hii, this geometry, please help haha!!

Hii, This Geometry, Please Help Haha!!

Answers

Answer 1

Answer:

its 6

Step-by-step explanation:

(16x+5) = 1

50 - 45 = 5

5+1=6

Answer 2

Answer:

x=5

Step-by-step explanation:

since both triangles are equivalent then both given angles add up to 95. So to find x you would see what value makes it equal 85 when it's plugged in to equal 180 in total.

16(5)+5=85+95=180


Related Questions

you as a broker sold a triangular piece of land for $900 per acre. what is the approximate amount of your commission at 7% if the land had a base of 1500 feet and a height of 600 feet?

Answers

The approximate commission at the rate of 7% is $650.82

What is area of triangle?

The area occupied by a triangle is known as area of triangle. The area if computed as 1/2*base*height

We are given the, base of 1500 feet and a height of 600 feet

Hence the area of triangle can be given as

Area= 0.5*1500*600

Area= 450000 ft^2

Now 1 acre costs as 43560 sqft

Hence the area of triangle in acres is

Area in acres = \(\frac{450000}{43560}\)

Area in acres= 10.33

Hence total amount for which the piece of land is sold = 10.33*900

Total amount= $9297

Now we have to find the 7% of this amount

Hence

\(=\frac{9297*7}{100}\\=650.82\)

Hence the amount received as commission is $650.82

To learn more about area of triangle please refer

https://brainly.com/question/17335144

#SPJ4

The temperature in degrees Fahrenheit, ofa warming room is given by the function F (m) = 2m +58, where m is the number of minutes the room has been warming. (a) Find the value of F (8) - F (2). Show or explain how you found your answer.

Answers

The difference between F(8) and F(2) is 12

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Given: Function of Warming Room = F(m) = 2m + 58

To Find: F(8) - F(2)

F(8) = 2*8 + 58 = 16+58 = 74

F(2) = 2*2 + 58 = 4+58 = 62

F(8) - F(2) = 74 - 62 = 12

The difference between F(8) and F(2) is 12

To learn more about Functions from the given link

https://brainly.com/question/22340031

#SPJ1

8 players to 10 players

Answers

Answer:

"I don't understand what this means but I will take my best shot, I guess, this is my answer based on the small amount of words this question gives"

Depending on skill level either of them could win, for example if the 10 players are able to overwhelm the 8 players they will win, but if the 8 players have better players they could win, depending on their skill, even though the 10 player team has a better chance to win, the 8 player team could win.

Simplify fully: 2a + 5b - 4b - 1

Answers

The simplified expression for 2a + 5b - 4b - 1 is 2a + b - 1.

To simplify this expression, we first combine like terms. We have 5b and -4b, which combine to give us b. We also have 2a and no other like terms, so we leave that as is. Finally, we have the constant term -1, which remains the same. Thus, our simplified expression is 2a + b - 1.

It is important to note that when combining like terms, we only combine terms with the same variables and same exponents. In this case, we had two terms with the variable b, but no other terms with that variable. Similarly, we had one term with the variable a, and no other terms with that variable. This allowed us to combine like terms and simplify the expression.

Know more about simplified expression click here:

https://brainly.com/question/18077352

#SPJ11

Is 20 - 5x = 50- 10x true ?

Answers

Answer:

Step-by-step explanation:

that is incorrect.

if it were to be equal, one side should equal each other when multiplied to make the ratio equal.

20-5x=40-10x (when multiplied by 2 on each side)

It CANNOT equal 50, if it were there would not be -10x

20-5x=100-25x

DIVIDE BY 2 to get 50 WOULD GIVE:

20-5x=50-17.5x

Answer:

Yes

Step-by-step explanation:

solve the equation for x , then evaluate and compare both sides

20 - 5x = 50 - 10x ( add 10x to both sides )

20 + 5x = 50 ( subtract 20 from both sides )

5x = 30 ( divide both sides by 5 )

x = 6

then

left side = 20 - 5x = 20 - 5(6) = 20 - 30 = - 10

right side = 50 - 10x = 50 - 10(6) = 50 - 60 = - 10

since both sides are equal then

20 - 5x = 50 - 10x is true

An architect wants to reduce a set of blueprints to make a portable set for easy access. The original dimensions of the blueprints are 24 inches by 36 inches. She reduces the blueprints by a scale factor of 13. She then decides that the reduced blueprints are a little too small and enlarges them by a scale factor of 1.25. Will the final image fit in a similar portfolio with an area of 160 square inches? Justify your response.

Answers

The final image will fit in a similar portfolio with an area of 160 square inches.

How to obtain the area of a rectangle?

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width.

The dimensions for this problem are given as follows:

24 inches, 36 inches.

With the reduction with a scale factor of 1/3, the dimensions are given as follows:

8 inches,  12 inches.

With the enlargement by a factor of 1.25, the dimensions are given as follows:

10 inches and 15 inches.

Hence the area is given as follows:

15 x 10 = 150 square inches.

As the area of 150 square inches is less than 160 square inches, the final image will fit in a similar portfolio with an area of 160 square inches.

More can be learned about the area of a rectangle at brainly.com/question/25292087

#SPJ1

50 POINTS! PLEASE HELP! Which graph represents the solution set of the system of inequalities?

{y≤2x+1 y>−2x−3

50 POINTS! PLEASE HELP! Which graph represents the solution set of the system of inequalities?{y2x+1
50 POINTS! PLEASE HELP! Which graph represents the solution set of the system of inequalities?{y2x+1

Answers

Step-by-step explanation:

the second one as the -2x-3 is only on the second one

2nd one I believe… all the number are positive so it has to go to a positive side…

The radius of a circle is 14 cm. Find its area in terms of π.

Answers

Answer:

A≈615.75cm²

Step-by-step explanation:

A=πr2=π·142≈615.75216cm²

Solve for b.
4b+5=1+5b

Answers

Answer:

b=4

Step-by-step explanation:

Answer:

b=4

Step-by-step explanation:

you subtract 4b from both sides and 1 from both sides leaving you with b=4

In a different plan for area codes, the first digit could be any number from 3 through 8, the second digit was either 2,3, or 4 and the third digit could be any number except 6,7, or 8. With this plan, how many different area codes are possible?

Answers

We count the total number of possibilities for the area codes in the next manner:

1. For the first digit of the codes, we have six options, these are; 3,4,5,6,7,8

2. For the second digit of the codes, three options\; 2,3,4

3. For the third digit of the codes with can put any digit number except 6,7 or 8, that restriction let us the following possibilities:0,1,2,3,4,5,9

We will use the multiplicative rule to count the total number of possible codes with this restrictions, that is we will apply a rule of the form:

\(total\text{ N' of codes=possibilities for the first digit}\times(possibilities\text{ for the second digid\rparen}\times(possibilities\text{ for the third digid\rparen}\)

In our the specific case

\(Total\text{ N' od codes=6}\times3\times7=126\)

Therefore, we conclude that with these restriction, the total number of codes is 126

M is the midpoint of segment JK. The coordinate of J are (-4, 7) and the coordinates of M are (2, 5). Find the coordinates of K.

M is the midpoint of segment JK. The coordinate of J are (-4, 7) and the coordinates of M are (2, 5).

Answers

The coordinates of K are (8,3).

There is a line segment JK with M as its midpoint. This means the length of JM = length of MK.

Also the coordinates of J is (-4,7) and the coordinates for M are (2,5).

As M is the midpoint, the x-distance and y-distance between (-4,7) and (2,5) are same as that between (2,5) and K.

x- distance between (-4,7) and (2,5) = 2- (-4) = 6

So x- coordinate of K = 2+6 = 8

y-distance between (-4,7) and (2,5) = 5-7 = -2

So y-coordinate of K = 5+(-2) = 3

Hence the coordinates of K are (8,3).

Learn more about co-ordinates at https://brainly.com/question/17206319

#SPJ1

Help and get what you want.

Help and get what you want.

Answers

Answer:

70°

Step-by-step explanation:

This is a question on angle properties.

Angle K + 35 + 75 = 180 (Sum of angles in a triangle)

Angle K + 110 = 180

Angle K = 180 - 110 = 70°

Answer:

angle k = \(\boxed {70}^\circ\)

Step-by-step explanation:

The angles in a triangle add up to 180°.

∴ ∠k + 75° + 35° = 180°

⇒ ∠k + 110° = 180°

⇒ ∠k = 180° - 110°

⇒ ∠k = 70°

I Need HELP PLEASE ANYONE U GET 5 STARS IF RIGHT ANSWER !

I Need HELP PLEASE ANYONE U GET 5 STARS IF RIGHT ANSWER !

Answers

Answer:

4√(7^5) and (4√7)^5

Step-by-step explanation:

7^5/4

The above can be expressed as follow: Method 1:

7^5/4

(7^5)^1/4

Recall:

(a^m)^1/n = n√(a^m)

Therefore,

(7^5)^1/4 = 4√(7^5)

Method 2:

7^5/4

(7^1/4)^5

Recall:

(a^1/m)^n = (m√a)^n

Therefore,

(7^1/4)^5 = (4√7)^5

From the illustration above, we can see that 7^5/4 can be expressed as 4√(7^5) and (4√7)^5

6) 5 mi
11 mi


7) 22 m
11 m


8) 22 yd
25 yd

6) 5 mi 11 mi7) 22 m 11 m8) 22 yd 25 yd

Answers

Answer:

#6=perimeter=32 area=55

#7=perimeter=66 area=242

#8=perimeter=94  area=550

Step-by-step explanation:

5+5+11+11=32

5x11=55

22+22+11+11=66

22x11=242

22+22+25+25=94

22x25=550

If six model cars cost $12 what is the price for the model cars

Answers

Answer:

72 dollars

Step-by-step explanation:

all you do is multiply

Roberto compró 6 cd's y 10 revistas en $ 900.00 pesos; en la misma tienda su amiga María compró 10 cd's y 4
revistas en $ 1.220.00 pesos. ¿ Cual es el sistema de ecuaciones con dos incognitas que representa el problema?

Answers

The system of linear equation that represent this problem is

6x + 10y = 900

10x + 4y = 1220

What is the system of equation?

Let's represent the number of CDs Roberto bought as x and the number of magazines as y

The problem states the following information:

Using the variables;  x and y as given;

1. Roberto bought 6 CDs and 10 magazines for $900.00 pesos. This can be represented as the equation:

  6x + 10y = 900

2. María bought 10 CDs and 4 magazines for $1,220.00 pesos. This can be represented as the equation:

  10x + 4y = 1220

So, the system of equations representing the problem is:

6x + 10y = 900

10x + 4y = 1220

learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

Translation: Roberto bought 6 cd's and 10 magazines for $900.00 pesos; In the same store, her friend María bought 10 CDs and 4

magazines at $1,220.00 pesos. What is the system of equations with two unknowns that represents the problem?

Last week a certain pet store had 52, 72, 96, 21, 58, 40, and 75 paying customers. Which data value(s) are outliers? Select all that apply.

Answers

There is one value greater than 148.25, which is 96. the value of 96 is considered an outlier in this Dataset.

To identify outliers in a dataset, we need to first calculate the interquartile range (IQR) and then use the following rule:Any data value less than Q1 - 1.5 x IQR or greater than Q3 + 1.5 x IQR is considered an outlier.

To find Q1 and Q3, we first need to order the data:

21, 40, 52, 58, 72, 75, 96

The median of the entire dataset is (58 + 72)/2 = 65, so Q2 (the second quartile) is 65.

The lower quartile Q1 is the median of the lower half of the data, which is:

21, 40, 52, 58

The median of this data is (40 + 52)/2 = 46, so Q1 is 46.

The upper quartile Q3 is the median of the upper half of the data, which is:

72, 75, 96

The median of this data is (75 + 96)/2 = 85.5, so Q3 is 85.5.

Now we can calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 85.5 - 46 = 39.5

Using the rule for outliers, any data value less than Q1 - 1.5 x IQR or greater than Q3 + 1.5 x IQR is considered an outlier.

Q1 - 1.5 * IQR = 46 - 1.5 x 39.5 = -23.25

Q3 + 1.5 * IQR = 85.5 + 1.5 x 39.5 = 148.25

Therefore, any data value less than -23.25 or greater than 148.25 is an outlier.

In this case, there are no values less than -23.25, but there is one value greater than 148.25, which is 96. Therefore, the value of 96 is considered an outlier in this dataset.

To know more about Dataset.

https://brainly.com/question/28168026

#SPJ11

determine the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2.

Answers

the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2 is \vec n = <0,0,-1>

A unit normal vector is a normal vector with magnitude 1, and it points in the direction that is perpendicular to the tangent to the curve at a given point.

To determine the unit normal vector to a curve, it's important to find the tangent first and then find the normal. In this case, we're looking for the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2.

To find the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2, it is necessary to find the tangent to the curve and then find the normal. This is a crucial step in understanding the geometry of curves in 3D space.

To find the tangent to the curve, we'll differentiate the vector equation with respect to t and evaluate it at t = 2. The derivative of \vec r (t) is given by:

d\vec r/dt = <1, -2t^-3, -4e^-t^-4>

So the tangent to the curve at t = 2 is:

d\vec r/dt = <1, -2(2)^-3, -4e^-2^-4> = <1, 1.5, -1.648721>

Next, we'll find the normal to the tangent by taking the cross product of the tangent with a fixed vector, for example, the unit vector i = <1,0,0>. The cross product of two vectors results in a vector that is perpendicular to both of them.

The cross product of the tangent and the unit vector i is given by:

\vec T x \vec i = <1, 1.5, -1.648721> x <1,0,0> = <0,0,-1.5>

Since the magnitude of the normal is not 1, we'll normalize it by dividing it by its magnitude:

\vec n = \vec T x \vec i / ||\vec T x \vec i|| = <0,0,-1.5> / ||<0,0,-1.5>|| = <0,0,-1>

So the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2 is given by:

\vec n = <0,0,-1>

This is the unit normal vector that points in the direction that is perpendicular to the tangent to the curve at t = 2. The magnitude of 1 ensures that it's a unit vector and the direction points towards the normal direction.

To know mare about unit normal vector  refer here:

https://brainly.com/question/29752499#

#SPJ11

The width of a rectangle is 3 meters more than half of the length. the perimeter is 516 meters. What is the length and the width?

Answers

Answer:

Length = 8 meters

Width = 5 meters

Step-by-step explanation:

2*(3 + (1/4)L + L) = 26 meters

1/4L + L = 26/2 - 3

1/4L + 4/4L = 10

5/4L = 10

L = 10 * 4/5

L = 40/5 = 8 meters

W = 3 + 1/4 L

W = 3 + 1/4 *8

W = 3 + 2

W = 5 meters

Hey there! I'm happy to help!

Let's write this out as a system of equations. We will have W be the width and L be the length.

W=0.5L+3

2L+2W=516

Since we know that W is equal to 0.5L+3, we can swap the W in the second equation with 0.5L+3 so we can solve for L!

2L+2(0.5L+3)=516

We use the distributive property to undo the parentheses.

2L+L+6=516

We combine like terms.

3L+6=516

We subtract 6 from both sides.

3L=510

We divide both sides by 3.

L=170

Now, we know that the width is 3 meters more than half the length. So, we take 1/2 of 170, which is 85, and then we add three, giving us 88.

So, our length is 170 meters and the width is 88 meters.

Have a wonderful day!

Is (-5,-8) a solution of y>3x+6?
Choose 1 answer:
A
Yes
B
No

Answers

Answer:  I am going to go with no...

Step-by-step explanation:

For linear regression, the model is f_{w,b}(x) = wx + bfw,b​(x)=wx+b.
Which are the inputs, or features, that are fed into the model and with which the model is expected to make a prediction?

Answers

The inputs or features that are fed into the model and with which the model is expected to make a prediction for the linear regression are x.

Linear regression is a statistical approach to establish a relationship between dependent and independent variables. In linear regression, the model is f_{w,b}(x) = wx + bfw,b​(x)=wx+b. The independent variable (x) is the feature that is fed into the model and with which the model is expected to make a prediction.

In the equation f_{w,b}(x) = wx + bfw,b​(x)=wx+b, w is the weight of the input feature x, and b is the bias term that makes an adjustment in the output. These parameters w and b are learned through training the model with input-output examples.

The purpose of linear regression is to create a mathematical model that defines the relationship between the input feature x and the output y. The model is then used to predict the outcome for new data points or to understand the relationship between the variables.

To know more "Linear regression" refer here:

https://brainly.com/question/29665935#

#SPJ11

What is the slope of the line?
3x-4y=73x−4y=7

Answers

Answer:

67x-7y2x-f8

Step-by-step explanation:

The amount of money in a bank account is given by the functiony = 200(1 + 0.05)^t, where y is in dollars and t is measured in months since the account was opened.What is the percent rate of growth of the bank account?Enter your answer in the box.

The amount of money in a bank account is given by the functiony = 200(1 + 0.05)^t, where y is in dollars

Answers

.Explanation

The question wants us to get the growth rate of the sum invested

To do this,

We have to use the general equation

\(\begin{gathered} y=P(1+\frac{r}{100})^t \\ \text{where P is the amount invested} \\ r=percent\text{ growth} \\ t=n\nu\text{mber of years} \end{gathered}\)

The given equation is

\(y=200(1+0.05)^t\)

To get the percentage growth rate, we will have to compare with the general formula

We will find out that

\(\begin{gathered} \frac{r}{100}=0.05 \\ \\ r=100\times0.05 \\ \\ r=5\text{ \%} \end{gathered}\)

Most engaged couples expect or at least hope that they will have high levels of marital satisfaction. However, because 54% of first marriages end in divorce, social scientists have begun investigating influences on marital satisfaction. (Data Source: These data were obtained from the National Center for Health Statistics. ) Suppose a counseling psychologist sets out to look at the role of having children in relationship longevity. A sample of 78 couples with children score an average of 51. 1 with a sample standard deviation of 4. 7 on the Marital Satisfaction Inventory. A sample of 94 childless couples score an average of 45. 2 with a sample standard deviation of 12. 1. Higher scores on the Marital Satisfaction Inventory indicate greater satisfaction.
Suppose you intend to conduct a hypothesis test on the difference in population means. In preparation, you identify the sample of couples with children as sample 1 and the sample of childless couples as sample 2. Organize the provided data by completing the following table:​

Answers

To organize the provided data, we can create a table comparing the samples of couples with children (sample 1) and childless couples (sample 2) as follows:

Sample Sample Size Sample Mean Sample Standard Deviation

1 78 51.1 4.7

2 94 45.2 12.1

In this table, we have listed the sample number (1 and 2), the sample size (number of couples in each group), the sample mean (average Marital Satisfaction Inventory score), and the sample standard deviation (measure of variability in the scores) for each group. This organization allows us to compare the data and proceed with hypothesis testing on the difference in population means between the two groups.

Learn more about  data from

https://brainly.com/question/30459199

#SPJ11

help me please im getting tired of getting no answers!

help me please im getting tired of getting no answers!
help me please im getting tired of getting no answers!

Answers

Answer:

The picture isnt popping up fix it and ill answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

change in time: 2

change in distance: 5.5

2:5.5

Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months. Month 2 3 4 5 Sales 924 91

Answers

Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

To learn more about time-series method visit:

brainly.com/question/32443421

#SPJ11

rack heights vary from a few rack units to many rack units. the most common rack heights are 24u and 42u. how tall is a 24u rack?

Answers

The height of the 24U rack is 42 inches.

A rack unit, or U, is a standard unit of measurement used in the computer industry to describe the height of server racks, equipment, and other hardware.

24U and 42U are two of the most common rack heights, and they are used to describe the height of a rack cabinet. In this article, we'll go over the height of a 24U rack in detail, so you can understand what this measurement means.

To calculate the height of a 24U rack, we need to first understand the height of a single U.

A single U is 1.75 inches tall.

To find the height of a 24U rack, we simply multiply the height of a single U by the number of U's in the rack.

So, the height of a 24U rack is

=> 24 U * 1.75 inches/U = 42 inches.

To know more about measurement here.

https://brainly.com/question/23816277

#SPJ4

14. MODELING REAL LIFE The data in the table show the
average speeds y (in miles per hour) of a pontoon boat
for several different engine speeds x (in hundreds of
revolutions per minute, or RPMs). Find a model for
the data. Use the model to estimate the average speed
of the pontoon boat when the engine speed is
2800 RPMs.

14. MODELING REAL LIFE The data in the table show theaverage speeds y (in miles per hour) of a pontoon

Answers

The estimated average speed of the pontoon boat when the engine speed is 2800 RPMs is approximately 20.5 miles per hour.

Explain about linear equation ?

A linear equation is an equation between two variables, x and y, that results in a straight line when plotted on a graph. The equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis).

The slope of the line determines how steep the line is. If the slope is positive, the line goes up as x increases. If the slope is negative, the line goes down as x increases. The magnitude of the slope tells us how much the line changes in y for each unit change in x.

According to the question:
To find a model for the data, we can plot the given points on a graph and see if there is a linear relationship between the two variables.

After plotting the points, we can see that there is a linear relationship between x and y. We can use linear regression to find the equation of the line that best fits the data. The equation of the line is of the form y = mx + b, where m is the slope and b is the y-intercept.

Using a calculator or software, we find that the equation of the line that best fits the data is y = 0.669x + 1.466.

To estimate the average speed of the pontoon boat when the engine speed is 2800 RPMs, we can substitute x = 28 into the equation and solve for y:

y = 0.669(28) + 1.466

y ≈ 20.5

Therefore, the estimated average speed of the pontoon boat when the engine speed is 2800 RPMs is approximately 20.5 miles per hour.

To know more about linear equation visit:
https://brainly.com/question/30310809
#SPJ1

a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it t/f

Answers

The statement that "a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect" is true.

The surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it is called a torus. The torus is a three-dimensional surface that can be thought of as a doughnut shape. The curve that generates the torus is called the generator, and the line about which the curve is rotated is called the axis of rotation. The torus has the interesting property that it has a hole in the center, and the distance from any point on the surface to the center of the torus is constant.

Learn more about torus here brainly.com/question/16653541

#SPJ4

After 3 minutes of exercise, Malcolm's heart rate is 80 beats per minute. After 5 minutes, itincreased to 94 beats per minute. Let a represent the number of minutes since Malcolm beganexercising, and let y represent Malcolm's heart rate (assume his heart rate increased at a constantrate). Write two linear equations (one in slope-intercept form and one in point-slope form) tomodel his heart rate. Then, calculate his heart rate after 12 minutes of exercise.♡14

Answers

Answer:

1. i. The slope-intercept equation is:

\(y=7x+59\)

1. ii. The point-slope equation is:

\(\begin{gathered} (y-80)=7(x-3) \\ OR \\ (y-94)=7(x-5) \end{gathered}\)

2. Malcolm's heart rate after 12 minutes is 143

SOLUTION

Problem Statement

The question tells us 3 minutes of exercise leads to 80 beats per minute with Malcolm's heart. The question goes on to say after 5 minutes, his beats per minute is 94 in magnitude.

We are asked to find two linear equations to model his heart rate.

Method

In order to solve this problem, we need to:

1. Calculate the slope (m) of the equation. To find the slope, we use the formula below:

\(\begin{gathered} m=\frac{y_2-y_1}{a_2-a_1} \\ \text{where,} \\ m=\text{slope} \\ _{}y_2=\text{the second heart rate} \\ y_1=\text{the frist heart rate} \\ x_2=\text{second minutes passed} \\ x_1=\text{first minutes passed} \end{gathered}\)

2. Find the value of the y-intercept of the linear equation.

3. Write out the heart-rate linear equation and find the value of the heart rate after 12 minutes

Implementation

1. Calculate the slope (m) of the equation. To find the slope, we use the formula below:

\(\begin{gathered} y_2=94,x_2=5 \\ y_1=80,x_1=3 \\ \\ \therefore m=\frac{94-80}{5-3} \\ m=7 \end{gathered}\)

Thus, the slope is 7

2. Find the value of the y-intercept of the linear equation.

The y-intercept can be gotten by substituting the value of x and y into the general equation of a line.

The equation of a line is given by:

\(\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope} \\ c=y-\text{intercept} \end{gathered}\)

Once we have substituted, it becomes a matter of making the y-intercept the subject of the formula. The values of x and y we can use can either be: (3, 80) or (5, 94)

\(\begin{gathered} \text{Given the general equation:} \\ y=mx+c \\ \text{choosing x=3 and y =80}.\text{ Remember that slope (m) = 7} \\ 80=3(7)+c \\ 80=21+c \\ \text{Subtract 21 from both sides} \\ 80-21=21-21+c \\ \therefore c=59 \end{gathered}\)

Thus, the y-intercept is 59

3. Write out the heart-rate linear equation and find the value of the heart rate after 12 minutes

The slope-intercept form equation of Malcolm's heart rate is:

\(\begin{gathered} y=mx+c \\ m=7,c=59 \\ \therefore y=7x+59 \end{gathered}\)

The point-slope form of Malcolm's heart rate is gotten using the formula given below:

\((y-y_1)=m(x-x_1)\)

Thus, the point-slope equation is gotten using either (3, 80) or (5, 94):

\(\begin{gathered} _{} \\ \text{ Using,} \\ x_1=3,y_1=80 \\ (y-80)=7(x-3) \\ \\ \text{using,} \\ x_2=5,y_2=94 \\ (y-94)=7(x-5) \\ \\ \therefore\text{The possible point-slope equations are:} \\ (y-80)=7(x-3) \\ (y-94)=7(x-5) \end{gathered}\)

Using the slope-intercept form of the equation to calculate Malcolm's heart rate after 12 minutes. This means that the value of x to be used is 12 and we are trying to find y.

Thus, we have:

\(\begin{gathered} y=7x+59 \\ \text{substituting x=12} \\ y=7(12)+59 \\ y=84+59 \\ \therefore y=143 \end{gathered}\)

Thus, his heart rate after 12 minutes is 143

Final Answer:

To recap,

1. i. The slope-intercept equation is:

\(y=7x+59\)

1. ii. The point-slope equation is:

\(\begin{gathered} (y-80)=7(x-3) \\ OR \\ (y-94)=7(x-5) \end{gathered}\)

2. Malcolm's heart rate after 12 minutes is 143

Other Questions
a 1.00 l solution saturated at 25c with lead(ii) iodide contains 0.54 g of pbi2. What are three applications for pressure treated lumber. Given the equation t(n)=3n-5 What is the 10th term? What is the equation of the line shown in the graph? Which sentence is an example of third-person narration?A. I asked the teacher to help me figure out a math problem.B. "Can you help me figure out the answer?" I asked the teacher.O C. She asked the teachem to help her figure out a math problem.O D. You ask the teacher to help you figure out a math problem. A large producer of household products purchases a glyceride used in one of its deodorant soaps from outside of the company. It uses the glyceride at a fairly steady rate of 40 pounds per month, and the company uses a 23 percent annual interest rate to compute holding costs. The glyceride can be purchased from two suppliers, A and B. Supplier A offers the following all- units discount schedule: Supplier A For all units of order size 0 Evaluate zodz, where c is the circle 12 - 11 = 1. [6]" I need some help so see if an equation is linear or not f(p)=2/5x-5 a) Identify ONE specific way in which the portrayal of the figures in the image reflects the political message presented in the painting.b) Identify ONE way in which the image reflects the relations between the Mughal Empire and other states during the period circa 1550-1650. c) Explain ONE reason that the political relations portrayed in the image changed in the period circa 1650-1850. (Can someone help me to answer these three questions? Thanks!!! Marcus dold a residential rental building for a gain of $30,000. He had originally purchased the building and placed it in service in March 2016 (the sale of land is not included in this question). The amount of depreciation allowed or allowable was $14250.There were no other adjustments to the basis of the property and Marcus did not sell any other property during the tax year. What is the amount and nature of Marcus gain?$15,700 gain taxed as long term capital gain and $14,250 gain taxed at a maximum of 25%$15,750 gain taxed as long term capital gain and $14, 250 gain added to business income$30,000 gain taxed as long term capital gain and $14, 250 gain taxed as a maximum of 25%$30,000 gain taxed as a long term capital gain and $14,250 gain added to business income HURRY ASAPThe table shows conversions of common units of length. Unit of Length Customary System Units Metric System Units 1 inch 2.54 centimeters 1 foot 0.3048 meters 1 mile 1.61 kilometers About how many inches are equivalent to 3 meters? Round the number(s) needed in the table to the nearest tenth to find the approximate answer. 10 inches, 75 inches ,100 inches ,or 120 inches 7204 divided by 9 only remainder no decimals A pair of parametric equations is given. x = 5t, y = t 3 (a) sketch the curve represented by the parametric equations. use arrows to indicate the direction of the curve as t increases. QUESTION 24 - 1 POINTA family picked 128 apples at the orchard. They eat the apples at a rate of 9 apples per day. Write a linear model in the forma(t) = mt + b where a represents the number of apples remaining 1 days after picking the apples. Be sure to include "a(t)="in your answer Mary had 3 baby lambs and 9 adult lambs. What is the ratio of adult lambs 5 pointsto baby lambs? *3:93:1O1:3 write the process of the formation of district co-ordination committee. You may research the following questions independently. Some of the material is covered in the text/slides and some information must be researched on the web or tested on a computer. When you have fin the marked price is 180. the rate of discount is 30% percent what is the discount and sale price? Will give brainlyist :D What kinds of activities would help to promote intrinsic motivation?