Use the distributive property to find two expressions that are equivalent to 73x = 4).​

The steps of completing the square assuming a parabolic equation of the form ax² + bx  + c is done to get

y = a(x + b/2a)² - (b² - 4ac)/4a = a(x - h)² + k

vertex is given by v(h, k) for h = b/2a and k = -(b² - 4ac)/4a

The standard equation of a parabola is ax² + bx  + c

completing the square is done as follows

write the equation ax² + bx  + c such that c is the other side of the equation

ax² + bx  = -c

divide through by a to get

x² + (b/a)x  = -c/a

add (b/2a)² to the both sides of the equation

x² + (b/a)x + (b/2a)² = (b/2a)² - c/a

solving each side differently,

(x + b/2a)² = x² + (b/a)x + (b/2a)² and

(b/2a)² - c/a = b²/4a² - c/a = (b² - 4ac)/4a²

hence

(x + b/2a)² = (b² - 4ac)/4a²

multiplying by a

a(x + b/2a)² = (b² - 4ac)/4a

rewriting the equation

y = a(x + b/2a)² - (b² - 4ac)/4a = a(x - h)² + k

therefore

h = b/2a

k = -(b² - 4ac)/4a

and vertex is v(h, k)

Learn more about quadratic equations at:

https://brainly.com/question/29244327

#SPJ1

Answer:

i really dont know this is hard hm

Step-by-step explanation:

Answer:

Marianne made an inference that is true based on the data. More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.

hope it help please mark me as brainliest

Hello !

you made a typo with the c^-2 because otherwise it does not make a round result

\(a^{2} *b^{2} *c^{2} \\\\= 1^{2} *2^{2}* (-3)^{2} \\\\= 1*4*9\\\\\boxed{= 36}\)

From the question, we are to plot the graph of

Using Desmos Graphing Calculator

The graph is as shown below

We may predict that, when rοunded tο the clοsest whοle number, 185 persοns οught tο be present at Sοcial Prοblems οn Sunday.

Detailed numbers the set οf integers that cοntains zerο and the natural numbers. nοt a decimal and fractiοn. Integer 0 thrοugh 2, 3, 4, 5, 6, 7, 8, 9, 10, and sο οn. a cοunting number, a negative number, οr zerο.

The library saw a sum οf 416 + 448 + 341 = 1205 visitοrs οn Saturday. By dividing the entire number οf visitοrs by the number οf visitοrs whο visited Sοcial Prοblems, and then multiplying the result by 100% tο represent the results as a percentage, we can determine what percentage οf these visitοrs visited Sοcial Issues:

Percentage οf visitοrs whο went tο Sοcial Issues = (448 ÷ 1205) x 100%

Percentage οf visitοrs whο went tο Sοcial Issues ≈ 37.18%

We may assume that a similar percentage οf Saturday's visitοrs will return οn Sunday in οrder tο estimate the number οf persοns whο can be expected tο attend Sοcial Prοblems οn that day. Tο determine hοw many peοple will visit Sοcial Prοblems οn Sunday, we can utilize the prοpοrtiοn mentiοned abοve:

Estimated number οf visitοrs tο Sοcial Issues οn Sunday = (37.18% οf 500 visitοrs)

Estimated number οf visitοrs tο Sοcial Issues οn Sunday ≈ 185

We may calculate that, if we rοund tο the next whοle number, 185 persοns shοuld be anticipated tο attend Sοcial Prοblems οn Sunday.

To know more about whole number visit:

https://brainly.com/question/13242016

#SPJ1

The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments

From the question, we have the following parameters that can be used in our computation:

The table of values

For the membership application, we have the following features

So, the function is

f(x) = 600 - 10x

For the membership available, we have the following features

So, the function is

g(x) = 20/3x

So, the functions are f(x) = 600 - 10x & g(x) = 20/3x

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

\(\Huge \boxed{\bold{\text{12 Boys}}}\)

\(\Huge \boxed{\bold{\text{30 Girls}}}\)

Step-by-step explanation:

Let the number of girls be \(g\) and the number of boys be \(b\).

According to the problem: \(b = \frac{2}{5} \times g\)

We also know that the total number of students is 42, so \(b + g = 42\).

Now, we have two equations with two variables:

We can solve these equations to find the values of \(b\) and \(g\).

Step 1: Solve for \(\bold{b}\) in terms of \(\bold{g}\)

From the first equation, we have\(b = \frac{2}{5} \times g\)

Step 2: Substitute the expression for \(\bold{b}\) into the second equation

Replace \(b\) in the second equation with the expression we found in step 1.

\(\frac{2}{5} \times g + g = 42\)

Step 3: Solve for \(\bold{g}\)

Now, we have an equation with only one variable, \(g\):

\(\frac{2}{5} \times g + g = 42\)

To solve for \(g\), first find a common denominator for the fractions:

\(\frac{2}{5} \times g + \frac{5}{5} \times g = 42\)

Combine the fractions:

\(\frac{7}{5} \times g = 42\)

Now, multiply both sides of the equation by \(\frac{5}{7}\) to isolate \(g\):

Step 4: Find the value of \(\bold{b}\)

Now that we have the value of \(g\), we can find the value of \(b\) using the first equation:

So, there are 12 boys and 30 girls in the class.

----------------------------------------------------------------------------------------------------------

Hi

to solve you must transcrive every word in math terms correctly.

so let's first give a name to our mysterious number. As you know, in math we generally call unknown by letter. " X"

so let's now play the detective.

what do we know on " X" ?

we add 3 to X so we have : X+3

then we multiply by 5. so. ( X+3) *5 .

if we do that we have twice X , so 2X

so ( X+3) * 5 = 2 X

now that we have translatted our data in math term, let's unmask. " X"

( X+3) *5 = 2X

5*X +3*5 = 2X

5X +15 = 2X

5X-2X = -15

3X = -15

X = -15/3

X = -5

So is " -5" is our guy.

let's check it out to be sure .

-5 +3 = -2

-2*5 = -10

-10 is twice -5. so -5 is the correct answer.

Ps : some operation are commonly implied. if you do not. know how I could write some line in the calculus, dont hesitate to ask in comments.

There is no mysteries in math everything is done according to rules and can be explained. So don't hesitate !

The coefficient of determination, given the total variation and the explained variation would be 0.898.

R-squared, or the coefficient of determination, represents the proportion of variation within a response variable that can be explained by the regression model. This calculation is achieved through dividing the explained variation by the total variation.

We are given the explained variation as 18. 592. We are also given the total variation as 20. 711.

The coefficient of determination is:

= explained variation / total variation

= 18. 592 / 20.711

= 0. 898

Find out more on coefficient of variation at https://brainly.com/question/13228462

#SPJ1

Full question is:

A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119.

Find the coefficient of determination. Round to three decimal place

A concentric square and circle intersect at 8 points. the area of A2, A6 is (3/4)s²

Generally, let's call the side length of the square s and the radius of the circle r.

We can set up the following equation:

(s/2)² + (r/2)² = (5/8) * s²

We can rearrange this equation to solve for r:

(r/2)² = (5/8)s² - (s/2)²

Evaluate the exponents

This gives

r²/4 = 5/8s² - s²/4

Multiply through by 4

So, we have

r² = 5/2s² - s²

Evaluate the like terms

This gives

r² = 3/2s²

Take the square roots of both sides

So, we have

r = s√(3/2)

Since A1, A3, A5, and A7 are the vertices of the square, the area of this region is (s/2)²,

When expanded, this gives

Area = 1/4s².

The area of A2, A6 can be found by subtracting the area of A1, A3, A5, and A7 from the area of the entire square.

This gives us:

A2, A6 = s² - (1/4)s²

Evaluate

A2, A6 = (3/4)s²

Read more about concentric square https://brainly.com/question/14690610

#SPJ1

Answer:

5 tickets for $12.50

Step-by-step explanation:

because in that deal the ticket only costs $2.05

and in the second deal which is 8 tickets for $20.60 the ticket costs 2.57

Answer:

.05 %

Step-by-step explanation:

Hi! I believe your answer is 4.7%. Simply move the decimal two places to the right. I hope this helps you! Good luck and have a great day. ❤️✨

Answer:

80 points

Step-by-step explanation:

If score in English is x points and score in math is 5% higher then score in math

y = x + 0.05x

where 0.05 = 5% expressed as decimal

0.05x refers to the 5% increase in score

y = math score

y = x(1 + 0.05)

y = 1.05x

Given score in math = 84 this becomes

84 = 1.05x

x = 84/1.05

x = 80

So Emily's score in English was 80 points

Considering the hypothesis tested and the p-value of the test, the correct option is given by:

There is sufficient evidence that there is a difference in mean cholesterol level when using medicine X and medicine Y.

At the null hypothesis, it is tested if there is no difference between the cholesterol levels, that is:

H₀:Hₓ-H

At the alternative hypothesis it is tested if there is a difference, hence:

H₀:Hₓ-H≠0

The p-value is of 0.003 < 0.01, hence we reject the null hypothesis and conclude that there has was a difference, hence the correct option is given by:

There is sufficient evidence that there is a difference in mean cholesterol level when using medicine X and medicine Y.

More can be learned about hypothesis tests at brainly.com/question/26454209

#SPJ1

Answer:

11.7 pounds

Step-by-step explanation:

Multiply the weight of one bag of oranges by 9 bags.

Answer:

B = 1320

\(A= \dfrac54B\)

Step-by-step explanation:

Let A = number of students at Branch A

Let B = number of students at Branch B

If the number of students taking classes at Branch A is 1/4 more than Branch B, then:

      \(A=1 \dfrac14B\)

\(\implies A= \dfrac54B\)

If Branch A has 1,650 students, then substitute A = 1650 and solve for B:

\(\implies 1650= \dfrac54B\)

\(\implies 1650 \times 4= 5B\)

\(\implies 6600 =5B\)

\(\implies B=\dfrac{6600}{5}\)

\(\implies B=1320\)

Answer: 1320

Step-by-step explanation:

If \($&f(x)=\frac{19}{x^{2}} \\\) then the inverse function exists  \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

An inverse function in mathematics exists function which "reverses" the another function.

Let f(x) = y, then the inverse function, \($x=f^{-1}(y)$\)

\($&f(x)=\frac{19}{x^{2}} \\\)

\($&y=\frac{19}{x^{2}} \\\)

\($&x^{2}=\frac{19}{y} \\\)

simplifying the equation, we get

\($&x=\sqrt{\frac{19}{y}} \\\)

\($&x^{-1}=f^{-1}(y)=\sqrt{\frac{19}{y}} \\\)

\($&f^{-1}(y)=\sqrt{\frac{19}{y}},\)  then \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

If \($&f(x)=\frac{19}{x^{2}} \\\) then the inverse function exists  \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

To learn more about inverse function refer to:

https://brainly.com/question/11735394

#SPJ9

(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

Read more on reflection here: brainly.com/question/27912791

#SPJ1

The graph shows that Connor traveled a total of seven blocks from his house to the store and then from the store to the bank.

Graph is a data structure used to represent data in a visual way. It is composed of a set of nodes and edges, where each node represents an object and each edge represents a connection between two objects. Graphs can be used to represent a variety of data structures, such as a network of roads, a family tree, or a list of friends. Graphs are powerful tools for understanding complex relationships in data.

It also shows that he stayed at the store and the bank for five and seven minutes respectively. After leaving the bank, he drove the remaining four blocks back home.

The graph also reveals that Connor was driving at a steady pace between the store and the bank and that the total journey time was twenty-two minutes. This time could have been reduced if he had driven faster. However, it is possible that he was being cautious due to the traffic or other conditions.

Overall, the graph provides a visual representation of Connor's journey and his decisions along the way. It also provides insight into his driving habits, as well as his ability to manage his time. Based on this data, it is clear that Connor was able to complete his errands in an efficient manner.

To know more about graph click-
https://brainly.com/question/19040584
#SPJ1

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

For similar question on equilateral triangle.

https://brainly.com/question/28063031

#SPJ8

The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

The current market price for the bond is $870 the yield to maturity is 14.13%

The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)

knowing that:

the formula is:

\(P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n\)

Putting the values:

\($870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13\)

Using the math we find that the percentage is  approximately 14.13%;

See more about percentage at brainly.com/question/32197511

#SPJ1

Answer:

c = 45 and e = 30

Step-by-step explanation:

Since we know that A = 45, B = 90, we can calculate C knowing that the total angle of a triangle is 180, so you do 180-45-90 = 45

Finding the angle C helps us find F by subtracting 45 from 180, since a straight line is 180 degrees, which is 135.

We know that E = 15, and what was said earlier about how the toal angle is 180 in a triangle, we can subtract 15 and 135 from 180, which is 30.

Hope that answers your question

The volunteers donated 1893 milliliters of blood.

Let's consider the following problem in writing expressions word problems:

During a blood drive, volunteers donated 3 pints and 2 cups of blood. Express the amount of blood donated in milliliters, given that there are 473 milliliters in 1 pint and 237 milliliters in 1 cup.

Solution:We have to express the amount of blood donated in milliliters. We can use the following conversion factors:1 pint = 473 mL1 cup = 237 mL

To find the amount of blood donated in milliliters, we can first convert 3 pints and 2 cups to milliliters:

3 pints x 473 mL/pint = 1419 mL2 cups x 237 mL/cup = 474 mLAdding these two amounts together, we get the total amount of blood donated in milliliters:1419 mL + 474 mL = 1893 mL

To learn more about : milliliters

https://brainly.com/question/30760941

#SPJ8

The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.

The Central limit theorem is used to find the probability

Data given:

sample size = 5.

mean, μ = 9.70 ounces

standard deviation, σ = 0.03 ounce.

To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.

x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

For the sample mean of 9.65 ounces in 5 boxes:

z = (9.65 - 9.70) / (0.03 / √5)

z ≈ -0.05 / (0.03 / √5)

Using a calculator, we find that the probability is approximately 0.4801.

Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.

Learn more about probability at: https://brainly.com/question/13604758

#SPJ1

Answer: D

Step-by-step explanation:

(lines parallel to each other have the same slope)

slope = m = 2

y = mx + b, (5,6)

6 = 2(5) + b

6 = 10 + b

b = -4

y = 2x - 4

y - 6 = 2(x - 5)

y - 6 = 2x - 10

y = 2x -4

The value of x is 58.51 degree.

We have,

Perpendicular= 8

Base = 4.9

Using trigonometry

tan x = Perpendicular/ Base

tan x = 8/4.9

tan x= 1.63265306122449

x = 58.51253064

Thus, the value of x is 58.51 degree.

Learn more about Trigonometry here:

https://brainly.com/question/12068045

#SPJ1

Answer/Step-by-step explanation:

1. Only one side and an included angle is known. To prove that both triangles are congruent by the SAS Congruence Theorem, an additional information such as a corresponding second side (KJ, and HJ) must be given to be equal to each other.

KJ = HJ

2. Additional information such as a second corresponding angle (angles C and W must be known to prove both triangles are congruent by SAS.

<C = <W

3. Additional information needed is a second corresponding angles must be known to prove the AAS.

4. Additional information needed is the corresponding angles, R and L, which should be equal to prove the ASA.

<R = L

5. Additional information needed: <C = <H

6. Additional information needed: equal hypotenuse lengths of both traingles.

Answer:

-16

Step-by-step explanation:

-16 + (-1) = -17