The points (-5, -6) and (-8, 9) fall on a particular line. What is its equation in point-slope
form?
leon

Answer:

The number 0 is a whole number, which is part of the rational numbers.

Step-by-step explanation:

I'M 50% SURE THAT THIS IS CORRECT SO SORRY IF I'M WRONG.

Answer:

answer is A

Step-by-step explanation:

The number 0 is a whole number, which is part of the rational numbers.

Answer: The midpoint will be at M (1,4)

Answer:  A  x = \(\sqrt{2}\)

Step-by-step explanation:

This is an isosceles right triangle.  The two sides will have the same length, 1.  The hypotenuse is calculated with the Pythagorean Theorem:

 \(1^{2}\) +  \(1^{2}\) = \(x^{2}\)

1 + 1  = \(x^{2}\)

x = \(\sqrt{2}\)

The term which contains A⁶ in the given binomial expansion as required to be determined is; 17010A⁶B⁴.

It follows from the task content that the term which contains A⁶ in the binomial expansion is to be determined.

From binomial expansions; the term containing A⁶ in the expansion would be the fifth term and it's coefficient would be; ¹⁰C⁴ = 210.

Therefore, the term would be; 210 (A)⁶ (3B)⁴.

= 210A⁶ • 81B⁴

= 17010A⁶B⁴.

Ultimately, the term that contains A⁶ in the binomial expansion is; 17,010A⁶B⁴.

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a) To analyze the correlation between umbrella sales and car accidents in Sylvester County in 2013, you would need the data for both variables.

b) To visualize the relationship between umbrella sales and car accidents, you can create a scatterplot.

c) The slope of the regression line represents the change in the number of car accidents associated with a one-unit increase in umbrella sales.

d) To predict the number of accidents if 150 umbrellas were sold in January 2014, you would use the regression equation obtained from the analysis of the 2013 data.

a) To analyze the correlation between umbrella sales and car accidents in Sylvester County in 2013, you would need the data for both variables. Let's assume you have collected data for umbrella sales (independent variable) and the number of car accidents (dependent variable) on a monthly basis. To find the regression equation, you would perform a linear regression analysis on the data. The regression equation will allow you to predict the number of car accidents based on umbrella sales. It will have the form:

Number of car accidents = b0 + b1 * Umbrella sales,

where b0 is the y-intercept and b1 is the slope of the regression line.

b) To visualize the relationship between umbrella sales and car accidents, you can create a scatterplot. The x-axis would represent the umbrella sales, and the y-axis would represent the number of car accidents. Each data point would represent a specific month's data. You would plot the points on the graph and then draw the least squares regression line (LSRL), which represents the linear relationship between the two variables.

c) The slope of the regression line represents the change in the number of car accidents associated with a one-unit increase in umbrella sales. However, it is important to note that correlation does not imply causation. The slope itself does not prove that umbrella sales directly cause car accidents. It simply indicates the relationship between the two variables in the given data. Other factors might be at play, such as weather conditions, driver behavior, road conditions, etc. Therefore, claiming that umbrella sales cause accidents solely based on the regression line would be misleading without considering other relevant factors.

d) To predict the number of accidents if 150 umbrellas were sold in January 2014, you would use the regression equation obtained from the analysis of the 2013 data. Plug in the value of umbrella sales (150) into the regression equation, and calculate the corresponding predicted number of car accidents. However, it's important to note that using the regression equation to make predictions outside the range of the available data introduces some uncertainty. The accuracy of the prediction may be affected by any changes in the underlying factors not captured by the regression analysis, such as changes in road conditions, driver behavior, or other external variables.

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After applying the coupon, the large pizza price came down to $13.00 from $16.25

We need to figure out the percentage change of this.

The formula for percent change is:

The amount of change (decrease) is:

16.25 - 13.00 = 3.25

The original amount is:

16.25

We substitute these information into the formula and figure out our answer:

Thus, the decrease is 20%.

We can say that the coupon was 20% off coupon.

The proportion that can be used to show that AC and CE has equal slope is: 2 - 0/3 - 0 = 4 - 2/6 - 3.

Using any two points on a given line, the formula to find the slope of the line is given as:

Slope (m) = change in y / change in x = rise/run or the line.

Given that triangles ABC and CDE are two similar right triangles, find the slope of AC and CE as explained below:

Point A is at (0, 0)

Point C is at (3, 2)

Point E is at (6, 4)

Slope of AC = change in y / change in x = 2 - 0/3 - 0 = 2/3

Slope of CE = 4 - 2/6 - 3 = 2/3

Thus, the proportion showing that the slope of AC and the slope of CE are the same would be expressed as:

2 - 0/3 - 0 = 4 - 2/6 - 3.

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Answer:

no

Step-by-step explanation:

Order of operations

18/2=9

9/3=3

5-2=3

3/3

1 (simplified)

The outcome is still the same but since you have to show your work.....That's the correct way to do it

Hope this helps. Have a nice day.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{84.5}}}}}\)

Step-by-step explanation:

Given data :

89 , 74 , 100 , 86 , 74 , 67 , 86 , 72 , 60 , 93 , 83 , 86

Arranging the data in ascending order, we have,

60 , 67 , 72 , 74 , 74 ,83 , 86 , 86 , 86 , 89 , 93 , 100

Here, n ( total no.of observation ) = 12

Now, finding the position of media :

\( \boxed{ \sf{position \: of \: median = ( \frac{n + 1}{2} ) ^{th} \: item}}\)

⇒\( \sf{ (\frac{12 + 1}{2} ) ^{th} item}\)

⇒\( \sf{( \frac{13}{2} ) ^{th} item}\)

⇒\( \sf{ {6.5}^{th} item}\)

6.5 th item is the average of 6 th and 7 th items.

Again,

\( \sf{median = \frac{ {6}^{th \: item} + {7}^{th} item}{2} }\)

⇒\( \sf{ \frac{83 + 86}{2} }\)

⇒\( \sf{ \frac{169}{2} }\)

⇒\( \sf{84.5}\)

Hope I helped!

Best regards!!

The nominal interest rate compounded semi-annually which is equivalent to 2.76% compounded quarterly is 1.37% (rounded to 2 decimal places).

Here, we are supposed to find the nominal interest rate compounded semi-annually which is equivalent to 2.76% compounded quarterly.

The relationship between a nominal interest rate (i) and the effective interest rate (i’), compounded (n) times a year, is given by;

(1 + i/n)^n

= 1 + i’/m(1)

Where m is the number of times interest is compounded per year.

So, we get the effective interest rate that corresponds to 2.76% compounded quarterly as follows;

Let i' be the effective interest rate that corresponds to 2.76% compounded quarterly.

Then; n = 4 and m = 1 (Quarterly compounding period and 1 year is divided into 4 quarters)i’

= (1 + 0.0276/4)^4 - 1

= 0.02806 (Rounded to 5 decimal places)

Now, to calculate the nominal interest rate compounded semi-annually,

we can use Equation (1);(1 + i/2)^2

= 1 + 0.02806i

= [1 + 0.02806]^(1/2) - 1

= 0.01367

≈ 1.37%(Rounded to 2 decimal places)

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The shadow length is increasing at a rate of approximately 3.16m/s when Regina is 7m away from the point under the light.

A streetlight hangs 5 meters above the ground.

Regina, who is 1.5 meters tall, walks away from the point under the light at a rate of 2 meters per second.

The objective is to find the rate at which her shadow is lengthening when she is 7 meters away from the point under the light.

Let AB be the pole of the light and C be the shadow of Regina and CB be her shadow. We have,

AB = 5m and AC = 1.5m

Also, it is given that Regina is moving away from the point at a rate of 2m/s.

Now, it is required to find the rate at which CB is increasing, i.e., to find d(CB)/dt when Regina is 7m away from the pole.

From the figure, we can observe that:  AB/BC = AC/CB

By differentiating w.r.t time t on both sides, we have:

d(AB)/dt / BC + AB / d(BC)/dt = - d(AC)/dt / CB - AC / d(CB)/dt

Now, we substitute the given values into the above equation, we get:

d(AB)/dt = 0, AB = 5m

BC = 7m

AC = 1.5m

d(AC)/dt = -2m/s

Substituting these values, we get;

0/7 + 5 / d(BC)/dt = -(-2) / CB - 1.5 / d(CB)/dt

On solving, we get;

d(CB)/dt = 60 / 19 ≈ 3.16m/s

Therefore, the shadow length is increasing at a rate of approximately 3.16m/s when Regina is 7m away from the point under the light.

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Answer:

5,740 more minutes i hope this helps

Step-by-step explanation:

The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

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Complete Question:-

Sum of Exterior Angles of Triangle is 360°.

Define Exterior Angle

The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.

Let's Prove: ∠1 + ∠2 + ∠3 = 360°

The angle that is created between one of a triangle's sides and its adjacent extended side is known as the external angle. A triangle has three external angles. Let's learn about the equation for adding a triangle's exterior angles.

From the figure, we can observe that ∠1, ∠2, and ∠3 are the exterior angles of triangle ABC. We know that the sum of all the exterior angles of any polygon is equal to 360°.

Thus, sum of all the exterior angles of a triangle = 360°

Therefore, In triangle ABC the sum of exterior angles,

∠1 + ∠2 + ∠3 = 360°

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Answer:

$28

Step-by-step explanation:

80% means 80/100

Of means multiplication

So, 80% of $35

= 80/100 X 35

= 0.8 X 35

= 28

Answer:

−7+y/3  is the same as that, but simplified.

Answer:

y/3-7

Step-by-step explanation:

The answer is the solved equation of -3+2/3y-4-1/3y.

Subtract 4 from -3 to get -7

= -7+2/3y-1/3y

Combine 2/3y and -1/3y to get 1/3y

-7+1/3, or just y/3-7.

Answer:

the slope is -3/2

Step-by-step explanation:

Basically just subtract the 3x from both sides and then divide the entrie equation by 2 to get the y by itself. and then the equation should be y=-3/2x-4 where -3/2 is the slope

Answer: The answer should be y = -3/2x-8

Step-by-step explanation:

you want the 2y by itself so you take the 3x and move it to the other side. so you subtract it to the other side.

2y = -3x-8

than you want the y alone so you divide it to get it to the other side

Answer:

30-j

Step-by-step explanation:

Start with 30, the store sold J

30-j is what the store would have left

Answer:

$1591.35

Explanation:

in the first year,

$1,500 × (100% + 3%)

= $1,500 × 103%

= $1,545

in the second year,

$1,545 × (100% + 3%)

= $1,545 × 103%

= $1591.35

do comment if you need any clarification. i hope this helps! :D

Answer:

2 days

Step-by-step explanation:

It takes four plumbers five days

total labor needed

4 * 5 = 20 days

How long would it take ten plumbers?

20 / 10 = 2 days

This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.

We have a pond which is completely filled with the water.

Area of the side face ( trapezium shaped)

= 1/2 x (1.4 + 0.6) x 2

= 2 m²

Volume = area x height (here width)

V = 2x1 = 2 m³

The level goes down by 20cm in the first 30 mins

Volume of water that will be taken down =

=0.2 x 1 x 2

=0.4 m³ ( upper water will form cuboid face)

Now,

⇒0.4 m³ water is taken out in 30 minutes

⇒1 m³ water is taken out in 30/0.4 minutes

⇒2 m³ water is taken out in 30/0.4 x 2 minutes

⇒30x2/0.4

⇒150 minutes.

So the pond will be completely empty in 150 min that is 2hrs30mins.

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Answer:

y = 6/7x + 68/7

Step-by-step explanation:

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Answer:

the last option

y = -x + 4

Step-by-step explanation:

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(f(x)=\cfrac{x-7}{x+4}\qquad \implies \qquad y=\cfrac{x-7}{x+4}\qquad \implies \qquad \stackrel{\textit{quick switcheroo}}{x=\cfrac{y-7}{y+4}} \\\\\\ xy+4x=y-7\implies 4x=y-7-xy\implies 4x+7=y-xy \\\\\\ 4x+7=y(1-x)\implies \hspace{5em}\cfrac{4x+7}{1-x}~~ = ~~\stackrel{f^{-1}(x)}{y} ~~ ; ~~ x\ne1\)

why x ≠ 1?  well, if that ever happens our denominator goes to 0 and the fraction goes poof, can't have that.

Boy = x

His Sister = y

Father = z

x = 2*y  

y = x/2

x = z-30 or z = x+30

3.8 m = 380 cm

x+y+z = 380

x + x/2 + x+30 = 380

multiply by 2

2x +x + 2x +60 = 760

5x = 700

x = 140 cm

y = x/2

 = 140 /2 = 70 cm

z = x+30

 = 140 + 30 = 170 cm

There  

x (Boy)             = 140 cm

y (His Sister)  = 70 cm

z (Father)        = 170 cm

Using an appropriate equation, the boy's height is 140  cm.​

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let Boy = x and His Sister = y

Father = z

So, x = 2*y  

y = x/2

x = z-30 or z = x+30

Now, substitute

3.8 m = 380 cm

Equation form;

x+y+z = 380

x + x/2 + x+30 = 380

then multiply by 2

2x +x + 2x +60 = 760

5x = 700

x = 140 cm

Thus,

y = x/2 = 140 /2 = 70 cm

z = x+30 = 140 + 30 = 170 cm

There  are x (Boy) = 140 cm

y (His Sister)  = 70 cm

z (Father)   = 170 cm

Hence, Using an appropriate equation, the boy's height is 140  cm.​

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Answer:

slope: -3

y-intercept: 5

Step-by-step explanation:

y=mx+b, where m=slope and b=y-intercept

Answer:

The slope is -3 and y is 5. hope that helped

Answer:

Graph b

Step-by-step explanation:

y = |x| is a "v"at x = 0

y = |x-1| is a "v" shifted to the right by 1 unit

Answer:

d=6 & p=13

Step-by-step explanation:

1. P+d=19

×9

2. 9p +5.50d=150

×1

9p+9d=171

-

9p +5.50d=150

3.5d=21

d=6

Substituting d=6 in 1.

P+6=19

P=13