If r=12 and t=20, find S.

ANSWER

D.

[tex]9 {y}^{2} - 4 {x}^{2}- 36y + 16x - 16 = 0[/tex]

EXPLANATION

The standard equation of the hyperbola is

[tex] \frac{ {(y - 2)}^{2} }{4} - \frac{ {(x - 2)}^{2} }{9} = 1[/tex]

We multiply through by 36 to obtain:

[tex]9 {(y - 2)}^{2} - 4( {x - 2)}^{2} = 36[/tex]

We now expand to get,

[tex]9( {y}^{2} - 4y + 4) - 4( {x}^{2} - 4x + 4) = 36[/tex]

Expand :

[tex]9 {y}^{2} - 36y + 36 - 4 {x}^{2} + 16x - 16 = 36[/tex]

To get the general form, we equate everything to zero to get,

[tex]9 {y}^{2} - 4 {x}^{2}- 36y + 16x - 16 = 0[/tex]

The correct choice is D.

Answer:

A

Step-by-step explanation:

Answer:

230 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

first draw you line down on the equal sign take 2x and devide itso it should be 14/2 you should get 7 2x is no longer there then bring down 9y and add d to 14 thats 23 so its x =23

We need to solve for x.

2x - 9y = 14

Move the 9y to the right side and use inverse operations.

2x = 14 + 9y

Divide both sides of the equation by 2.

x = 7 + 9/2y or x = 7 + 4.5y

I will attach a picture of the graph as well in case that’s what you were looking for.

Answer: it’s definetly C

Step-by-step explanation:

The answer is C.

Hope this helps!

Answer:

D.) 1237 spots

Step-by-step explanation:

We have been given the following regression line;

y= 89.5 + 0.409x

It is reasonable to argue that the number of commuters determines the number of parking spots and as such commuters is our explanatory variable (x). On the other hand, the number of parking spots is our response or dependent variable (y).

We are required to predict the number of parking spots at the Metro-North Station of Greenwich which has 2804 commuters. We are simply asked to determine the value of y when x is 2804 using the regression line;

y = 89.5 + 0.409(2804)

y = 1236.336

y = 1237

D. All rational numbers are integers

All rational numbers are integers

Step-by-step explanation:

answer for this question is 3.85 units squared

Answer:

[tex]\boxed{\text{38.5 units}^{2}}[/tex]

Step-by-step explanation:

The polygon is a trapezoid on its side.

The formula for the area of a trapezoid is  

A = ½(a + b)h,

where a and b are the lengths of the parallel sides and h is the distance between them.

AD = a = 2 – (-2) = 2 + 2 = 4 units

BC = b = 2 – (-5) = 2 + 5 = 7 units

AB = h = 3 – (-4) = 3 + 4 = 7 units

A = ½(4 + 7) × 7 = ½ × 11 × 7 = 38.5 units²

[tex]\boxed{\text{A = 38.5 units}^{2}}[/tex]

Answer:

A≈644.58

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

7m+8=8m

7m-8m= -8

Whenever you move a number for the opposite side , you change the sign. For example, the number is 6 , then you move it to the other side. The sign becomes negative 6.

-m=-8

The m cannot be a negative sign. So you multiply it by -1 and for -8.

-1(-m)= -1(-8)

m= 8

Double check answer if you want to:

7m+8=8m

Substitute the answer for m.

7(8)+8=8(8)

64=64

So the answer is correct. m=8

Postulate SAS can be used to prove triangle [tex]ABC[/tex] is congruent to triangle [tex]AED.[/tex]

" Triangle is defined as the two dimensional closed figure with three vertices, three sides, and three angles enclosed in it."

According to the question,

Given,

In triangle [tex]ABC[/tex] and [tex]AED[/tex]

[tex]\angle ADE = 120\° \ \ \ \ \ \ \ \ \ (1)[/tex]

[tex]\angle ACD = 60\°\\\\\angle ACD + \angle ACB = 180\° (linear \ pair)\\\\\implies \angle ACB = 180\° -60\°\\\\\implies \angle ACB = 120\° \ \ \ \ \ \ \ \ \ \ (2)[/tex]

From [tex](1)[/tex] and [tex](2)[/tex] we get

[tex]\angle ADE \cong \angle ACB[/tex]

[tex]AC \cong AD\\\\BC \cong ED[/tex]

By SAS postulate ,

Triangle ABC is congruent to triangle AED.

Hence, Option 3 is the correct answer.

Learn more about triangle here

brainly.com/question/2773823

#SPJ2

Answer:

D. 0.43, because 13 of the 30 days were cloudy

Step-by-step explanation:

The fist thing that you should do is divide 100 by 30.  We will do this so taht our percentages add up to 100.  When we do this we get 3.333.  Next we need to multiply this by the nubert of cloudy days 13 to get the answer D.

Answer:

Step-by-step explanation:

The formula of a volume of a rectangular prism:

V = lwh

The fomula of a surface area of a rectangular prism:

SA = 2(lw + lh + wh)

l - length

w - width

h - height

We have l = 10cm, w = 6.5cm and h = 8.3cm. Substitute:

V = (10)(6.5)(8.3) = 539.5 cm³

SA = 2[(10)(6.5) + (10)(8.3) + (6.5)(8.3)] = 2(65 + 83 + 53.95)

= 2(201.95) = 403.9 cm²

Answer:

see attached picture

Step-by-step explanation:

I got this by using the free app desmos, you should check it out!

Answer:     2 to 1          and          2;1

Step-by-step explanation:

in general there are 3 ways to write these ratios. A fraction, the one using to, and the ones with semicolans. This is how you will always want to write your ratios on the problems you are solving with your ratios when it asks that.

Answer:

[tex]\frac{2}{1}, 2:1,[/tex]2

Step-by-step explanation:

We can actually use three forms here.

[tex]\frac{x}{y}[/tex]

[tex]x:y[/tex]

x to y.

Use the format for a ratio.

[tex]x:y[/tex]

So

[tex]x=2 \\ y = 1[/tex]

Now we can plug in.

[tex]\frac{2}{1} \\ \\ 2:1 \\ \\[/tex]

2 to 1

Answer:

78%

Step-by-step explanation:

Answer:

Part 1) The measure of angle C is 90°

Part 2) The measure of angle B is 35°

Part 3) The measure of angle A is 55°

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

step 1

Find the measure of angle C

The diameter divide the circle into two equal parts

so

If AB is a diameter

arc AB=180°

∠C=(1/2)[arc AB]

∠C=(1/2)[180°]=90°

step 2

Find the measure of angle B

arc AC=70°

∠B=(1/2)[arc AC]

∠B=(1/2)[70°]=35°

step 3

Find the measure of angle A

The sum of the internal angles of a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

substitute

∠A+35°+90°=180°

∠A=180°-(35°+90°)

∠A=55°

Answer:

m = ($55,000 - $40,000)/(9 - 3)

= $15,000/6 = $2,500

A salesperson's salary will increase by about $2,500 per year of employment.

So in a gallon there is 4 quarts, and in 1 quart there are 2 pints and in 1 pint there are 2 cups.

So for the 1 quart of onion that would equal 4 cups. Then for the 4 pints of broth there would be 8 cups and then the 6 cups and 2 cups just stay the same. So if you add those number of cups up you would get 20 cups. Divide that by 4 to see how many bowls she would need.

The answer is she would need 5 bowls

Answer:

A we can use the sampling distribution to infer about the behavior of all students in the specific district

Step-by-step explanation:

A sample is usually studied or analyzed in order to make inference about the population. It will be more time consuming and costly to study the entire population due to the large number of participants.

In our case, the samples are obtained from a specific school district Michigan. This implies that the researcher is interested in this particular school district and is thus our population of interest. Therefore, we can use the sampling distribution to infer about the behavior of all students in the specific district

We can use the sampling distribution to infer about the behavior of all students in the specific district  

Answer:

Part 1) [tex]42=\frac{1}{2}x(x-5)[/tex]

Part 2) The length of the base is [tex]x=12\ m[/tex]

Step-by-step explanation:

Part 1) Which equation would be help solve the following problem?

Let

x----> the length of the base of a triangle

y----> the height of a triangle

we know that

The area of a triangle is

[tex]A=\frac{1}{2}xy[/tex]

[tex]A=42\ m^{2}[/tex]

so

[tex]42=\frac{1}{2}xy[/tex] ------> equation A

[tex]y=x-5[/tex] -----> equation B

Substitute equation B in equation A  

[tex]42=\frac{1}{2}x(x-5)[/tex]

Part 2) Find the length of the base

we have

[tex]42=\frac{1}{2}x(x-5)[/tex]

solve for x

[tex]84=x^{2}-5x\\x^{2}-5x-84=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=12\ m[/tex]

see the attached figure

Answer:

[tex]\large\boxed{\sqrt[3]{3^{15}}=243}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{3^{15}}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt[3]{3^{5\cdot3}}=\sqrt[3]{(3^5)^3}\\\\\text{use}\ \sqrt[n]{a^n}=a\\\\=3^5=243[/tex]

Answer:

15 dollars

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Divide 640 by 64 to find 1/64.

640/64=10

Or multiply 1/64*640=10

Answer:

125.66 in. ³

Step-by-step explanation:

2 × π × r × h  +  2 × π × r²

We only know the length of the diameter, but we have to find the radius. So we divide by 2 because the radius is half the diameter.

4 ÷ 2 = 2

So r = 2.

h = 8

2 × π × r × h

2 × 3.14 × 2 × 8 = 100.48

2 × π × r²

2 × 3.14 × 2²

2 × 3.14 × 4 = 25.12

Now add them up.

100.48 + 25.12 = 125.66

Hope this helps... :)

Equation of line is doubling

Answer:Hello there!

2y + 4 = 0

2y = -4

y = -2

My assumption is that you'd graph this as a horizontal line at (0,-2) but PLEASE double check with your teacher/instructor because I'm not sure if I'm right.

Hope this helped!

Step-by-step explanation:

Answer:

Step-by-step explanation:

You'll need to share the graphs mentioned in this problem statement.

One can solve  2y + 4 = 0  for y and thus obtain an equation which is easy to graph:

2y + 4 = 0 becomes

2y = -4, or

 y = -2

The graph of this function is the horizontal line y = -2.  Find (0, -2) on your set of coordinate axes and plot a dark dot there.  Then draw a horizontal line thru it.  This line has a slope of zero (0) and a y-intercept of -2.

The equation that matches the function shown in the graph is y = 2x + 4

Which equation matches the function shown in the graph?

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

The graph

A linear equation is represented as

y = mx + c

Where

m = slope

c = y-intercept

From the graph, we have the point (0, 4)

This means that

c = 4

So, we have

y = mx + 4

Using the point (-2, 0) on the graph, we have

-2m + 4 = 0

This gives

2m = 4

m = 2

Recall that

y = mx + 4

So, we have

y = 2x + 4

Hence. the equation is y = 2x + 4

Answer:

S = 1/2 n (n+1)

Step-by-step explanation:

1 + 2 + 3 + ... + n

Now write in reverse order:

n + n-1 + n-2 + ... + 1

Add together:

n+1 + n+1 + n+1 + ... + n+1

n (n+1)

Since this is double the sum:

S = 1/2 n (n+1)

Answer:

1/2n(n+1)

Step-by-step explanation:

The formula for volume of a sphere is 4/3 x PI x r^3

Solve for r:

288PI = 4/3 x PI x r^3

Divide both sides by PI:

288 = 4/3 x r^3

Divide both sides by 4/3:

216 = r^3

Take the cubic root of 216 for r:

r = ∛216

r = 6

The radius is 6 cm.