Is (8, 3) a solution to the system?
- x + 4y = 4
- x + 3y = 1

Answer:

Equal volumes

Step-by-step explanation:

Given

[tex]h \to[/tex] height of cone

[tex]d \to[/tex] diameter of cone

[tex]H \to[/tex] height of cylinder

[tex]D \to[/tex] diameter of cylinder

Such that:

[tex]d = 2D[/tex]

[tex]h =\frac{3}{4}H[/tex]

Required

The relationship between the volumes

The volume of a cylinder is:

[tex]V_1 = \pi R^2H[/tex]

Where

[tex]R = 0.5D[/tex]

So:

[tex]V_1 = \pi (0.5D)^2H[/tex]

[tex]V_1 = \pi *0.25*D^2H[/tex]

[tex]V_1 = 0.25\pi D^2H[/tex]

The volume of the cone is:

[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]

Where

[tex]r =0.5d[/tex]

[tex]r = 0.5 * 2D[/tex]

[tex]r = D[/tex]

and

[tex]h =\frac{3}{4}H[/tex]

So, we have:

[tex]V_2 = \frac{1}{3}\pi * D^2 * \frac{3}{4}H[/tex]

[tex]V_2 = \frac{1}{4}\pi * D^2H[/tex]

[tex]V_2 = 0.25\pi * D^2H[/tex]

[tex]V_2 = 0.25\pi D^2H[/tex]

So, we have:

[tex]V_1 = 0.25\pi D^2H[/tex]

[tex]V_2 = 0.25\pi * D^2H[/tex]

[tex]V_1 = V_2[/tex]

Answer: : When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of this circle is (x - 2)^2 + (x + 3)^2 = 36.

The center of the circle is at (h, k):  (2, -3), and the radius, r, is 6.

Answer: 1306.5 m^3

Step-by-step explanation:

1. The formula for the volume of a cylinder is: V=[tex]\pi[/tex]r^2h

2. If you substitute the values into the equation, you get

V = pi * 5.7^2 * 12.8 = 1306.5

3. 1306.5 is already to the nearest tenth, so that is the answer.

Answer:

24 miles

Step-by-step explanation:

Given that the cost of the company consist of two elements; a fixed cost equivalent to $4 and a variable cost element which depends on the miles driven. If the car travels x miles then the cost will be

= 4 + 1*x

= 4 + x

If the total cost is $28 then

4 + x = 28

Subtract 4 from both sides

x = 28 - 4

= 24  

The car ride is

24/1 = 24 miles

Answer:

(1,0) and (3,0)

Step-by-step explanation:

The roots are always shown where the parabola crosses the x-axis.

In this particular graph, the parabola crosses at (1, 0) and (3, 0). Which means the roots are:

x = 1 and x = 3

Answer:

216 cubic centimeters

Step-by-step explanation:

I divided the shape as two separate rectangular prisms.

4 times 6 times 6 = 144

3 times 4 times 6 = 72

144 + 72 = 216

I hope this helps! :-)

Answer:

4,500

Step-by-step explanation:

150,000x.03=4500

The commission of the real estate agent is 4500 which is 3% of 150,000.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A real estate agent earns a 3% commission on each house she sells and she sells a 150,000 house.

So, His commission is 3% of 150,000.

Therefore,

Commission = (3/100)×150000.

Commission = 4500.

So, The commission of the real estate agent is 4500.

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Answer:

A unit rate is the rate of change in a relationship where the rate is per 1.

The rate of change is the ratio between the x and y (or input and output) values in a relationship.  Another term for the rate of change for proportional relationships is the constant of proportionality.

If the rate of change is yx, then so is the constant of proportionality.  To simplify things, we set  yx=k, where k represents the constant of proportionality.  

If you solve a yx=k equation for y, (like this: y=kx), it is called a direct variation equation. In a direct variation equation, y varies directly with x. When x increases or decreases, y also increases or decreases by the same proportion.

To find y in a direct variation equation, multiply x by the constant of proportionality, k.

For example: Given the relationship y=7x, the constant of proportionality k=7,  so if x=3,  then y=3×7 or 21.

Given the same relationship, if x=7,  then y=7×7, or 49.  

Step-by-step explanation:

Answer:

Yes it is. Y=2.5x

Step-by-step explanation:

So, lets start with bthe first values of the table and work our way down:

2x=5y

Lets just divide both sides by the 2:

x=5/2y

This means that for every 1 x, there should be 5/2y's.

Or, for every 1 x, there should be 2.5ys.

Lets check the next few to see if thats correct:

3x=7.5y

Divide both sides by 3:

x=7.5/3

This means for every one x, there are again, 2.5ys.

Lets check one more just to be sure:

4x=10y

Divide both sides by 4:

x=10/4

This means for everyone one x, y equals 2.5ys, yet again,

So we can conclude that the poprotional relationship between x and y is:

When x equals 1, y=2.5

Or

Y=2.5x

Hope this helps!

Answer:

A = 37.5

Step-by-step explanation:

The formula for finding the are of a trapezoid is (a + b)/2(h)

a = base

b = base

h = height

A = (6.1 + 8.9) / 2(5)

A = 37.5

Answer:

The answer is 37.5.

Step-by-step explanation:

The area for a triangle is A=1/2 bh.

In this case, we have 2 triangles, so we just make it one rectangle.

Each triangle is (1.4*5)/2. (1.4*5)*2/2=7.

You do 2/2 because the half and the two triangles cancel out.

6.1*5=30.5.

30.5+7=37.5

Answer:

[tex]130cm^{2}[/tex]

Step-by-step explanation:

1) Calculate the entire rectangle and subtract the right triangle area

15 x 10 = 150 Entire rectangle area

(5 x 8) ÷ 2 = 20 Triangle area

150 - 20 = 130 Area of shaded region

Answer:

please provide the choices of this question

Answer:

3x2 – 5x + 2 = ( 3x-2)( x-1)

Step-by-step explanation:

I hope this helps you!

Have a nice dayyy <3

Answer:

[tex](3x-2)(x-1)[/tex]

Step-by-step explanation:

Answer:

1) Use translation to coincide the center of a circle with the center of the other circle.

2) We construct the respective loci for the circles.

3) Compare each loci by direct inspection ([tex]f(x,y)[/tex] must be the same and radii must be different but constant) to conclude the similarity of the two circles.

Step-by-step explanation:

Geometrically speaking, a circle is formed after knowing its center and radius.

1) Use translation to coincide the center of a circle with the center of the other circle. In this case, we translate the center ([tex]C_{A} (x,y) = (6,7)[/tex]) of the circle A to the location of the center of the circle B ([tex]C_{B}(x,y) = (2,4)[/tex]):

[tex]C_{A'} (x,y) = (6,7) + [(2,4) - (6,7)][/tex]

[tex]C_{A'} (x,y) = (2,4)[/tex]

2) We construct the respective loci for the circles.

By Analytical Geometric, a circle is represented by the following locus:

[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]

Where:

[tex]x, y[/tex] - Coordinates of a point of the circunference.

[tex]h, k[/tex] - Coordinates of the center of the circle.

[tex]r[/tex] - Radius of the circle.

3) Compare each loci by direct inspection ([tex]f(x,y)[/tex] must be the same and radii must be different but constant) to conclude the similarity of the two circles.

Then, the circles A' and B are represented by the following loci:

Circle A'

[tex](x-2)^{2} + (y-4)^{2} = 16[/tex]

Circle B

[tex](x-2)^{2} + (y-4)^{2} = 256[/tex]

Since both the [tex]f(x,y)[/tex] component of each circle is the same and radii are different but constant, then we conclude that circle A is similar to circle B.

Hence,

Hope it helps you. Please don't mind my rude handwriting. Just pretend it get bent due to a cyclone.

Answer:

[tex]n=-2[/tex]

Step-by-step explanation:

[tex]-4(8+6n)=-2(n-6)\\ -32-24n=-2n+12\\-32-12=-2n+24n\\-44=22n\\n=-2[/tex]

Answer: It’s 5%

Step-by-step explanation:45 divided by 9 is 5 so that the answer :)

Answer:

a b c and f

Step-by-step explanation:

rectangle parallelogram square and rhombus

Answer:

Step-by-step explanation:

I need help

Answer: just do 3x136

step-by-step explanation:

bfui3qtwsd3wa CAF

The number of sodas sold is 102 and the number of Hot dogs sold is 34.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, At a hockey game, a vendor sold a combined total of 136 sodas and hot dogs.

Let "x" be the number of hot dogs sold

Since The number of sodas sold was three times the number of hot dogs sold.

thus,

Number of Sodas sold = 3 * x

Since total items sold = 136

x + 3x = 136

4x = 136

x = 34

Thus, the number of Sodas sold = 34 * 3

the Number of Sodas sold = 102

therefore, the number of sodas sold is 102 and the number of Hot dogs sold is 34.

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Answer:

uhhhh.....wut?

Step-by-step explanation:

The measure of the angle WSV is 38 degrees.

Complementary Angles Two angles are Complementary when they add up to 90 degrees.

The value of x is;

[tex]\rm 5x+17=9x-11\\\\ 5x-9x=-11-17\\\\-4x=-28\\\\x =\dfrac{-28}{-4}\\\\x=7[/tex]

The angle VST is equlas to;

[tex]\angle \rm VST=9x-11=9(7)-11=63-11=52 \ degrees[/tex]

The angle VST and angle WSV are the complementary angles;

[tex]\angle \rm WSV+\angle VST=90\\\\\angle \rm WSV+52=90\\\\ \angle \rm WSV=90-52\\\\\angle \rm WSV=38[/tex]

Hence, the measure of the angle WSV is 38 degrees.

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Answer:

Grey Hairs? Try some of our free Pi-Lights

Step-by-step explanation:

Answer:

87 %

Step-by-step explanation:

Answer:

a⁸=112 is the answer.

Step-by-step explanation:

a⁸=32(1/2)⁷

a⁸=32(7/2)

a⁸=112

The last name I am pretty sure of it.

Answer:

Zarathustra is the answer

Answer:

D

Step-by-step explanation:

Answer:

1884.96 cm squared

Answer:

Step-by-step explanation:

Answer:

Mean

Step-by-step explanation:

I said mean because it would allow both Carl and Tamera to average their scores and compare one side by side rather than comparing 6 each which would just be time consuming and it seems like it wouldn't be any other choices.