MULTIPLE CHOICE
A sphere has the same radius as a cylinder. In the cylinder, the radius equals the height. If
the cylinder has a volume of 150 cubic units, what is the volume of the sphere?
A
450 cubic units
B
200 cubic units
С
112.5 cubic units
D
50 cubic units

Answer:

a. a = 1, b = -5, c = -14

b. a = 1, b = -6, c = 9

c. a = -1, b = -1, c = -3

d. a = 1, b = 0, c = -1

e. a = 1, b = 0, c = -3

Step-by-step explanation:

a. x-ints at 7 and -2

this means that our quadratic equation must factor to:

[tex](x-7)(x+2) = 0[/tex]

FOIL:

[tex]x^2 + 2x - 7x - 14 = 0[/tex]

Simplify:

[tex]x^2 - 5x - 14 = 0[/tex]

a = 1, b = -5, c = -14

b. one x-int at 3

this means that the equation will factor to:

[tex](x-3)^2=0[/tex]

FOIL:

[tex]x^2 - 3x - 3x +9 = 0[/tex]

Simplify:

[tex]x^2 - 6x + 9 = 0[/tex]

a = 1, b = -6, c = 9

c. no x-int and negative y must be less than 0

This means that our vertex must be below the x-axis and our parabola must point down

There are many equations for this, but one could be:

[tex]-x^2-x-3=0[/tex]

a = -1, b = -1, c = -3

d. one positive x-int, one negative x-int

We can use any x-intercepts, so let's just use -1 and 1

The equation will factor to:

[tex](x+1)(x-1)=0[/tex]

This is a perfect square

FOIL:

[tex]x^2-1=0[/tex]

a = 1, b = 0, c = -1

e. x-int at [tex]\sqrt{3} , -\sqrt{3}[/tex]

our equation will factor to:

[tex](x+\sqrt{3} )(x-\sqrt{3)} =0[/tex]

This is also a perfect square

FOIL and you will get:

[tex]x^2 - 3 = 0[/tex]

a = 1, b = 0, c = -3

Answer:

2/6 chance of landing on 2 or 3

Step-by-step explanation:

Answer:

C. 314.2 cm²

Step-by-step explanation:

Surface area for cylinder

[tex]\text{SA} = 2 \pi r^2 + 2 \pi r h[/tex],
where r is radius and h is height.

[tex]2\pi r^2[/tex] comes from two times the area of the circle, [tex]2 \pi r h[/tex] is the area of the curved surface.

Given information:

r = 5 cm

h = 5 cm

Insert the values into the formula and evaluate

[tex]\text{SA} = 2 \pi r^2 + 2 \pi r h\\\text{SA} = 2 \pi (5)^2 + 2 \pi (5)(5)\\\text{SA} = 2 \pi (25) + 2 \pi (25)\\\text{SA} = 50 \pi+ 50\pi \\\text{SA} = 100\pi \approx 314.159\\\text{SA} = 314.2 \text{ cm}^2[/tex]

Answer:

Yes

Step-by-step explanation:

Because when you draw it u get a right angle

Answer:

256cm

Step-by-step explanation:

I'm assuming 16 and 16 are the 2 legs of the triangle.

The equation to get the area of a triangle is b x h /2

16cm x 16cm / 2 = 128cm

128cm x 2 triangles = 256cm

The next step to complete the construction will connect the in-center to one of the sides of the triangle.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

Samuel is trying to construct the inscribed circle of a triangle.

Using the angle bisectors to find the in-center.

Where two angles bisector meets, the point called in-center.

Next step will be: connect the in-center to one of the sides of the triangle.

Thus, the next step to complete the construction will be connect the in-center to one of the sides of the triangle.

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The equation used for finding the length of Harold's bridge will be 3H-7M=0 Length will be H = 1/√2

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Here we have the following data:-

Matthew's bridge length is

 1(1/2)=3/2

Now we have that Harold made a bridge that was 2 1/3 times as long as Matthew’s. From this data the equation will be:-

[tex]H=2\dfrac{1}{3}M\\\\\\H-\dfrac{7}{3}M=0\\\\\\3H-\dfrac{7\times 3}{2}=0\\\\\\H=\dfrac{1}{\sqrt{2}}[/tex]

The equation used for finding the length of Harold's bridge will be 3G-7M=0 Length will be H = 1/√2

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Answer:

138, 460 m²

Step-by-step explanation:

How To Find Volume of Pyramid With Slant Height? If 'x' is the base length, 's' is the slant height, and 'h' is the height of a regular pyramid, then they satisfy the equation (the Pythagoras theorem) (x/2)2 + h2 = s2.

Answer:

132 is the one to the right of it and next one going clockwise wold probably be 48 continueing clockwise the next would be 132 again

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

You can get 1/2 the unknown just by looking at the givens. The slope is just given -- no need to modify it.

The y intercept is a little harder. You need the point for that.

Givens

Slope = 1/2

point = (-6,8)

Formula

y = mx + b

Solution

m = 1/2

y = 1/2x + b              To find b,

8 = 1/2(-6) + b

8 = -3 + b                 Add 3 to both sides

8 + 3 = b

b = 11

Answer

y = 1/2x + 11

Answer:

y = 1/2x+11

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

y = 1/2x +b

We can use the point on the line to find b

8 = 1/2(-6) +b

8 = -3+b

Add 3 to each side

8+3 =-3+3 b

11 = b

y = 1/2x+11

Answer:

$336

Step-by-step explanation:

how to find this is very simple, she raised d =(total amount of money raised) in dollars, average means we assume that with any amount of people one person gave 28 dollars each.

Our problem would read out to be d(total amount she raised) is equal to $28 times x(amount of people who sponsored her) or d = 28 * x

If 12 people sponsored her

original equation:

d = 28 * x

equation with x known(12 people)

d = 28 * 12

to solve all we do is multiply 28 times the amount of people who sponsored her, in this case, its 12.

d = 336

we know that if 12 people sponsor her d, or the total amount she raised, is equal to $336

For the rectangle to have a perimeter of 36 units, the sum of the length and the width must equal 18 units

The given parameter is:

Perimeter = 36 units

The perimeter of a rectangle is:

Perimeter = 2 * (Length + Width)

So, we have;

36 = 2 * (Length + Width)

Divide both sides by 2

Length + Width = 18

This means that for the rectangle to have a perimeter of 36 units, the sum of the length and the width must equal 18 units

So, the possible table of values is:

Length  Width

  5           13

  8           10

  9           9

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Answer:

B

Step-by-step explanation:

add 8 to both sides and multiply both y and 8 by 4 to get 4y and 32

The value of variable x of provided quadratic function at h(x) = 18 are 6.56 and -0.13. These points explain solution of the equation.

Quadratic formula is the formula which is used to find the roots of a quadratic equation.The standard form of the quadratic equation is,

ax²+bx+c=0

For the above equation, the quadratic formula can be given as,

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The equation of variable x is given as,

h(x) = 7x²-45x + 12,

The value of h(x) = 18 has to be found out. Put 18 on the place of h(x) in the above equation.

18 = 7x²-45x + 12

0= 7x²-45x + 12-18

0=7x²-45x -6

Find the roots of the equation using the quadratic formula:

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\dfrac{-(-45)\pm\sqrt{(-45)^2-4(7)(-6)}}{2(-6)}\\x=6.56,-0.13[/tex]

Thus, the value of variable x of provided quadratic function at h(x) = 18 are 6.56 and -0.13. These points explain the solution of the equation.

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Answer:

Two

Step-by-step explanation:

3,5 or 7 out of possible 12 spins

3 / 12  of the time she will win

$ 4 is   8 spins

8 spins * 3/12 = 2 wins

ANSWER
2 prizes

Step-by-step explanation:

$4 ÷ $0.5 = 8

Total points on spinner = (1,2,3,4,5,6,7,8,9,10,11,12)

Required for winning = (3, 5, 7)

5+7 = 12

3/12

P(win) = 3/12 simplified is  1/4

(1/4) × (8) = 2

Therefore, the answer is two prizes

On August 5, 1861, President Lincoln imposes the first federal income tax by signing the Revenue Act. Strapped for cash with which to pursue the Civil War, Lincoln and Congress agreed to impose a 3 percent tax on annual incomes over $800.

Answer:

Answer below :)

Step-by-step explanation:

128 = $76.20132= $77.80134= $78.60144= $82.60

Answer: 128 = $76.20132= $77.80134= $78.60144= $82.60

[tex]\begin{cases} x+y=1\\\\ 3y=-3x+3 \end{cases}\hspace{5em}\stackrel{\textit{using the 1st equation}}{x+y=1\implies y=1-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3\stackrel{y}{(1-x)}~~ = ~~-3x+3\implies 3-3x=-3x+3}\implies 0~~ = ~~0[/tex]

now... the result could have been 3 = 3, or hmmm something like so, which is a bit of a flag hmmm let's take a closer look at the 2nd equation

[tex]\begin{cases} \boxed{x+y=1}\\\\ 3y=-3x+3 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 3y=-3x+3\implies 3y=3(-x+1)\implies \cfrac{3y}{3}=-x+1 \\\\\\ y=-x+1\implies \boxed{x+y=1}[/tex]

let's notice, the 2nd equation is really the 1st one in disguise, so both equations are exactly equal.  So what's the solution to that?  well, there isn't one solution per se, if we were to graph both lines, it'll be the graph on one line pancaked on top of the other, and where they touch each other is the solution, well, hell they touch each other everywhere, and since both lines go to infinity, then they have infinitely many solutions.

Answer: X = 12

Step-by-step explanation:

Answer:

im not really sure what that means im so sorry

Step-by-step explanation:

Answer:

good luck passing

Step-by-step explanation: -3 -2 1 x 1 2

Step-by-step explanation:

69 bc it is the difference between the largest number and the smallest number

Answer:

[tex]\textsf{i)} \quad \text{T} &=2 \pi r^2 + \dfrac{26}{r}[/tex]

ii)  radius = 1.27 cm (3 sf)

   height = 2.55 cm (3 sf)

Step-by-step explanation:

[tex]\text{Volume of a cylinder}=\pi r^2 h \quad \text{(where r is radius and h is height)}[/tex]

Given volume = 13 cm³, rewrite the equation making h the subject:

[tex]\implies 13=\pi r^2 h[/tex]

[tex]\implies h=\dfrac{13}{\pi r^2}[/tex]

Substitute found expression for h into the Surface Area equation to find the expression for the total surface area, T:

[tex]\begin{aligned}\text{Surface Area of a cylinder} & =2 \pi r^2 + 2 \pi r h\\\implies \text{Surface Area} & =2 \pi r^2 + 2 \pi r \left(\dfrac{13}{\pi r^2}\right)\\& =2 \pi r^2 + \dfrac{26 \pi r}{\pi r^2}\\ \implies \text{T} &=2 \pi r^2 + \dfrac{26}{r}\end{aligned}[/tex]

To find the radius of the minimum surface area, differentiate T with respect to r:

[tex]\begin{aligned}\text{T}& =2 \pi r^2 +26r^{-1}\\\implies \dfrac{dT}{dr} & =(2)2 \pi r^{(2-1)}+(-1)26r^{(-1-1)}\\ & =4 \pi r-26r^{-2}\\ & =4 \pi r-\dfrac{26}{r^2}\\ & = \dfrac{4 \pi r^3-26}{r^2} \end{aligned}[/tex]

Set it to zero, and solve for r:

[tex]\begin{aligned}\dfrac{dT}{dr} & = 0 \\\implies \dfrac{4 \pi r^3-26}{r^2} & = 0 \\\impliles 4 \pi r^3-26 & = 0 \\4 \pi r^3 & = 26 \\r^3 & = \dfrac{13}{2 \pi} \\r & = \sqrt[3]{\dfrac{13}{2 \pi}} \end{aligned}[/tex]

To find the height, substitute the found value of r into the equation for height (found previously):

[tex]\begin{aligned}h & =\dfrac{13}{\pi r^2} \\\implies h & =\dfrac{13}{\pi \left(\sqrt[3]{\dfrac{13}{2 \pi}}\right)^2} \\& =2.548499134\end{aligned}[/tex]

Therefore,

Answer I think it is a

Step-by-step explanation: A

Answer:

The graph I expect to have a negative correlation is the third graph.

Step-by-step explanation:

Positive correlation is when the the x-values increase with a corresponding increase in y-values.

Negative correlation is when the x-values increases with a corresponding decrease in y-values.

No correlation is when only x or y variable changes.

From the graphs given the only one that has a negative correlation is the third graph.

The linear equation that passes through points (-2,7) and (6,-9) is given by:

y = -2x + 3

A linear function is modeled by:

y = mx + b

In which:

The line passes through points (-2,7) and (6,-9), hence the slope is given by:

m = (-9 - 7)/(6 - (-2)) = -2.

Hence, since when x = -2, y = 7, when x = 0, y = 7 - 2 x (0 - (-2)) = 3, which means that the y-intercept is of b = 3, and the equation is given by:

y = -2x + 3.

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