Consider the polynomial 9n2+60n+100.
What are the square roots of the first and last terms?

square root of first term:

square root of last term:

Answer:

Answer choice D

Step-by-step explanation:

So we need to get r to the right side. First we can multiply by 3 to get rid of the fraction:

3V=4[tex]\pi[/tex][tex]r^{3}[/tex]

Then we can divide both sides by 4[tex]\pi[/tex] to get r by itself:

[tex]\frac{3V}{4\pi } = r^{3}[/tex]

Then cube both sides:

[tex]\sqrt[3]{\frac{3V}{4\pi } } =r\\[/tex]

Answer choice D

Answer:

300 + 2,000 = 2,300

Step-by-step explanation:

349 = 300

1,978 = 2,000

because the 4 is less than 5 and any number greater than 5 is rounded up and any number less than 5 is rounded down

Answer:

The equation of perpendicular bisector is:

[tex]y = 2x-2[/tex]

Step-by-step explanation:

Given the points

First, we need to find the midpoint of the points (-4, 3) and (8, -3)

[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)[/tex]

[tex]=\left(\frac{8-4}{2},\:\frac{-3+3}{2}\right)[/tex]

[tex]=\left(2,\:0\right)[/tex]

Thus, the midpoint of the points is: (2, 0)

Now, finding the slope between (-4, 3) and (8, -3)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)[/tex]

[tex]m=-\frac{1}{2}[/tex]

Therefore, the slope m = -1/2

The slope of the line perpendicular to the segment = [-1] / [-1/2] = 2

Using the point-slope form of the equation of the line, the equation of perpendicular bisector is:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where m is the slope of the line

substituting the slope 2 and the point (2, 0)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y - 0 = 2 (x-2)[/tex]

[tex]y = 2x-2[/tex]

Therefore, the equation of perpendicular bisector is:

[tex]y = 2x-2[/tex]

Answer:

Step-by-step explanation:

1). Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

   m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

   Therefore, slope of the line passing through two points (2, -10) and (-2, 18) will be,

   m = [tex]\frac{-10-18}{2+2}[/tex]

  m = -7

2). From the table attached,

    Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

    Slope of line passing through (4, -6) and (0, -2) will be,

    Slope = [tex]\frac{-6+2}{4-0}[/tex]

    Slope = -1

Answer:

The answer is not 1 or 0

I think its D. infinitely many

Step-by-step explanation:

Hey there!

The solution to the system is [tex](\frac{1}{2}, 13)[/tex]

To solve the system, we can multiply the second equation by -1:

[tex]-2x - y = -12[/tex]

Then, we add the two equations together, and solve for x:

[tex]4x = -2[/tex]

[tex]x = \frac{-1}{2}[/tex]

Now, we plug the x value into one of the equations, and solve for y:

[tex]2(\frac{1}{2} ) + y = 12[/tex]

[tex]-2 + y = 12[/tex]

[tex]y = 13[/tex]

Now we know that the solution to the system is [tex](\frac{1}{2}, 13)[/tex]

Hope it helps and have an amazing day!

Answer:

(-1/2, 13)

Step-by-step explanation:

Multiply the 2nd equation by -1, obtaining the following system:

6x + y = 10

-2x  - y = -12

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

Combine like terms, obtaining:

6x + y = 10

-2x  - y = -12

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

4x     = -2

Dividing both sides by 4 yields x = -2/4, or x = -1/2

Substituting -1/2 for x in the second equation yields:

2(-1/2) + y = 12, or

-1 + y = 12.  Then y = 13, and the solution is

(-1/2, 13)

Answer:

Yes they are. “X” is basically 1x becuase if you multiply 1 by x its still x. So they are like terms, if you combine them you’ll get 6x becuase 5x+x=6x

Answer:

89.03

Step-by-step explanation:

29x3.07=89.03

Step-by-step explanation:

im not sure

Answer: 1/6

Step-by-step explanation:

5/6 - 4/6 = 1/6

Answer:

1

-

6

Step-by-step explanation:

Answer:

I(20) is 600 dollars

Step-by-step explanation:

From the given function, I(p) = p(50 - p)

Where I is the income in dollars and p is price dollars.

To determine I(20), that is, to determine the income in dollars when the ticket price is 20 dollars.

From

I(p) = p(50 - p)

When p = 20

Then,

I(20) = 20(50 - 20)

I(20) = 20(30)

I(20) = 20 × 30

I(20) = 600

Hence, I(20) is 600 dollars

That is, the income is 600 dollars when the ticket price is 20 dollars.

Answer:

On the side length of the triangle

Step-by-step explanation:

On the side length of the triangle

Answer:

No solution exists

Step-by-step explanation:

Answer:

its b because

Step-by-step explanation:

24÷12 is 2 and if u do 12 × 2 and keep going u will get the next answer

Answer:

The 2 angles are supplementary.  This means they have to add up to 180 degrees.  The first angle is 8x and the second is x+27.  So set both of them equal to 180.

8x + x + 27 = 180

9x = 153

x = 17

Angle 1 = 8(17) = 136

Angle 2 = (17) + 27 = 44

Check: Angle 1 + Angle 2 = 180

136 + 44 = 180

Step-by-step explanation:

Answer:

Step-by-step explanation:

12). By applying Pythagoras theorem in the given right triangle,

      Hypotenuse² = (Leg 1)² + (Leg 2)²

      x² = 7² + 7²

      x² = 2(7)²

      x = [tex]\sqrt{2(7)^{2} }[/tex]

      x = [tex]7\sqrt{2}[/tex]

13). By sine rule,

      sin(60)° = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

      [tex]\frac{\sqrt{3}}{2}=\frac{9\sqrt{3} }{y}[/tex]

      y = [tex]\frac{18\sqrt{3} }{\sqrt{3} }[/tex]

      y = 18

      By cosine rule,

      cos(60)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

      [tex]\frac{1}{2}=\frac{x}{y}[/tex]

      x = [tex]\frac{y}{2}[/tex]

      x = [tex]\frac{18}{2}=9[/tex]

14). By applying Pythagoras theorem in the given right triangle,

      12² = x² + x²

      144 = 2x²

      72 = x²

      x = √72

      x = 6√2

Answer:

Answer

Step-by-step explanation:

Answer:

The correct option is C) Yes; the change in x is constant and the change in y is constant.

Step-by-step explanation:

Consider the table shown.

x     y

0    8

1     1

2   -6

3   -13

Now observe the changes in x and y coordinates, if changes are constant then the given function is linear.

Consider the change in x coordinate.

1-0=1,  2-1=1 and 3-2=1

Now consider the change in y coordinate.

1-8=-7,  -6-1=-7  and -13-(-6)=-13+6=-7

Since the change in x and y is constant the given relationship is linear.

Therefore, the correct option is (C) Yes; the change in x is constant and the change in y is constant.

9514 1404 393

Answer:

  (c)  16πx^6y^10

Step-by-step explanation:

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

__

Putting the expression for r in the formula, you have ...

  A = πr^2

  A = π(4x^3y^5)^2 . . . . . substitute for r

  A = π(4^2)(x^(3·2))(y^(5·2)) = 16πx^6y^10

Answer:

£129.60

Step-by-step explanation:

10% =  £16.2

20% = £32.4

£162 - £32.40 = £129.60

Answer:

2

Step-by-step explanation:

Hope this helps!! Have a blessed day!

Answer:

1 + 1 = 2

Step-by-step explanation:

This is because if you count on your fingers one and one, you get two. I hope this helps!!

The question is incomplete :

The amount sabrina earns varies directly with the number boxes of cookies she sells.How much does Sabrina earn for eah box of cookies that she sells?

Earning (y) : ____ 5 ____ 10 ____ 15 ____ 20

Boxes sold (x) :__ 2 ____ 4 _____ 6 ____ 8

Answer:

$2.5

Step-by-step explanation:

Given:

Earning varies directly as the number of boxes of cookies sold

y α x

y = kx - - - (1)

k = constant of proportionality (earning per box of cookies sold)

Taking any 2 points :

y = 10 ; x = 4

10 = k4

10 = 4k

Divide both sides by 4

10/4 = 4k/4

2.5 = k

Hence, the amount earned per box of cookies sold is $2.5

Answer:

the answer is SAS

side angle side

Answer:

Inspection fee = $50

h = 2 hours

Step-by-step explanation:

Let

x = the inspection fee

Charge per hour = $22

Number of hours = 4

A customer with a coupon for 40% off the inspection fee

This means the customer paid 60% of the inspection fee

118 = 60% of x + 22(4)

118 = 0.6x + 88

118 - 88 = .6x

30 = .6x

x = 30/0.6

x = $50

Inspection fee = x = $50

How many hours are worked when a customer pays $94 without a coupon?

94 = 50 + 22h

94 - 50 = 22h

44 = 22h

h = 44/22

h = 2 hours

Answer:

-4

Step-by-step explanation:

Answer:s

slope of -4x-3: m=-4

Answer:

x=44444444444444444444444444444444

Step-by-step explanation:

Answer:

.2

Step-by-step explanation: