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3 years ago

Factor 391, 291, 387, 113, 451, 37, 411, 239, and 459 to prime factors

Mathematics

1 answer:

Zigmanuir [339]3 years ago

3 0

Answer:

391 = 17 × 23

291 = 3 × 97

387 = 3 × 3 × 43 = 3^2 × 43

113 is prime

451 = 11 × 41

37 is prime

411 = 3 × 137

239 is prime

459 = 3 × 3 × 3 × 17 = = 3^3 × 17

Step-by-step explanation:

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Isosceles triangles have two equal sides. true or false

melomori [17]

True
isosceles triangles
have 2 equal sides

5 0

3 years ago

Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different

N76 [4]

Answer:

(a) As time increases, the amount of water in the pool increases.

11 gallons per minute

(b) 65 gallons

Step-by-step explanation:

From inspection of the table, we can see that as time increases, the amount of water in the pool increases.

We are told that Ann adds water at a constant rate. Therefore, this can be modeled as a linear function.

The rate at which the water is increasing is the rate of change (which is also the slope of a linear function).

Choose 2 ordered pairs from the table:

$\textsf{let}\:(x_1,y_1)=(8, 153)$

$\textsf{let}\:(x_2,y_2)=(12,197)$

Input these into the slope formula:

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11$

Therefore, the rate at which the water in the pool is increasing is:

11 gallons per minute

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

$y-y_1=m(x-x_1)$

$\implies y-153=11(x-8)$

$\implies y-153=11x-88$

$\implies y=11x-88+153$

$\implies y=11x+65$

When Ann had added no water, x = 0. Therefore,

$y=11(0)+65$

$y=65$

So there was 65 gallons of water in the pool before Ann starting adding water.

3 0

2 years ago

Read 2 more answers

Solve the following system of equations. {y=−2x−92x+3y=−3 Write your answer as an ordered pair in the form (x,y).

Over [174]

Answer:

(x, y) = (-6, 3)

Step-by-step explanation:

Maybe you want to solve ...

y = -2x -9
2x +3y = -3

Use the first equation to substitute for y in the second:

2x +3(-2x -9) = -3

2x -6x -27 = -3

-4x = 24 . . . . . . . . . add 27, simplify

x = -6 . . . . . . . . . . . divide by -4

y = -2(-6) -9 = 12 -9 = 3

The solution is (x, y) = (-6, 3).

6 0

3 years ago

muminat

Answer:

y = 3x + 3

Step-by-step explanation:

when you check, only that equation delivers the correct x and y pairs.

x = 0, => y = 3×0 + 3 = 3

x = 1, y = 3×1 + 3 = 3+3 = 6

x = 2, y = 3×2 + 3 = 6 + 3 = 9

x = 3, y = 3×3 + 3 = 9 + 3 = 12

it all fits.

6 0

2 years ago

11. Mis the midpoint of QR. Q is at (-8, 2) and M is at (4, -3). Find the coordinates of the endpoint R.

tamaranim1 [39]

Answer:

R(16,-8)

Step-by-step explanation:

if (x1,y1) and (x2,y2) are coordinates of two points and (x,y) the coordinate of midpoint.

then x=(x1+x2)/2

and y=(y1+y2)/2

let coordinates of R are (x,y)

4=(-8+x)/2

8=-8+x

x=8+8=16

-3=(2+y)/2

-6=2+y

y=-6-2=-8

so R is (16,-8)

8 0

3 years ago