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Tema [17]
3 years ago
10

Apply the distributive property to create an equivalent expression. 7(4p + 2q + 3r) =?

Mathematics
1 answer:
Nookie1986 [14]3 years ago
4 0

Answer:

The equivalent expression is 28p+14q+21r

Step-by-step explanation:

The distributive property says for any numbers <em>a, b c</em>, and <em>d</em>

d*(a+b+c)=a*d+b*d+c*d

which basically says you should multiply the coefficient d by every term in the parenthesis to get an equivalent expression.

Applying the distributive proper to the expression 7(4p+2q+3r) we get:

7(4p+2q+3r)=7*4p+7*2q+7*3r

=\boxed{28p+14q+21r}

which is an equivalent expression to 7(4p+2q+3r).

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Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.
Rufina [12.5K]

Answer: k = -1 +/- √769

<u>Step-by-step explanation:</u>

48x - ky = 11

<u>-48x        </u>  <u> -48x</u>

         -ky = -48x + 11

         \frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}    

           y =\frac{48x}{k} - \frac{11}{k}

Slope: \frac{48}{k}

*************************************************************************

 (k + 2)x + 16y = -19

<u>- (k + 2)x          </u>   -<u>(k + 2)x </u>

                 16y = -(k + 2)x - 19

                  \frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}

                  y = -\frac{(k + 2)x}{16} - \frac{19}{16}

Slope: -\frac{(k + 2)}{16}

**********************************************************************************

\frac{48}{k} and -\frac{(k + 2)}{16} are perpendicular so they have opposite signs and are reciprocals of each other.  When multiplied by its reciprocal, their product equals -1.

-\frac{(k + 2)}{16} *  \frac{k}{48} = -1

\frac{(k + 2)k}{16(48)} = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769



5 0
3 years ago
Shane wrapped the kite with paper. How many square inches of paper did Shane use to cover the front and back? 45 POINTS
arsen [322]

Answer:

576

Step-by-step explanation:

First off, we can use the area of a kite formula, (D1*D2)/2 to get the area of one side of the kite, which is simplified to 18 * 32 : which gets us 288. But because we are looking for the area of the front and back side, we multiply 288 by 2- getting the final answer of <u>576</u>.

7 0
3 years ago
Read 2 more answers
HELP PLS
Dmitry [639]

volume cylinder

=3.14×3^2×5

=141.3 cubic inches

volume sphere

=4/3×3.14×3^3

=113.04 cubic inches

difference between volume of cylinder and sphere

=141.3-113.04

=28.26 cubic inches

6 0
3 years ago
The original price of a motorcycle was reduced by $275 p = motorcycle, whats the expression
Nostrana [21]

i think it would be p+275

8 0
3 years ago
What is the best approximation of the length of segment QS? (Note: cos 80° = 0.17)
matrenka [14]

Answer: QS=11.8cm


Step-by-step explanation:

1. You have the following information:

- The lenght of RS is 2 centimeters.

- The angle m∠S=80°.

- Cos80°=0.17

2. Therefore, you can calculate the lenght of the segment QS as following:

cos80=\frac{adjacent}{hypotenuse}

adjacent=2cm\\hypotenuse=QS\\cos80=0.17

3. Substitute values and solve for QS:

0.17=\frac{2cm}{QS}\\QS=\frac{2cm}{0.17} \\QS=11.76cm

4. To the nearest tenth:

QS=11.8cm

6 0
3 years ago
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