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3 years ago

15

Expand the expression −11(3c−2d) using the Distributive Property.

1 answer:

Sladkaya [172]3 years ago

5 0

Answer:

-33c+22d

Step-by-step explanation:

=(−11)(3c+−2d)

=(−11)(3c)+(−11)(−2d)

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Each person in the United States eats about 65 fresh apples a year based on this estimate. How many apples do 3 families of 4 ea

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Solve the triangle. Round your answers to the nearest tenth.

mixas84 [53]

Answer:

Angles: $\angle A = 43^{\circ}$ $\angle B = 55^{\circ}$ $\angle C = 82^{\circ}$

Sides: $BC = 20$ $AB = 29$ $AC =24$

Step-by-step explanation:

See attachment for complete question

From the attachment, we have:

$AB = 29$

$AC =24$

$\angle C = 82^{\circ}$

Required

Complete the missing side and missing angles

To calculate angle B, we apply sine laws:

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

In this case:

$\frac{AB}{sinC}=\frac{AC}{sinB}$

This gives:

$\frac{29}{sin(82^{\circ})}=\frac{24}{sinB}$

$\frac{29}{0.9903}=\frac{24}{sinB}$

Cross Multiply

$sinB * 29 = 24 * 0.9903$

Divide both sides by 29

$sinB = \frac{24 * 0.9903}{29}$

$sinB = 0.8196$

Take arcsin of both sides

$B = sin^{-1}(0.8196)$

$B = 55^{\circ}$

So:

$\angle B = 55^{\circ}$

To solve for the third angle, we make use of:

$\angle A + \angle B + \angle C = 180^{\circ}$

This gives:

$\angle A + 55^{\circ} + 82^{\circ} = 180^{\circ}$

$\angle A + 137^{\circ}= 180^{\circ}$

$\angle A = 180^{\circ}- 137^{\circ}$

$\angle A = 43^{\circ}$

Hence, the angles are:

$\angle A = 43^{\circ}$ $\angle B = 55^{\circ}$ $\angle C = 82^{\circ}$

To calculate the length of the third side, we apply cosine law

$BC^2 = AB^2 + AC^2 - 2*AB*AC*cosA$

$BC^2 = 29^2 + 24^2 - 2*29*24*cos(43^{\circ})$

$BC^2 = 841+ 576 - 1392*cos(43^{\circ})$

$BC^2 = 841+ 576 - 1392*0.7314$

$BC^2 = 841+ 576 - 1018.11$

$BC^2 = 398.89$

Take the square root of both sides

$BC = \sqrt{398.89$

$BC = 19.9722307217$

$BC = 20$

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Step-by-step explanation:

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Leslie mows lawns to earn money. For each customer, she charges $2.00 for gas and $3.00 per 12 hour of work. Let x represent the

RUDIKE [14]

Answer:

See Explanation

Step-by-step explanation:

Given

$Gas = \$2.00$

$Rate = \$3.00/12hr$

$\begin{array}{ccc}{Row} & {Hours} & {Earnings} & {A} & {2} & { } & {B} & {4} & { } & {C} & {6} &{ } \ \end{array}$ ---- Missing table

Required

Complete the table and plot the graph

First, we determine the equation of the table:

$Gas = \$2.00$

$Rate = \$3.00/12hr$ implies that:

$Rate = \$0.25/hr$

So:

$y = Gas + Rate * x$

$y = 2+ 0.25* x$

$y = 2+ 0.25 x$

To complete the table, we have:

$x = 2$

$y = 2+ 0.25 x = 2+0.25 * 2 = 2.5$

$x = 4$

$y = 2+ 0.25 x = 2+0.25 * 4 = 3$

$x = 6$

$y = 2+ 0.25 x = 2+0.25 * 6 = 3.5$

So, the complete table is:

$\begin{array}{ccc}{Row} & {Hours} & {Earnings} & {A} & {2} & {2.5} & {B} & {4} & {3} & {C} & {6} &{3.5} \ \end{array}$

See attachment for graph

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