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2 years ago

Mr. Moss had 2 gallons of paint. He painted 3 doors. How many benches can he paint with the paint that is left? Show your work.

Mathematics

1 answer:

RUDIKE [14]2 years ago

8 0

Answer:

uh depends on how much paint he used for the doors and how much paint he needs for the benches

Step-by-step explanation:

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Determine the number of possible solutions for a triangle with B=37 degrees, a=32, b=27

vladimir1956 [14]

Answer:

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}=\frac{c}{Sin(C)}$

we have

$a=32\ units$

$b=27\ units$

$B=37\°$

step 1

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}$

substitute the values

$\frac{32}{sin(A)}=\frac{27}{Sin(37\°)}$

$sin(A)=(32)Sin(37\°)/27=0.71326$

$A=arcsin(0.71326)=45.5\°$

The measure of angle A could have two measures

the first measure-------> $A=45.5\°$

the second measure -----> $A=180\°-45.5\°=134.5\°$

step 2

Find the first measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=45.5\°$

$B=37\°$

$45.5\°+37\°+C=180\°$

$C=180\°-(45.5\°+37\°)=97.5\°$

step 3

Find the first length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(97.5\°)}$

$c=Sin(97.5\°)\frac{32}{sin(37\°)}=52.7\ units$

therefore

the measures for the first solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=97.5\°$ , $b=52.7\ units$

step 4

Find the second measure of angle C with the second measure of angle A

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=134.5\°$

$B=37\°$

$134.5\°+37\°+C=180\°$

$C=180\°-(134.5\°+37\°)=8.5\°$

step 5

Find the second length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(8.5\°)}$

$c=Sin(8.5\°)\frac{32}{sin(37\°)}=7.9\ units$

therefore

the measures for the second solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=8.5\°$ , $b=7.9\ units$

6 0

2 years ago

Question 11 Find the value of y. X+ 13 45° No links please! Thanks for the help!

9966 [12]

Answer:

First option: $13 \sqrt{2}$

Step-by-step explanation:

$cosθ = \frac{adj}{hyp}$

$cos45° = \frac{13}{y}$

Multiply both sides by y:

$y(cos45°) = 13$

$y ( \frac{ \sqrt{2} }{2} ) = 13$

$y = 13 \div \frac{ \sqrt{2} }{2}$

$y = 13 \times \frac{2}{ \sqrt{2} }$

$y = \frac{26}{ \sqrt{2} } ( \frac{ \sqrt{2} }{ \sqrt{2} } )$

$y = \frac{26 \sqrt{2} }{2}$

$y = 13 \sqrt{2}$

7 0

2 years ago

Read 2 more answers

The Jets play 16 football games this season. So far they have 3 wins and 4 losses. If they can win all the rest, how many wins a

brilliants [131]

Answer:

12 wins and 4 losses

Step-by-step explanation:

3 wins and 4 losses means they have played so far 7 games.

They play a total of 16 games in a season.

16 - 7 = 9

They still have to play 9 more games.

Add 9 wins to the 3 wins.

9 + 3 = 12

That means they'd finish the season with 12 wins and 4 losses.

6 0

2 years ago

If line segment are you is considered the base of a parallelogram are STU what is the corresponding height of the parallelogram

Westkost [7]

Answer: Hello your question lacks some data hence i will provide a general solution within the scope of your question.

answer:

Height = Area of parallelogram / base of parallelogram

Step-by-step explanation:

The corresponding height of the parallelogram can be calculated using the general equation below :

Height = Area of parallelogram / base of parallelogram

Kindly input the values you have into the relation to get the corresponding height of the parallelogram.

6 0

2 years ago

Solve the system of equations by substitution.<br> 4x−3y=18 <br> x+2y=−1

Oksana_A [137]

Answer:

Step-by-step explanation:

4x - 3y = 18

-4x - 8y = 4

-11y = 22

y = -2

4x + 6 = 18

4x = 12

x = 3

(3, -2)

3 0

2 years ago

Mr. Moss had 2 gallons of paint. He painted 3 doors. How many benches can he paint with the paint that is​ left? Show your work.

Mr. Moss had 2 gallons of paint. He painted 3 doors. How many benches can he paint with the paint that is left? Show your work.