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2 years ago

Calculate the value of x to one decimal place. inches

Mathematics

1 answer:

kakasveta [241]2 years ago

5 0

Use the law of cosines: $c^2=a^2+b^2-2ab\cos C$

We have:

$c=x\\a=3in\\b=7in\\C=54^o$

substitute:

$\cos54^o\approx0.5878\\\\c^2=3^2+7^2-2\cdot3\cdot7\cdot0.5878\\\\c^2=9+49-24.6876\\\\c^2=33.3129\to c=\sqrt{33.3129}\\\\c\approx5.8$

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What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth

uysha [10]

Answer:

The perimeter of the trapezoid is $38.25\ units$

Step-by-step explanation:

we know that

The perimeter of the trapezoid is the sum of its four side lengths

In this problem

$P=QR+RS+ST+QT$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

$Q(8, 8), R(14, 16), S(20, 16),T(22, 8)$

step 1

Find the distance QR

$Q(8, 8), R(14, 16)$

substitute the values in the formula

$d=\sqrt{(16-8)^{2}+(14-8)^{2}}$

$d=\sqrt{(8)^{2}+(6)^{2}}$

$d=\sqrt{100}$

$QR=10\ units$

step 2

Find the distance RS

$R(14, 16), S(20, 16)$

substitute the values in the formula

$d=\sqrt{(16-16)^{2}+(20-14)^{2}}$

$d=\sqrt{(0)^{2}+(6)^{2}}$

$d=\sqrt{36}$

$RS=6\ units$

step 3

Find the distance ST

$S(20, 16),T(22, 8)$

substitute the values in the formula

$d=\sqrt{(8-16)^{2}+(22-20)^{2}}$

$d=\sqrt{(-8)^{2}+(2)^{2}}$

$d=\sqrt{68}$

$ST=8.25\ units$

step 4

Find the distance QT

$Q(8, 8),T(22, 8)$

substitute the values in the formula

$d=\sqrt{(8-8)^{2}+(22-8)^{2}}$

$d=\sqrt{(0)^{2}+(14)^{2}}$

$d=\sqrt{196}$

$QT=14\ units$

step 5

Find the perimeter

$P=10+6+8.25+14=38.25\ units$

6 0

2 years ago

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You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x x djemb

MissTica

326 = 12m + 6c + x = 18 rounded to 19

8 0

1 year ago

a car travels 30 1/2 miles in 2/3 of an hour. what is the average speed, in miles per hour, of the car ?

Contact [7]

Answer:

speed=225.75 miles per hour

Step-by-step explanation:

given:

s=301/2

t=2/3

we have,

v=s/t

v=(301/2)/(2/3)

=(301/2)×3/2

=903/4

v=225.75

therefore, speed of car will be 225.75 miles per hour

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1 year ago

Colin leaves school to go home. He walks 3 blocks south and then 9 blocks west. If Colin could walk in a straight line to the sc

White raven [17]

Answer:

9.48*

Step-by-step explanation:

This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :

3^2 + 9^2 = C^2

9 + 81 = C^2

90 = C^2

9.48 = C

* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.

5 0

1 year ago

The area of a second soup can’s base is 5 pi inches squared. The can has a height of 10 inches. How would you use that informati

Ilia_Sergeevich [38]

Answer:

The amount of soup the can will hold is;

50π inches cubed = 157.08 inches cubed

Step-by-step explanation:

The amount of soup the can will hold is equal to the volume of the can.

Volume of the can = base area × height

Given;

Base Area = 5π inches squared

height = 10 inches

Volume of can = 5π × 10 = 50π inches cubed

The amount of soup the can will hold is;

50π inches cubed = 157.08 inches cubed

8 0

2 years ago

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