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3 years ago

10

Complementary angles sum up to equal 90 degrees. Find the measure of each angle in the figure below. Note that since the angles

make up a right angle, they are complementary to each other.

1 answer:

laiz [17]3 years ago

3 0

#1 and #2 both equal 30 or x=30

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The diagonal of a TV set is 13 inches long. It’s length is 7 inches more than the height. Find the dimensions of the TV set.

alukav5142 [94]

Answer: The length is 12 inches while the height is 5 inches

Step-by-step explanation: It the Television has a diagonal of 13 inches, and a height of H inches, then the length would be (H + 7) inches. It’s length is 7 inches more than the height. At this point we can draw up a right angled triangle with the hypotenuse as 13 (diagonal side) and the other two sides as H and (H + 7)

Then we can apply the Pythagoras theorem which states that

AC^2 = AB^2 + BC^2

(Where AC is the hypotenuse and AB and BC are the two other sides)

Hence,

13^2 = H^2 + (H + 7)^2

169 = H^2 + (H^2 + 14H + 49)

169 = 2H^2 + 14H + 49

By collecting like terms we now have

169 - 49 = 2H^2 + 14H

120 = 2H^2 + 14H

By re-arranging all terms on one side of the equation, we arrive at

2H^2 + 14H - 120 = 0

Divide all sides by 2

H^2 + 7H - 60 = 0

To solve the quadratic equation, we now factorize and we have,

H^2 + 12H - 5H - 60 = 0

(H + 12) (H - 5) = 0

Therefore

Either H + 12 = 0 OR

H - 5 = 0

Hence, Either H = -12 or H = 5

The dimension can not be a negative value so we shall take h equals 5.

Having calculated the height of the television as 5 inches, the length which was given as H + 7 can now be calculated as

Length = H + 7

Length = 5 + 7

Length = 12

Therefore, the length of the Television is 12 inches and the height is 5 inches

4 0

3 years ago

A.The observation deck of tall skyscraper 370 m above the street. Determine the time required for a penny to free fall from the

Ainat [17]

Answer:

8.68 seconds

Step-by-step explanation:

Given:

Height of the deck above the street, s = 370 m

Since the condition is of free falling

thus,

initial speed, u = 0

Acceleration of the penny = acceleration due to gravity, g = 9.81 m/s²

Now,

from Newton's equation of motion, we have

$s=ut+\frac{1}{2}at^2$

here,

s is the distance

a is the acceleration

t is the time

on substituting the values, we get

$370=0\times t+\frac{1}{2}\times9.81\times t^2$

or

t² = 75.433

or

t = 8.68 seconds

8 0

4 years ago

1.Solve the inequality (x-2)(x+1) ≥ 0 .

scoray [572]

Answer:

#1: inequality form: x ≤ –1 or x ≥ 2

interval notion: ( -∞,-1] U [2,∞)

#2: false/no solution

#3: A) point form: (3,9)(-1,1)

equation form: x= 3,y=9 and x= -1,y=1

B)point form: (1,7)(7,1)

equation form: x=1,y=7 and x=7,y=1

Step-by-step explanation:

#1: solve for x by simplifying both sides of the inequality, then isolating the variable.

#2: N/A

#3: solve for the first variable in one of the equations, then substitute the results into the other question.

5 0

3 years ago

What is 5 minus 7/16

nekit [7.7K]

$Hello.
$
$Convert.$
$5 = 80/16$
$80/16 - 7/16 = 73/16$
$Simplify.$
$73/16 = 4 \frac{9}{16}$
$Thus, 5 - 7/16 = 4 \frac{9}{16}$
You're welcome.

3 0

3 years ago

What is 2/3 divided by 4 in the Simplest form?

dsp73

Answer:

2/3 divided by 4 = .16

4 0

3 years ago

Read 2 more answers