Identify the percent of change (POC) as an increase or decrease. Then find the percent of change. Round to the nearest tenth of a percent if necessary.-12 inches to 36 inches
-50 punds to 35 pounds
-10 gallons to 24 gallons
-16 centimeters to 44.2 centimeters

If you could explain this as simple as possible with the work, for I have problems understanding things well, then that would be a HUGE help!

If you can answer all 4, I'm awarding 20 points!!

Answers

Answer 1

Answer: percent change=(change/original) tiimes 100 change= |original-new| so 12 to 36 |12-36|=|-24|=24 so pcercent change=100 times (24/12)=100 times 2=200% 50 to 35 |50-35|=|15|=15 percent change=100 times (15/50)=100 times 100 times 0.30=30% 10 to 24 |10-24|=|-14|=14 percent change=100 times (14/10)=100 times 1.4=140% 16 to 44.2 |16-44.2|=|-28.2|=28.2 percent change=100 times (28.2/16)= 100 times 1.7625=176.25% answers are -12 inches to 36 inches: 200% -50 punds to 35 pounds: 30% -10 gallons to 24 gallons: 140% -16 centimeters to 44.2 centimeters: 176.25%

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Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Answers

Answer:

The correct prove will be:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$ $= (1)/(8)$

Step-by-step explanation:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$

Multiply and Divide by $2cos((\pi )/(14))$

= $(2sin((\pi )/(14))cos((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14)))/(2cos((\pi )/(14)))$

⇒ Let $(\pi )/(14)$ = Ф and 7Ф = $(\pi )/(2)$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin((\pi )/(14))sin((3\pi )/(14))sin((5\pi )/(14))$ $= (1)/(8)$

Keywords: prove, sinФ, cosФ

Learn more about trigonometric functions from brainly.com/question/7331447

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The points (-6, r) and (10,4) lie on a line with slope 1/2Find the missing coordinate r.

Answers

Answer:

r = -4

Step-by-step explanation:

The slope of a line is given by

m= (y2-y1)/(x2-x1)

1/2 = (4-r)/(10 - -6)

1/2 = (4-r) (10+6)

1/2 =( 4-r) /16

Multiply each side by 16

16*1/2 = 4-r

8 = 4-r

Subtract 4 from each side

8-4= 4-r-4

4 = -r

Multiply each side by -1

-4 = r

Answer:

-4

Step-by-step explanation:

½ = (r - 4)/(-6 - 10)

½ = (r - 4)/(-16)

r - 4 = -8

r = -4

recall that two angles are comlementary if the sum of their measures is 90. find the measures of two complementary angles if one angle is twenty-nine times the other angle.