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3 years ago

Cameron is creating a chart of numbers and their opposites

Mathematics

1 answer:

lesantik [10]3 years ago

6 0

-8645 is not the opposite to -8645. 8645 is the correct opposite to -8645

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What is the value of x? Please show step by step.

3241004551 [841]

Start by using trig to find the length of the line LJ

The triangle KJL (big right angled triangle) has been given the following dimensions

Hypotenuse = $8 \sqrt{2}$
The adjacent angle is 30 degrees

Since we have the hypotenuse and the angle we must use the equation
opposite = Sin(angle) x Hypotenuse

Opposite= sin30 x $8 \sqrt{2}$

Opposite= $4 \sqrt{2}$

Therefore line LJ is $4 \sqrt{2}$

Now look at the smaller right angled triangle (LMJ)

Hypotenuse is the line LJ which is $4 \sqrt{2}$

The adjacent angle is 45

Since we have hypotenuse and angle we must use the equation opposite = sin(angle) * h

therefore
x= $4 \sqrt{2}$ * sin45= 4

3 0

3 years ago

The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. The length of the h

Alex17521 [72]

Answer:

Step-by-step explanation:

Let x represent the length of the hypotenuse.

Let y represent the length of the the shorter leg.

Let z represent the length of the longer leg.

The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. It means that

z = 2y + 20

The length of the hypotenuse is 22 inches more than twice the length of the shorter leg. It means that

x = 2y + 22

We would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

(2y + 22)² = y² + (2y + 20)²

(2y + 22)(2y + 22) = y² + (2y + 20)(2y + 20)

= 4y² + 44y + 44y + 484 = y² + 4y² + 40y + 40y + 400

4y² + 88y + 484 = y² + 4y² + 80y + 400

4y² + 88y + 484 = 5y² + 80y + 400

5y² - 4y²+ 80y - 88y + 400 - 484

y² - 8y - 84 = 0

y² + 6y - 14y - 84 = 0

y(y + 6) - 14(y + 6)

y - 14 = 0 or y + 6 = 0

y = 14 or y = - 6

The shorter length cannot be negative hence y = 14 inches

The length of the shorter side is 14 inches.

The length of the hypotenuse is

(2 × 14) + 22 = 50 inches

The length of the longer side is

(2 × 14) + 20 = 48 inches

7 0

3 years ago

PLEASE HELP ME!!! Ryan worked at a store for 3.5 days. He was paid $53.30 per day. He spent $24.75 to buy a gift for his mother.

Nadusha1986 [10]

Answer: 161.8

Step-by-step explanation:

6 0

3 years ago

You have $9.30 plus 6 percent of tax what is the total costs

mario62 [17]

Answer:

$ 9.86

Step-by-step explanation:

Tax = 6% of 9.30

= 0.06 * 9.30

= $ 0.558

Total costs = 9.30 + 0.558

= 9.858

= $ 9.86

4 0

3 years ago

Waylon is typing a paper for keyboarding class. He has typed 648 words in 8 minutes. He types at the same rate each minute. Whic

Vlad1618 [11]

Answer:

that is the correct answer

7 0

2 years ago