Evaluate: 6.7 × $99.99 =<br> O $692.43<br> O $106.69<br> O $669.93<br> O $14.92

A hockey puck strikes a wall at an angle of 30 degrees. the puck then travels away from the wall at the same angle.

patriot [66]

Two or more angles whose sum is 180° are called supplementary angles. The measure of the ∠y is 120°.

<h3>What are supplementary angles?</h3>

Two or more angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Given the puck strikes the wall at an angle of 30°, it goes away at the same angle of 30°. Therefore, the measure of angle y can be found using the sum of the angle as a supplementary angle. Thus, we can write,

30° + ∠y + 30° = 180°

60° + ∠y = 180°

∠y = 180° - 60° = 120°

Hence, the measure of the ∠y is 120°.

Learn more about Supplementary Angles:

brainly.com/question/2882938

#SPJ1

5 0

2 years ago

Assume the equation has a solution for z.<br> -cz+ 6z = tz + 83<br>z=?

solong [7]

Answer:

z = 83 / (- c + 6 - t)

Step-by-step explanation:

Given:

-cz+ 6z = tz + 83

z=?

-cz+ 6z = tz + 83

Collect like terms

-cz+ 6z - tz = 83

Factorize

z(- c + 6 - t) = 83

Divide both sides by (- c + 6 - t)

z(- c + 6 - t) / (- c + 6 - t) = 83 / (- c + 6 - t)

z = 83 / (- c + 6 - t)

5 0

3 years ago

Triangle X Y Z is cut by line segment C D. Line segment C D goes from side X Y to side Y Z. The length of C D is 15, the length

Marizza181 [45]

The length of DZ is 4 units ⇒ 3rd answer

Step-by-step explanation:

Triangle X Y Z is cut by line segment C D, where

C lies on side XY and D lies on the side YZ
The length of C D is 15
The length of X Z is 18
The length of C Y is 25
The length of Y D is 20
C D and X Z are parallel
CX = 5 units

We need to find the length of DZ

In Δ XYZ

∵ C ∈ XY and D ∈ YZ

∵ CD // XZ

∴ m∠YCD = m∠YXZ ⇒ alternate angles

∴ m∠YDC = m∠YZX ⇒ alternate angles

In Δs YCD and YXZ

∵ m∠YCD = m∠YXZ

∵ m∠YDC = m∠YZX

∵ ∠Y is a common angle

∴ Δ YCD is similar to Δ YXZ by AAA postulate

- There is a constant ratio between their corresponding sides

∴ $\frac{YC}{YX}=\frac{CD}{XZ}=\frac{YD}{YZ}$

∵ YC = 25 units

∵ CX = 5 units

∵ YX = YC + CX

∴ YX = 25 + 5 = 30 units

∵ YD = 20 units

∵ YZ = YD + DZ

∴ YZ = 20 + DZ

Let us use the ratio of the corresponding side

∵ $\frac{YC}{YX}=\frac{YD}{YZ}$

∴ $\frac{25}{30}=\frac{20}{20+DZ}$

- Simplify $\frac{25}{30}$ by dividing up and down by 5

∵ $\frac{25}{30}=\frac{5}{6}$

∴ $\frac{5}{6}=\frac{20}{20+DZ}$

- By using cross multiplication

∴ 5(20 + DZ) = 6(20)

∴ 100 + 5 DZ = 120

- Subtract 100 from both sides

∴ 5 DZ = 20

- Divide both sides by 5

∴ DZ = 4 units

The length of DZ is 4 units

Learn more:

You can learn more about triangles in brainly.com/question/3202836

#LearnwithBrainly

8 0

3 years ago

Need the formula for 8% of 575

Nitella [24]

The formula of that is 24

7 0

3 years ago

Read 2 more answers

A worker has job offers from two companies. The information below summarizes the job offer from each company.Company A:Starting

Zanzabum

Using linear functions, we have that:

A.

For Company A: $S_A(n) = 31000 + 3000n$

For Company B: $S_B(n) = 38000 + 2000n$

B. The salaries will be the same after 7 years.

A linear function is given by:

$y = mx + b$

In which:

m is the slope, which is the rate of change.
b is the y-intercept, which is the initial value.

Item a:

For Company A, the salary starts at $31,000, with a raise of $3,000 each year. Thus, $b = 31000, m = 3000$ , and the salary after n years is given by:

$S_A(n) = 31000 + 3000n$

For Company B, the salary starts at $38,000, with a raise of $2,000 each year. Thus, $b = 38000, m = 2000$ , and the salary after n years is given by: