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nata0808 [166]
3 years ago
5

A and B are vertical angles. If m A = (3x+3)° and m B= (4x-8)°, then find the value of x.

Mathematics
1 answer:
iogann1982 [59]3 years ago
6 0

Answer: x=11

Step-by-step explanation:

First, since angle A and angle B are vertical angles, that means that they are congruent. If they are congruent, then the m of angle A equals the measure of angle B. So, (3x+3)=(4x-8). Simplify using algebra so that in the end, you will find that x=11.

3x+3=4x-8

3=x-8

11=x

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Step-by-step explanation:

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3 years ago
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liraira [26]

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3 years ago
One operator is holding a laser pointer at a height of 9 feet whose beam is reflected on a horizontal reflecting surface at a po
lutik1710 [3]

Answer:

The height (in feet) at which the laser will impact the wall is 6.75 feet

Step-by-step explanation:

The given parameters are;

The height from which the laser beam operator is holding the laser = 9 feet

The horizontal distance away from the pointer the beam is reflected = 8 feet

Given that we have;

f(x) = \dfrac{9}{8} \times \left | x - 8\right | = y

When x = 8, the point of reflection, the height, f(x) is given as follows;

f(x) = \dfrac{9}{8} \times \left | 8 - 8\right | = 0

When x = 7, the point of reflection, the height, f(x) is given as follows;

f(x) = \dfrac{9}{8} \times \left | 7 - 8\right | = \dfrac{9}{8}

Therefore, given that the point of reflection is at an elevation of 0 relative to the 9 feet of the laser source (pointer), by tan rule, we have;

tan(\theta) = \dfrac{Opposite \ side}{Adjacent \ side} =\dfrac{9}{8} = \dfrac{h}{7}

Where;

h = The height at which the laser meets the wall

h = \dfrac{9 \times  7}{8} =7.875

Given that the wall the laser meets is at the point x with elevation 9/8, the height, y, at which the laser meets the wall is therefore;

y = \dfrac{9 \times  7}{8} - \dfrac{9}{8} = \dfrac{54}{8} = 6.75 \ feet

The height (in feet) at which the laser will impact the wall = 6.75 feet.

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3 years ago
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Step-by-step explanation:

see the attachment...............

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3 years ago
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