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2 years ago

Find the height of the lamppost to the nearest inch.

Mathematics

1 answer:

diamong [38]2 years ago

7 0

<h3>The height of lamp post to nearest inch is 110 inches</h3>

<em><u>Solution:</u></em>

We have to find the height of lamppost

From the figure in question,

Given is a right angled triangle

Where,

base = 40 inches

height = ?

By definition of tan,

$tan\ 70 = \frac{opposite}{base}\\\\tan\ 70 = \frac{height}{40}\\\\height = tan\ 70 \times 40\\\\height = 2.7474 \times 40\\\\height = 109.89 \approx 110$

Thus height of lamp post to nearest inch is 110 inches

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Consider this system of equations. Which shows the second equation written in slope-intercept form? y = 3 x minus 2. 10 (x + thr

Arte-miy333 [17]

Question

Consider this system of equations. Which shows the second equation written in slope-intercept form?

$y = 3x - 2.$

$10(x + \frac{3}{5} ) = 2y$

A. $y = 5x + \frac{3}{10}$

B. $y = 5x + 3$

C. $y = \frac{1}{5} x + \frac{3}{25}$

D. $y = \frac{1}{2} x + 6$

Answer:

B. $y = 5x + 3$

Step-by-step explanation:

Given

Equation 1: $y = 3x - 2.$

Equation 2: $10(x + \frac{3}{5} ) = 2y$

Required:

Equivalent of equation 2

To get an equivalent of equation 2 (in slope intercept form), first we have to simplify equation 2

$10(x + \frac{3}{5} ) = 2y$

Open the bracket

$10*x + 10 *\frac{3}{5} = 2y$

$10x + \frac{30}{5} = 2y$

Simplify fraction

$10x + 6 = 2y$

Divide through by 2

$\frac{10x}{2} + \frac{6}{2} = \frac{2y}{2}$

$5x + 3 = y$

Re-arrange

$y = 5x + 3$

The next step is to compare each of option A through D with $y = 5x + 3$

$y = 5x + \frac{3}{10}$ is not equal to $y = 5x + 3$

We check the next available option

$y = 5x + 3$ is equal to $y = 5x + 3$

This option is equivalent to the second equation in slope-intercept form.

We check further if there are more equivalent options

$y = \frac{1}{5} x + \frac{3}{25}$

Convert fraction to decimal

$y = 0.2x + 0.12$

This is not equal to $y = 5x + 3$

$y = \frac{1}{2} x + 6$

Convert fraction to decimal

$y = 0.5x + 6$

This is not equal to $y = 5x + 3$

Hence, the only equation that is equivalent to the second equation written in slope intercept form is Option B

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2 years ago

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Given \qquad \overline{PQ}\perp\overline{PS} PQ ⊥ PS start overline, P, Q, end overline, \perp, start overline, P, S, end over

Tomtit [17]

Answer: 40 degrees

Step-by-step explanation:

did this on khan! :)

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2 years ago

Find the dependent and independent variable in r = 5s + 3.

Firdavs [7]

Answer:

The independent variable is s and the dependent variable is r

Step-by-step explanation:

r = 5s+3

The independent variable is s and the dependent variable is r

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2 years ago

Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average

lutik1710 [3]

Let the distance of the first part of the race be x, and that of the second part, 15 - x, then
x/8 + (15 - x)/20 = 1.125
5x + 2(15 - x) = 40 x 1.125
5x + 30 - 2x = 45
3x = 45 - 30 = 15
x = 15/3 = 5

Therefore, the distance of the first part of the race is 5 miles and the time is 5/8 = 0.625 hours or 37.5 minutes
The distance of the second part of the race is 15 - 5 = 10 miles and the time is 1.125 - 0.625 = 0.5 hours or 30 minutes.

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2 years ago

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You and three friends own a paint shop. The shop's profit was $536 in the first month. You always divide the profits equally. In

alexandr1967 [171]

C. $360

$224x4=896 (total profit)

$896 (total) - $536 (first month profit) = $360 (second month profit)

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2 years ago

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