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3 years ago

8

How many solutions does the equation 5x+17=4(3x−1) have?

1 answer:

Stella [2.4K]3 years ago

4 0

<u>Answer:</u>

one solution = 3

<u>Step-by-step explanation:</u>

Let's solve your equation step-by-step.

5x+17=4(3x−1)

Step 1: Simplify both sides of the equation.

5x+17=4(3x−1)

5x+17=(4)(3x)+(4)(−1)(Distribute)

5x+17=12x+−4

5x+17=12x−4

Step 2: Subtract 12x from both sides.

5x+17−12x=12x−4−12x

−7x+17=−4

Step 3: Subtract 17 from both sides.

−7x+17−17=−4−17

−7x=−21

Step 4: Divide both sides by -7

-7x/-7 = -21/-7 = 3

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Answer:

$Owl= 67.14ft$

Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

$22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}$

$22^{\circ} 8'6'' = 22.135^{\circ}$

$30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}$

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Considering Jason's position:

$tan(22.135^{\circ}) = \frac{H}{x + 48}$

Where x = distance between the tree and Alison

Make H the subject

$H = (x + 48)tan(22.135^{\circ})$

Considering Alison's position

$tan(30.675^{\circ}) = \frac{H}{x}$

Make H the subject

$H = xtan(30.675^{\circ})$

$H = H$

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$(x + 48) *0.4068 = x* 0.5932$

Open bracket

$x *0.4068 + 48 *0.4068 = 0.5932x$

$0.4068x + 19.5264 = 0.5932x$

Collect Like Terms

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$-0.1864x = -19.5264$

$0.1864x = 19.5264$

Make x the subject

$x = \frac{19.5264}{0.1864}$

$x = 104.76$

Substitute 104.76 for x in $H = xtan(30.675^{\circ})$

$H = 104.76 * tan(30.675^{\circ})$

$H = 104.76 * 0.5932$

$H = 62.14$

The above represents the height of the tree.

The height of the owl is:

$Owl= H + 5$

$Owl= 62.14 + 5$

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