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3 years ago

Please help with geometry

Mathematics

1 answer:

Mariana [72]3 years ago

6 0

Answer: The angle of depression is 51.34°.

Step-by-step explanation:

1. You can make the diagram shown in the figure attached. Where $A$ is the point where the clue is and $B$ is the point where Tyler is.

2. To calculate the angle of depression, which is identified in the diagram as $\alpha$ , you can use $tan^{-1}$ , as following:

$tan^{-1}(\alpha)=\frac{3.5}{2.8}$

3. Then, you obtain the following angle of depression from the clue to the point where Tyler is:

$\alpha=51.34$ °

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Select steps that could be used to solve the equation 1 + 3x = -x + 4.

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Answer:

A, C & D

Step-by-step explanation:

A) 1 + 3x = -x + 4 {subtract 1}

1 + 3x -1 = -x + 4 - 1

3x = -x + 3 {add x}

3x + x = -x + 3 + x

4x = 3 {Divide by 4}

4x/x = 3/4

x = 3/4

C) 1 + 3x = -x +4 {Add x}

1+ 3x + x = - x +4 + x

1 + 4x = 4 {subtract 1}

4x = 4 - 1

4x = 3 {Divide by 4}

D) 1 + 3x = -x + 4 { Subtract 3x}

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Given:

The given expression is $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$

We need to determine the equivalent expression.

Option A: -1

Solving the expression, we get;

$\frac{3}{2} x+14-\frac{3}{2} x+15$

Simplifying, we get;

$14+15=29$

Thus, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is not equivalent to -1.

Hence, Option A is not the correct answer.

Option B: 29

Solving the expression, we get;

$\frac{3}{2} x+14-\frac{3}{2} x+15$

Simplifying, we get;

$14+15=29$

Thus, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is equivalent to 29.

Hence, Option B is the correct answer.

Option C: $2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]$

Let us rewrite the given expression.

$2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]$

Thus, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is equivalent to $2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]$

Thus, Option C is the correct answer.

Option D: $2\left(\frac{3}{4} x\right)+2(7)+3\left(\frac{1}{2} x\right)+3(-5)$

Rewriting the expression, we get;

$2\left(\frac{3}{4} x+7\right)+(-3)\left[\frac{1}{2} x+(-5)\right]$

Hence, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is equivalent not to $2\left(\frac{3}{4} x\right)+2(7)+3\left(\frac{1}{2} x\right)+3(-5)$

Thus, Option D is not the correct answer.

Option E: $2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)$

Multiplying the terms within the bracket, we get;

$2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)$

Hence, the expression $2\left(\frac{3}{4} x+7\right)-3\left(\frac{1}{2} x-5\right)$ is equivalent to $2\left(\frac{3}{4} x\right)+2(7)+(-3)\left(\frac{1}{2} x\right)+(-3)(-5)$

Thus, Option E is the correct answer.

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