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3 years ago

If DE= 4x–1, EF= 9, and DF= 9x–22 , find the value of x

Mathematics

1 answer:

dybincka [34]3 years ago

6 0

Answer:

The correct answer is x = 6.

Step-by-step explanation:

To solve this problem, we first must recognize that DE + EF = DF.

From this information, we can set up the following equation when we substitute in the given values:

DE + EF = DF

(4x-1) + 9 = 9x - 22

Our first step is going to be to combine like terms on the left side of the equation. This is modeled below:

4x - 1 + 9 = 9x - 22

4x + 8 = 9x - 22

Then, we should subtract 4x from both sides of the equation.

8 = 5x - 22

Now, we can add 22 to both sides of the equation.

30 = 5x

Finally, we can divide both sides by 5.

x = 6

Therefore, the correct answer is x = 6.

Hope this helps!

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Answer:

A. 34°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Trigonometry

[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] tanθ = opposite over adjacent
Inverse Trig

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = x

Opposite leg AC = 24

Adjacent leg CB = 35

Step 2: Solve for x

Substitute in variables [Tangent]: $\displaystyle tanx^\circ = \frac{24}{35}$
Inverse Trig [Tangent]: $\displaystyle x^\circ = tan^{-1}(\frac{24}{35})$
Evaluate: $\displaystyle x = 34.439^\circ$
Round: $\displaystyle x \approx 34^\circ$

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