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30°<br> 8 + 6x<br> 4x + 2 <br> in a triangle

andrey2020 [161]

Answer:

x=12

Step-by-step explanation:

Simplifying

30 + 4x + 2 = 8 + 6x

Reorder the terms:

30 + 2 + 4x = 8 + 6x

Combine like terms: 30 + 2 = 32

32 + 4x = 8 + 6x

Solving

32 + 4x = 8 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation.

32 + 4x + -6x = 8 + 6x + -6x

Combine like terms: 4x + -6x = -2x

32 + -2x = 8 + 6x + -6x

Combine like terms: 6x + -6x = 0

32 + -2x = 8 + 0

32 + -2x = 8

Add '-32' to each side of the equation.

32 + -32 + -2x = 8 + -32

Combine like terms: 32 + -32 = 0

0 + -2x = 8 + -32

-2x = 8 + -32

Combine like terms: 8 + -32 = -24

-2x = -24

Divide each side by '-2'.

x = 12

Simplifying

x = 12

4 0

3 years ago

Solve for x. (e^x-e^-x)/((e^x+e^-x)=t

Sergio [31]

$\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t\\\\
\dfrac{e^{2x}-1}{e^{2x}+1}=t\\\\
e^{2x}-1=t(e^{2x}+1)\\\\
e^{2x}-1=e^{2x}t+t\\\\
e^{2x}-e^{2x}t=t+1\\\\
e^{2x}(1-t)=t+1\\\\
e^{2x}=\dfrac{t+1}{1-t}\\\\
e^{2x}=-\dfrac{t+1}{t-1}\\\\
2x=\ln\left(-\dfrac{t+1}{t-1}\right)\\\\
x=\dfrac{\ln\left(-\dfrac{t+1}{t-1}\right)}{2}\qquad t\in(-1,1)



$

8 0

4 years ago

Read 2 more answers

To find the surface area of the pyramid, in square inches, Vikram wrote (33.2) (34.2) + 4 (one-half (34.2) (28.4)). What error d

madam [21]

Answer:

B. He used the wrong expression to represent the area of the base of the pyramid.

Step-by-step explanation:

Given

See attachment for pyramid

$Area = (33.2)(34.2) + 4 * \frac{1}{2} * 34.4 * 28.4$

Required

Vikram's error

The surface area of a square pyramid is:

$Area = Base\ Area + 4 * Area \triangle$

Where

$Base\ Area = Length * Length$

$Base\ Area = 34.2 * 34.2$

$4 * Area \triangle = 4 * \frac{1}{2} * Base * Height$

$4 * Area \triangle = 4 * \frac{1}{2} * 34.2 * 28.4$

So:

$Area = Base\ Area + 4 * Area \triangle$

$Area = 34.2 * 34.2 + 4 * \frac{1}{2} * 34.2 * 28.4$

By comparing the calculated expression with

$Area = (33.2)(34.2) + 4 * \frac{1}{2} * 34.4 * 28.4$

Option (b) is correct

3 0

3 years ago

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of eac

Natasha_Volkova [10]

Let x be the number of 5 points question.
Let y be the number of 2 points question.

Total number of questions is 38
x + y = 38

Total points is 100
5x + 2y = 100

x + y = 38 ------------- (1)
5x + 2y = 100 ---------(2)

From (1):
x + y = 38
x = 38 - y -------------- sub into (2)
5(38 - y) + 2y = 100
190 - 5y + 2y = 100
3y = 90
y = 30 ------------------ sub into (1)
x + 30 = 38
x = 38 - 30
x = 8

There are 8 5-point questions and 30 2-point questions

5 0

4 years ago

Read 2 more answers

Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team memebers who do not wear glasses, 30

GarryVolchara [31]

the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade is 14%.

Given, the members of the junior varsity swim team wear glasses is 55%.

And the members of junior varsity swim team who do not wear glasses and in 10th grade is 30%.

Let the total no. of members be x.

So, the members of the junior varsity swim team wear glasses (55%),will be

$0.55x$ .