Find the length of side x in simplest radical form with a rational denominator

Answer:2x+15+6x-37/2=3x+5

We move all terms to the left:

2x+15+6x-37/2-(3x+5)=0

We add all the numbers together, and all the variables

8x-(3x+5)+15-37/2=0

We get rid of parentheses

8x-3x-5+15-37/2=0

We multiply all the terms by the denominator

8x*2-3x*2-37-5*2+15*2=0

We add all the numbers together, and all the variables

8x*2-3x*2-17=0

Wy multiply elements

16x-6x-17=0

We add all the numbers together, and all the variables

10x-17=0

We move all terms containing x to the left, all other terms to the right

10x=17

x=17/10

x=1+7/10

The value of RS is 31.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

If RS and UT are parallel, then their corresponding sides are proportional. Thus,

RS/UT = (2x + 15)/(6x - 37)

Now,

RS/UT = (2x + 15)/(6x - 37)

Cross-multiplying.

(2x + 15)UT = RS(6x - 37)

Expanding and simplifying.

2xUT + 15UT = 6xRS - 37RS

Rearranging.

6xRS - 2xUT = 15UT + 37RS

Factorizing.

2x(3RS - UT) = 15UT + 37RS

Dividing both sides by (3RS - UT):

2x = (15UT + 37RS)/(3RS - UT)

Substituting RS = 2x + 15 and UT = 6x - 37:

2x = (15(6x - 37) + 37(2x + 15))/(3(2x + 15) - (6x - 37))

Simplifying

2x = (90x - 555 + 74x + 555)/(6x + 36)

2x = (164x)/(6x + 36)

Multiplying both sides by (6x + 36):

12x² + 72x = 164x

Simplifying

12x² - 92x = 0

Factoring out 4x.

4x(3x - 23) = 0

So,

x = 0 or x = 23/3.

Since x cannot be 0 (as it would make UT = -37, (which is not possible),

x = 23/3.

Substituting this value of x into RS = 2x + 15.

RS = 2(23/3) + 15 = 31

Thus,

The value of RS is 31.

Learn more about expressions here:

https://brainly.com/question/3118662

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Answer: See Explanation

Step-by-step explanation:

ABC and DBE = Vertical

DBC and ABC = Adjacent

CBD and EBA = Vertical

EBA and ABC = Adjacent

Adjacent angles are two angles that have a common vertex and a common side but do not overlap.

Vertical angles are angles opposite each other where two lines cross.

Hope I could help!

Answer:

Percent symbol 2 I think

Answer:

0.03

Step-by-step explanation:

Percent increase= amount of increase/ original amount  

66 - 64 / 66 = 2 / 66 = 0.0303030303

Answer:

1 hour

Step-by-step explanation:

Answer:

minimum, Q1, median, Q3, maximum.

Step-by-step explanation:

i did the test

Answer:

minimum, Q1, median, Q3, maximum.

Answer:

3/5

Step-by-step explanation:

The question is incomplete. Let us use this as the complete version;

Of the people at a tennis club 2/5 are women. The rest of the people are men. What fraction of the people are men?

Let the total people be 1

Given

Fraction that are women = 2/5

Fraction that are men = 1 - 2/5

Fraction that are men = (5-2)/5

Fraction that are men = 3/5

Answer:

19

Step-by-step explanation:

9 + 10 = 19

Answer: 89.4427

Step-by-step explanation: I apologize if I am wrong; I used Pythagorean Thyreom, and I used the formula a=√c^2-b^2 since we are solving for side a.

a=√120^2−80^2

a=√14400−6400

a=√8000

a=89.4427

I hope this is what you are looking for :)

Pythagoras is the sum of the square of two sides is equal to the square of the longest side. Then the height of the tower is 89.44 m.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

The length of a guy's wire supporting a cell tower is 120 meters.

The guy wire is anchored to the ground at a distance of 80 meters from the base of the tower.

We know that the Pythagoras theorem.

[tex]\rm H^2 = P^2 + B^2[/tex]

We have

H = 120 m

B = 80 m

Then by the Pythagoras theorem, we have

[tex]\rm P = \sqrt{H^2 - B^2}\\\\P = \sqrt{120^2 - 80^2}\\\\P = \sqrt{14400 - 6400}\\\\P = \sqrt{8000} = 89.44[/tex]

Thus, the height of the tower is 89.44 m.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

Answer:

e

Step-by-step explanation:

Answer:

5+7x

Step-by-step explanation:

1/2(6-4x) +2 +9x

3-2x+2+9x

5+7x

Answer:

n/3 = 9

Step-by-step explanation:

the quotient is the result you get from division

Answer:

negative one third

Step-by-step explanation:

So you go to the 1 and half

Answer:

B

Step-by-step explanation:

Answer:

It is the first answer choice

Answer:

Step-by-step explanation:

1. 3.52 tax for the game, 2.09 for the book

difference between the two, 1.43

2. 3.68 in tax for the book, 2.18 for the book

difference between the two, 1.50

3. It was purchased in Contra Costa county with 11.5% sales tax

Answer:

c 116

Step-by-step explanation:

Answer:

The answer is c

Step-by-step explanation:

Answer:

$15.5

Step-by-step explanation:

33.50-18=15.5

jope it helps ypu a lot.

Answer:

im pretty sure that it is B please correct me if i am wrong:D

Answer:

B. 70°

Step-by-step explanation:

Answer: x=56

Step-by-step explanation:

I started off by figuring out what’s the total internal angles for a pentagon which is 540

Then i did 72+ 3x +2x+89+99 = 540

And i solved for x=56

Answer:

the correct answer is d.

Step-by-step explanation:

i hope this helps :)

Answer:

D.

Step-by-step explanation:

The line crosses the x-axis at 4 and the y-axis at -2.

Answer: D.

Answer:

Richard's gross pay for the month was $ 4,512.5.

Step-by-step explanation:

Given that Richard Klein works as auto mechanic and earns the following commission rates: 3.00 percent for oil changes, 5.00 percent for tune ups and 6.25 percent on auto parts sales; and he is guaranteed a minimum salary of $ 2,450.00 per month, if last month he brought in $ 2,500.00 in oil changes, $ 4,500.00 in tune ups and sold $ 28,200.00 in parts, to determine what is his gross pay for the month the following calculation must be performed:

2,450 + (2,500 x 0.03) + (4,500 x 0.05) + (28,200 x 0.0625) = X

2,450 + 75 + 225 + 1,762.5 = X

2,450 + 2,062.5 = X

4,512.5 = X

Thus, Richard's gross pay for the month was $ 4,512.5.

Answer:

y = x+1

Step-by-step explanation:

Slope-intercept form

(y = mx+b)

m = slope and b = y-intercept

The line crosses the y-axis at (0, 1), therefore the y-intercept (b) = 1

The slope (m) = 1

Because the slope is 1, it does not need to be written in the equation, as any number multiplied by 1 is that number.

Answer:

sin^-1 square root 2/2

=90

Answer:

1352 miles

Step-by-step explanation:

since city t, s, and P make a right angle we can use the Pythagorean theorem to find the hypotenuse (distance from t to p) 1180 squared=1,392,400 and 660 squared =435,600 so now we add them together and take its square root which is 1352.0

Answer:

(8, 4)

Step-by-step explanation:

i hope this helps :)

Answer:

3:1 in simplest form

Step-by-step explanation: