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NNADVOKAT [17]
3 years ago
9

Find x and y, given that line WS and line VT are parallel. Show all work!!

Mathematics
1 answer:
slavikrds [6]3 years ago
5 0
Given that those lines are parallel they will form similar traingles. This means the lengths of the sides of the triangles will be proportional through a ratio.

Find the ratio:  divde the given small side by the given big side(they must be the same sides of the triangles though)

For example:
I found the ratio by dividing 8 / (20) and simplify to 2/5

Next step: multiply 22 by the fraction to get "y"
\frac{y}{22} = \frac{2}{5}
22*\frac{2}{5}= y
y=8.8 units


To find x :

Step 1: write an equation for the length of side US.
US= 5+x-2= x+3

Step 2: DIVIDE 5 by the ratio (must divide to get longer side DO NOT multiply)
US= 5/(2/5)= 12.5 units

Step 3: set the expression you found for US equal to 12.5 

12.5= x+3
subtract 3 from both sides to isolate x.
x= 9.5 units

My answers:
x= 9.5 units
y= 8.8 units
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Let ​ f(x)=x2+5x−36 ​. Enter the x-intercepts of the quadratic function in the boxes.
san4es73 [151]
Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     x^2-5*x-(36)=0 

Step by step solution:<span> Step 1:</span> Trying to factor by splitting the middle term

<span> 1.1 </span>    Factoring <span> x2-5x-36</span> 

The first term is, <span> <span>x2</span> </span> its coefficient is 1.
The middle term is, <span> -5x </span> its coefficient is  - 5.
The last term, "the constant", is <span> -36 </span>

Step-1: Multiply the coefficient of the first term by the constant <span> <span> 1</span> • -36 = -36</span> 

Step-2: Find two factors of  -36  whose sum equals the coefficient of the middle term, which is - 5.

<span><span>     -36   +   1   =   -35</span><span>     -18   +   2   =   -16</span><span>     -12   +   3   =   -9</span><span>     -9   +   4   =   -5   That's it</span></span>


Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  4 
                     <span>x2 - 9x</span> + 4x - 36

Step-4: Add up the first 2 terms, pulling out like factors :
                    x • (x-9)
              Add up the last 2 terms, pulling out common factors :
                    4 • (x-9)
Step-5: Add up the four terms of step 4 :
                    (x+4)  •  (x-9)
             Which is the desired factorization

<span>Equation at the end of step  1  :</span> (x + 4) • (x - 9) = 0 <span>Step  2  :</span>Theory - Roots of a product :

<span> 2.1 </span>   A product of several terms equals zero.<span> 

 </span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span> 

 </span>We shall now solve each term = 0 separately<span> 

 </span>In other words, we are going to solve as many equations as there are terms in the product<span> 

 </span>Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

<span> 2.2 </span>     Solve  :    x+4 = 0<span> 

 </span>Subtract  4  from both sides of the equation :<span> 
 </span>                     x = -4 

Solving a Single Variable Equation :

<span> 2.3 </span>     Solve  :    x-9 = 0<span> 

 </span>Add  9  to both sides of the equation :<span> 
 </span>                     x = 9 

6 0
3 years ago
Read 2 more answers
PLEASE HELP IM STUCK
kkurt [141]

Answer:

y= 2x + 10

Step-by-step explanation:

The variable depends on the $2 so, the green box should be 2

4 0
1 year ago
The exponential function y= a(b)^x passes through the points (3,25) and (8,10). Which of the following is closest to the value o
Yuki888 [10]

If the exponential function y=ab^x passes through the points (3,25) and (8,10), the value of b is 0.833

The given exponential equation is:

y=ab^x

The function passes through the points (3, 25) and (8, 10)

Substitute x = 3 and y = 25 into the function y=ab^x

25=ab^3............................(1)

Substitute x = 8 and y = 10 into the function y=ab^x

10=ab^8.............................(2)

Divide equation (2) by equation (1)

\frac{10}{25}=\frac{ab^8}{ab^3}  \\\\0.4=b^5\\\\b=0.4^\frac{1}{5} \\\\b=0.4^{0.2}\\\\b=0.833

Therefore, if the exponential function y=ab^x passes through the points (3,25) and (8,10), the value of b is 0.833

Learn more on exponential functions here: brainly.com/question/12940982

6 0
2 years ago
Search the Internet for a number that can be expressed as a Power of 10 and then, rewrite your number as a Power of 10.
Serhud [2]
10 to the power of 10 would be 10,000,000,000
7 0
3 years ago
Simplify the equation.​
Phoenix [80]

Answer:

C. 3j^{3}l

Step-by-step explanation:

1) First you cancel k^{2} because they are completely the same. then you take out the constants and simply.

2)You then have to use the Quotient Rule:

\frac{x^{a} }{x^{b} } =x^{a - b}

You should have ...

3j^{6-3} l^{5-4}

3) Simplify 6 − 3 to 3.

3j^{3} l^{1}

4) Simplify 5 − 4 to 1.

5) Use Rule of One: x^{1} =x

Answer is !!!

3j^{3} l

5 0
3 years ago
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