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AnnZ [28]
2 years ago
11

TU = 3, RS = 15, TW = 4, TR = 9; Assume that the sides of triangle TUW are proportional to the sides of triangle TRS. What is th

e length of WS? 8 12 15 24

Mathematics
2 answers:
sertanlavr [38]2 years ago
5 0
The answer is 8. Hope it helped!
VMariaS [17]2 years ago
3 0

Answer:

  WS=8\ units

Step-by-step explanation:

we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal and the corresponding angles are also equal

In this problem

\frac{TU}{TR}=\frac{UW}{RS}=\frac{TW}{TS}

we have

TU=3\ units, RS=15\ units, TW=4\ units,TR=9\ units

Find the value of TS

\frac{TU}{TR}=\frac{TW}{TS}

substitute

\frac{3}{9}=\frac{4}{TS}

TS=36/3=12\ units

WS=TS-TW

WS=12-4=8\ units

see the attached figure to better understand the problem

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

 </span>Add  9  to both sides of the equation :<span> 
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Tems11 [23]
B = hourly rate for babysitting and w = hourly rate for working at water park

3b + 10w = 109...multiply by -8
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----------------------
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---------------------add
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2 years ago
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vovangra [49]

Answer: Option A) 729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12} is the correct expansion.

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on applying binomial theorem,  (a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r

Here a=3c, b=d^2 and n=6,

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2 years ago
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anzhelika [568]
<span>this is pretty hard but here is your answer 
</span>

y = x^2 - 10x + 25 - 25

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<span> x-5 = +/-sqrt(y+25) </span>

 

<span> And you get TWO inverses: </span>

 

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Luden [163]

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See explanation below

Step-by-step explanation:

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Now, <u>Student A:</u>

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For <u>Student B:</u>

Similarly, both answers are correct for this student as well, looking at the equivalence we showed first.

Also, "-" (negative) in front of the parenthesis and inside parenthesis here doesn't matter.

Hence,

Student A and Student B both answered 2 questions correctly.

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