The mistake is there is no parenthesis around 4x+12
Answer: 1 = 4.20, 2 = 8.40 3 = 12.60 4 = 16.80
This is a direct variation.
Step-by-step explanation:
Hey ! there
Answer:
- Value of missing side i.e. TE is <u>1</u><u>2</u><u> </u><u>feet</u>
Step-by-step explanation:
In this question we are provided with a <u>right</u><u> </u><u>angle </u><u>triangle</u> having <u>TS </u><u>-</u><u> </u><u>35</u><u> </u><u>ft </u><u>and</u><u> </u><u>SE </u><u>-</u><u> </u><u>37</u><u> </u><u>ft </u>. And we are asked to find the missing side that is <u>TE </u>using Pythagorean Theorem .
<u>Pythagorean Theorem :</u> -
According to Pythagorean Theorem sum of squares of perpendicular and base is equal to square of hypotenuse in a right angle triangle i.e.
<u>Where </u><u>,</u>
- H refers to <u>Hypotenuse</u>
- P refers to <u>Perpendicular</u>
<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>
In the given triangle ,
- Perpendicular = <u>TS </u><u>(</u><u> </u><u>35</u><u> </u><u>feet </u><u>)</u>
- Hypotenuse = <u>SE </u><u>(</u><u> </u><u>37</u><u> </u><u>feet </u><u>)</u>
Now applying Pythagorean Theorem :
![\quad \longmapsto \qquad \:SE {}^{2} = TS {}^{2} + TE {}^{2}](https://tex.z-dn.net/?f=%20%5Cquad%20%5Clongmapsto%20%5Cqquad%20%5C%3ASE%20%7B%7D%5E%7B2%7D%20%20%3D%20TS%20%7B%7D%5E%7B2%7D%20%20%2B%20TE%20%7B%7D%5E%7B2%7D%20)
Substituting values :
![\quad \longmapsto \qquad \:37 {}^{2} = 35 {}^{2} + TE {}^{2}](https://tex.z-dn.net/?f=%20%5Cquad%20%5Clongmapsto%20%5Cqquad%20%5C%3A37%20%7B%7D%5E%7B2%7D%20%20%3D%2035%20%7B%7D%5E%7B2%7D%20%20%2B%20TE%20%7B%7D%5E%7B2%7D%20)
Simplifying it ,
![\quad \longmapsto \qquad \:1369 = 1225 + TE {}^{2}](https://tex.z-dn.net/?f=%20%5Cquad%20%5Clongmapsto%20%5Cqquad%20%5C%3A1369%20%3D%201225%20%20%2B%20TE%20%7B%7D%5E%7B2%7D%20)
Subtracting 1225 on both sides :
![\quad \longmapsto \qquad \:1369 - 1225 = \cancel{1225} + TE {}^{2} - \cancel{1225}](https://tex.z-dn.net/?f=%20%5Cquad%20%5Clongmapsto%20%5Cqquad%20%5C%3A1369%20-%201225%20%20%3D%20%5Ccancel%7B1225%7D%20%20%2B%20TE%20%7B%7D%5E%7B2%7D%20%20-%20%20%5Ccancel%7B1225%7D)
We get ,
![\quad \longmapsto \qquad \:144 = TE {}^{2}](https://tex.z-dn.net/?f=%20%5Cquad%20%5Clongmapsto%20%5Cqquad%20%5C%3A144%20%3D%20TE%20%7B%7D%5E%7B2%7D)
Applying square root to both sides :
![\quad \longmapsto \qquad \ \sqrt{ 144} = \sqrt{TE {}^{2}}](https://tex.z-dn.net/?f=%20%5Cquad%20%5Clongmapsto%20%5Cqquad%20%5C%20%5Csqrt%7B%20144%7D%20%3D%20%20%5Csqrt%7BTE%20%7B%7D%5E%7B2%7D%7D)
We get ,
![\quad \longmapsto \qquad \: \red{\underline{\boxed{\frak{TE = 12 \: feet}}}} \quad \bigstar](https://tex.z-dn.net/?f=%20%5Cquad%20%5Clongmapsto%20%5Cqquad%20%5C%3A%20%20%20%20%20%5Cred%7B%5Cunderline%7B%5Cboxed%7B%5Cfrak%7BTE%20%20%3D%2012%20%5C%3A%20feet%7D%7D%7D%7D%20%5Cquad%20%5Cbigstar)
- <u>Henceforth</u><u> </u><u>,</u><u> </u><u>value </u><u>of </u><u>missing </u><u>side </u><u>is </u><em><u>1</u></em><em><u>2</u></em><em><u> </u></em><em><u>feet </u></em><em><u>.</u></em>
<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>
Now we are verifying our answer using Pythagorean Theorem . We know that according to Pythagorean Theorem ,
Substituting value of SE , TS and TE :
- 37² = 35² + <u>1</u><u>2</u><u>²</u>
<u>Therefore</u><u> </u><u>,</u><u> </u><u>our</u><u> answer</u><u> is</u><u> correct</u><u> </u><u>.</u>
<h2>
<u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>
Answer:
x = 8
Step-by-step explanation:
We solve the equation:
4x + 6 = 38
4x = 38 - 6
4x = 32
x = 32 ÷ 4
x = 8