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ozzi
3 years ago
13

4-(2y-1)=2(5y+9)+y please help quick

Mathematics
2 answers:
stich3 [128]3 years ago
7 0

Step-by-step explanation:Step 1: Simplify both sides of the equation.

4−(2y−1)=2(5y+9)+y

4+−1(2y−1)=2(5y+9)+y(Distribute the Negative Sign)

4+−1(2y)+(−1)(−1)=2(5y+9)+y

4+−2y+1=2(5y+9)+y

4+−2y+1=(2)(5y)+(2)(9)+y(Distribute)

4+−2y+1=10y+18+y

(−2y)+(4+1)=(10y+y)+(18)(Combine Like Terms)

−2y+5=11y+18

−2y+5=11y+18

Step 2: Subtract 11y from both sides.

−2y+5−11y=11y+18−11y

−13y+5=18

Step 3: Subtract 5 from both sides.

−13y+5−5=18−5

−13y=13

Step 4: Divide both sides by -13.

−13y

−13

=

13

−13

y=−1

 Answer: y =-1

kiruha [24]3 years ago
3 0

Here, this is a linear equation in one variable because only one variable is there, y. We need to find the solution i.e the value of y.

Given, equation:

4 - (2y - 1) = 2(5y + 9) + y

We need to find y, So let's isolate y in any one side of the equation. Before that, let's open the parentheses.

4 - 2y + 1 = 10y + 18 + y

5 - 2y = 11y + 18

Now, let's add 2y to both sides, So that -2y on the left hand side gets cancel.

5 - 2y + 2y = 11y + 18 + 2y

5 = 13y + 18

Flipping the equation for easy calculation,

13y + 18 = 5

Solving further,

13y =  - 13

y =  \frac{ - 13}{13}

\boxed{y =  - 1}

Hence, we are done !!

<u>━━━━━━━━━━━━━━━━━━━━</u>

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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.

  • H² = P² + B²

<u>Where </u><u>,</u>

  • H refers to <u>Hypotenuse</u>

  • P refers to <u>Perpendicular</u>

  • B refers to <u>Base</u>

<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>

In the given triangle ,

  • Base = <u>TE </u>

  • 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}

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\quad \longmapsto \qquad \:37 {}^{2}  = 35 {}^{2}  + TE {}^{2}

Simplifying it ,

\quad \longmapsto \qquad \:1369 = 1225  + TE {}^{2}

Subtracting 1225 on both sides :

\quad \longmapsto \qquad \:1369 - 1225  = \cancel{1225}  + TE {}^{2}  -  \cancel{1225}

We get ,

\quad \longmapsto \qquad \:144 = TE {}^{2}

Applying square root to both sides :

\quad \longmapsto \qquad \ \sqrt{ 144} =  \sqrt{TE {}^{2}}

We get ,

\quad \longmapsto \qquad \:     \red{\underline{\boxed{\frak{TE  = 12 \: feet}}}} \quad \bigstar

  • <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 ,

  • SE² = TS² + TE²

Substituting value of SE , TS and TE :

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  • 1369 = 1225 + 144

  • 1369 = 1369

  • L.H.S = R.H.S

  • Hence , Verified .

<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>
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