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3 years ago

12

Find the value of x.

1 answer:

vagabundo [1.1K]3 years ago

6 0

Answer:

X = 44

because the bottom triangle's sides are equal, which means that both angles are equal. so you can add 68 to 68 and get 136. then you need to subtract it by 180 to get the final angle which is 44 and because there is a vertical pair of angles, they both equal the same value. So for the top triangle because both sides are also equal it will make both corner angles equal to each other.

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KIM [24]

The answer is = 7 11/12

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3 years ago

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Shayla's rideshare fare from the airport was $28.50, and she added a 15% tip. How much did Shayla pay in total

Elodia [21]

15 percent of 28.50 is 4.275
So 28.50 + 4.275 = 32.775
So $32.77

8 0

3 years ago

Prove that 1³+2³+....n³=n²(n+1)²/4. principle of mathematics induction

alex41 [277]

<h3>The Simplified Question:-</h3>

$\sf 1^3+2^3\dots n^3=\dfrac{n^2(n+1)^2}{2}$

$\\ \sf\longmapsto 1^3+2^3+\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2$

<h3>Solution:-</h3>

Let

$\\ \sf\longmapsto P(n)=1^3+2^3\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2$

For n=1

$\\ \sf\longmapsto P(1)=\left(\dfrac{1(1+1)}{2}\right)^2$

$\\ \sf\longmapsto P(1)=\left(\dfrac{1(2)}{2}\right)^2$

$\\ \sf\longmapsto P(1)=\left(\dfrac{2}{2}\right)^2$

$\\ \sf\longmapsto P(1)=(1)^2$

$\\ \bf\longmapsto P(1)=1=1^3$

Let k be any positive integer.

$\\ \sf\longmapsto P(k)= 1^3+2^3\dots k^3=\left(\dfrac{k(k+1)}{2}\right)^2$

We have to prove that p(k+1) is true.

consider

$\sf 1^3+2^3\dots k^3+(k+1)^3$

$\\ \sf\longmapsto \left(\dfrac{k(k+1)}{2}\right)^2+(k+1)^3$

$\\ \sf\longmapsto \dfrac{k^2(k+1)^2}{4}+(k+1)^3$

$\\ \sf\longmapsto \dfrac{k^2(k+1)^2+4(k+1)^3}{4}$

$\\ \sf\longmapsto \dfrac{k+1)^2\left\{k^2+4k+4\right\}}{4}$

$\\ \sf\longmapsto \dfrac{(k+1)^2(k+2)^2}{4}$

$\\ \sf\longmapsto \dfrac{(k+1)^2(k+1+1)^2}{4}$

$\\ \sf\longmapsto \left(\dfrac{(k+1)(k+1+1)}{2}\right)^2$

$\\ \sf\longmapsto (1^3+2^3+3^3\dots k^3)+(k+1)^3$

Thus P(k+1) is true whenever P(k) is true.

Hence by the Principal of mathematical induction statement P(n) is true for $\bf n\epsilon N.$

Note:-

We can solve without simplifying the Question .I did it for clear steps and understanding .

<h3>Learn More:-</h3>

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Susan threw a softball 42 yards on her first try and 51 and a half yards on her second try.

ExtremeBDS [4]

The answer would be 28 ft. and 6 in.

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Celesta used to spend 90 minutes a day on the phone. Now she spends 60 minutes a day. What is the PERCENT DECREASE?

Andrews [41]

Answer:

-210

Step-by-step explanation:

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3 years ago