PleASEE HELP!!! I HAVE TO GET AN A PLEASE

The hypotenuse of a right triangle is 6 cm and one side is 2 cm longer than the other side. Find the length of each side to one

MA_775_DIABLO [31]

Answer:

The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

Step-by-step explanation:

Let x be one leg of the right triangle.

Since the other leg is two centimeters longer, it can be represented by the expression:

$x + 2 \text{ cm}$

According to the Pythagorean Theorem, for a right triangle:

$a^2 + b^2 = c^2$

Where c is the hypotenuse and a and b are the two legs.

The hypotenuse is given to be 6 cm and the two legs are x and (x + 2). Hence:

$(x)^2 + (x+2)^2 = 6^2$

Solve for x. Simplify:

$x^2 + (x^2 + 4x + 4) = 36$

Simplify:

$2x^2 + 4x + 4 = 36$

Subtract:

$2x^2 + 4x - 32 =0$

Divide:

$x^2 + 2x - 16 = 0$

The equation is not factorable, so we can consider using the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}$

In this case, a = 1, b = 2, and c = -16. Substitute:

$\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}$

And evaluate:

$\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}$

Hence, our two solutions are:

$\displaystyle x = -1 + \sqrt{17} \approx 3.1\text{ or } x = -1 - \sqrt{17} \approx -5.1$

Lengths cannot be negative, so we can ignore the second solution.

Hence, the value of x or the first side length is about 3.1 centimeters.

Since the other side length is two centimeters longer, the other side is about 5.1 centimeters.

In conclusion, the two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

4 0

3 years ago

What is another way to write 300+70+5/10+30070.508

N76 [4]

Answer:

375÷10+30070.508

Step-by-step explanation:

4 0

4 years ago

Hardware store sells a 5 pound box of nails for $16.80. The store is having a 20% off sale on all merchandise. What is the sale

DENIUS [597]

The correct answer is $13.44

7 0

3 years ago

Read 2 more answers

Note that the proportion of students who went Home for winter break was 0.35 (or 35%). Briefly explain why it would not be appro

tensa zangetsu [6.8K]

Answer:

Is not appropiate to refer a estimation or a statistic as a paramter because the statistic just give informaation about the sample selected and not about all the population of interest. What we can do is inference with this sample proportion or confidence intervals in order to see on what limits our real parameter of interest p lies.

Step-by-step explanation:

Description in words of the parameter p

$p$ represent the real population proportion of students who went Home for winter break

$\hat p$ represent the estimated proportion of students who went Home for winter break

n is the sample size selected

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

For this case we assume that the proportion given 0.35 is an estimation for the real parameter of interest p, that means $\hat p = 0.35$

On this case the estimated proportion is calculated from the following formula:

$\hat p = \frac{X}{n}$

Where X are the people in the sam with the characteristic desired (students who went Home for winter break) and n the sample size selected.

Is not appropiate to refer a estimation or a statistic as a paramter because the statistic just give informaation about the sample selected and not about all the population of interest. What we can do is inference with this sample proportion or confidence intervals in order to see on what limits our real parameter of interest p lies.

7 0

3 years ago

Solve on the interval 0 2pi. 2sec(x)+4=0

bazaltina [42]

So look at this it’s should help you .

5 0

3 years ago