Find the circumcenter of triangle EFG with E(4, 4), F(4, 2), and G(8, 2).

The length of one side of a triangle is 2 feet less than three times the length of its second side. The length of the third side

Zanzabum

Using a system of equations, it is found that the lengths of the sides of the triangle are given as follows:

0.91 feet, 0.73 feet, 1.23 feet.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are the lengths, given by x, y and z.

The length of one side of a triangle is 2 feet less than three times the length of its second side, hence:

y = 3x - 2.

The length of the third side is 3/4 of the sum of the lengths of the first two sides, hence:

$z = \frac{3(x + y)}{4} = \frac{3(4x - 2)}{4}$

The perimeter of the triangle is 17.5 feet, hence:

$x + y + z = 17.5$

$x + 3x - 2 + \frac{3(4x - 2)}{4} = 17.5$

$4x + \frac{3(4x - 2)}{4} = 19.5$

$16x + 12x = 25.5$

x = 25.5/28

x = 0.91.

Then the other sides are:

y = 3x - 2 = 3(0.91) - 2 = 0.73 feet.

$z = \frac{3(4 x 0.91 - 2)}{4} = 1.23 feet$

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

4 0

2 years ago

Use the graph to write an equation that shows the distance y in terms of the number of hours x.

Andrews [41]

Answer:

50/1, 100/2, 250/5, 400/8

7 0

3 years ago

Calculus 2 Master needed, show steps with partial fraction decomposition <img src="https://tex.z-dn.net/?f=%5Cint%283x%5E2-26x%2

Vladimir79 [104]

Answer:

-ln|x−5| + 2 ln(x²+4) + 3 tan⁻¹(x/2) + C

Step-by-step explanation:

The fraction will be split into a sum of two other fractions.

The first fraction will have a denominator of x − 5. The numerator will the a polynomial of one less order, in this case, a constant A.

The second fraction will have a denominator of x² + 4. The numerator will be Bx + C.

$\frac{3x^{2}-26x+26}{(x-5)(x^{2}+4)}=\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}$

Combine the two fractions back into one using the common denominator.

$\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}=\frac{A(x^{2}+4)+(Bx+C)(x-5)}{(x-5)(x^{2}+4)}$

This numerator will equal the original numerator.

$A(x^{2}+4)+(Bx+C)(x-5)=3x^{2}-26x+26\\Ax^{2}+4A+Bx^{2}-5Bx+Cx-5C=3x^{2}-26x+26\\(A+B)x^{2}+(C-5B)x+(4A-5C)=3x^{2}-26x+26$

Match the coefficients.

$A+B=3\\C-5B=-26\\4A-5C=26$

Solve the system of equations.

$A=-1\\B=4\\C=-6$

So we can rewrite the integral as:

$\int {(\frac{-1}{x-5}+\frac{4x-6}{x^{2}+4}) } \, dx$

Solving:

$\int {\frac{-1}{x-5}\, dx + \int {\frac{4x}{x^{2}+4}} \, dx - \int {\frac{6}{x^{2}+4} } \, dx$

$-\int {\frac{1}{x-5}\, dx + 2\int {\frac{2x}{x^{2}+4}} \, dx - 6\int {\frac{1}{x^{2}+4} } \, dx$

$-ln|x-5| + 2ln(x^{2}+4) - 6(\frac{1}{2} tan^{-1}(\frac{x}{2} )) + C$

$-ln|x-5| + 2ln(x^{2}+4) - 3 tan^{-1}(\frac{x}{2} ) + C$

5 0

3 years ago

I need help can someone please help me

makkiz [27]

Answer:

The measure of ∠A is 66°.

Step-by-step explanation:

∠A = 3x + 18
∠D = 4x + 2
∠D = ∠A

<u>Now, let's solve the equation. ∠D = ∠A.</u>

=> 3x + 18 = 4x + 2
=> -2 + 18 = x
=> 16 = x

<u>Now, let's substitute the value of x into any equation.</u>

=> 4x + 2
=> 4(16) + 2
=> <u>66°</u>

Hence, the measure of ∠A is 66°.

7 0

3 years ago

Hiiiooo! Can someone please help❤️

ICE Princess25 [194]

Answer: it is either A or B im leaning more to B..im so sorry if im worng.

Step-by-step explanation:

Have a good day! :) ^-^ ❤️

5 0

3 years ago