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3 years ago

10

Pythagorean Theorem

1 answer:

Usimov [2.4K]3 years ago

5 0

A(squared)+B(squared)=C(squared)

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What is the x-value of the solution to the system of equations?

ValentinkaMS [17]

Answer:

The solution to the system of equations is:

$x=4,\:y=-3$

Step-by-step explanation:

Given the system of equations

$5x + 4y =8$

$2x- 3y = 17$

solving the system of equations

$\begin{bmatrix}5x+4y=8\\ 2x-3y=17\end{bmatrix}$

$\mathrm{Multiply\:}5x+4y=8\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:10x+8y=16$

$\mathrm{Multiply\:}2x-3y=17\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:10x-15y=85$

$\begin{bmatrix}10x+8y=16\\ 10x-15y=85\end{bmatrix}$

$10x-15y=85$

$-$

$\underline{10x+8y=16}$

$-23y=69$

$\begin{bmatrix}10x+8y=16\\ -23y=69\end{bmatrix}$

solve for y

$-23y=69$

Divide both sides by -23

$\frac{-23y}{-23}=\frac{69}{-23}$

$y=-3$

$\mathrm{For\:}10x+8y=16\mathrm{\:plug\:in\:}y=-3$

$10x+8\left(-3\right)=16$

$10x-24=16$

$10x=40$

Divide both sides by 10

$\frac{10x}{10}=\frac{40}{10}$

$x=4$

Thus, the solution to the system of equations is:

$x=4,\:y=-3$

7 0

2 years ago

What is f(+3) if f(x) = 5 x

Damm [24]

Answer:

$f(x) = 5x \\ f(3) = 5(3) = \boxed{15}$

<h3><u>f(</u><u>3</u><u>) =15</u> is the right answer.</h3>

4 0

2 years ago

Please help me so stressed

mr Goodwill [35]

Answer:

Meron ka nang loptap bakit humihingi ka pa nang answer

8 0

3 years ago

8) Factor each sum or difference of cubes completely.<br> a. 8x3 + 27

ASHA 777 [7]

Answer:

$\large\boxed{(2x+3)(4x^2-6x+9)}$

Step-by-step explanation:

$8=2^3\\\\8x^3=2^3x^3=(2x)^3\\\\27=3^3\\\\8x^3+27=(2x)^3+3^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+3)\bigg((2x)^2-(2x)(3)+3^2\bigg)=(2x+3)(4x^2-6x+9)$

4 0

3 years ago

B is the midpoint of ac. Ab = x+9 and bc = 3x-7 find x and ac

natali 33 [55]

To solve this problem, we need to know 2 relationships:

<h2>1. AC = AB + BC</h2>

The distance of AC is the sum of AB and BC.

$AC = AB + BC$

We know this since the distance of going from A to C (AC) is the same as going from A to B (AB), then B to C (BC).

<h2>2. AB = BC</h2>

The distance of AB is the same as AC.

$AB = BC$

We know this since B is in the middle of AC, so the distance from B to A (BA) is the same as the distance from B to C (BC).

You can see the attached image (at the bottom) for a visualization of this.

<h2>Putting them together</h2>

Since we know the values of AB and BC...

$AB = x+9\\BC = 3x-7$

...we can put these values into our 2nd equation and solve for x:

$AB = BC\\x + 9 = 3x -7$

Add 7 to both sides:

$x + 16 = 3x$

Subtract x from both sides:

$16 = 2x$

Divide both sides by 2:

$8 = x\\x = 8$

Knowing x, we can find the distance of AC using our first equation.

$AC = AB + BC$

Let's put in the values of AB and BC:

$AC = (x+9) + (3x-7)$

Before we put in x = 8, we can simplify this:

$AC = (x+9) + (3x-7)\\AC = x + 9 + 3x -7\\AC = x + 3x + 9 -7\\AC = 4x + 9 - 7\\AC = 4x+2$

We group x and 3x and add those together. Then we subtract 7 from 9.

With this equation, we can put in x = 8:

$AC = 4x +2\\AC = 4*8 + 2$

Since 4 * 8 = 32:

$AC = 4 * 8 + 2\\AC = 32 + 2\\AC = 34$

Finally, we have found both x and AC.

<h2>Answer</h2>

x = 8

AC = 34

7 0

3 years ago