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Alexus [3.1K]
3 years ago
9

I’m in Algebra 2 and we’re currently on the subject of “Solving Absolute Value Equations” and I’m having trouble with this equat

ion. Please help!

Mathematics
1 answer:
saw5 [17]3 years ago
6 0

let's bear in mind that an absolute value expression is in effect a piece-wise expression,  namely it has a ± versions of the same expression.

\bf 5|3x-4| = x+1\implies |3x-4|=\cfrac{x+1}{5}\implies \begin{cases} +(3x-4)=\cfrac{x+1}{5}\\[1em] -(3x-4)=\cfrac{x+1}{5} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ +(3x-4)=\cfrac{x+1}{5}\implies 3x-4=\cfrac{x+1}{5}\implies 15x-20=x+1 \\\\\\ 14x-20=1\implies 14x=21\implies x = \cfrac{21}{14}\implies \boxed{x=\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill\\\\ -(3x-4)=\cfrac{x+1}{5}\implies -3x+4=\cfrac{x+1}{5}\implies -15x+20=x+1 \\\\\\ 20=16x+1\implies 19=16x\implies \boxed{\cfrac{19}{16}=x}

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The midpoint of GH is M( 6,-4). One endpoint is G(8,-2). Find the coordinates of endpoint H.
Finger [1]

Using the midpoint formula, the coordinates of endpoint H are (4, -6).

<h3>The Midpoint Formula</h3>

The midpoint formula is given as: (x_m, y_m) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )

<em>Where</em>,

(x_m, y_m) = coordinates of the midpoint

(x_1, y_1) = coordinates of the first point

(x_2, y_2) = coordinates of the second point

Given the following:

(x_m, y_m) = M( 6,-4)

(x_1, y_1) = G(8,-2)

(x_2, y_2) = H(?, ?)

Plug in the values into the midpoint formula

M(6, -4) = (\frac{8 + x_2}{2}, \frac{-2 + y_2}{2} )

Solve for the x-coordinate and y-coordinate separately

6 = \frac{8 + x_2}{2}

  • Multiply both sides

6 \times 2 = 8 + x_2\\\\12 = 8 + x_2\\\\12 - 8 = x_2\\\\4 = x_2\\\\\mathbf{x_2 = 4}

-4 = \frac{-2 + y_2}{2}\\\\-8 = -2 + y_2\\\\-8 + 2 = y_2\\\\-6 = y_2\\\\\mathbf{y_2 = -6}

Therefore, using the midpoint formula, the coordinates of endpoint H are (4, -6).

Learn more about midpoint formula on:

brainly.com/question/13115533

3 0
2 years ago
Demarco has a piece of fabric 6yd long. He uses a piece 3yd long. He cuts the rest into strips that are each 3\4 yd long. How ma
Kobotan [32]

Answer: 4

Step-by-step explanation:

Hi, to answer this question, first, we have to subtract the amount of fabric used (3yd) to the total fabric that Demarco has (6yd)

6 -3 =3yd

Finally, we have to divide the result by the length of each strip piece (3/4yd)

3÷ 3/4= 4 pieces  

There are 4 3/4 yd long strips.

Feel free to ask for more if needed or if you did not understand something.

4 0
3 years ago
If f(x) = e^X, and W(f, g) = 3e^x, find g(x).
trasher [3.6K]

Answer:

g(x)=3

Step-by-step explanation:

Let's find the answer.

W(f,g)=3e^x which can be written as:

W(f,g)=(3)*(e^x), notice that:

(e^x)=f(x) so:

W(f,g)=3*f(x), establishing:

W(f,g)=g(x)*f(x) then:

g(x)=3

In conclusion, g(x)=3.

5 0
3 years ago
How kany doulutions does this equation have 25 - 4x=15-3x+10-x
natima [27]
Since it's a one-variable equation, it has only one solution:

25 - 4x = 15 - 3x + 10 - x

25 - 4x + x = 15 - 3x + 10

25 - 3x = 15 - 3x + 10

- 3x = 15 - 3x + 10 - 25

- 3x = 15 - 3x - 15

- 3x + 3x = 15 - 15

0 = 15 - 15

0 = 0




Hope it helped,



BioTeacher101
4 0
4 years ago
isac walks 6/10 of a mile in 1/5 of an hour if his rate remains constant what is isac walking rate in miles per hour
Slav-nsk [51]

Answer:amazing

Step-by-step explanation:

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