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3 years ago

What is the reason for each step in the solution of the equation?

1 answer:

8 0

The correct reason <span>for each step in the solution of the equation would be as follows:
</span>
12 − 5x + 6x = 4 - Given

12 + x = 4 - Combine Like Terms

x= −8 - Subtraction Property of Equality

Hope this answers the question. Have a nice day.

You might be interested in

Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.

koban [17]

Answer:

$x^2 + 4x + y^2 +8y = 0$

Step-by-step explanation:

Given

$A = (-1,-2)$

$B = (2,4)$

$AP:BP = 1 : 2$

Required

The locus of P

$AP:BP = 1 : 2$

Express as fraction

$\frac{AP}{BP} = \frac{1}{2}$

Cross multiply

$2AP = BP$

Calculate AP and BP using the following distance formula:

$d = \sqrt{(x - x_1)^2 + (y - y_1)^2}$

So, we have:

$2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

$2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

Take square of both sides

$4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2$

Evaluate all squares

$4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16$

Collect and evaluate like terms

$4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20$

Open brackets

$4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20$

Collect like terms

$4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0$

$3x^2 + 12x + 3y^2 +24y = 0$

Divide through by 3

$x^2 + 4x + y^2 +8y = 0$

3 0

3 years ago

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x - 7x + 11?

Maksim231197 [3]

Answer:

±1, ±11, ±1/5, ±11/5

Step-by-step explanation:

f(x) = 5x³ - 7x + 11

constant term: 11

leading coefficient: 5

factors of the constant term: ±1, ±11

factors of the leading coefficient: ±1, ±5

possible rational roots = factors of the constant term/factors of the leading coefficient = ±1, ±11, ±1/5, ±11/5

6 0

3 years ago

Find three right triangles based upon the Pythagorean Triple of 8, 15, and 17. Explain how you know these are triangles.

Luba_88 [7]

A^2 + b^2 = c^2
8^2 + 15^2 = 17^2
64 + 225 = 289
289=289
It is a triangle because the numbers match the Pythagorean Theorem.

7 0

3 years ago

PLS HELP ME ASAP WILL MARK BRAINLIEST!!

My name is Ann [436]

Answer:

1. Rational

2. Integer

3. Irrational

4. Irrational

5. Imaginary

8 0

3 years ago

Nina and Jo both ran an 8 km race. Nina took 55 minutes to run the whole race. Jo started the race 3 minutes later than Nina but

grin007 [14]

Answer:

Step-by-step explanation:

First we figure out how fast Nina can run. If Nina can run 8 km in 55 minutes, then her rate is

$\frac{8km}{55min}=.145\frac{km}{min}$ and we can use that in a d = rt table:

d = r * t

Nina .145

Now we can fill in the distance which is 6 for both, since that is the distance where they met:

d = r * t

Nina 6 = .145

Jo 6 =

Now we go to the info given about the time. If Jo started the race 3 minutes after Nina, that means that Nina is running 3 minutes longer than Jo. Filling in the time info:

d = r * t

Nina 6 = .145 * t + 3

Jo 6 = r * t

As you can see, right now we have 2 unknowns in Jo's row. But we don't have to! We will go to Nina's row where the only unknown is time and solve for t. If d = rt, then

6 = .145(t + 3) and

6 = .145t + .435 and

5.55 = .145t so

t = 38.379 minutes. This means that Jo was running 38.379 minutes when she caught up to Nina (it took Nina 3 minutes longer than that to go 6 km since she was already running for 3 minutes when Jo started the race). If Jo's time is 38.379, we can use that in her row for t and solve for r. If d = rt, then

6 = r(38.379) and

r = .16 km/min

Let's check it without the rounding (rounding takes away from the accuracy). If 6 = .145(t + 3) and Nina's rate not rounded is .145454545 and t = 38.37931034, then, rewriting without rounding:

6 should equal .145454545( 38.37931034 + 3)

6 ?=? .145454545(41.37931034)

6 ?=? 6.0 so

Jo's rate is .16 km/min rounded

6 0

3 years ago