Which expression to a+ (c+7)?<br>

Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

4 0

2 years ago

When Emily arrived home from school, she spent 8 minutes eating a snack. Then, she spent 15 minutes playing with her dog and 32

ziro4ka [17]

Answer: 1 hour and 40 minutes

Explanation: Add all the time together and you get 100 minutes.

100 - 60 = 40

(I’m not very good at explaining it)

7 0

2 years ago

Read 2 more answers

Natasha is a bank teller. She received a 5% raise last year and a subsequent merit raise of 3% this year. What is the accumulati

Anvisha [2.4K]

Answer:

The correct answer is C. 8.15%.

Step-by-step explanation:

Given that Natasha is a bank teller, and she received a 5% raise last year and a subsequent merit raise of 3% this year, to determine what is the accumulative or compound effect of these two raises as a percentage, the following calculation must be performed, assuming, as an example, that her starting salary was $ 2,000:

(2,000 x 1.05) x 1.03 = X

2,100 x 1.03 = X

2,163 = X

2,000 = 100

2,163 = X

2,163 x 100 / 2,000 = X

216,300 / 2,000 = X

108.15 = X

108.15 - 100 = 8.15

Thus, the compound effect of both salary increases is a salary increase of 8.15%.

8 0

2 years ago

Midpoint of the x intercepts of f(x)=(x-4)(x+4)

lorasvet [3.4K]

The x-intercept is defined to be the value of x when y is zero. Based on the graph of the function: f(x) = (x-4)(x+4), the x-intercepts are located at (-4, 0) and (4,0). At these points the graph intersects the x-axis. The midpoint of the x-intercepts is located at the middle of the two points. In this case, the graph shows that it is at the origin or at (0,0).

5 0

2 years ago

Read 2 more answers

Solve the inequality. |2x + 10| > 26

neonofarm [45]

Answer:

x > 8

x < -16

Step-by-step explanation:

2x + 10 > 26

2x + 10 - 10 > 26 - 10

2x > 16

2x/2 > 16/2

x > 8

2x + 10 < -26

2x + 10 - 10 < - 26 - 10

2x < -36

2x/2 < -36/2

x < -16

6 0

2 years ago

Read 2 more answers

Which expression to a+ (c+7)?​

Which expression to a+ (c+7)?