The graph shows a proportional relationship. Which equation matches the

What is the solution of

kobusy [5.1K]

Answer:

Third option: x=0 and x=16

Step-by-step explanation:

$\sqrt{2x+4}-\sqrt{x}=2$

Isolating √(2x+4): Addind √x both sides of the equation:

$\sqrt{2x+4}-\sqrt{x}+\sqrt{x}=2+\sqrt{x}\\ \sqrt{2x+4}=2+\sqrt{x}$

Squaring both sides of the equation:

$(\sqrt{2x+4})^{2}=(2+\sqrt{x})^{2}$

Simplifying on the left side, and applying on the right side the formula:

$(a+b)^{2}=a^{2}+2ab+b^{2}; a=2, b=\sqrt{x}$

$2x+4=(2)^{2}+2(2)(\sqrt{x})+(\sqrt{x})^{2}\\ 2x+4=4+4\sqrt{x}+x$

Isolating the term with √x on the right side of the equation: Subtracting 4 and x from both sides of the equation:

$2x+4-4-x=4+4\sqrt{x}+x-4-x\\ x=4\sqrt{x}$

Squaring both sides of the equation:

$(x)^{2}=(4\sqrt{x})^{2}\\ x^{2}=(4)^{2}(\sqrt{x})^{2}\\ x^{2}=16 x$

This is a quadratic equation. Equaling to zero: Subtract 16x from both sides of the equation:

$x^{2}-16x=16x-16x\\ x^{2}-16x=0$

Factoring: Common factor x:

x (x-16)=0

Two solutions:

1) x=0

2) x-16=0

Solving for x: Adding 16 both sides of the equation:

x-16+16=0+16

x=16

Let's prove the solutions in the orignal equation:

1) x=0:

$\sqrt{2x+4}-\sqrt{x}=2\\ \sqrt{2(0)+4}-\sqrt{0}=2\\ \sqrt{0+4}-0=2\\ \sqrt{4}=2\\ 2=2$

x=0 is a solution

2) x=16

$\sqrt{2x+4}-\sqrt{x}=2\\ \sqrt{2(16)+4}-\sqrt{16}=2\\ \sqrt{32+4}-4=2\\ \sqrt{36}-4=2\\ 6-4=2\\ 2=2$

x=16 is a solution

Then the solutions are x=0 and x=16

5 0

3 years ago

Can some one help with this question?

vesna_86 [32]

Answer:

Step-by-step explanation:

log₂125 = log₂(5²) = 2log₂5 = 2k

3 0

3 years ago

What is 2 + 24 in a pound of a mile that has touched a cliff

geniusboy [140]

Answer:

26

Step-by-step explanation:

4 0

3 years ago

How do you write 59/50 as a percent

Free_Kalibri [48]

Answer:118

Step-by-step explanation:

Convert from a fraction to percent. Here is the answer to the question: 59/50 as a percentage or how to convert the fraction 59/50 to percent. Use the fraction to percent calculator below to write any fraction as a percent.

Please, input values in this format: a b/c or b/c.

Examples: Three tenths should be typed as 3/10. One and one-half should be typed as 1 1/2. Note that there is a space between the the integer and the fraction.

6 0

3 years ago

Read 2 more answers

Please help and explain how you did it

jenyasd209 [6]

To determine the lengths of the sides from shortest to longest, you need to calculate the corresponding angles. The higher angles will correspond to longer sides.

To find the angles, you have to solve for x. You’re already given that angle A is 76. To find the others, you know that angle C is 180-(16x+16) since it’s supplemental to the exterior angle. Then, you know the sum of the angles of the entire triangle is 180, so add up A, B, and C

A+B+C=180
76+6x+(180-16x-16)=180
240-10x=180
-10x=-60
x=6

So to find angle B, you use 6x or 6(6)=36.

To find angle C, you use 180-(16x-16) or 180-16(6)-16=68

So now match up the angles with their corresponding sides to find the length from shortest to longest.

Angle A (76) corresponds with BC
Angle B (36) corresponds with AC
Angle C (68) corresponds with AB

Again, the higher the degree, the longer the corresponding side, so AC is shortest, AB is next, and BC is the longest.

5 0

3 years ago