Greatest to least: 17/20, 19/20, 0.19, 0.24

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

Given the same triangle from part C, if line segment AB measures 12 inches and line segment BC measures 5 inches what is the mea

exis [7]

Answer:

4.615 in

Step-by-step explanation:

Triangle ABC and ABD are similar because they have two corresponding congruent triangles that is right angle and ∠A. Triangle ABC and BCD are similar because they have two corresponding congruent triangles that is right angle and ∠C. Therefore Triangle ABC, ABD and BCD are similar. Since they are similar, then their sides are proportional in length.

In triangle ABC, using Pythagoras theorem:

AC² = AB² + BC²

AC² = 12² + 5²

AC² = 144 + 25 = 169

AC² = 169

AC = √169 = 13 in

Using similar triangle for ΔABC and ΔABD:

$\frac{AC}{AB}= \frac{BC}{BD} \\\\\frac{13}{12}=\frac{5}{BD}\\\\BD=\frac{12*5}{13}\\ BD=4.615\ in$

5 0

2 years ago

The graph of a linear equation has a slope of -2 and passes through the point (-4,3) what is the equation of the line

valentinak56 [21]

Answer:

I need points

Step-by-step explanation:

nononon

3 0

2 years ago

Please answer correctly !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!

xxTIMURxx [149]

Answer:

x=57 degree

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

What is the sum of all the integers between the square root of 19 and the square root of 77?

Artist 52 [7]

Since we are only dealing with integers, we do not need to worry about decimals. Therefore, finding the exact values of sqrt(19) and sqrt(77) is not important. We can just estimate.

19 is between 16 and 25 (which are 4^2 and 5^2), so the square root of 18 is some number between 4 and 5.

77 is between 64 and 81 (which are 8^2 and 9^2), so the square root of 77 is some number between 8 and 9.

So the integers (whole numbers) that are between our two sqaure roots are 5, 6, 7, and 8.

Add them up and we have our answer.

5+6+7+8 = 26

4 0

3 years ago