All categories

2 years ago

What is the solution to the equation below? √ x-5 = x-11

Mathematics

1 answer:

Anuta_ua [19.1K]2 years ago

6 0

Answer:

x= 14

Step-by-step explanation:

sqrt( x-5) = x-11

Square each side

(sqrt( x-5))^2 = (x-11)^2

x-5 = x^2 - 22x +121

Subtract (x-5) from each side

x-5-x+5 = x^2 -22x +121 -x+5

0 = x^2 -23x +126

Factor

0 = ( x-14) ( x-9)

Using the zero product property

x-14 = 0 x-9=0

x=14 x=9

Check the solutions

sqrt( x-5) = x-11

sqrt( 14-5) = 14-11

sqrt(9) = 3

3=3

solution

sqrt( x-5) = x-11

sqrt(9-5) = 9-11

sqrt(4) =-2

2 = -2

not a solution

You might be interested in

The area of the rectangle shown is 17.36 square yards. What is the perimeter?

Nostrana [21]

Answer:

16.67

Step-by-step explanation:

Each side is about 4.167 yards so the perimeter is roughly 16.67 yards

5 0

2 years ago

Identify the transformations y = |x| ‐ 6

siniylev [52]

Thé transformation is that the function moved 6 units down

4 0

2 years ago

I need some help with this

masya89 [10]

Answer:

A, C, D

Step-by-step explanation:

Consider triangles NKL and NML. These triangles are right triangles, because

$m\angle K=m\angle M=90^{\circ}$

In these right triangles:

$\overline{NL}\cong \overline {NL}$ - reflexive property;
$\angle KLN\cong \angle MLN$ - given

Thus, triangles NKL and NML by HA postulate. Congruent triangles have congruent corresponding parts, so

$\overline{KN}\cong \overline{NM}\\ \\\overline{KL}\cong \overline{LM}\ [\text{option D is true}]$

Since

$\overline{KN}\cong \overline{NM},$

then

$7x-4=5x+12\\ \\7x-5x=12+4\\ \\2x=16\\ \\x=8\ [\text{option A is true}]\\ \\MN=KN=7\cdot 8-4=56-4=52\ [\text{option C is true}]$

Option B is false, because KN=52 units.

Option E is false, because LN is congruent KN, not LM

4 0

2 years ago

ASAP: Four cards are chosen from tens, jacks, queens and aces . What is the probability that there are at least three queens?

olasank [31]

Answer:

1 out of 4

Step-by-step explanation:

4 0

3 years ago

Please helpppp ty giving brain liest trying to get more:)

olya-2409 [2.1K]

The answer I believe would be 3/4

Remember to count from point to point using rise/run

I hope this helped :D

8 0

2 years ago

Read 2 more answers