MATHEMATICS HIGH SCHOOL

If JK=20-x^2, KL=2-x, and JL=10 find x

Answers

Answer 1
Answer: 0\ and\ 2-x > 0\ and\ 20-x^2 < 10\ and\ 2-x < 10\\x\in(-\sqrt{20};\ \sqrt{20})\ and\ x < 2\ and\\x\in(-\infty; -\sqrt{10})\ \cup\ (\sqrt{10};\ \infty)\ and\ x >-8\\\\x\in(-\sqrt{20};-\sqrt{10})\\\\|JL|=|JK|+|KL|\\\\20-x^2+2-x=10\\\\-x^2-x+22=10\ \ \ \ \ |subrtact\ 10\ from\ both\ sides\\\\-x^2-x+12=0\\\\-(x^2+x-12)=0\\\\x^2+x-12=0\\\\x^2+4x-3x-12=0\\\\x(x+4)-3(x+4)=0\\\\(x+4)(x-3)=0\iff x+4=0\ or\ x-3=0\\\\x=-4\in D\ or\ x=3\notin D\\\\Answer:\boxed{x=-4}" alt="|JK|=20-x^2;\ |KL|=2-x;\ |JL|=10\\D:20-x^2 > 0\ and\ 2-x > 0\ and\ 20-x^2 < 10\ and\ 2-x < 10\\x\in(-\sqrt{20};\ \sqrt{20})\ and\ x < 2\ and\\x\in(-\infty; -\sqrt{10})\ \cup\ (\sqrt{10};\ \infty)\ and\ x >-8\\\\x\in(-\sqrt{20};-\sqrt{10})\\\\|JL|=|JK|+|KL|\\\\20-x^2+2-x=10\\\\-x^2-x+22=10\ \ \ \ \ |subrtact\ 10\ from\ both\ sides\\\\-x^2-x+12=0\\\\-(x^2+x-12)=0\\\\x^2+x-12=0\\\\x^2+4x-3x-12=0\\\\x(x+4)-3(x+4)=0\\\\(x+4)(x-3)=0\iff x+4=0\ or\ x-3=0\\\\x=-4\in D\ or\ x=3\notin D\\\\Answer:\boxed{x=-4}" align="absmiddle" class="latex-formula">

Related Questions

HIGH SCHOOL

Under a dilation centered at the origin, the image is congruent to the preimage. What is the scale factor? A.
–1 or 0
C.
only 1
B.
0 or 1
D.
–1 or 1

Answers

The scale factor is D. -1 or 1
MIDDLE SCHOOL

Which equation has a graph parallel to the graph of 7x=14y-8 A y=-2x-7
B y=-1/2x+4
C y=1/2x+1
D y=2x+9

Answers

Answer:

C

Step-by-step explanation:

Parallel graphs have the same slope. To find the slope of 7x=14y-8 convert it to y=mx+b.

7x=14y-8

7x+8=14y

7/14 x + 8/14 = y

1/2 x +4/7 = y

The slope here is 1/2. And C has the same slope of 1/2. They are parallel.

MIDDLE SCHOOL

 what are irrational numbers/

Answers

To put it simply, irrational numbers are numbers that cannot be expressed as a fraction. In other words, irrational numbers are numbers that cannot be terminated(stop repeating) or continuously repeated as a single repeating number(.666 or .333 for example). So pi is a irrational number since it repeats but with different numbers repeating each time.
MIDDLE SCHOOL

What is one-tenth of 12.5?

Answers

First write 1/10 in decimal form using your knowledge of place value.

.1

then multiply by 12.5

12.5 × .1 = 1.25 or 1 1/4
HIGH SCHOOL

Anais bought 2 1/2 yards of ribbon. She had 1 foot 6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?

Answers

2 1/2 yards = 7.5 ft
7.5-1.5= 6
6 ft = 72 in
Anais used 72 inches of ribbon to trim the curtains.
COLLEGE

6 (r - 4) + r + 30 - 7r

Answers

6r-24+r+30-7r (the we divide the regular numbers on one side and the others on the other side)Like this:
(6r+r-7r)+(-24+30)
(7r-7r)+6
And the final answer is 6
MIDDLE SCHOOL

The work of a student to find the dimensions of a rectangle of area 8 + 12x and width 4 is shown below: Step 1: 8 + 12x

Step 2: 4(2) 4x2)

Step 3: 4(4 + 8x)

Step 4: Dimensions of the rectangle are 4 and 4 + 8x
In which step did the student first make an error and what is the correct step?

Step 2: 4(2) + 4x(2)

Step 2: 4(2) + 4(3x)

Step 3: 4 + (4+8x)

Step 3: 4 + (4• 8x)

Answers

Answer:

Step 2: 4(2) + 4(3x)

Step-by-step explanation:

By definition, the area of a rectangle is given by:

Area = Length × Width

In this case, we know that:

Area = 8 + 12x

Width = 4

Therefore:

Step 1: 8 + 12x

Step 2: 4(2) + (4)(3x)

Step 3: 4(2 + 3x)

Therefore, the dimensions of the rectangle are 4 and 2 + 3x.

The mistake was made in STEP 2. Instead of 4(2) + 4(x2) it should be  4(2) + 4(3x). Which is the second option.

HIGH SCHOOL

What is the square root of 64

Answers

8 times 8 is 64 so the answer answeris 8
MIDDLE SCHOOL

9 workers working 8 hours a day to complete a piece of work in 52 days. How long will it take 13 workers to complete the same job by working 6 hours a day? Please show all the steps. Correct answer will get

Answers

It will take them 16 days because 13 x 6 is 78 and we know there's 24 hours in a day so we have to do 52 x 24 and get 1248 then divide it by 78 and get 16 correct me if I'm wrong
Random Questions
Read the passage from Animal Farm. When it was all over, the remaining animals, except for the pigs and dogs, crept away in a body. They were shaken and miserable. They did not know which was more shocking—the treachery of the animals who had leagued themselves with Snowball, or the cruel retribution they had just witnessed. In the old days there had often been scenes of bloodshed equally terrible, but it seemed to all of them that it was far worse now that it was happening among themselves. Since Jones had left the farm, until today, no animal had killed another animal. Not even a rat had been killed. They had made their way on to the little knoll where the half-finished windmill stood, and with one accord they all lay down as though huddling together for warmth—Clover, Muriel, Benjamin, the cows, the sheep, and a whole flock of geese and hens—everyone, indeed, except the cat, who had suddenly disappeared just before Napoleon ordered the animals to assemble. For some time nobody spoke. Only Boxer remained on his feet. He fidgeted to and fro, swishing his long black tail against his sides and occasionally uttering a little whinny of surprise. Finally he said: "I do not understand it. I would not have believed that such things could happen on our farm. It must be due to some fault in ourselves. The solution, as I see it, is to work harder. From now onwards I shall get up a full hour earlier in the mornings." Which statement best explains how Boxer's response supports the author’s purpose in writing an allegory? Orwell uses Boxer's inability to understand the carnage on the farm to show the rising consciousness of workers. Orwell uses Boxer's decision to avoid more carnage by working hard to show how the working class was manipulated. Orwell uses Boxer's decision to work harder to show that the working class would ultimately succeed in rebelling. Orwell uses Boxer's surprise at the carnage to show that the working class realized that they were being manipulated.