MATHEMATICS
HIGH SCHOOL

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">

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

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

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/

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?

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

.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?

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.

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

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

(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)

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

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

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