MATHEMATICS
HIGH SCHOOL

Answer: The ratio of areas is given by:

A1 / A2 = 400/25 = k ^ 2

Therefore, the relationship of the sides is given by:

L1 / L2 = k

Clearing k we have:

k = root (400/25)

Rewriting we have:

L1 / L2 = k = 20/5

Answer:

The ratio of their corresponding sides is:

20: 5

A1 / A2 = 400/25 = k ^ 2

Therefore, the relationship of the sides is given by:

L1 / L2 = k

Clearing k we have:

k = root (400/25)

Rewriting we have:

L1 / L2 = k = 20/5

Answer:

The ratio of their corresponding sides is:

20: 5

Answer:

Answer: 16:1

simplify 400:25 by dividing 400 by 25, which is 16.

MIDDLE SCHOOL

Mr Wallace took 600mg of medicine. This was 75% of the full dose. What was the full dose?

Set up a proportion.

75% = 0.75

600/0.75 = x/1

Cross multiply:

0.75x = 600

Divide 0.75 to both sides:

x = 800

So the full does is 800mg.

75% = 0.75

600/0.75 = x/1

Cross multiply:

0.75x = 600

Divide 0.75 to both sides:

x = 800

So the full does is 800mg.

.25 x 600 = 150

150 + 600 = 750mg

150 + 600 = 750mg

MIDDLE SCHOOL

The difference of 2x and 5 is greater than -3 and less than or equal to 11

Answer:

-3 < x ≤ 8

Step-by-step explanation:

First, write this statement with symbols:

2x - 5 > -3, but also:

2x - 5 ≤ 11

Adding 5 to both sides of the first inequality yields 2x > 2. pr x > 1.

Adding 5 to both sides of the second inequality results in 2x ≤ 16, or x ≤ 8.

Thus, -3 < x ≤ 8 is the shortest way in which to write the given information.

MIDDLE SCHOOL

Explain why 4/10 and 40/100 have unlike denominators but are equivalent fractions

4/10 and 4/100 are the same because all you had to do was multiply both the numerator and denominator by 10. It is still the same amount. Hope this helps!

MIDDLE SCHOOL

there were 180 people at a civic club fundraiser. members paid 4.50 per ticket, no members paid 8.25 per ticket. if the total receipts amounted to 1222.50 how many members and how many nonmembers attended the fundraiser

X= # of members

y= # of nonmembers

QUANTITY EQUATION

x + y= 180

COST EQUATION

$4.50x + $8.25y= $1222.50

STEP 1:

Use substitution or elimination to solve. I'm using elimination. Multiply quantity equation by -4.50 to eliminate the x term and solve for y.

-4.50(x + y)= -4.50(180)

-4.50x - 4.50y= -810

STEP 2:

Add the cost equation and the step 1 equation together. The x term is cancelled and we solve for y.

$4.50x + $8.25y= $1222.50

-4.50x - 4.50y= -810

3.75y= 412.50

divide both sides by 3.75

y= 110 nonmembers

STEP 3:

Substitute the y value into either original equation to solve for x.

x + y= 180

x + 110= 80

subtract both sides by 110

x= 70 members

CHECK:

use the opposite equation as chosen for step 3.

$4.50x + $8.25y= $1222.50

4.50(70) + 8.25(110)= 1222.50

315.00 + 907.50= 1222.50

1222.50= 1222.50 √

ANSWER: There were 70 members and 110 nonmembers attending.

Hope this helps! :)

y= # of nonmembers

QUANTITY EQUATION

x + y= 180

COST EQUATION

$4.50x + $8.25y= $1222.50

STEP 1:

Use substitution or elimination to solve. I'm using elimination. Multiply quantity equation by -4.50 to eliminate the x term and solve for y.

-4.50(x + y)= -4.50(180)

-4.50x - 4.50y= -810

STEP 2:

Add the cost equation and the step 1 equation together. The x term is cancelled and we solve for y.

$4.50x + $8.25y= $1222.50

-4.50x - 4.50y= -810

3.75y= 412.50

divide both sides by 3.75

y= 110 nonmembers

STEP 3:

Substitute the y value into either original equation to solve for x.

x + y= 180

x + 110= 80

subtract both sides by 110

x= 70 members

CHECK:

use the opposite equation as chosen for step 3.

$4.50x + $8.25y= $1222.50

4.50(70) + 8.25(110)= 1222.50

315.00 + 907.50= 1222.50

1222.50= 1222.50 √

ANSWER: There were 70 members and 110 nonmembers attending.

Hope this helps! :)

COLLEGE

What two numbers multiply to give you -210 but add to give you -23

The answer is 15 and 8 because they equals 23 and when you multiply them it equals 210

MIDDLE SCHOOL

Which statement shows the associative property of addition? (d + 4) + 17 = 17 + (d + 4)

13 + 5a = 5a + 13

7⋅(4⋅x)=(7⋅4)⋅x

(18 + 6) + y = 18 + (6 + y)

Answer:

(18 + 6) + y = 18 + (6 + y)

Step-by-step explanation:

Answer:

the answer is (18 + 6) + y = 18 + (6 + y )

Step-by-step explanation:

i did the quiz and got it right!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

hope this helps!!!!!!!!!!!!!!!!!!!11

COLLEGE

it takes 45 pounds of seeds to completely plant a 5 acre field how many acres can be planted per pound of seed

Find the unit rate:

45 pounds

__________ = 9 acres per pound of seeds

5 acres

45 pounds

__________ = 9 acres per pound of seeds

5 acres

1/9 acres. It's 9lbs/acre so you dive that by 9 and get 1/9 acres/lbs.

COLLEGE

Which of the binomials below is a factor of this trinomial? 4x2 + 20x - 24

A. x + 4

B. x + 1

C. x - 1

D. x - 4

Answer: the correct option is (C) x - 1.

Step-by-step explanation: We are given to select the correct binomial that is a factor of the following trinomial :

To select the factor, we need to factorize expression (i). To factorize, we need two integers with sum 20 and product -96.

From (i), we have

So, the factors of the given trinomial are 4, (x + 6) and (x - 1).

Since 4 and ( x + 6) are not in the options, so (x - 1), is the correct binomial.

Thus, (C) is the correct option.

4x²+20x-24

Simplify by 4:

x²+5x-6

(x+6)(x-1)

The answer is x-1.

Simplify by 4:

x²+5x-6

(x+6)(x-1)

The answer is x-1.

HIGH SCHOOL

What is the absolute value of -8 and 8?

Step-by-step explanation: The absolute value of an integer is its distance from zero on a number line. Since -8 is 8 units from zero, the absolute value of -8 is +8. Notice that I put the "+" in front of 8 to show that it's positive.

On the other hand, 8 would also be 8 units from zero so the absolute value of 8 would also be +8.

Because taking an absolute value of a number means making positive, then we can conclude that the absolute value of both numbers are 8.

|-8| = 8

|8| = 8

|-8| = 8

|8| = 8