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1 year ago

Easy math question n

Mathematics

1 answer:

kolbaska11 [484]1 year ago

7 0

Answer: $|x| \leq 5$ (the last option)

Step-by-step explanation: When you plug in values from the given solution set, the number is positive because of the absolute value symbol. This causes the range of possible values to be from 0 to 5, which are all less than or equal to 5.

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How many gallons of 30% alcohol solution and how many of 60% alcohol solution must be mixed to produce 18 gallons of 50% solutio

allochka39001 [22]

Answer:

x = 6 gallons (of 30% alcohol)

y = 12 gallons (of 60% alcohol)

Step-by-step explanation:

Let

x = liters of 30% alcohol

y = liters of 60% alcohol

There are two unknowns, we need two equations

x + y = 18. (1)

0.30x + 0.60y = 0.50(x+y) (2)

From (1)

x + y = 18

y = 18-x

Substitute the value of y into (2) and solve for x:

0.30x + 0.60y = 0.50(x+y)

0.30x + 0.60(18-x) = 0.50(x+18-x)

0.30x + 10.8 - 0.60x = 0.50(18)

10.8 - 0.30x = 9

-0.30x = -1.8

Divide both sides by -0.30

x = 6 gallons (of 30% alcohol)

Substitute x=6 into (1) and solve for y:

x + y = 18

6 + y = 18

y = 12 gallons (of 60% alcohol)

5 0

3 years ago

Tyler's father is a used car salesman. He receives 5% commission for every car he sells. How much commission does he earn if he

hoa [83]

Answer:

$23,100

Step-by-step explanation:

First you find 5% of 22,000 which is 1,100. You earn commission so you add 1,100 to 22,000. Therefore getting your answer of $23,100.

4 0

3 years ago

A recipe calls for 2 cups of milk for every 6 1/4 cups of flour. If you increase the flour to 43 3/4 cups, how many cups of milk

balu736 [363]

First you must convert 1/4 to a decimal which is 0.25 then multiply that by 6= 1.5, so for every 1.5 cup of flour, you add 2 cups of milk basically.
If you increase the flower to 43 3/4, you need to again, turn 3/4 into a decimal which is 0.75 and multiply 0.75 by 43 = 32.25, then 32.25 divided by 1.5 = 21.5

CONCLUSION: You will use 21.5 cups of milk!
Hope this helped:))

6 0

4 years ago

Read 2 more answers

Given the points R(6, -2) and T(-9, -7), find the coordinates of point S on line segment RT such that the ratio of RS to ST is 3

Kay [80]

Answer:

The coordinates of the point are (-3,-5)

Step-by-step explanation:

Here, we want to find the coordinates of the point that divides the segment in the ratio 3:2

We shall use the internal division formula;

(x,y) = (mx2 + nx1)/(m + n) , (my2 + ny1)/(m+ n)

Where in this case;

(x1,y1) = (6,-2)

(x2,y2) = (-9,-7)

(m, n) = 3,2

Substituting these values;

(x,y) = (3(-9) + 2(6))/(3+2) , (3(-7) + 2(-2))/(3+2)

(x,y) = (-27 + 12)/5 , (-21 -4)/5

(x ,y) = (-15/5, -25/5)

(x , y) = (-3,-5)

8 0

3 years ago

A dolphin in an aquarium is 12 feet long. A scale model of the dolphin is 3.5 inches long. What is the scale factor of the mode?

polet [3.4K]

Assuming the life sized dolphin is 12 ft long, what we want to know is what factor do you multiply 12 ft by to get 3.5 inches so converting this to an equation gives: 12*f=3.5 solving for f gives f=3.5/12=.29166...The units on the factor are inches/foot.

So to get the size if anything linear in the small scale you just multiply it's dimension in the full scale by f.

3 0

3 years ago