400 written as a product of its prime factors is 2 x 2 x 2 x 2 x 5 x 5.
Write 800 as a product of its prime factors.

Answer:

240g of 10% salt solution and 160g of 5% salt solution

Step-by-step explanation:

Simpler way:

Let X be the amount of 10% salt solution and Y be the amount of 5% salt solution.

Then X:Y = 3:2 as you need more 10% salt solution than 5% salt solution to create a 8% salt solution. The ratio 3:2 is given as 10 - 8 = 2 and 8-5 = 3.

If X:Y = 3:2 = 60:40, then 60% of the 400g of 8% salt solution must be the 10% solution and 40% of the 400g of 8% salt solution must be the 5% solution. Therefore, 240g of the 10% salt solution and 160g of the 5% salt solution is needed to create 400g of the 8% salt solution.

This is correct as the amount of salt in the solution is equal to (10% X 240g = 24g) + (5% of 160g = 8g). So the total amount (24+8) 32g should be equal to the amount of salt in the 400g of 8% salt solution.

8% of 400g = 32g which means our answer is correct.

More complex way:

A more complex way is to use algebra.

Let X be the amount of 10% salt solution and Y be the amount of 5% salt solution.

X + Y = 400g

and 10% of X + 5% of Y = 8% of 400

so 1/10 X + 1/20 Y = 32

2X + Y = 640 (multiply the previous equation by 20)

Now from the first line we know that X + Y = 400

So if we subtract (2X+Y) by (X+Y) we can get the value of X:

(2X+Y) - (X+Y) = 640 - 400

2X+Y - X - Y = 240

Therefore X = 240

And since X + Y = 400, Y = 160.

Answer:

ee

Step-by-step explanation:

e

Answer:

1^2 and 2^2

Step-by-step explanation:

1^2 is 1

2^2 is 4

3 is a number in between

Answer:

1 and 4 or [tex]1^{2} and 2^{2}[/tex]

Step-by-step explanation:

[tex]1^{2}[/tex] = 1

[tex]2^{2}[/tex] = 4

The number that comes in between is 1 and 4 is 3.

Answer:

6\8

Step-by-step explanation: Because 3/4 times 2/2 is 6/8

Answer:

40°

Step-by-step explanation:

Since triangle ABC is identical to triangle A'B'C', it has the same measures of respective sides and angles, and ang A is therefore equal to angle A'.

After rotational transformation, the measure of angle ∠A' = 40°.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction on the coordinate plane. In both transformations the size and shape of the figure stays exactly the same.

For the given situation,

The diagram shows the two triangles.

Triangle ABC is the original triangle and A'B'C' is the triangle obtained after the rotation of -120°.

From the definition, in rotational transformation the size and shape of the figure stays exactly the same. Then the angle measures are also remains the same.

Thus the measure of angle A' is [tex]\angle A' = \angle A = 40[/tex]

Hence we can conclude that after rotational transformation, the measure of angle ∠A' = 40°.

Learn more about rotation transformation here

https://brainly.com/question/12865301

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Answer:

Step-by-step explanation:

You are to assume in both problems that the two triangles are similar. That is a very dangerous assumption -- especially in later math classes. But in this case, there is no other way to do the problem. The two sets of triangles look like they are proportional.  So set up two ratios that are = to each other

On the left

long side small triange / long side large triangle = base small triangle / base large triangle

On the right

hypotenuse/longest leg = hypotenuse / longest leg.

Problem A

Set up the similar Proportion

5/40 = x/20                Cross Multiply

40x = 20*5

40x = 100                   Divide by 40

x = 100/40

x = 2.5

Problem B

Again set up the similar triangle proportion

15/10 = x/2                  Multiply by 2

15*2/10 = x              

3 = x

Answer:

([tex]n^{2}[/tex]+4)-3

Step-by-step explanation:

since it says "and four" i think it means it is in parenthesis

Answer:

n^2 + 1

Step-by-step explanation:

Let the unknown number be n.  Then "a number squared and four" is

n^2 + 4, and 3 fewer than this result is

n^2 + 3 - 3, or n^2 + 1

Answer:

30:34

Step-by-step explanation:

30 = thick crust pizza

4 = thin crust pizza

total = 34

=

30:34

Answer:

9)-1=x+19

-x =19+1

-x=20

-x÷-1=20÷-1

x=20.

Answer:

Step-by-step explanation

Answer:

1

Step-by-step explanation:

divide both side by 11 and you get 1:7

Answer:

I'd guess 54

Step-by-step explanation:

If the sections are all equal sized, there's an equal chance the arrow/spinner would land on them. If you divide 240 by 5, you get 48. The closest number to 48 is 54.

Answer:

y = 1/2 - 3/2

Step-by-step explanation:

All we need to do is find the y-intercept of the line using the formula for slope intercept form [ y = mx + b ].

-3 = 1/2(-3) + b

-3 = -1.5 + b

-1.5 = b

We can put all the information we know/solved for into the formula.

y = 1/2 - 1.5

Best of Luck!

Answer:

The equation of the line is y = 1/2x - 3/2

Step-by-step explanation:

Plug in point (-3, 3) with slope 1/2 into y = mx + b

-3 = 1/2(-3) + b

-3 = -3/2 + b

+3/2     +3/2

-------------------

-3/2 = b

hence, y = 1/2x - 3/2

Answer: 26

Step-by-step explanation:

mean is the same thing as finding the average

you add up all the numbers then divide by the amount of numbers there are

24+27+31+21+27=130

130\5=26

Answer

Because velocity and speed differ each other by direction, in a 100 m sprint race the person moves in a straight path without changing its direction where as in a 400 m race. The person moves in a lap around the race track and the direction changes as he turns according to the race track.

Step-by-step explanation:

<3

Answer:

14

Step-by-step explanation:

5x + 2 + 48 = (180-120)+30 +30

5x+50 = 60+30+30

5x+50=120

5x=120-50

5x = 70

x = 70/5

x = 14

Answer:

3/8

Step-by-step explanation:

In 1 day = 1/8

In 3 days = 1/8 x 3 = 3/8

Answer:

It is ⅜ hours

Step-by-step explanation:

[tex]{ \sf{1 \: day = \frac{1}{8} \: hours}} \\ \\ { \sf{3 \: days = (3 \times \frac{1}{8} ) \: hours}} \\ \\ = \frac{3}{8} \: hours[/tex]

its one of the maritime climates

Answer:

$44

Step-by-step explanation:

Let the total amount of money be represented by Y

Amount spent on fresh food =

[tex] \frac{4}{7} \times y[/tex]

Remainder =

[tex]y - \frac{4}{7}y = \frac{3}{7} y[/tex]

Amount spent on frozen foods = two-thirds of remainder = $22

[tex] = \frac{2}{3} \times \frac{3}{7} y = \frac{2}{7} y[/tex]

[tex]\frac{2}{7} y = 22 \\ y = 22 \times \frac{7}{2} \\ y = 77[/tex]

The total amount for grocery shopping is $77

Therefore, Brittany spent $44 on fresh foods

[tex] = \frac{4}{7} \times 77 \\ = 4 \times 11 \\ = 44[/tex]

Answer:

y= -x+2

Step-by-step explanation:

Using the equation, y = mx+b, you know you have to find the slope. Find the slope using two coordinate points, (-2,4) and (0,2).

Subtract 2-4/0+2 - the answer is -1. Your slope is -1 and the y axis is given so the equation is y=-x+2

Answer:

the answer would be C.

Step-by-step explanation:

C is your answer

Answer:

answer b

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

45/15=x/3

3*3=x

x=9

Answer:

3*5=15 so __*4=45 so answer is 45/5=9

Step-by-step explanation:

Answer:

a is right angle

Step-by-step explanation:

Answer:

1. 245 = 5 × 7 × 7

2. 510 = 2 × 3 × 5 × 17

3. 250 = 2 × 5 × 5 × 5

4. 1089 = 3 × 3 × 11 × 11

5. 4725 = 3 × 3 × 3 × 5 × 5 × 7

6. 900 = 2 × 2 × 3 × 3 × 5 × 5

18. 27000 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5