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Brilliant_brown [7]
3 years ago
11

You are trying to recreate flubber because you are obsessed with that movie and you thought it was the coolest. you take 70% sli

me solution and some 40% slime solution to obtain 120 gallons of a 50% slime solution. how much of the 40% slime solution do you need to create your mixture?
a. 40

b. 80

c. 50

d. 70

can you help me solve?
Mathematics
1 answer:
german3 years ago
8 0

Let x be the amount (gal) of the 40% slime solution you end up using. You want to end up with 120 gal of the 50% solution, so that you would use 120-x gal of the 70% solution.

You want the final solution to consist of 50% slime, or 60 gal of slime. Each gal of the 40% solution contributes 0.4 gal of slime, while each gal of the 70% solution contributes 0.7 gal of slime. This means

0.4x+0.7(120-x)=0.5\cdot120=60

\implies0.4x+84-0.7x=60

\implies24=0.3x

\implies x=80

so the answer is B.

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Solve for x and explain how you got your answer <br> 3x + 4 = 16
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Answer:

X = 4

Step-by-step explanation:

3x=16-4

3x= 12

X=12/3

X= 4

5 0
3 years ago
Please help. Thank you​
love history [14]

Answer:

The length of side x is x = \sqrt{6}

Step-by-step explanation:

Pythagorean Theorem:

In a right triangle, with sides a and b, and hypothenuse h, we have that:

a^2 + b^2 = h^2

In this question:

The vertical line on the sides means that both are equal, that is, measuring x, so a = b = x.

Hypothenuse is the square root of 12. So h = \sqrt{12}

x^2 + x^2 = (\sqrt{12})^2

2x^2 = 12

x^2 = \frac{12}{2}

x^2 = 6

x = \sqrt{6}

The length of side x is x = \sqrt{6}

8 0
2 years ago
A climber who is 6 feet tall, casts a shadow that is 20 feet tall, at the same time that a tree casts a shadow which is 90 feet
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The tree is about 27.3 ft. tall.
8 0
3 years ago
Read 2 more answers
The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo
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Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY =  \sqrt{x^2+y^2}

Therefore, the length between points AB is

length AB = \sqrt{(-4 - (-2))^2+(-1-3)^2}

= \sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2}  = \sqrt{20}  = 4.472 units

Similarly, length BC is given by

Length BC =  \sqrt{(-4)^2+1^2} =  \sqrt{17} = 4.123 units

Length CD = \sqrt{(-2)^2+5^2} =  \sqrt{29} = 5.385 units

Length DA = \sqrt{(8)^2+(-2)^2} =  \sqrt{68} = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A =  \sqrt{(7)^2+(0)^2} =  \sqrt{49} =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

 S_{\bigtriangleup} = (\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|

= (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

S_{{\bigtriangleup}ABC} = (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|

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Triangle ACD'

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C(2,2)

D'(3, -1)

S_{{\bigtriangleup}ACD'} = (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

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Area of polygon ABCD' = 19.5 units².

7 0
3 years ago
A barn silo, excluding the top, is a cylinder. The silo is 7 m in
Elenna [48]

The volume of the silo is 461.81 m³

Step-by-step explanation:

A barn silo, excluding the top, is a cylinder

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  • Its height is 12 m

We need to find the volume of the silo

∵ The silo is shaped a cylinder

∵ The volume of a cylinder = base area × height

∵ The base is shaped a circle

∵ Area a circle = π r², where r is the radius of the circle

∴ The volume of the silo = π r² × h

∵ The diameter of the silo = 7 m

∵ The radius of a circle is half the diameter

∴ The radius of the silo = \frac{1}{2} × 7 = 3.5 m

∵ The height of the silo = 12 m

- Substitute the values of r and h in the rule of volume

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∴ The volume of the silo = 147 π = 461.81 m³

The volume of the silo is 461.81 m³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

#LearnwithBrainly

7 0
3 years ago
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