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2 years ago

There are 22 animals in the barn. Some are ducks and some are oxen. There are 72 legs in all.

Mathematics

1 answer:

xeze [42]2 years ago

7 0

Answer:

14 oxen
8 ducks

Step-by-step explanation:

Let x represent the number of oxen. Then the number of ducks is 22-x and the number of legs is ...

4x +2(22 -x) = 72

2x +44 = 72 . . . . . . . simplify

x +22 = 36 . . . . . . divide by 2

x = 14 . . . . . . . . . subtract 22; the number of oxen

22-x = 8 . . . . . the number of ducks

There are 8 ducks and 14 oxen in the barn.

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At what values of x, does f(x) = 0?

Alex

Answer:

C. 4, D. 2, A. -1

Step-by-step explanation:

On the graph, the points at 0 are 4, 2, and -1.

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2 years ago

2 gal 1 qt - 2 qt 1 pt

jekas [21]

Make all of the units equal.
1 gal = 4 quarts = 8 pints
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18 pt - 5 pt

13 pints or

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3 years ago

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Vladimir79 [104]

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3 years ago

Jenny is making tie-dyed shirts for her class with her school colors,blue and yellow.she used a total of 8 ounces of fabric pain

Elodia [21]

Question:

Jenny is making tie-dyed shirts for her class with her school colors, blue and yellow. She used a total of 8 ounces of fabric paint. The amount of blue paint is 3 times the amount of yellow paint. Make a diagram to show the ratio of blue paint to yellow paint

Answer:

The ratio of blue paint to yellow paint is 3 : 1

Solution:

Let "x" be the amount of blue paint in ounces

Let "y" be the amount of yellow paint in ounces

She used a total of 8 ounces of fabric paint

Therefore,

x + y = 8 -------- eqn 1

The amount of blue paint is 3 times the amount of yellow paint

Amount of blue paint = 3 times the amount of yellow paint

x = 3y ------- eqn 2

Substitute eqn 2 in eqn 1

3y + y = 8

4y = 8

Divide both sides by 4

y = 2

Substitute y = 2 in eqn 2

x = 3(2)

x = 6

Therefore , the amount of blue paint is 6 ounces and the amount of yellow paint is 2 ounces

Find the ratio

To find out the ratio of blue paint to yellow paint, divide the amount of blue paint by the amount of yellow paint

$\frac{x}{y} = \frac{6}{2} = \frac{3}{1}$

Which means, of every 4 parts of paint, three parts are blue and one part is yellow

The diagram is attached below

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3 years ago

Answer the Blanks:

vfiekz [6]

Answer:

1. 90°

2. 90°

3. 40°

4. 45°

5. 45°

Step-by-step explanation:

Given: ΔABC,

CD⊥AB,

m∠A=50°,

m∠ACB=85°

Solution:

1. ∠ADC is a right ange, because CD⊥AB, so

$m\angle ADC=90^{\circ}$

2. ∠CDB is a right ange, because CD⊥AB, so

$m\angle CDB=90^{\circ}$

3. Consider triangle ACD. The sum of the measures of all interior angles is always 180°, so

$m\angle A+m\angle ADC+m\angle ACD=180^{\circ}\\ \\50^{\circ}+90^{\circ}+m\angle ACD=180^{\circ}\\ \\m\angle ACD=180^{\circ}-50^{\circ}-90^{\circ}=40^{\circ}$

4. By Angle Addition Postulate,

$m\angle ACD+m\angle BCD=m\angle ACB\\ \\40^{\circ}+m\angle BCD=85^{\circ}\\ \\m\angle BCD=85^{\circ}-40^{\circ}=45^{\circ}$

5. Consider triangle ABC. The sum of the measures of all interior angles is always 180°, so

$m\angle A+m\angle ACB+m\angle B=180^{\circ}\\ \\50^{\circ}+85^{\circ}+m\angle B=180^{\circ}\\ \\m\angle B=180^{\circ}-50^{\circ}-85^{\circ}=45^{\circ}$

6 0

3 years ago