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3 years ago

The Big Paint “Mix-Up”

Mathematics

1 answer:

sladkih [1.3K]3 years ago

3 0

Answer:

1. 8 quarts of blue

2. 12 quarts of yellow

3. 10 pints of red

4. 24 pints of yellow

5. 16 quarts of light blue

6. 9 quarts of red

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Construct a triangle whose sides are 3 in., 1 1/2 in., 2 3/8 in., 2 in., 3 1/2 in.

Luda [366]

That's 5 lengths for a three sided shape... Are you sure that is the instructions?

6 0

3 years ago

The number of apples in a box decreased from 150 to 135. What is the percent decrease of the number of apples in the box?

goblinko [34]

Answer:

10% decrease

Step-by-step explanation:

The formula for percent change is:

$\frac{\textrm{New}-\textrm{Old}}{\textrm{Old}} \times 100$

Therefore, for this example:

$\frac{\textrm{New}-\textrm{Old}}{\textrm{Old}} \times 100=\frac{135-150}{150} \times 100=-10\%$

The negative value indicates that the change was a decrease. Therefore, there was a 10% decrease.

5 0

3 years ago

7x + 6(-3 + 4x) = 199<br>what does x equal?

tresset_1 [31]

Simplify. Note the equal sign. What you do to one side, you do to the other. Follow PEMDAS.

Isolate the x.

First, distribute 6 to all terms within the parenthesis

6(-3) = -18

6(4x) = 24x

7x - 18 + 24x = 199

Simplify. Combine like terms

31x - 18 = 199

Isolate the x. Add 18 to both sides

31x - 18 (+18) = 199 (+18)

31x = 199 + 18

31x = 217

Isolate the x. Divide 31 from both sides

31x/31 = 217/31

x = 217/31

x = 7

7 is your answer for x

hope this helps

8 0

3 years ago

Please help me out :P

Veseljchak [2.6K]

cos θ = $\frac{-4\sqrt{65} }{65}$ , sin θ = $\frac{-7\sqrt{65} }{65}$ , cot θ = 4/7, sec θ = $\frac{-\sqrt{65} }{4}$ , cosec θ = $\frac{-\sqrt{65} }{7}$

<h3>What are trigonometric ratios?</h3>

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = $\sqrt{7^{2} + 4^{2} }$ = $\sqrt{49+16}$ = $\sqrt{65}$

sin θ = opposite/ hyp = $\frac{7}{\sqrt{65} }$

Rationalize, $\frac{7}{\sqrt{65} }$ x $\frac{\sqrt{65} }{\sqrt{65} }$ = $\frac{7\sqrt{65} }{65}$

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - $\frac{7\sqrt{65} }{65}$

cos θ = adj/hyp = $\frac{4}{\sqrt{65} }$

By rationalizing and knowing that cos θ is negative, cos θ = - $\frac{-4\sqrt{65} }{65}$

cot θ = 1/tan θ = 1/7/4 = 4/7

sec θ = 1/cos θ = 1/ $\frac{4}{\sqrt{65} }$ = - $\frac{-\sqrt{65} }{4}$

cosec θ = 1/sin θ = 1/ $\frac{\sqrt{65} }{7}$ = $\frac{-\sqrt{65} }{7}$

Learn more about trigonometric ratios: brainly.com/question/24349828

#SPJ1

5 0

1 year ago

Factor 125x^3-1000. Show your work.

Salsk061 [2.6K]

The left term is (5x)³.

The right term is 10³.

So, you can use the formula for the factorization of the difference of cubes.

... a³ - b³ = (a-b)(a² +ab +b²)

Here, you have a=5x, b=10, so the factorization is

... 125x³ -1000 = (5x-10)(25x² +50x +100)

4 0

2 years ago