5. The number −6 is 2 more than an unknown number. Find the unknown number.

What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y?

gregori [183]

The GCF is 5x because 5x goes into all the sets.

8 0

3 years ago

write an equation for the line that passes through the given point and has the given slope m (4,-5);m= -1/4

EastWind [94]

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Answer: $\textsf{y = -1/4x - 4}$

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Given: $\textsf{Slope = -1/4, Point through = (4, -5)}$

Find: $\textsf{Equation for the line that passes through the given point}$

Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.

Plug in the values

$\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}$

$\textsf{y - (-5) = -1/4(x - 4)}$

Simplify and solve for y

$\textsf{y + 5 = -1/4(x - 4)}$

$\textsf{y + 5 = -1/4x + 1}$

$\textsf{y + 5 - 5 = -1/4x + 1 - 5}$

$\textsf{y = -1/4x - 4}$

Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.

5 0

2 years ago

Create a ratio table for making lemonade with a lemon juice to water of ratio of 1:3 show how much lemon juice would be needed i

Ganezh [65]

There is 1 serving of lemon juice to 3 cups water. Hence why it's 1:3 ratio.

Since it's 1:3, then 2 servings to 6 cups of water, so on and so forth.

Multiply your lemon juice servings by 3 to find out how many cups of water for the table.

To find how much lemon juice for 36 cups of water, just divide 36 by 3 to get 12. 12 servings of lemon juice is just right for your 36 cups of water.

8 0

3 years ago

Read 2 more answers

Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first

Bumek [7]

A function assigns the values. The list of 6 ordered pairs to show the height of the candle inches are (1,8.5), (1,8), (1,7.5), (1,7), (1,6.5), and (1,6).

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

The rate at which the candle burns down is 0.5 inches per hour. Now, if we substitute the value of the point (0,9) in the function of a line, and the rate as well, we will get,

y = mx +c

9 = -0.5(0) + c

c = 9

Now, the equation that can represent the height of the candle at any hour after it is lit will be,

y= -0.5x+9

substitute the value of x as 1, 2, 3, 4, 5, and 6 to get the value of y and form ordered pairs.

y=-0.5(1)+9 = 8.5 inches ⇒ (1,8.5)
y=-0.5(2)+9 = 8 inches ⇒ (1,8)
y=-0.5(3)+9 = 7.5 inches ⇒ (1,7.5)
y=-0.5(4)+9 = 7 inches ⇒ (1,7)
y=-0.5(5)+9 = 6.5 inches ⇒ (1,6.5)
y=-0.5(6)+9 = 6 inches ⇒ (1,6)

Hence, the list of 6 ordered pairs to show the height of the candle inches are (1,8.5), (1,8), (1,7.5), (1,7), (1,6.5), and (1,6).

Learn more about Function:

brainly.com/question/5245372

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8 0

2 years ago

Find the volume of the figure. 2.25 m 4 m 2.5 m no

liberstina [14]

Given:

Given that the figure is a triangular prism.

The length of the prism is 4 m.

The base of the triangle is 2.5 m.

The height of the triangle is 2.25 m.

We need to determine the volume of the triangular prism.

Volume of the triangular prism:

The volume of the triangular prism can be determined using the formula,

$V=\frac{1}{2}bhl$

where b is the base of the triangle,

h is the height of the triangle and

l is the length of the prism.

Substituting b = 2.5, h = 2.25 and l = 4 in the above formula, we get;

$V=\frac{1}{2}(2.5)(2.25)(4)$

$V=\frac{1}{2}(22.5)$

$V=11.25 \ m^3$

Thus, the volume of the triangular prism is 11.25 m³

4 0

3 years ago