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Otrada [13]
3 years ago
15

How many marbles do you need to be able to arrange them into the shape of an equilateral triangle with 75 rows

Mathematics
1 answer:
zysi [14]3 years ago
5 0

Answer:

2850

Step-by-step explanation:

1+2+3+4+5+6+7...74+75

just add up all the numbers from 1 to 75

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Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to
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Answer:

about 3.2 gallons. (3.2, 12)

Step-by-step explanation:

If gas costs $3.75 per gallon and Berto has $12, then he can purchase 12/3.75 gallons. This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12)

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Is 4y=x a direct variation
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The direct variation equation is y =kx

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3 years ago
choose the slope-intercept form of 3x 2y = 5. y = 3/2x - 5/2 y = -3/2x 5/2 y = -2/3x 5/3 y = 2/3x – 5/3
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3x + 2y = 5
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Calculate the distance between each line and the point. round your answer to one decimal place.
Dmitry [639]

                                     Solving Equation A

Given the equation A

y=4x-2

and point (-3, 3)

The distance from the point (x₀, y₀) to the line Ax+By+C=0 is given by

d=\frac{\left|Ax_0+By_0+C\right|}{\sqrt{A^2+B^2}}

To apply this formula, we first need to express the line in standard form

y=4x-2

4x-y-2=0

After substituting: A=4, B=-1, C=2, x₀=-3, y₀=3

d=\frac{\left|\left(4\right)\left(-3\right)+\left(-1\right)\left(3\right)+\left(-1\right)\right|}{\sqrt{4^2+\left(-1\right)^2}}

d=\frac{\left|-12-3-2\right|}{\sqrt{4^2+\left(-1\right)^2}}

d=\frac{17}{\sqrt{4^2+\left(-1\right)^2}}

d=\sqrt{17}

d=4.1 units

Therefore, the distance between the line y = 4x - 2 and the point (-3, 3) will be:

  • d=4.1 units

                                             Solving Equation B

Given the equation B

y = -x + 5

and point (-1, -2)

The distance from the point (x₀, y₀) to the line Ax+By+C=0 is given by

d=\frac{\left|Ax_0+By_0+C\right|}{\sqrt{A^2+B^2}}

To apply this formula, we first need to express the line in standard form

y = -x + 5

x+y-5=0

After substituting: A=4, B=1, C=-5, x₀=-1, y₀=-2

d=\frac{\left|\left(1\right)\left(-1\right)+\left(1\right)\left(-2\right)+\left(-5\right)\right|}{\sqrt{1^2+\left(1\right)^2}}

d=\frac{\left|-1-2-5\right|}{\sqrt{1+1}}

d=\frac{\left|-8\right|}{\sqrt{2}}

d=\frac{8}{\sqrt{2}}

d=4\sqrt{2}

d=5.7 units

Therefore, the distance between the line y = -x + 5 and the point (-1, -2) will be:

  • d=5.7 units
8 0
3 years ago
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