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2 years ago

What inequality describes the solutions of 2y less than or equal to 8?

Mathematics

1 answer:

In-s [12.5K]2 years ago

4 0

Answer:

*View attached graph*

Step-by-step explanation:

$2y\leq 8$

$/2$ $/2$

$y\leq 4$

Hope this helps!

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Find the distance between the point (-2, -3) and the line with the equation y=4-2/3x

otez555 [7]

Answer:

$D = \frac{25\sqrt{13}}{13}$

Step-by-step explanation:

Given

$y = 4 - \frac{2}{3}x$

$(x_1,y_1) = (-2,-3)$

Required

Determine the distance

$y = 4 - \frac{2}{3}x$

Write the above equation in standard form:

$Ax + By + C = 0$

So, we have:

$\frac{2}{3}x+y - 4 = 0$

By comparison:

$A = \frac{2}{3}$ $B = 1$ and $C = -4$

The distance is calculated using:

$D = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$

Where:

$(x_1,y_1) = (-2,-3)$

$A = \frac{2}{3}$ $B = 1$ and $C = -4$

This gives:

$D = \frac{|\frac{2}{3} * (-2) + 1 * (-3) - 4|}{\sqrt{(\frac{2}{3})^2 + 1^2}}$

$D = \frac{|-\frac{4}{3} -3 - 4|}{\sqrt{\frac{4}{9} + 1}}$

Take LCM

$D = \frac{|\frac{-4-9-12}{3}|}{\sqrt{\frac{4+9}{9}}}$

$D = \frac{|\frac{-25}{3}|}{\sqrt{\frac{13}{9}}}$

$D = |\frac{-25}{3}|/\sqrt{\frac{13}{9}}$

$D = \frac{25}{3}/\sqrt{\frac{13}{9}}$

Split the square root

$D = \frac{25}{3}/\frac{\sqrt{13}}{\sqrt{9}}$

Change / to *

$D = \frac{25}{3}*\frac{\sqrt{9}}{\sqrt{13}}$

$D = \frac{25}{3}*\frac{3}{\sqrt{13}}$

$D = \frac{25}{\sqrt{13}}$

Rationalize

$D = \frac{25}{\sqrt{13}} * \frac{\sqrt{13}}{\sqrt{13}}$

$D = \frac{25\sqrt{13}}{13}$

Hence, the distance is:

$D = \frac{25\sqrt{13}}{13}$

4 0

2 years ago

To make a shirt 2 whole number 1/2m of cloth is required. how many shirts can be made with 70 m of cloth.

11111nata11111 [884]

Answer:

28 shirts

Step-by-step explanation:

1 shirt=2 l/2

70m ×2/5=28

3 0

1 year ago

The radius of a circle is 18 yards. What is the circle's area? Use 3.14 for .

IrinaVladis [17]

Solution:

We know that:

Radius: 18 yards
πr² = Area of circle
π = 3.14

Finding the area of the circle:

(π)(r²) = Area of circle
=> (3.14)(18²) = Area of circle
=> (3.14)(324) = Area of circle
=> Area of circle = 3.14 x 324 = 1017.36 yards²

3 0

2 years ago

Read 2 more answers

An education researcher randomly selected 48 middle schools from across the country and interviews every teacher of the selected

swat32

Answer:

graphs

Step-by-step explanation:

the answer is graph

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2 years ago

There are 5 students in class. each will be assigned a grade of a, b or

antiseptic1488 [7]

There could be five in each class.

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3 years ago