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3 years ago

What is the slope of a line that is perpendicular to the line whose equation is 7x−3y=107x−3y=10?

1 answer:

4 0

This is the concept of algebra, to get the slope of the line we need to rewrite the equation in slope intercept form y=mx+c, where m=slope, c=y-intercept.
Therefore re-writing our expression in slope-intercept form we get:
7x-3y=10
-3y=-7x+10
y=7/3x-10/3
The slope=7/3
hence we conclude that the slope of the line perpendicular to this is -3/7

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What is the distance between the points (5, 1) and (-3,-5)?

Reil [10]

Answer: THIRD OPTION.

Step-by-step explanation:

For this exercise you need to use the formula for calculate the distance between two points. This is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Given the following points:

$(5, 1)$ and $(-3,-5)$

You can identify that:

$x_2=-3\\x_1=5\\\\y_2=-5\\y_1=1$

Knowing these values, the next step is to substitute them into the equation for calculate the distance between two points and then evaluate.

Therefore, the distance between $(5, 1)$ and $(-3,-5)$ is:

$d=\sqrt{(-3-5)^2+(-5-1)^2}\\\\d=10$

8 0

3 years ago

Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-c

natali 33 [55]

Answer: By the slope formula.

Step-by-step explanation:

Given: ABC is a triangle (shown below),

In which A≡(6,8), B≡(2,2) and C≡(8,4)

And, D and E are the mid points of the line segments AB and BC respectively.

Prove: DE║AC and DE = AC/2

Proof:

Since, And, D and E are the mid points of the line segments AB and BC respectively.

Therefore, By mid point theorem,

coordinate of D are $(\frac{2+6}{2} , \frac{2+8}{2} ) = (\frac{8}{2} , \frac{10}{2} )= (4,5)$

Coordinate of E are $(\frac{2+8}{2} , \frac{2+4}{2} ) = (\frac{10}{2} , \frac{6}{2} )= (5,3)$

By the distance formula,

$DE=\sqrt{(5-4)^2+(3-5)^2}=\sqrt{5}$

$AC=\sqrt{(8-6)^2+(4-8)^2}=2\sqrt{5}$

By the slope formula,

Slope of AC = $\frac{4-8}{8-6} = \frac{-4}{2} = -2$

Slope of DE = $\frac{3-5}{5-4} = \frac{-2}{1} = -2$

Statement Reason

1. The coordinate of D are (4,5) and 1. By the midpoint formula

the coordinate of E are (5,3)

2. The length of DE = √5 2. By the Distance formula

The length AC = 2√5 ⇒ Segment DE

is half the length of segment AC

3. The slope of DE = -2 and the 3. By the slope formula

slope of AC = -2

4. DE║AC 4. Slopes of parallel lines are equal

7 0

3 years ago

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mixas84 [53]

Answer:

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Step-by-step explanation:

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4 years ago

Alicia says that 6÷2+5 is the same as 5+6÷2. is Alicia correct or incorrect

liq [111]

It is not correct because of the order the problem is organized in.

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3 years ago

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prisoha [69]

Answer:

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Step-by-step explanation:

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7 0

3 years ago

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