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2 years ago

Which equation represents a line that is perpendicular to y = 5x +2 and goes through

Mathematics

1 answer:

tia_tia [17]2 years ago

5 0

Answer:

y = -1/5x + 1

Step-by-step explanation:

By definition, the product of the slopes of two perpendicular lines, neither of which is vertical, is always -1.

Given the linear equation, y = 5x + 2, and the point (-10, 3):

Since the slope of the original linear equation is 5, then it means that the slope of the perpendicular line must be -1/5 (because if you multiply -1/5 by 5, the result is -1).

Therefore, the slope of the perpendicular line is -1/5.

Next, we'll use the slope of the perpendicular line and the coorindates of the given point, (-10, 3). Let (x1, y1) = (-10, 3)

We'll plug these values into the point-slope form:

y - y1 = m(x - x1)

y - 3 = -1/5[x - (-10)]

y - 3 = -1/5(x + 10)

y - 3 = -1/5x - 2

Add 3 on both sides to isolate the y:

y - 3 + 3 = -1/5x - 2 + 3

y = -1/5x + 1

Therefore, the equation of the line that is perpendicular to y = 5x + 2 is:

y = -1/5x + 1

Please mark my answers as the Brainliest if my explanations were helpful :)

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Write the equation of a line, in slope-intercept form, that has a slope of m=9 and passes through the point (4, 31) .

Zinaida [17]

Answer:

$\sf y=9x-5$

Step-by-step explanation:

$\begin{aligned}&\sf y-y_1=m(x-x_1) \\&\sf y-31=9(x-4) \\&\sf y-31=9x-36 \\&\sf y=9x-36+31 \\&\boxed{\sf y=9x-5} \end{aligned}$

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6x +8=5x=4 <br> what is the value of x

Free_Kalibri [48]

Answer:

x = -4/11

Step-by-step explanation:

add the x values.

11x+8=4

subtract 8 from each sides

11x=-4

divide by 11

x=-4/11

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3 years ago

A.Calculate the mean,median and mode.(3 points each) 1.)1,2,3,4,5 2.)2,3,4,5,6,6 3.)6,7,5,4,5,6,2,5

zlopas [31]

Answer:

Step-by-step explanation:

1.)1,2,3,4,5

mean=sum of all values/number of values

=1+2+3+4+5/5

=15/5

mean=3

Mode :

In the given data, no observation occurs more than once.

Hence the mode of the observations does not exist, means mode=0.

Median

1,2,3,4,5

Middle value is 3 so the median is 3.

2.)2,3,4,5,6,6

mean=sum of all values/number of values

=2+3+4+5+6+6/6

=26/6

mean =4.33

Mode

is that value of the observation which occurs maximum number of times so here mode is 6.

Median

2,3,4,5,6,6

4+5/2

9/2

median=4.5

3.)6,7,5,4,5,6,2,5

mean=sum of all values/number of values

=6+7+5+4+5+6+2+5/8

=40/8

mean =5

Mode

is that value of the observation which occurs maximum number of times so here mode is 5

Median

2,4,5,5,5,6,6,7

5+5/2

10/2

median=5

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3 years ago

11 POINTS PLZ HELP EMERGENCY

Bad White [126]

Part A

The given expression is:

$(-5(1+2i)+3i(3-4i)$

We expand to get:

$-5-10i+9i-12i^2$

Note that $i^2=-1$

$12-5-10i+9i$

$-5-10i+9i+12$

$7-i$

Part Bi)

The given expression is;

$\sqrt{-50}$

We simplify to get:

$\sqrt{25\times 2\times -1}$

$\sqrt{25\times} \sqr{2}\times \sqrt{-1}$

Note that:

$\sqrt{-1}=i$

$5\sqr{2}i$

This is now of the form $a+bi$ , where $a=0,b=5\sqr{2}$ .

This explains why it is a complex number;

Part bii)

The given expression is :

$\frac{\sqrt{-50} }{\sqrt{5}}$

We simplify to get

$\sqrt{\frac{-50 }{5}}$

$\sqrt{-25}$

$\sqrt{-25}=\sqrt{25}\times \sqrt{-1}$

$\sqrt{-25}=5\times i$

$\sqrt{-25}=5i$

Part C

We want to simplify:

$i^{22}$

We rewrite in terms of $i^2$

$i^{22}=(i^2)^{11}$

$i^{22}=(-1)^{11}$

$i^{22}=-11$

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Step-by-step explanation:

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