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2 years ago

Find the equation of the line the line is perpendicular to the graph of x - 5y=6 and contains 2,-10

1 answer:

4 0

<h3>Answer: </h3><h3>y + 10 = - 5 (x - 2) [point-slope form] OR</h3><h3>y = - 5 x [slope-intercept form]</h3><h2 /><h3>Step-by-step explanation:</h3>

<u>Identify the slope of the given line</u>

If we rewrite the equation given, we can easily identify the slope

x - 5y = 6

- 5y = - x + 6

y = ¹/₅ x - ⁶/₅

∴ the slope of x - 5y = 6 is ¹/₅

<u>Find the slope of the perpendicular line</u>

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

⇒ since the slope of this line = ¹/₅

then the slope of the perpendicular line (m) = - 5

<u>Determine the equation of perpendicular line</u>

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

⇒ y - (-10) = - 5 (x - 2)

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

since y + 10 = - 5 (x - 2)

<h3> y = - 5 x</h3><h3 /><h3>∴ the slope-intercept equation of the perpendicular line is y + 10 = - 5 (x - 2) OR y = - 5 x. </h3><h3 /><h3 />

<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>

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Line segment AB has endpoints A(-1.5, 0) and B(4.5 8). Point C is on line segment AB located at (0, 2)

Pie

Answer:

The ratio of AC/CB=1/3

Step-by-step explanation:

We use the section formula:

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

We substitute the point A(-1.5,0) and B(4.5,8).

We plug in the points to get:

$(\frac{4.5m - 1.5n}{m+n},\frac{8m+n \times 0}{m+n})$

This is supposed to be equal to: (0,2).

$(\frac{4.5m - 1.5n}{m+n},\frac{8m+n \times 0}{m+n}) = (0,2)$

We can equate, corresponding coordinates to find m and n.

$\frac{4.5m - 1.5n}{m + n} = 0$

This implies that:

$4.5m - 1.5n = 0$

$4.5m = 1.5n$

$\frac{m}{n} = \frac{1.5}{4.5}$

$\frac{m}{n} = \frac{1}{3}$

Therefore the ratio is m:n=1:3

4 0

3 years ago

You need to wrap a present that you will put inside a cylindrical container. You’ll need to know how much will fit in the conta

nirvana33 [79]

Answer:

149.28 sq. inches

137.5 cubic inches.

Step-by-step explanation:

The cylindrical container has length or height (h) 7 inches and has a diameter of 5 inches i.e. radius (r) 2.5 inches.

Now, total surface area of the container = $2\pi r^{2} + 2\pi rh$

= $\frac{2 \times 22 \times (2.5)^{2} }{7} + \frac{2 \times 22 \times 2.5 \times 7}{7}$

= 39.28 + 110

= 149.28 sq. inches (Answer)

Again the volume of the container will be $\pi r^{2}h$

= $\frac{22 \times (2.5)^{2} \times 7}{7}$

= 137.5 cubic inches. (Answer)

6 0

3 years ago

If P = (3, 1) and Q = (-3, -7), find The distance PO

Monica [59]

Answer:

10 units

Step-by-step explanation:

Given data

P = (3, 1) and Q = (-3, -7)

x1=3

y1=1

x2= -3

y2= -7

The expression for the distance between two coordinate is

d=√((x_2-x_1)²+(y_2-y_1)²)

Substitute

d=√((-3-3)²+(-7-1)²)

d=√((-6)²+(-8)²)

d=√36+64

d=√100

d=10 units

Hence the distance is 10 units

7 0

3 years ago

The probability that Jane will go to a ballgame (event A) on a Monday is 0.73, and the probability that Kate will go to a ballga

sergiy2304 [10]

Answer:

dependent events since P(A and B) is not equal to P(A) * P(B)

Step-by-step explanation:

According to the Question,

Given, The probability that Jane will go to a ballgame (event A) on a Monday is 0.73, and the probability that Kate will go to a ballgame (event B) the same day is 0.61. The probability that Kate and Jane both go to the ballgame on Monday is 0.52.

Thus, The events A, B and A∩B are:

A - Jane will go to a ballgame on Monday;

B - Kate will go to a ballgame on Monday;

A∩B - Kate and Jane both go to the ballgame on Monday.

P(A)=0.73, P(B)=0.61, P(A∩B)=0.52.

Pr(A)⋅Pr(B) = 0.73⋅0.61 = 0.4453 ≠ 0.52

So, events A and B are dependent events since P(A and B) is not equal to P(A) * P(B)

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3 years ago

REWARDING BRAINLY!!!! THERE ARE 4 PROBLEMS BUT ONLY 3 SCREENSHOTS

Tcecarenko [31]

#1: The whole value of data is 21.

There are 21 data values on the dot plot.

#2: The number of data values is 14.

#3: The unit is: 21 ÷ 14.

And it is 1.5.

#4: A statistical question can be answered by collecting data and where there will be variability in that data.

For example, how many students enjoy playing game?

5 0

2 years ago

Read 2 more answers