Pls I Need Help!

For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the ne

SVEN [57.7K]

Answer:

The answer is below

Step-by-step explanation:

a) y=3x-1

The standard equation of a line is given by:

y = mx + c

Where m is the slope of the line and c is the intercept on the y axis.

Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:

3 × d = -1

d = -1/3

To find the equation of the perpendicular line passing through (0,0), we use:

$y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x$

To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

$y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12$

b) y=1/4 x+2

Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:

1/4 × f = -1

f = -4

To find the equation of the perpendicular line passing through (0,0), we use:

$y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x$

To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

$y=-4}x\\ 4=-4x\\x=-1$

8 0

2 years ago

The length of an object's shadow varies directly with It's heigt. If a can is 13 cm tall casts a shadow that is 7.5 cm long, a b

svetoff [14.1K]

X = Can/Bottle height, y = Shadow length
x = 13 cm, y = 7.5 cm
x = 2.5 cm, y = 14.2 cm
I'm assuming your question is asking for an equation to model this. Since there are only two data points the only equation that can be made is linear
y = mx + c
m = (y2 - y1)/(x2 - x1) <- Let 14.2 be y2, and 2.5 be x2 (it is important)
m = (14.2 - 7.5)/(2.5 - 13)
m = 6.7/-10.5
m = -0.638
y = -0.638x + c
To find c we can sub any one of the two coordinates, i'm choosing (2.5,14.2)
14.2 = -0.638(2.5) + c
14.2 = -1.595 + c
14.2 + 1.595 = c
15.795 = c
So the final equation is y = -0.638x + 15.795

6 0

2 years ago

Sociology graduates, upon entering the workforce are normally distributed and earn a mean salary of $30,000 with a standard devi

GrogVix [38]

Answer:

0.62% probability that randomly chosen salary exceeds $40,000

Step-by-step explanation:

Problems of normally distributed distributions are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu = 30000, \sigma = 4000$

What is the probability that randomly chosen salary exceeds $40,000

This is 1 subtracted by the pvalue of Z when X = 40000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{40000 - 30000}{4000}$

$Z = 2.5$

$Z = 2.5$ has a pvalue of 0.9938

1 - 0.9938 = 0.0062

0.62% probability that randomly chosen salary exceeds $40,000

7 0

2 years ago

Alexander has nickels, dimes, and quarters in the ratio of 2:1:8, if 40 of Alexander's coins are quarters, how many nickels and

ch4aika [34]

Answer:

He has 10 nickels and 5 dimes

Step-by-step explanation:

We can take advantage of the ratio by dividing 40 by 8, giving us that every 1 in the ratio = 5. So we can multiply 2 x 5 = 10 and 1 x 5 = 5.

Hope this Helps!

4 0

2 years ago

The area of the square rug is 121 square feet. what is the length of the side of the rug

hram777 [196]

Answer:

11 feet

Step-by-step explanation:

Squares have the same length and width. So you just take the square root of teh area to find both.

√121 = 11

7 0

3 years ago