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2 years ago

Write the equation of the line perpendicular to y = -3/4x that passes through the point (3,-8)

Mathematics

1 answer:

arlik [135]2 years ago

4 0

Answer:

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

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - $\frac{3}{4}$ x ← is in slope- intercept form

with slope m = - $\frac{3}{4}$ , c = 0

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{3}{4} }$ = $\frac{4}{3}$ , then

y = $\frac{4}{3}$ x + c ← is the partial equation

To find c substitute (3, - 8) into the partial equation

- 8 = 4 + c ⇒ c = - 8 - 4 = - 12

y = $\frac{4}{3}$ x - 12 ← equation of perpendicular line

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Alex sold wrapping paper rolls (r) as part of a school fundraiser. He earned a total of 156 reward points from his sales. Using

Eva8 [605]

Answer:

Step-by-step explanation:

Alex earned 156 reward points for selling wrapping paper rolls.

Using the given equation

3r = 156

r = 156/3

r = 52

Alex sold 52 wrapping paper rolls

5 0

2 years ago

In studies for a medication, 3 percent of patients gained weight as a side effect. Suppose 643 patients are randomly selected.

timofeeve [1]

Part a)

It was given that 3% of patients gained weight as a side effect.

This means

$p = 0.03$

$q = 1 - 0.03 = 0.97$

The mean is

$\mu = np$

$\mu = 643 \times 0.03 = 19.29$

The standard deviation is

$\sigma = \sqrt{npq}$

$\sigma = \sqrt{643 \times 0.03 \times 0.97}$

$\sigma =4.33$

We want to find the probability that exactly 24 patients will gain weight as side effect.

P(X=24)

We apply the Continuity Correction Factor(CCF)

P(24-0.5<X<24+0.5)=P(23.5<X<24.5)

We convert to z-scores.

$P(23.5 \: < \: X \: < \: 24.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 1.20) \\ = 0.051$

Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.

P(X≤24)

We apply the continuity correction factor to get;

P(X<24+0.5)=P(X<24.5)

We convert to z-scores to get:

$P(X \: < \: 24.5) = P(z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P(z \: < \: 1.20) \\ = 0.8849$

Part c)

We want to find the probability that

11 or more patients will gain weight as a side effect.

P(X≥11)

Apply correction factor to get:

P(X>11-0.5)=P(X>10.5)

We convert to z-scores:

$P(X \: > \: 10.5) = P(z \: > \: \frac{10.5 - 19.29}{4.33} ) \\ = P(z \: > \: - 2.03)$

$= 0.9788$

Part d)

We want to find the probability that:

between 24 and 28, inclusive, will gain weight as a side effect.

P(24≤X≤28)=

P(23.5≤X≤28.5)

Convert to z-scores:

$P(23.5 \: < \: X \: < \: 28.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{28.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 2.13) \\ = 0.1494$

3 0

2 years ago

Timin

Brums [2.3K]

I think I just had a stroke trying to read this

6 0

2 years ago

Which statement is true about the sum of (5y/y^2)+(y-4/5y) ? A: The denominator of the simplified sum is y2 + 5y. B: The denomin

lora16 [44]

Answer:

Dude the answer is B

Step-by-step explanation:

7 0

2 years ago

The city has a section of land that is 3,694.7 feet long. The city wants to partition this lengths to form 10 equal-sized garden

Soloha48 [4]

Answer:

369.47 ft

Step-by-step explanation:

Each plot is 1/10 of the total length, so has length ...

(3694.7 ft)/10 = 369.47 ft

5 0

2 years ago