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3 years ago

Write an equation of a line perpendicular to y=3x+5 that contains the points (-3,-4)

Mathematics

1 answer:

Vlad [161]3 years ago

5 0

The equation of line is:

$y = - \frac{1}{3}x-5$

Further explanation:

Given equation of line is:

y = 3x+5

The standard form of point-slope form is:

y = mx+b

Comparing the given equation with the standard form is:

m = 3

We know that product of slopes of two perpendicular lines is -1

Let m2 be the slope of line perpendicular to y = 3x+5

Then

$3 * m_2 = -1\\m_2 = -\frac{1}{3}$

Putting the value of slope in standard form

$y = -\frac{1}{3}x + b$

To find the value of b, putting (-3,-4) in equation

$-4 = -\frac{1}{3}(-3) + b\\-4 = 1 + b\\b = -4-1\\b = -5$

Putting the values of slope and b in equation

$y = - \frac{1}{3}x-5$

Keywords: Slope, Point-intercept form

Learn more about perpendicular lines at:

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Which relation is a function?

Annette [7]

Answer:

B is the answer because a function is if none of the x values are the same with different y values.

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2 years ago

Is the figure a rectangle? Explain.

luda_lava [24]

The correct option is b. No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

<h3>How to explain the information?</h3>

The figure is a parallelogram and one diagonal measure 28 units.

In this case, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

Therefore, the correct option is B.

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2 years ago

I need help with this promblem it’s ALGEBRA 2!

AlekseyPX

Answer:

$(f\circ h)(2)=2$

Step-by-step explanation:

<u>Composite Function </u>

Given f(x) and h(x) real functions, the composite function named $(f\circ h)(x)$ is defined as:

$(f\circ h)(x)=f(h(x))$

It can be found by substituting h into f.

We are given the functions:

$f(x)=2x^2-9x+2$

$h(x)=x^2-4$

It's required to find $(f\circ h)(2)$

As defined above:

$(f\circ h)(x)=f(h(x))$

Thus:

$(f\circ h)(2)=f(h(2))$

Find h(2):

$h(2)=2^2-4=0$

h(2)=0

Now:

$(f\circ h)(2)=2(0)^2-9(0)+2$

$(f\circ h)(2)=2$

8 0

2 years ago

Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats . what is the probability th

Neko [114]

The probability that a kid who goes to the doctor has a sore throat given that he has a fever is <u>0.30 or 30%</u>. Computed using conditional probability.

The probability of any event A given that event B has already taken place is found using the formula P(A|B) = P(A ∩ B)/P(B). This is known as conditional probability, where P(A ∩ B) is the probability of events A and B, and P(B) is the probability of event B.

In the question, we are given that 70% of kids who visit a doctor have a fever and 21% of kids have a fever and sore throats.

We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever.

We suppose the event of going to the doctor while having a fever to be B, and going to a doctor while having a sore throat to be A.

We are given that 70% of kids who visit a doctor have a fever, that is, the probability of event B, P(B) = 70% = 0.7.

We are given that 21% of kids who visit a doctor have a fever and sore throats, that is, the probability of event A and event B, P(A ∩ B) = 21% = 0.21.

We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever, that is, we are asked to find the conditional probability of event A, when event B has already taken place, that is, P(A|B).

By formula, we know that:

P(A|B) = P(A ∩ B)/P(B) = 0.21/0.70 = 0.30.

Thus, the probability that a kid who goes to the doctor has a sore throat given that he has a fever is <u>0.30 or 30%</u>.

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3 0

1 year ago

Cara started working for $9 per hour. She earns a 4% raise every year. What is her

shutvik [7]

Answer:

Caras hourly wage is $10.08 after 3 years

Step-by-step explanation:

4% of 9

0.04 x 9 = 0.36

then you multiply 0.36 by 3 because you are solving for 3 years.

0.36 x 3 = 1.08

then you add 1.08 to 9 because Cara's wage goes up $1.08 in 3 years

1.08 + 9 = 10.08

answer:

Cara's hourly wage is $10.08 after 3 years of working

5 0

3 years ago