MATHEMATICS COLLEGE

PLEASE HELP ASSIGNMENT DUE TODAY NEED TO PASS 1)
You have 2 lines. The first goes through points (6, 2) and (4, 6). The second goes through points (5,-1) and (1, 1). These lines are:

A) perpendicular

B) parallel

C) horizontal and vertical

D) none of the above

2) You have 2 lines. The first goes through points (7, 0) and (4, 6). The second goes through points (1, 1) and (5,3). These lines are:

A) perpendicular

B) parallel

C) horizontal and vertical

D) none of the above

Answers

Answer 1

Answer:

Answer:

1. D

2. A

Step-by-step explanation:

To determine the type of line, find the slope.

Slopes which are the same are parallel
Slopes which are negative reciprocals are perpendicular
Slopes which are undefined (0 in the denominator) are horizontal.
Slopes which are 0 are vertical.

1. Find the difference in y values over the difference in x values. Calculate the slope using the formula:

$(y_2-y_1)/(x_2-x_1) = (6-2)/(4-6)=(4)/(-2)=-2$

$(y_2-y_1)/(x_2-x_1) = (1--1)/(1-5)=(2)/(-4)=(-1)/(2)$

These are reciprocals of each but not the negative or opposite signs of each other. This is none.

2. Find the difference in y values over the difference in x values. Calculate the slope using the formula:

$(y_2-y_1)/(x_2-x_1) = (6-0)/(4-7)=(6)/(-3)=-2$

$(y_2-y_1)/(x_2-x_1) = (3-1)/(5-1)=(2)/(4)=(1)/(2)$

These are reciprocals of each and the negative or opposite signs of each other. These are perpendicular.

Related Questions

Jill is making a long cape. She needs 7 1/3 yards of blue fabric for the outside of the cape. She needs 6 2/3
yards of purple fabric for the lining of the cap
How much more blue fabric than purple fabric should Jill buy?

Answers

Answer: 2/3yards

Step-by-step explanation:

From the question, we are informed that Jill is making a long cape and that she needs 7 1/3yards of blue fabric for the outside of the cape and that she needs 6 2/3yards of purple fabric for the lining of the cap.

To calculate the yards of blue fabric that'll be needed more than purple fabric,, we subtract 6 2/3 from 7 1/3. This will be:

= 7 1/3 - 6 2/3

= 2/3

She needs 2/3yards of blue fabric more.

The sum of seven and 5 times a number is 48

Answers

Answer:

The sum of seven and five is 12 so the number would be 4 because 12 times 4 is 48 so the answer is "4" please give me brainliest!!

The average starting salary of this year's vocational school graduates is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Answers

Answer:

Minimum: $25,200

Maximum: $44,800

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

$Z = (X - \mu)/(\sigma)$

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:

$\mu = 35000, \sigma = 5000$

What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Minimum: 50 - (95/2) = 2.5th percentile.

Maximum: 50 + (95/2) = 97.5th percentile

2.5th percentile:

X when Z has a pvalue of 0.025. So X when Z = -1.96.

$Z = (X - \mu)/(\sigma)$

$-1.96 = (X - 35000)/(5000)$

$X - 35000 = -1.96*5000$

$X = 25200$

The minimum is $25,200

97.5th percentile:

X when Z has a pvalue of 0.975. So X when Z = 1.96.

$Z = (X - \mu)/(\sigma)$

$1.96 = (X - 35000)/(5000)$

$X - 35000 = 1.96*5000$

$X = 44800$

The maximum is $44,800

brody is working two summer jobs, making $10 per hour babysitting and making $15 per hour cleaning tables. In a given week, he can work a maximum of 13 total hours and must earn at least $150. If x represents the number of hours babysitting and y represents the number of hours cleaning tables, write and solve a system of inequalities graphically and determine on possible solution.

Answers

The solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).

Given:

Brody can work a maximum of 13 hours: x + y ≤ 13

Brody must earn at least $150: 10x + 15y ≥ 150

These are the two inequalities we need to solve graphically.

Graph the first inequality: x + y ≤ 13

This inequality represents the total number of hours Brody can work, which cannot exceed 13 hours. We'll plot the line x + y = 13 and shade the region below it.

Graph the second inequality: 10x + 15y ≥ 150

This inequality represents the total earnings Brody needs to make, which should be at least $150. Let's simplify it to 2x + 3y ≥ 30. We'll plot the line 2x + 3y = 30 and shade the region above it.

Now, let's find the point where the shaded regions of both inequalities overlap. This point will represent the feasible solution where Brody's working hours and earnings satisfy both conditions.

Solving the system of inequalities graphically, you will find the point of intersection. However, since I can't create a graphical representation here, I'll explain how to calculate the solution point algebraically:

First, solve the equation x + y = 13 for y:

y = 13 - x

Now substitute this value of y into the equation 2x + 3y = 30:

2x + 3(13 - x) = 30

2x + 39 - 3x = 30

-x = -9

x = 9

Now substitute the value of x back into the equation y = 13 - x:

y = 13 - 9

y = 4

So, the solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).

To know more about inequalities:

brainly.com/question/20383699

#SPJ3

Graph y≤13−x (shading down)

graph y≥10− 3/2x (shading up)

uppose a small cannonball weighing 16 pounds is shot vertically upward, with an initial velocity v0 = 290 ft/s. The answer to the question "How high does the cannonball go?" depends on whether we take air resistance into account. If air resistance is ignored and the positive direction is upward, then a model for the state of the cannonball is given by d2s/dt2 = −g (equation (12) of Section 1.3). Since ds/dt = v(t) the last differential equation is the same as dv/dt = −g, where we take g = 32 ft/s2. If air resistance is incorporated into the model, it stands to reason that the maximum height attained by the cannonball must be less than if air resistance is ignored. (a) Assume air resistance is proportional to instantaneous velocity. If the positive direction is upward, a model for the state of the cannonball is given by m dv dt = −mg − kv, where m is the mass of the cannonball and k > 0 is a constant of proportionality. Suppose k = 0.0025 and find the velocity v(t) of the cannonball at time t.

Answers

Answer:

Given in the explanation

Step-by-step explanation:

Given

w = 16 pounds

v₀ = 290 ft/s

g = 32 ft/s²

k = 0.0025 (Kg/s)

$m(dv)/(dt)= -mg - kv^(2)$

Solving the differential equation we obtain

$v(t)=((1)/(0.0125))*tan((-2*(t+C_(1) )/(5) )$

If v(0) = 290 ft/s, we have

$290=((1)/(0.0125))*tan((-2*(0+C_(1) )/(5) )$

⇒ C₁ = -3.254

Finally, we have

$v(t)=((1)/(0.0125))*tan((-2*(t-3.254 )/(5) )$

Tom is the deli manager at a grocery store.He needs to schedule employees to staff the deli department at least 260 person-hours per week.Tom has one part-time employee who works 20 hours per week.Each full-time employee works 40 hours per week.Write an inequality to determine f, the number of full time employees Tom must schedule, so that his employees will work at least 260 person-hours per week. Solve and graph. !PLEASE HELP!

Answers

I hope this is right but:
Let n=number of full time employees

260<=20+n*40
260-20<=N*40
240<=n*40
n>=240/40
n>=6 full time employees

which means he would have to hire at least 6 or more fully time employees

Though I'm not sure if the attached file is the graph you are looking for

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