A coordinate map of a college campus gives the coordinates (x,y) of three major buildings as follows: computer center, (3.5,-1.5); engineering lab, (0.5,0.5); andlibrary, (-1,-2.5). Find the equations in slope-intercept form of the lines connecting (a) the engineering lab and the computer center and (b) the engineering lab with the library. Are these two paths perpendicular to each other?

Answers

Answer 1

Answer:

a) [tex]y = -\frac{2}{3}x + \frac{5}{6}[/tex]

b) [tex]y = 2x - \frac{1}{2}[/tex]

These two paths are not perpendicular to each other.

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope of the line and b is the y-intercept.

If two lines are perpendicular, the multiplication of their slopes is -1.

(a) the engineering lab and the computer center

Coordinates (3.5,-1.5) and (0.5,0.5)

The slope is given by the change in y divided by the change in x.

Change in y: 0.5 - (-1.5) = 0.5 + 1.5 = 2

Change in x: 0.5 - 3.5 = -3

Slope: [tex]m = \frac{2}{-3} = -\frac{2}{3}[/tex]

So

[tex]y = -\frac{2}{3}x + b[/tex]

Now, to find the y-intercept, we replace one of these points into the equation.

(0.5,0.5) means that when [tex]x = 0.5 = \frac{1}{2}, y = 0.5 = \frac{1}{2}[/tex]

So

[tex]y = -\frac{2}{3}x + b[/tex]

[tex]0.5 = -\frac{2}{3}(0.5) + b[/tex]

[tex]b = \frac{1}{2} + \frac{1}[3}[/tex]

[tex]b = \frac{5}{6}[/tex]

So

[tex]y = -\frac{2}{3}x + \frac{5}{6}[/tex]

(b) the engineering lab with the library.

(0.5,0.5) and (-1,-2.5).

First, we find the slope:

Change in y:-2.5 - 0.5 = -3

Change in x: -1 - 0.5 = -1.5

The slope is: [tex]m = \frac{-3}{-1.5} = 2[/tex]

So [tex]y = 2x + b[/tex]

Now we find b

[tex]y = 2x + b[/tex]

[tex]0.5 = 2(0.5) + b[/tex]

[tex]b = -0.5 = -\frac{1}{2}[/tex]

So

[tex]y = 2x - \frac{1}{2}[/tex]

The multiplication of their slopes, is

[tex]2*\frac{-2}{3} = -\frac{4}{3}[/tex]

Since it is different of one, these paths are not perpendicular to each other.


Related Questions

Answer the question

Answers

Answer:

D

Step-by-step explanation:

demos

According to order of operations, which operation should be done first in this
problem:
45 - 9.5 + 8
a. multiplication
b. addition
c. division

Answers

D) division (PEMDAS)

Find the area of the parallelogram shown below.

Answers

Answer:

120 square units

Step-by-step explanation:

Given,

Base of the parallelogram = 10

Height of the parallelogram = 12

Therefore,

Area of the parallelogram = base × height

= 10 × 12

= 120

Hence,

Area of the parallelogram is 120 square units (Ans)

2. Determine whether segment AB is tangent to the given circle
12 pol
2. AB
А
12
B
13
Yes
No

Answers

Answer:

no

Step-by-step explanation:

13² should be equal to 4² + 12² for that

checking, we get that 169 is not equal to 16+144= 160

so it's not right angle

to be tangent, it should be right angle

Plz help me on this one.

Answers

Answer: 2

Step-by-step explanation:

Answer:

To find the value of x, add 5 to each side.

x - 5 = 13

+5 +5

x = 18

:)

Decrease $260 in the ratio 3:5​

Answers

$260 / 8 = $32.50
32.5 x 3= $97.50
32.5 x 5 = $162.50
$97.50:$162.50

please help me i really need help please please please

Answers

Answer: ≈117.15375m (if you're expected to round make sure you do so!)

Explanation: Because this a right triangle, you can apply the pythagorean theorem which is a^2 + b^2 = c^2. a and b can be any side except the hypotenuse (the one across from the 90° angle). You take 90^2 + 75^2 = c^2. This equals 13,725 after that you can take the square root of it and you're left with ≈ 117.15375m

Hope this helped! :)

Use f(x)=-2x+5 to find x when f(x)=11

Answers

When it asks this question, ultimately you want to plug 11 into x because its f(x). 11=-2+5.

Then you subtract 5 on both sides because of the opposite of addition is subtraction.

6=-2x

now divide on both sides

x=-3

Explain how 17.526 could be rounded to both 18 and 17.5.

Answers

Answer:

Step-by-step explanation:

If you round it to the nearest whole number, then 17.526  becomes 18 because if the first digit after the decimal(in this case,5) is 5 or greater you round to the next whole number.

If you round it to the nearest tenth, it would result in 17.5, because if the second digit after the decimal (in this case, 2) is 5 or greater you round to the next tenth of decimal.

Hope this helps!

Answer:

Step-by-step explanation:

It can be rounded down to 17.5 if rounding to 1 decimal place. If you are rounding to the nearest whole number, you would round to 18.

Hope this helps :)

Please tell me if I got it right

Answers

Answer:

1/9

Step-by-step explanation:

1/3 / 3 = 1/9

she will run 1/9

jog 1/9

and walk 1/9

to check all of them equal 1/3

1/9+1/9+1/9 = 3/9 = 1/3

find the area of the shaded region

Answers

Answer:

D) 54.9 cm^2

Step-by-step explanation:

I found the area of the circle wwith the formula A= πr^2

A= π•64

then I found the area of the square, 256

then I subtracted the area of the circle from the area of the square and got approx. 54.9

hope this helps <3

Need help pls ASAP no jokes need this badly

Answers

Answer:

x=64°

................

Answer:  x = 64

=============================================================

Explanation:

Combining all of the angles shown in the diagram leads to 360 degrees. This is because there are 360 degrees in a full rotation.

Let's add up the angles shown and set the sum equal to 360. Keep in mind that the square angle marker represents 90 degrees (aka a right angle).

180+26+x+90 = 180

x+296 = 360

x = 360-296

x = 64

After simplifying, what will x be equivalent to?
a2a4=ax

Answers

Answer:

x=8a

Step-by-step explanation:

Given data

We have the expression

a2a4=ax

Simplifying the LHS(Left Hand Side)

8a^2=ax

8a=x

Hence x will simplify to

x=8a


PLEASE HELP !! ILL GIVE BRAINLIEST !!

Answers

Answer:

<HIK to <GFD

Step-by-step explanation:

Alternate exterior angles are angles that are on the exterior sides alternately on a transversal

Answer:

∠HIK and ∠GFD

Step-by-step explanation:

Alternate exterior angles are angles that lie on the same parts of the parallel lines, but on alternate (different) sides.

∠HIK is on the lower left.

∠GFD is on the upper right.

Evaluate 2w2+8, when w=−4.


HELP ASAP

Answers

Answer:

-8

Step-by-step explanation:

Plug in -4 for w,  2(-4)2+8     (2x-4x2+8)

2 x -4 x 2 =-16

-16+8= -8

Jesse has three one-gallon containers. The first
3
one has of a gallon of juice, the second has
gallon of juice and the third has of a gallon of juice.
How many total gallons of juice does Jesse have?

Answers

Step-by-step explanation:

Total gallons of juice = No. of containers x one gallon of juice

= 3x1

= 3 gallons of juice

Which of these choices are square roots of 144? Check all that apply. ​

Answers

Answer:

E

Step-by-step explanation:

whats the are and perimeter for this pls help

Answers

Answer:

the area is 64 the perimeter is 30

Step-by-step explanation:

The diameter of a circle is 8 centimeters. What is the circle's circumference?

Answers

Answer:

25.13 centimeters

Step-by-step explanation:

Answer #1 please ASAP

Answers

Answer:

4.5

Step-by-step explanation:

To find the median, put the data in order from smallest to largest

1,2,2,3,4,4,5,5,8,10,10,11

The count up the number of data points

12

Divide by 2

12/2

Split the data into 2 groups, 6 in each, starting at the beginning

1,2,2,3,4,4,   5,5,8,10,10,11

Since there is an even number

Add the last number in first group and the first number in the last group and divide by 2

(4+5)/2 = 9/2 = 4.5

The median is 4.5

the correct answer is 4.5

Joey compared the cost of 9 different toys.

$2, $8, $4, $7, $8, $5, $8, $4, $6

What is the median cost of the books?

Question 1 options:

$8


$5


$6

Answers

Put in order
2,4,4,5,6,7,8,8,8
Look for middle one
So it’s $6

Answer:

6$

Step-by-step explanation:

$2, $8, $4, $7, $8, $5, $8, $4, $6

2, 4, 4, 5,6,7,8,8,8

6$

The length of a room is 19 feet. When using a 1/4 inch = 1 foot scale, what would be
the length of the wall on a floor plan?

Answers

Answer:

1 Expert Answer

19.5 ft would be represented, in the floor plan, as ¼ of 19.5 inches, i.e. 4.875 inches (four and seven eighths inches).

Please like and give me brainliest and rate!

The length of the wall on the floor plan will be 4.75 in


Step by step

The length of the wall is 19 ft
1/4 of an inch = 1 ft
19/4 = 4.75in (4 3/4 in)

Valerie and Bret have a total 18 dog show ribbons. Bret has twice as many ribbons as
Valerie
How many ribbons does each have?
no

Answers

Twice = double, double means x2 so 18/2 is 9 9x2=18 so valerie has 9 ribbons — hope this helps!

Answer: Valerie has 9 and Bret has 18

Step-by-step explanation:

27-18= 9

Hailey made the following statement
"It is impossible to build a rectangular prism with a volume of 40 units it one side measures 5 units."
Key
represents
1 cubic unit
Select the two figures below that prove Hailey's statement is false

Answers

Answer:

D

Step-by-step explanation:

Devon can take one of three different buses to and from work (bus a, b or c). he randomly catches one bus in the morning and another one on teh way home. teh table list the sample space of outcomes

Answers

Answer:

BB

Step-by-step explanation:

Answer:

ca

Step-by-step explanation:

URGENT GIVING BRAINLIEST
no links no scams no fake answers no guessing use evidence if you get it correct with evidence i will give you 100 points

Answers

Answer: The mode is 3

The range is 12

Step-by-step explanation:

The mode is the most frequently appearing number

3

The range is the difference between the highest and lowest numbers

12 - 0 = 12

slant height =15.2 in. height =14 in.base width =12 in .What is the surface area of the pyramid?​

Answers

Answer: 605.08 hope this helps.

Step-by-step explanation:

Emiliano firmó hoy un pagaré por la cantidad de $ 92.000. la tasa de interés estipulada es un 20% anual
Cuantos dias se necesitan para los intereses de la playa $ 8.000

Answers

Answer:

159 días.

Step-by-step explanation:

Dado que Emiliano firmó hoy un pagaré por la cantidad de $ 92.000 a una tasa de interés estipulada de un 20% anual, para determinar la cantidad de días que se necesitan para que dicho interés genere unos $8.000 se debe realizar el siguiente calculo:

92.000 x 0.2 = X

18.400 = X

18.400 / 365 = 50,41

8.000 / 50,41 = X

158.69 = X

Así, se necesitarán 159 días para que se generen $8.000 en intereses.

Combine the like terms to create an equivalent expression.
2q+2+9

Answers

Answer:

the answer is 2q + 11 because 2 and 9 are like terms so you can add them

Answer:

2q+11

Step-by-step explanation:

khan said so

Evaluate A2-B2 for A = 3 and B = -4.
O-2
0-7
Lenovo

Answers

Answer:

3×2+(-4)×(-2)=6+8=14

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