1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivan
2 years ago
8

What is the equation that represents the line that passes through the points (9, -2) and (12, -5)?

Mathematics
1 answer:
garik1379 [7]2 years ago
8 0

Hi there!

\large\boxed{y = -x + 7}

To begin, we must use the slope formula to calculate the slope of the line:

m = \frac{y_2-y_1}{x_2-x_1}

Plug in the coordinates:

m = \frac{-5-(-2)}{12-9}

Simplify:

m = \frac{-3}{3} =-1

Recall that the equation for a line in point-slope form is:

y - y1 = m(x - x1)

Plug in coordinates into the equation along with the slope:

y - (-2) = -1(x - 9)

Simplify:

y + 2 = -x + 9

y = -x + 7

You might be interested in
Mona's math certificate is 10 inches tall and 14 inches wide. Mona wants to put the certificate in a fancy frame that costs $1.0
swat32

Answer:

$48.96

Step-by-step explanation:

Given data

Length= 10inches

Width=14 inches

Let us find the perimeter of the  certificate

P=2L+2W

P= 2*10+2*14

P=20+28

P= 48 inches

Hence if 1 inche cost $1.02

Then 48 inches will cost x

cross multiply we

x= 48*1.02

x= $48.96

Hence it will cost $48.96 to frame the certificate

6 0
3 years ago
Express (16³) 1/4 in simplest radical form.
Doss [256]

Answer:

70

Step-by-step explanation:

4 0
1 year ago
I really need help please answer
belka [17]

Answer: Choice B) between 6:48 AM and 5:12 PM

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

Explanation:

I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.

We want to find values of t that satisfy f(t) > 25

This is the same as trying to solve f(t) - 25 > 0

So we have,

f(t) = 24 - 5\cos\left(\frac{\pi}{12}t\right)\\\\   f(t)-25 = 24 - 5\cos\left(\frac{\pi}{12}t\right)-25\\\\   f(t)-25 = -1 - 5\cos\left(\frac{\pi}{12}t\right)\\\\   f(t)-25 > 0\\\\ -1 - 5\cos\left(\frac{\pi}{12}t\right) > 0\\\\

To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.

Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.

Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)

Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.

When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.

Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.

Then focusing on the point  (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours

1700 hours in military time = 17-12 = 5 pm

The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.

We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).

--------------------------

In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.

Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.

8 0
3 years ago
SOLVE x^4 − 15x^2 − 16 = 0 <br> What are the roots of the equation?
kakasveta [241]

Answer:

roots : 4, -4, i, -i

Step-by-step explanation:

This gets a bit tricky.

We have to substitude x^2 as u in this problem.

Now to rewrite x^4 − 15x^2 − 16 = 0 with u, we get

u^2 - 15u - 16 = 0

( u - 16) (u + 1)

U = 16

U = -1

<em>This is not the end of the problem. </em>

Now we have to substitute x^2 back to u.

x^2 = 16  --> we get the roots 4 and -4

x^2 = -1 --> we get the roots i and -i

tadah!

8 0
2 years ago
Select the term that best describes the statement A triangle is acute provided all the angles have a measure of less than 90 deg
Burka [1]
I think the correct answer is conjunction...
3 0
3 years ago
Other questions:
  • If y = 9 and x = 12, what additional information is necessary to show that
    6·1 answer
  • A square patio has an area of 143 square feet. How long is each side of the patio to the nearest tenth?
    13·1 answer
  • Round 12,351 to the nearest hundred
    15·1 answer
  • Find the area of this parallelogram?
    12·1 answer
  • Katherine is shopping for cupcakes and donuts. She can purchase at most 30 items in total. She also wants the number of cupcakes
    12·2 answers
  • How do I find the y intercept when all that is given is the x intercept?​
    8·1 answer
  • What is the equation of the line that passes through the point (4, 12) and has a y-intercept of -2?
    14·1 answer
  • What point is shared by two lines?
    8·2 answers
  • Solve 3-²<br>I need work shown​
    9·1 answer
  • (2x+1)/(x²-3) simplified
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!