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
densk [106]
3 years ago
5

How many square units are in the area of the triangle whose vertices are the x and y intercepts of the curve y = (x-3)^2 (x+2)?

Mathematics
1 answer:
pantera1 [17]3 years ago
6 0

The intercepts can be read from the equation as (-2, 0), (0, 18), (3, 0). These define a triangle with a base of 5 and an altitude of 18, so the area is

... A = (1/2)·5·18 = 45 . . . . square units


_____

The x-intercepts are those values of x that make one or another of the factors be zero. (x-3) is zero when x=3; (x+2) is zero when x=-2.

The y-intercept is the value when x=0. That is (-3)²·(2) = 9·2 = 18.

You might be interested in
Mark recorded the growth of a plant over 8 weeks. The equation y=0.2x+2 represents the height y, in inches, after x weeks.
bezimeni [28]

The statements could be true are:

The height of the plant after week 3 was about 2.6 inches. ⇒ A

The height of the plant after week 9 was about 3.8 inches. ⇒ C

Step-by-step explanation:

Mark recorded the growth of a plant over 8 weeks

The equation y = 0.2x + 2, represents the height y, in inches, after x weeks

From the equation

  • 0.2 represents the rate of increasing of the height of the plant per week
  • 2 represents the initial height of the plant

∵ y represents the height of the plant after x week

∴ x is the number of the weeks

∵ y = 0.2x + 2

∵ x = 3

- Substitute x in the equation by 3

∴ y = 0.2(3) + 2

∴ y = 0.6 + 2

∴ y = 2.6

∴ The height of the plant after 3 weeks is 2.6 inches

∵ x = 9

- substitute x by 9 in the equation

∴ y = 0.2(9) + 2

∴ y = 1.8 + 2

∴ y = 3.8

∴ The height of the plant after 9 weeks is 3.8 inches

The statements could be true are:

The height of the plant after week 3 was about 2.6 inches.

The height of the plant after week 9 was about 3.8 inches.

Learn more:

You can learn more about the linear equations in brainly.com/question/1284310

#LearnwithBrainly

5 0
3 years ago
Find the percent of increase from 40 gallons to 89 gallons. Round to the nearest tenth of a percent if necessary.
tiny-mole [99]

Answer:

50

Step-by-step explanation:

because 89-49=49 49 rouded to the nearest ten is 50

3 0
2 years ago
How do you solve this?
motikmotik
Pemdas helps so first you do Parentheses Exponet multiply divide add and subtract
3 0
3 years ago
Read 2 more answers
Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally dis
nikitadnepr [17]

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 ​minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72​, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = <u><em>the interval of time between the eruptions</em></u>

So, X ~ N(\mu=72, \sigma^{2} =23^{2})

The z-score probability distribution for the normal distribution is given by;

                            Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = population mean time = 72 minutes

           \sigma = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is given by = P(X > 82 min)

       P(X > 82 min) = P( \frac{X-\mu}{\sigma} > \frac{82-72}{23} ) = P(Z > 0.43) = 1 - P(Z \leq 0.43)

                                                           = 1 - 0.6664 = <u>0.3336</u>

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let \bar X = <u><em>sample mean time between the eruptions</em></u>

The z-score probability distribution for the sample mean is given by;

                            Z  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean time = 72 minutes

           \sigma = standard deviation = 23 minutes

           n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P(\bar X > 82 min)

       P(\bar X > 82 min) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{82-72}{\frac{23}{\sqrt{13} } } ) = P(Z > 1.57) = 1 - P(Z \leq 1.57)

                                                           = 1 - 0.9418 = <u>0.0582</u>

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let \bar X = <u><em>sample mean time between the eruptions</em></u>

The z-score probability distribution for the sample mean is given by;

                            Z  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean time = 72 minutes

           \sigma = standard deviation = 23 minutes

           n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P(\bar X > 82 min)

       P(\bar X > 82 min) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{82-72}{\frac{23}{\sqrt{34} } } ) = P(Z > 2.54) = 1 - P(Z \leq 2.54)

                                                           = 1 - 0.9945 = <u>0.0055</u>

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 ​minutes, then we conclude that the population mean must be more than 72​, since the probability is so low.

6 0
3 years ago
If oranges cost $0.75 for 1/3 of a dozen, how many oranges can you buy for $3.00?? ❗️Please help❗️
pishuonlain [190]
75 + 75 + 75. = 2.25 so no
6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the x intercept of the parabola with vertex -3,-4 and y intercept 0,13
    6·1 answer
  • What is 110% of 80<br> (With work please)
    8·2 answers
  • #16. Do the ordered pairs (-5,19), (-1,7),(3,-5),(6,-14), and (9,-23) represent a linear function? How do you know?
    14·1 answer
  • A single, six-sided die is rolled. Find the probability of rolling an odd number or a number less than 4.
    5·2 answers
  • I Really Need Help With This Problem, Please
    10·2 answers
  • What is 5 divided by 23
    10·1 answer
  • Combine value to find 615 minus 342
    12·1 answer
  • One factor of f(x)=4x^3-4x^2-16x+16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
    6·1 answer
  • 1. Find m1<br><br> [] 30<br> [] 33<br> [] 57<br> [] 63
    14·2 answers
  • 1/8 quarters is how many gallons
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!