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JulsSmile [24]
2 years ago
5

Which describes the graph of y = (x - 5)2 - 4?

Mathematics
1 answer:
Schach [20]2 years ago
4 0

Answer:

A. Opens up with a vertex at (5,-4)

Step-by-step explanation:

Apex

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Mr. Varello is paid semimontnly. His annual salary is $64,333. What is his semimonthly
scoray [572]

Answer: His semimonthly salary is $2,680.54.

Step-by-step explanation:

64,333/12 = 5,361.08

5,361.08/2 = 2,680.54

8 0
3 years ago
Explain why f(x) = x^2+4x+3/x^2-x-2 is not continuous at x = -1.
liberstina [14]

Answer:

The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)

Step-by-step explanation:

We have the following expression

f(x) = \frac{x^2+4x+3}{x^2-x-2}

Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.

Now we search that values of x make 0 the denominator factoring the polynomial x^2-x-2

We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.

These numbers are -2 and 1

Then the factors are:

(x-2) (x + 1)

We do the same with the numerator

x^2+4x+3

We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.

These numbers are 3 and 1

Then the factors are:

(x+3)(x + 1)

Therefore

f(x) = \frac{(x+3)(x+1)}{(x-2)(x+1)}

Note that \frac{(x+1)}{(x+1)}=1 only if x \neq -1

So since x = -1 is not included in the domain the function has a discontinuity in x = -1

3 0
3 years ago
1. Find the volume of a cone with a diameter of 14 cm and a height of 25 cm.
slega [8]

Answer:

V≈1282.82

Step-by-step explanation:

V=πr^2h

3=π·72·25

3≈1282.817

8 0
2 years ago
g In R simulate a sample of size 20 from a normal distribution with mean µ = 50 and standard deviation σ = 6. Hint: Use rnorm(20
Illusion [34]

Answer:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

> sqrt(var(a))

[1] 7.470221

Step-by-step explanation:

For this case first we need to create the sample of size 20 for the following distribution:

X\sim N(\mu = 50, \sigma =6)

And we can use the following code: rnorm(20,50,6) and we got this output:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

> sqrt(var(a))

[1] 7.470221

5 0
3 years ago
(-10x)(2) is there any chance you can help please and thanks
Svetllana [295]
The answer is -20x, because the parentheses show they are being multiplied, so you multiply -10x and 2, which would be -20x.
7 0
2 years ago
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