MATHEMATICS COLLEGE

To graph the function g(x) = (x – 5)2 – 9, shift the graph of f(x) = x2 5 units and 9 units.

Answers

Answer 1

Answer:

Answer:

The graph of f(x) shifts 5 units right and 9 units down to graph g(x).

Step-by-step explanation:

The general form of the parabola is

$h(x)=a(x-h)^2+k$

Where, (h,k) is the vertex of the parabola and a is stretch factor.

The parent function is

$f(x)=x^2$

The vertex of the parabola is (0,0).

The given function is

$g(x)=(x-5)^2-9$

The vertex of the parabola is (5,-9).

The vertex of the parabola shifts from (0,0) to (5,-9), therefore the graph of f(x) shifts 5 units right and 9 units down to graph g(x).

Answer 2

Answer: To graph the function g(x) = (x – 5)2 – 9, shift the graph of f(x) = x2 ✔ right
5 units and ✔ down 9 units.

Related Questions

Find the area of the combined figure. A figure is made up of a triangle and a rectangle. The triangle has a height of 8.5 inches and a base of 10 inches. The rectangle has dimensions of 9 inches x 10 inches. What is the area of the figure? a 102.5 square inches b 132.5 square inches C 110.2 square inches d 140.2 square inches
A firm has 18 senior and 22 junior partners. A committee of three partners is selected at random to represent the firm at a conference. In how many ways can at least one of the junior partners be chosen to be on the committee?
Help a homie out here
6x − 2y = 3 (equation 1) 5x + 3y = 4 (equation 2)
What’s the square root of 9/100

Write an equation that represents the line. Use exact numbers.

Answers

Answer:

y=3x/4 +2

Step-by-step explanation:

(0;2) and (4;5)

(x1;y1) ; (x2;y2)

y=mx+b

m=(y2-y1)/(x2-x1)

m=(5-2)/4-0)

m=3/4

y=mx+b=> 2=3/4 *0+b; => b=2

So, y=3x/4 +2

Suppose that P dollars in principal is invested for t years at the given interest rates with continuous compounding. Determine the amount that the investment is worth at the end of the given time period.=P$10,000, =t112 yr

(a) 1% interest

(b) 4% interest

(c) 4.5% interest

Answers

Answer: (a )$30648.54 (b)$882,346.73 (c) $1,544,700.15

Step-by-step explanation:

Formula: $A=Pe^(rt)$ , where P= principal , r=rate of interest, t= time

Given : P= $10,000, t = 112 years

(a) r = 1% = 0.01

$A=(10000)e^(0.01*112)$

$A=(10000)e^(1.12)=10000(3.06485420)\approx 30648.54$

Hence, Amount = $30,648.54

(b) r = 4% = 0.04

$A=(10000)e^(0.04*112)$

$A=(10000)e^(4.48)=10000(88.2346726757)\approx 882346.73$

Hence, Amount = $882,346.73

(c) r = 4.5% = 0.045

$A=(10000)e^(0.045*112)$

$A=(10000)e^(5.04)=10000(154.470015026)\approx 1544700.15$

Hence, Amount = $1,544,700.15

Final answer:

For 1% interest, the investment will be worth $10100.50. For 4% interest, it will be worth $10420.96, and for 4.5% interest, it will be worth $10451.65.

Explanation:

To determine the amount that an investment is worth at the end of a given time period with continuous compounding, we can use the formula A = P * e^(rt), where A is the final amount, P is the principal, r is the interest rate, and t is the time in years.

(a) For 1% interest:

A = 10000 * e^(0.01 * 1) = $10100.50

(b) For 4% interest:

A = 10000 * e^(0.04 * 1) = $10420.96

A = 10000 * e^(0.045 * 1) = $10451.65

Learn more about Continuous compounding here:

brainly.com/question/32594953

#SPJ11

A normal population has the mean of 10 and the variance of 25 . A random sample of size n-28 is selected. (a) Find the standard deviation of the sample mean. Round your answer to two decimal places (e.g. 98.76)
(b) How large must the sample be if you want to halve the standard deviation of the sample mean?

Answers

Answer:

Step-by-step explanation:

Given that:

population mean = 10

variance $\sigma^2$ = 25 ; $\sigma$ = $√( 25)$ = 5

sample size n = 28

The standard deviation of the sample mean:

= ${(5)/(√(28))$

= 0.95

To halve the standard deviation of the sample mean, the size of how large the sample will be can be computed as follows:

$(sd_1)/(sd_2) = ((\sigma)/(√(n)) )/((\sigma)/(√(n)) )$

$\implies ((5)/(√(28)) )/((5)/(√(28)) )$

$= (5)/(√(28)) * (√(28))/(5)$

= 2

n = 4 × 28

n = 112

The standard deviation is 0.95 and if the standard deviation is halved then the sample mean is 112.

What is a standard deviation?

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

A normal population has a mean of 10 and a variance of 25.

A random sample of sizes n-28 is selected.

A. The standard deviation will be

$\sigma = (√(Var(x)))/(n) \n\n\sigma = (√(25))/(√(28)) \n\n\sigma = 0.95$

B. The sample be if you want to halve the standard deviation of the sample mean

$\rm (SD_1)/(SD_2) = 2 = (√(n))/(√(28))\n\nn = 4*28 \n\nn= 112$

More about the standard deviation link is given below.

brainly.com/question/12402189

Compact and oversized tires are produced on two different machines. The table shows the number of each type of tire produced, y, depending on the number of hours, x, the machines work.

Answers

Answer:

OPTION B: 57x - 3

Step-by-step explanation:

Total tires produced is the sum of number of over-sized tires and the number of compact tires.

So, we have when x = 1, tires, y = 23 + 31 = 54

When x = 2, total tires y = 48 + 63 = 111

When x = 3, total tires y = 73 + 95 = 168

When x = 4, total tires y = 98 + 127 = 225

We can substitute the options to check which one will be the correct representation.

Option A: 55x - 1

When x = 1, y = 55(1) - 1 = 54

When x = 2, y = 55(2) - 1 = 109 $\ne$ 111

So, this option is eliminated.

Option B: 57x - 1

When x = 1, y = 57(1) - 3 = 54

When x = 2, y = 57(2) - 3 = 111

When x = 3, y = 57(3) - 3 = 168

When x = 4, y = 57(4) - 3 = 225

These values exactly match with the values from the table. So, Option B is the right answer.

Option C: 110x - 2

When x = 1, y = 110(1) - 2 = 108 $\ne$ 54

Hence, this option is incorrect.

Option D: 114x - 6

When x = 1, y = 114(1) - 6 $\ne$ 54

Hence, this option is also eliminated.

Option B is the required answer.

Answer: D

Step-by-step explanation:

the person above me was on the right track but needed to multiply the sum of the y values by 2. Therefore the answer should be D

According to the line plot what is the total number of the dog toys

Answers

Answer: 4 3/4

Step-by-step explanation:

3/8 +3/8 + 1/8 +1/2 +1/2 +1/2 +1/2 + 5/8 +5/8 +5/8=

3/8+3/8+1/8+2+5/8+5/8+5/8=

11/4 + 2=

2 · 4 /4 + 11/4=

2 · 4 + 11 / 4=

19/4 =

4 3/4

What property allows us to determine the congruency of the two triangles in the diagram?A. SSS
B. ASA
C. HL
D. SAS

Answers

A. SSS

That is because the diagram only shows that the sides are congruent and does not show anything else. (Like angles or anything)

The correct answer is A.SSS.

P.S. I am only answering this question so you could give the brainliest to the person who answered first :)

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