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
Pavlova-9 [17]
3 years ago
11

Which statements describe transformations performed in f (x) = x^2 to create g (x) = 2x^2 + 5? select all that apply.

Mathematics
1 answer:
snow_tiger [21]3 years ago
8 0

Answer:

The statements describe transformations performed in f(x) to create g(x) are:

a translation of 5 units up ⇒ c

a vertical stretch with a scale factor of 2 ⇒ d

Step-by-step explanation:

  • If f(x) stretched vertically by a scale factor m, then its image g(x) = m·f(x)
  • If f(x) translated vertically k units, then its image h(x) = f(x) + k

Let us use these rule to solve the question

∵ f(x) = x²

∵ g(x) is created from f(x) by some transformation

∵ g(x) = 2x² + 5

→ Substitute x² by f(x) in g(x)

∴ g(x) = 2f(x) + 5

→ Compare it with the rules above

∴ m = 2 and k = 5

→ That means f(x) is stretched vertically and translated up

∴ f(x) is stretched vertically by scal factor 2

∴ f(x) is translated 5 uints up

The statements describe transformations performed in f(x) to create g(x) are:

  • a translation of 5 units up
  • a vertical stretch with a scale factor of 2
You might be interested in
A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random
Yuliya22 [10]

Answer:

b) independent samples t-test

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: \mu_1 = \mu_2  

Alternative hypothesis: \mu_1 \neq \mu_2  

Or equivalently:  

Null hypothesis: \mu_1 - \mu_2 = 0  

Alternative hypothesis: \mu_1 -\mu_2\neq 0  

Our notation on this case :  

n_1 =5 represent the sample size for group 1  

n_2 =5 represent the sample size for group 2  

We can calculate the mean and deviation for eaach group with the following formulas:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X_1 =5.92 represent the sample mean for the group 1  

\bar X_2 =5.74 represent the sample mean for the group 2  

s_1=1.88 represent the sample standard deviation for group 1  

s_2=1.81 represent the sample standard deviation for group 2  

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:  

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}  

And now we can calculate the statistic:  

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

The degrees of freedom are given by:  

df=5+5-2=8

And now we can calculate the p value using the altenative hypothesis:  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

7 0
3 years ago
What is the <br> The product of -2 and a number minus six is greater than -18.
Fed [463]
Answer: x>-6

Explanation: -2x -6>-18
-2x >-12
-x>6
X>-6
6 0
3 years ago
Which of the following equations is of a parabola with a vertex at (3, 0)?
bixtya [17]

Answer:

D. y = (x - 3)²

Step-by-step explanation:

The parabola formula in vertex form is:

y = a(x - h)² + k

where the vertex is located at (h, k). Replacing with vertex (3, 0) we get:

y = a(x - 3)² + 0

y = a(x - 3)²

In all possible options the leading coefficient <em>a</em> is equal to one. Therefore:

y = (x - 3)²

7 0
3 years ago
Part A: The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the a
Debora [2.8K]

Answer:

What am I supposed to be solving please

4 0
3 years ago
Need Help ASAP algebra 2​
Anastasy [175]

Answer:

a = √10

Step-by-step explanation:

a² + b² = c²

a² + 9² = (√91)²

a² + 81 = 91

a² = 10

a = √10

hope this helps :)

7 0
3 years ago
Read 2 more answers
Other questions:
  • What are the domain restrictions of the expression h^2+3h−10/h^2−12h+20 ?
    11·2 answers
  • Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre
    7·1 answer
  • A password is 4 characters long and must consist of 3 letters and 1 of 10 special characters. If letters can be repeated and the
    12·2 answers
  • Kevin is responsible for delivering sacks of grains to a grocery shop on the tenth floor of a departmental store. Each sack weig
    13·1 answer
  • A pitcher is full of lemonade. Which unit of liquid volume best describes the amount of lemonade in the pitcher?
    15·1 answer
  • Geometry Vertical angles and Parallel lines
    9·1 answer
  • Which expression is equivalent to 5y + 2y + 6x + 2y - x
    11·1 answer
  • Keith rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 97 cents for each mile d
    7·2 answers
  • Can someone help me with this problem
    10·1 answer
  • URGENT ANSWER LLEASE DUE IN 3 MINUTES!!!!!!!!!!!
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!