The correct answers are: 
1) A;
2) A;
4) D
3 cannot be done because the graph is not shown.

Explanation: 
1) Shifting a graph to the left, we would normally think of subtracting 1 from the function. However, horizontal translations are the opposite; left means adding 1 to x, while right means subtracting 1 from x.

2) A reflection in the x-axis means the y-coordinate will be negated (the opposite sign). This means that g(x)=-f(x)=-(x^2+5=-x^2-5.

4) To perform a vertical stretch of a function, we multiply by the factor; this gives us y=6x.

3 0

3 years ago

Read 2 more answers

Find the values of a and b such that x^2-2x+2=(x-a)^2+b

vekshin1

Answer:

a = 1, b = 1

Step-by-step explanation:

Expand the right side and compare the coefficients of like terms on both sides, that is

right side

(x - a)² + b ← expand factor using FOIL

= x² - 2ax + a² + b

Compare to left side x² - 2x + 2

Compare the coefficients of the x- term

- 2a = - 2 ( divide both sides by - 2 )

a = 1

Compare the constant terms

a² + b = 2 ( substitute a = 1 )

1² + b = 2

1 + b = 2 ( subtract 1 from both sides )

b = 1

Thus a = 1, b = 1

6 0

2 years ago

A glacier in Alaska moves about 29.9 meters a day. About how much farther will mobe in 1,000 days than it will move in 100 days

Reptile [31]

Answer:

26,910 meters

Step-by-step explanation:

The glacier moves 29.9 meters a day.

In 100 days it will move 29.9(100)=2990 meters.

In 1000 days it will move 29.9(1000)=29900 meters.

29,900-2,990=26,910 meters

7 0

3 years ago

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 o

xeze [42]

Answer:

a) 95% of the widget weights lie between 29 and 57 ounces.

b) What percentage of the widget weights lie between 12 and 57 ounces? about 97.5%

c) What percentage of the widget weights lie above 30? about 97.5%

Step-by-step explanation:

The empirical rule for a mean of 43 and a standard deviation of 7 is shown below.

a) 29 represents two standard deviations below the mean, and 57 represents two standard deviations above the mean, so, 95% of the widget weights lie between 29 and 57 ounces.

b) 22 represents three standard deviations below the mean, and the percentage of the widget weights below 22 is only 0.15%. We can say that the percentage of widget weights below 12 is about 0. Equivalently we can say that the percentage of widget weights between 12 an 43 is about 50% and the percentage of widget weights between 43 and 57 is 47.5%. Therefore, the percentage of the widget weights that lie between 12 and 57 ounces is about 97.5%

c) The percentage of widget weights that lie above 29 is 47.5% + 50% = 97.5%. We can consider that the percentage of the widget weights that lie above 30 is about 97.5%

3 0

2 years ago