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3 years ago

Cassie has 1/2 pound of sugar in her cabinet. Her cake recipe calls for 2/10 of a pound of sugar. How many cakes can she make?

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

5 0

1/2 = 5/10

she can make 2 cakes

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The graph of f(x) shown below has the same shape as the graph of g (x) = x^2 but it is shifted to the left 2 units. what is the

mariarad [96]

Answer:

C. F(x) = (x+2)²

Step-by-step explanation:

A horizontal shift to the right by "h" units is achieved by replacing x with (x-h). The shift we want is to the left by 2 units, so h = -2, and we have ...

f(x) = g(x -(-2)) = g(x+2)

f(x) = (x+2)²

8 0

3 years ago

Find all the zeros of the function <br> g(x)=x^3-4x^2-x+22

vagabundo [1.1K]

Answer:

x = -2, x = 3 − i√8, and x = 3 + i√8

Step-by-step explanation:

g(x) = x³ − 4x² − x + 22

This is a cubic equation, so it must have either 1 or 3 real roots.

Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.

g(-1) = 18

g(1) = 18

g(-2) = 0

g(2) = 12

g(-11) = 1782

g(11) = 858

g(-22) = -12540

g(22) = 8712

We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.

g(x) = x³ − 4x² − 12x + 11x + 22

g(x) = x (x² − 4x − 12) + 11 (x + 2)

g(x) = x (x − 6) (x + 2) + 11 (x + 2)

g(x) = (x (x − 6) + 11) (x + 2)

g(x) = (x² − 6x + 11) (x + 2)

x² − 6x + 11 = 0

Quadratic formula:

x = [ 6 ± √(36 − 4(1)(11)) ] / 2

x = (6 ± 2i√8) / 2

x = 3 ± i√8

The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.

5 0

3 years ago

Pringles is planning their sales force spending for the next year. Each of their sales people spends about 3400 hours annually a

LUCKY_DIMON [66]

Answer:

459 sales people.

Step-by-step explanation

Time per call (t) = 45 min = 0.75 h

Hours per sales person (H) = 3,400 hours

Number of customers (n) = 40,000 customers

Call frequency (f)= 52 calls per year

The total number of sales people (S) needed, is given by the total time spent on calls for the year, divided by the amount of hours each person spends on sale:

$S=\frac{40,000*0.75*52}{3,400}\\ S=458.8$