MATHEMATICS COLLEGE

Which of the following functions has the greatest y-intercept?f(x)
X: -3, -2, -1, 0, 1, 2
Y: 15, -8, -1, 3, 6, 10

g(x) = –4 sin(5x) + 3

Options:
A. f(x)
B. g(x)
C. f(x) and g(x) have the same y-intercept
D. Not enough information

Answers

Answer 1
Answer:

Answer:

C. f(x) and g(x) have the same y-intercept

Step-by-step explanation:

To find the y-intercept, we need to plug in x = 0

f(x) is given in table values.

When x = 0, y = 3 from the table values.

Therefore, y-intercept of f(x) = 3

g(x) = -4 sin(5x) + 3

Plug in x = 0

y = -4 sin(5.0) + 3

y = -4 sin 0 + 3         [sin 0 = 0]

y = 0 + 3

y = 3

Therefore, y-intercept of g(x) = 3

Answer: C. f(x) and g(x) have the same y-intercept

Hope this will helpful.

Thank you.
Answer 2
Answer: C, just consider when x=0,find the y

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How to work the problems and explain step by step by showing the work

Answers

well, you're asked to simply grab the second version of that amount, or balance, and provide a common factored version of it, is all

so \bf A_2=(P+Pr)+(P+Pr)r\n\n\textit{now, let's take common factor}\n\nA_2=\underline{(P+Pr)}+\underline{(P+Pr)} r\impliedby \textit{see the common factor?}\n\nA_2=\underline{(P+Pr)}(1+r)

Rewrite the function by completing the square.
f(x) = x^2 – 10x—96

Answers

Answer:

f(x) = (x - 5)^(2) - 121.

Step-by-step explanation:

The goal is to rewrite f(x) in the vertex form a\, (x - h)^(2) + k by completing the square (where a, h, and k are constants.)

Expand the vertex form expression:

\begin{aligned}& a\, (x - h)^(2) + k\n &= a\, (x - h)\, (x - h) + k \n &= a\, \left(x^2 - h\, x - h\, x + h^2\right) + k \n &= a\, \left(x^2 - 2\, h\, x + h^2\right) + k\n &= a\, x^2 - 2\, a\, h\, x + \left(a\, h^2 + k\right) \end{aligned}.

Compare this expression to f(x) = x^2 - 10\, x - 96 and solve for the constants a, h, and k. Make sure that the coefficient of each term matches:

  • Coefficient for the x^2 term: a in the expanded expression and 1 in the expression for f(x). Hence, a = 1.
  • Coefficient for the x term: (-2\, a\, h) in the expanded expression and (-10) in the expression for f(x). Hence, -2\, a\, h = -10.
  • Coefficient for the constant term: \left(a\, h^2 + k\right) in the expanded expression and (-96) in the expression for f(x). Hence, a\, h^(2) + k = -96.

Substitute a = 1 into the second equation, -2\, a\, h = -10, and solve for h.

-2 \, h = -10.

h = 5.

Substitute both a = 1 and h = 5 into the third equation, a\, h^(2) + k = -96, and solve for k.

5^2 + k = -96.

k = -121.

Therefore, a\, (x - h)^(2) + k becomes (x - 5)^2 + (-121).

Hence, the vertex form of the parabola f(x) would be:

f(x) = (x - 5)^(2) - 121.

Answer:

(x - 5)² -121 = 0

Step-by-step explanation:

if you need to find the roots you can take the square root of each side:

(x-5)² = 121

(x-5)² = 121

square root of (x-5)² is x-5

square root of 121 is ±11

first root:  x-5 = 11

x = 16

second root: x-5 = -11

x = -6

How much is `10\%` of `10` liters of milk?

Answers

the answer would be 1 liter of milk

Answer:

one

Step-by-step explanation:

Steven wants to make some extra money using a CD account. He wants $22,000 in his account after 5 yearscompounded continuously. How much principal will he have to start with, at an interest rate of 6.625%?

Answers

Answer: You got to multiply 22,000 times 5 and that will equal 110,000

Step-by-step explanation:

Final answer:

To have a final balance of $22,000 in a CD account after 5 years with continuous compounding at an interest rate of 6.625%, Steven needs to initially deposit approximately $15,895.68.

Explanation:

To calculate how much principal Steven should start with in his CD account, we need to use the formula for continuous compounding, which is A = Pe^(rt), where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • e is the base of the natural logarithm, approximately equal to 2.71828.
  • r is the annual interest rate (decimal).
  • t is the time the money is invested for in years.

In Steven's case, he wants A = $22,000 after t = 5 years, at an interest rate r of 6.625% or 0.06625 in decimal format. Substituting these values into our formula and solving for P, we get:

P = A / e^(rt)

P = 22000 / e^(0.06625 * 5)

After calculating this expression, we find that Steven needs to deposit approximately $15,895.68 into his CD account to have $22,000 after 5 years with continuousinterest compounding at 6.625%.

Learn more about Continuous Compounding here:

brainly.com/question/36501885

#SPJ2

A 15° sector in a circle has an area of 11.9 m2. What is the area of the circle?

Answers

A 15° sector in a circle has an area of 11.9 m2. What is the area of the circle?
The area of the circle will be found as follows:
the fraction of the sector=15/360=1/24
the area of the circle will be:
area=(fraction of the circle)/(fraction of the sector)*(area of the sector)
=1/(1/24)×11.9
=285.6 m²

Gabriella swims 2 laps per minute. What is the associated rate? ___ minute per lapA.2
B.4
C.1/4
D.1/2


ANSWER QUICKKK

Answers

Answer:

The answer is D.

Step-by-step explanation:

ItisgiventhatGabriellaswims2lapsfor1minute.Soinordertofindhowmanyminutesdidheswimforeachlap,youhavetodivideitby2:

2 laps = 1 minute

2 laps ÷ 2 = 1 minute ÷ 2

1 lap = 1/2 minute

= 30 seconds

Test:

Gabriella swim 1/2 min per lap. So if he swim 2 laps, you have to multiply it by 2 :

1/2 × 2 = 1 minute

Answer:

The answer is D

Step-by-step explanation:

HOPE THIS HELPS
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