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3 years ago

7

Write the rule for the following arithmetic sequence: 11, 15, 19, 23, …

1 answer:

miv72 [106K]3 years ago

5 0

11,15,19,23

an = 11 + 4(n-1)
an = 11 + 4n - 4
an = 4n + 7

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I think of a number. If I divide the sum of 6 and the number by 3,the result is 4 more than one quarter of the number. Find the

Alex17521 [72]

Answer:

24

Step-by-step explanation:

Let the number be x.

Sum of the number and 6: $6+x$

Divide it by 3: $\frac{6+x}{3}$

Result is 4 more than one quarter of the number:

$\frac{6+x}{3} =4+\frac{1}{4} x$

Multiply both sides by 12:

$\frac{6+x}{3}\cdot \:12=4\cdot \:12+\frac{1}{4}x\cdot \:12$

Simplify:

$4\left(x+6\right)=48+3x$

Expand:

$4x+24=48+3x$

Subtract 24 from both sides:

$4x+24-24=48+3x-24$

$4x=3x+24$

Subtract 3x from both sides:

$4x-3x=3x+24-3x$

$x=24$

The number is 24.

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3 years ago

Does the graph below represent a proportional relationship?

aleksklad [387]

The answer is A.
The reason being straight lines mean equal proportions, while curved lines are exponential or quadratic.

6 0

3 years ago

Read 2 more answers

Which equation is a related equation? x + 15 =24

AleksandrR [38]

Your answer would be A hope this helps!

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3 years ago

Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of

victus00 [196]

Answer:

g(x), f(x) and h(x)

Step-by-step explanation:

Given

Interval: (0,3)

See attachment for functions f(x), g(x) and h(x)

Required

Order from fastest to slowest decreasing average rate of change

The average rate of change is calculated as:

$Rate = \frac{f(b) - f(a)}{b - a}$

In this case:

$(a,b) = (0,3)$

i.e.

$a = 0\\b=3$

For f(x)

$f(x) = 16(\frac{1}{2})^x$

$Rate = \frac{f(b) - f(a)}{b - a}$

$Rate = \frac{f(3) - f(0)}{3 - 0}$

$Rate = \frac{f(3) - f(0)}{3}$

Calculate f(3) and f(0)

$f(x) = 16(\frac{1}{2})^x$

$f(3) = 16(\frac{1}{2})^3 = 16 * \frac{1}{8} = 2$

$f(0) = 16(\frac{1}{2})^0 = 16 * 1 = 16$

So:

$Rate = \frac{f(3) - f(0)}{3}$

$Rate = \frac{2 - 16}{3}$

$Rate = -\frac{14}{3}$

For g(x)

$Rate = \frac{g(b) - g(a)}{b - a}$

$Rate = \frac{g(3) - g(0)}{3 - 0}$

$Rate = \frac{g(3) - g(0)}{3}$

From the table of g(x)

$g(3) = 1$

$g(1) = 27$

So:

$Rate = \frac{1 - 27}{3}$

$Rate = -\frac{26}{3}$

For h(x)

$Rate = \frac{h(b) - h(a)}{b - a}$

$Rate = \frac{h(3) - h(0)}{3 - 0}$

$Rate = \frac{h(3) - h(0)}{3}$

From the graph of h(x)

$h(3) = -3$

$h(0) = 4$

So:

$Rate = \frac{-3 - 4}{3}$

$Rate = -\frac{7}{3}$

So, the calculated rates of change are:

$f(x) = -\frac{14}{3}$ $= -4.67$

$g(x) = -\frac{26}{3}$ $=-8.67$

$h(x) = -\frac{7}{3}$ $=-2.33$

By comparison:

From the fastest decreasing to slowest, the order is: <em>g(x), f(x) and h(x)</em>

4 0

3 years ago

Kendrick’s bill for lunch was $24.50. He left the server an 18% tip. What is the total amount that Kendrick paid for lunch inclu

Mice21 [21]

Answer:

$28.91

Step-by-step explanation:

The first step is to calculate the amount of the tip. You multiply the price (24.50) by the tip amount (18% or 0.18). The product is 4.41. Then, you add the tip to the bill. 24.50+4.41=28.91.

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3 years ago