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3 years ago

For any linear function f(x) = mx + b, when does kf(x) = f(kx)?

Mathematics

1 answer:

iogann1982 [59]3 years ago

4 0

Only when b = 0 or k = 1.

If f(x) = mx + b, then

f (kx) = m (kx) + b = mkx + b

while

k f(x) = k (mx + b) = kmx + kb

The two expression are identical only if

kb = b ===> kb - b = 0 ===> b (k - 1) = 0 ===> b = 0 or k = 1

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How to solve multi step inequality

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3 years ago

A jacket usually sells for $69.00. If the jacket is 30% off, and sales tax is 8%, what is the total price of the jacket, includi

Ivan

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3 years ago

It takes Mr. Martin 12 minutes to drive his bus route without stopping to pick up any passengers. For each passenger stop, he es

PtichkaEL [24]

14 = 0.5p + 12 <== ur equation

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3 years ago

Read 2 more answers

Please help! alg 1! I really need a explaintion fastttt

Gelneren [198K]

Answer:

y = -5x +10
(0, 10)
(1, 5)
see attached

Step-by-step explanation:

1. Subtract 5x from both sides to put the equation in slope-intercept form:

y = -5x +10

2. The y-intercept is the point corresponding to x=0. The y-value when x=0 is the constant in the equation: 10. Then the point is ...

(x, y) = (0, 10)

You may notice this is one of the points listed in part 4, and is also used in question 3.

3. The x-value computed is 1; the y-value computed is 5. The point is ...

(x, y) = (1, 5)

You may notice this is one of the points listed in part 4.

4. See attached

7 0

3 years ago

30 years ago zoe was 2/3 as old as luke, 18 years ago zoe was 5/6 as old as luke how old are they now

barxatty [35]

Based on the mathematical statements, Zoe is 56 years old and Luke is 66 years old, now

<h3>How to determine how old they are now?</h3>

From the question, we have the following statements that can be used in our computation:

30 years ago

Zoe was 2/3 as old as Luke

18 years ago

Zoe was 5/6 as old as Luke

Let their present ages be represented as

Zoe = x

Luke = y

So, we have the following representations

30 years ago

Zoe was 2/3 as old as Luke

x - 36 = 2/3(y - 36)

18 years ago

Zoe was 5/6 as old as Luke

x - 18 = 5/6(y - 18)

So, we have the following system of equations

x - 36 = 2/3(y - 36)

x - 18 = 5/6(y - 18)

Make x the subject in x - 18 = 5/6(y - 18)

x = 5/6(y - 18) + 16

Substitute x = 5/6(y - 18) + 16 in x - 36 = 2/3(y - 36)

5/6(y - 18) + 16 - 36 = 2/3(y - 36)

Open the brackets

5/6y - 15 + 16 - 36 = 2/3y - 24

Evaluate the like terms

5/6y - 35 = 2/3y - 24

Multiply through by 6

5y - 210 = 4y - 144

Evaluate the like terms

y = 66

Substitute y = 66 in x = 5/6(y - 18) + 16

x = 5/6(66 - 18) + 16

Evaluate

x = 56

Recall that

Zoe = x

Luke = y

So, we have

Zoe = x = 56

Luke = y = 66

Hence, they are 56 and 66 years, now