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2 years ago

If f(x) = 4x-3, which of the following is the inverse of f(x)?

Mathematics

1 answer:

GalinKa [24]2 years ago

5 0

Answer:

$\huge\boxed{f^{-1}(x)=\dfrac{x+3}{4}=\dfrac{1}{4}x+\dfrac{3}{4}}$

Step-by-step explanation:

$f(x)=4x-3\to y=4x-3\\\\\text{exchange}\ x\ \text{to}\ y\ \text{and vice versa}\\\\x=4y-3\\\\\text{solve for}\ y\\\\4y-3=x\qquad|\text{add 3 to both sides}\\\\4y-3+3=x+3\\\\4y=x+3\qquad|\text{divide both sides by 4}\\\\\dfrac{4y}{4}=\dfrac{x+3}{4}\\\\y=\dfrac{x+3}{4}\to y=\dfrac{1}{4}x+\dfrac{3}{4}$

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A 34-foot pole casts a 30-foot shadow. At the same time, a nearby tree casts a 24-foot shadow. How tall is the tree?

artcher [175]

Answer:

27.2 ft

Step-by-step explanation:

Let's set up a ratio that represents the problem:

Object's Height (ft) : Shadow (ft)

Substitute with the dimensions of the 34 foot pole and its 30 foot shadow.

34 : 30

Find the unit rate:

The unit rate is when one number in a ratio is 1.

Let's make the Shadow equal to one by dividing by 30 on both sides.

Object's Height (ft) : Shadow (ft)

34 : 30

/30 /30

1.13 : 1

Now, let's multiply by 24 on both sides to find the height of the tree.

Multiply:

Object's Height (ft) : Shadow (ft)

1.13 : 1

x24 x24

27.2 : 24

Therefore, the tree is 27.2 feet tall.

7 0

3 years ago

14(0.89)^x+4.5 =162

lisabon 2012 [21]

$14(0.89)^{x + 4.5} = 162$
$\frac{14(0.89)^{x + 4.5}}{14} = \frac{162}{14}$
$0.89^{x + 4.5} = 11\frac{4}{7}$
$ln(0.89^{x + 4.5}) = ln(11\frac{4}{7})$
$(x + 4.5)ln(0.89) = ln(11\frac{4}{7})$
$\frac{(x + 4.5)ln(0.89)}{ln(0.89)} = \frac{ln(11\frac{4}{7})}{ln(0.89)}$
$x + 4.5 = -2101.14032500$
$x = 2105.64032500$

3 0

3 years ago

Julia has five cards face down on the table. They are numbered 6, 7, 8, 9, and 10.

9966 [12]

6+7+8+9+10=40 ********************

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3 years ago

Read 2 more answers

Now heres the tricky part

loris [4]

13. Answer: n ≥ 108

Step-by-step explanation:

18 ≤ n ÷ 6

×6 ×6

108 ≤ n → n ≥ 108

Note: The line under the inequality symbol represents a closed dot

Graph: 108 ·---------------→

************************************************************************************

14. Answer: x > -4

Step-by-step explanation:

-3x < 12

÷(-3) ÷(-3)

x > -4 Flip the inequality sign when × or ÷ by a negative

Note: No line under the inequality symbol represents an open dot

Graph: -4 o-----------→

4 0

3 years ago

A metal bar weighs 8.15 ounces. 93% of the bar is silver. how many ounces of silver are in the bar

Zielflug [23.3K]

7.5795 ounces of the bar are silver.

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3 years ago