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3 years ago

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

Mathematics

1 answer:

GalinKa [24]3 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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The camping supply store sells bags of charcoal in a 20 pound size for 5.79 the same brand sells a 50 pound size for 14.29 Wich

Paul [167]

Answer:

50 pounds for $14.29 is the better option.

Step-by-step explanation:

$5.79÷20=$0.2895 per pound

$14.29÷50=$0.2858 per pound

$0.2895-$0.2858=$0.0037 saved per pound.

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2 years ago

WILL GIVE BRAINLIEST

mafiozo [28]

Answer:

(6x - 1) • (2x + 9)

Step-by-step explanation:

STEP

Equation at the end of step 1

((22•3x2) + 52x) - 9

STEP

Trying to factor by splitting the middle term

2.1 Factoring 12x2+52x-9

The first term is, 12x2 its coefficient is 12 .

The middle term is, +52x its coefficient is 52 .

The last term, "the constant", is -9

Step-1 : Multiply the coefficient of the first term by the constant 12 • -9 = -108

Step-2 : Find two factors of -108 whose sum equals the coefficient of the middle term, which is 52 .

-108 + 1 = -107

-54 + 2 = -52

-36 + 3 = -33

-27 + 4 = -23

-18 + 6 = -12

-12 + 9 = -3

-9 + 12 = 3

-6 + 18 = 12

-4 + 27 = 23

-3 + 36 = 33

-2 + 54 = 52 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 54

12x2 - 2x + 54x - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (6x-1)

Add up the last 2 terms, pulling out common factors :

9 • (6x-1)

Step-5 : Add up the four terms of step 4 :

(2x+9) • (6x-1)

Which is the desired factorization

HOPE IT HELPS! :))

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2 years ago

Examine this right triangle. A right triangle has a side length of 16 meters and hypotenuse of 20 meters. Which equation can be

Sergeu [11.5K]

The equation can be used to find the missing leg in the triangle $20^{2} = 16^{2} +a^{2}$ .

<h3>What is the right triangle?</h3>

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

It is given that a right triangle has a side length of 16 meters and a hypotenuse of 20 meters.

From a Pythagoras theorem

$b^{2} = c^{2} +a^{2} \\20^{2} = 16^{2} +a^{2}\\20^{2}-16^{2} =a^{2}\\a^{2} = 20^{2}-16^{2} \\$