What is the inverse of the function f(x) = 1/4x - 12?

Answers

Answer 1

Answer: Hello,

1) if the equation is
y=1/4 * x-12 then x=1/4 y-12==>1/4y=x+12==>y=x/4+3

2) if the equation is
y=1/(4x-12) then x=1/(4y-12)==>4y-12=1/x==>4y=1/x+12==>y=1/(4x)+3

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Your family went out to dinner at Applebee's and left the waiter an 18% tip. If the total before the tip for the dinner was $47.98 what should be paid to the waitress as a tip

Answers

Answer:

The amount that should be paid to the waitress as a tip would be $8.64

Step-by-step explanation:

0.18 x $47.98=$8.64

Find the missing side and round to the nearest tenth

Answers

To solve for the missing side. Do sin 33 degrees = 16/x and rearrange the equation to solve for X. X=16/sin 33

given a rectangle of length a and width b if A and B are both rational numbers would the perimeter be irrational or rational? Give an example choosing your own values for a and b

Answers

The perimeter would be rational due to both the width and length being rational numbers. A rational number is a number that can be written as a fraction such as 8 it can be written as 8/1, but a irrational would be a decimal number which in this case there would be none because both length and width is rational number. For example, Lets say the width is 8 and the length is 10. once both are written into fraction form such as 8/1 and 10/1 we add them to get a perimeter of 18.
Hope this helps!

Which polynomial can be simplified to a difference of squares? 10a2 + 3a – 3a – 16 16a2 – 4a + 4a – 1 25a2 + 6a – 6a + 36 24a2 – 9a + 9a + 4

Answers

16a² - 4a + 4a - 1 can be simplified to a difference of squares:

16a² - 4a + 4a - 1 =
16a² - 1 =
(4a)² - 1² =
(4a-1)(4a+1)

Answer:

2. $16a^2-4a+4a-1$

Step-by-step explanation:

We have to find the polynomial can be simplified to a difference of squares.

1. $10a^2+3a-3a-16$

Combine like terms

$10a^2-16$

10 in $10a^2$ is not a perfect square number because when a number end with one zero then the number is not perfect square number.

Therefore, it can not be simplified to a difference of squares.

2. $16a^2-4a+4a-1$

$16a^2-1$

Combine like terms

$(4a)^2-(1)^2$

Hence, the polynomial can be simplified as difference of squares.

3. $25a^2+6a-6a+36$

Combine like terms

$25a^2+36$

$(5a)^2+(6)^2$

Hence, the polynomial can not be simplified as difference of squares because the polynomial can be simplified as sum of squares.

4. $24a^2-9a+9a+4$

Combine like terms

$24a^2+4$

$24a^2+(2)^2$

$24=2* 2* 3* 2$

24 is not a perfect square number because when factorize 24 then 2 and 3 are not paired.

Hence, the polynomial can not be simplified as difference of squares.

Solve 3x2 + 12x = 3.

Answers

Answer:

The solutions to the quadratic equation are: $x=-2+√(5),\:x=-2-√(5)$

Step-by-step explanation:

To solve the quadratic equation $3x^2+12x=3$ you must:

Subtract 3 from both sides and simplify

$3x^2+12x-3=3-3\n\n3x^2+12x-3=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)$

$\mathrm{For\:}\quad a=3,\:b=12,\:c=-3$

$x=(-12+√(12^2-4\cdot \:3\left(-3\right)))/(2\cdot \:3)=(-12+√(180))/(2\cdot \:3)=(-12+6√(5))/(6)=(6\left(-2+√(5)\right))/(6)=-2+√(5)$

$x=(-12-√(12^2-4\cdot \:3\left(-3\right)))/(2\cdot \:3)=(-12-√(180))/(2\cdot \:3)=(-12-6√(5))/(6)=-(6\left(2+√(5)\right))/(6)=-2-√(5)$

The solutions to the quadratic equation are:

$x=-2+√(5),\:x=-2-√(5)$

$3 x^(2) + 12x = 3$
$3 x^(2) + 12x - 3 = 0$
Using the quadratic formula
$x = \frac{-b (+ or -) \sqrt{b^(2 - 4ac) } }{2a}$
$x = \frac{-12 + \sqrt{12^(2 - 4(3)(-3)) } }{2(3)}$ OR $x = \frac{-12 - \sqrt{12^(2 - 4(3)(-3)) } }{2(3)}$
$x = (-12 + √(180) )/(6)$ OR $x = (-12 - √(180) )/(6)$
∴ x = 0.236 and x = -4.236

A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table. A 4-column table with 3 rows. Column 1 has entries in band, not in band, total. Column 2 is labeled play a sport with entries a, d, g. Column 3 is labeled do not play a sport with entries b, e, h. Column 4 is labeled total with entries c, f, i.

Which of the following correctly represents the given data in the problem?

A: a = 24, g = 48, h = 22, i = 80
B: a = 22, c = 80, d = 24, i = 48
C: a = 24, b = 48, c = 22, i = 48
D: a = 24, c = 48, e = 22, i = 80

Answers

Answer:

It's D

Step-by-step explanation:

I took the lesson E2020

Answer:

b = 24

d = 10

f = 32

g = 34

h = 46

Step-by-step explanation:

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