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3 years ago

Please help!!! ive been stuck on this for 30 minutes now!

Mathematics

1 answer:

max2010maxim [7]3 years ago

7 0

Answer:

f^-1 = 4(x-3)

Step-by-step explanation:

If f(x) = 1/4(x) + 3 we ned to find f^-1.

To find the inverse function, we need to solve the equation for "x", as follows:

f(x) = 1/4(x) + 3

y = 1/4(x) + 3

y-3 = 1/4(x)

4(y-3) = x

Now, change the "x" for an "y". And change the "y" for an "x":

4(x-3) = y

The solution is the last one.

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Which point lies on a circle that is centered at A(-3, 2) and passes through B(1, 3)?

My name is Ann [436]

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the center
r - the radius

$\hbox{the center: } A(-3,2) \\
h=-3 \\ k=2 \\ \\
\hbox{the equation:} \\
(x+3)^2+(y-2)^2=r^2 \\ \\
\hbox{the circle passes through B(1,3)} \\
x=1 \\ y=3 \\ \Downarrow \\
(1+3)^2+(3-2)^2=r^2 \\
4^2+1^2=r^2 \\
16+1=r^2 \\
17=r^2 \\ \\
\hbox{the equation is:} \\
(x+3)^2+(y-2)^2=17$

Plug the coordinates of the points into the equation and check:
$C(-1,-2) \\
(-1+3)^2+(-2-2)^2=17 \\
2^2+(-4)^2=17 \\
4+16=17 \\
20=17 \\
not \ true \\ \\
D(-6,3) \\
(-6+3)^2+(3-2)^2=17 \\
(-3)^2+1^2=17 \\
9+1=17 \\
10=17 \\
not \ true$

$E(-3,-3) \\
(-3+3)^2+(-3-2)^2=17 \\
0^2+(-5)^2=17 \\
25=17 \\
not \ true \\ \\
F(-2,6) \\
(-2+3)^2+(6-2)^2=17 \\
1^2+4^2=17 \\
1+16=17 \\
17=17 \\
true$

The answer is F(-2,6).

8 0

3 years ago

(4x-3)(2x^2-7x+1) what is the product of this please help!

goblinko [34]

Answer:

$8x^{3}-34x^{2}+25x-3$

Step-by-step explanation:

In order to solve this problem, lets take the two terms in the binomial (4x and -3) and, for each one, multiply them by each term in the trinomial (2x^2, -7x, and 1):

$(4x-3)(2x^{2}-7x+1)$

$(4x*2x^{2})+(4x*-7x)+(4x*1)+(-3*2x^{2})+(-3*-7x)+(-3*1)$

$8x^{3}+(-28x^{2})+4x+(-6x^{2})+21x+(-3)\\$

$8x^{3}-28x^{2}+4x-6x^{2}+21x-3$

Let's combine like terms to get our final answer:

$8x^{3}-28x^{2}-6x^{2}+4x+21x-3$

$8x^{3}-34x^{2}+25x-3$

6 0

3 years ago

In the polynomial below, what number should replace the question mark to produce a difference of squares? X^2 + ?x -49 A. 0 B. 1

Mrac [35]

Answer:

Step-by-step explanation:

The difference of squares formula is a² - b² = (a + b)(a - b). We want this polynomial to be in the form a² - b². We notice that x² and 49 are perfect squares already which means that we don't need the x term. To get rid of it, its coefficient must be 0 because 0 times anything is 0, thus the x term will be removed and we'll be left with x² - 49 which is a difference of squares.

5 0

3 years ago

C=5/9(F-32) solve for F

mina [271]

F= 9/5 C + 32
or
F= 9/5(C+32)
 Hoped this helped:)

7 0

3 years ago

Write an exponential model given the two points (10,130) and (11,240).

enot [183]

Answer:

y = 130(24/13)^(x -10)

Step-by-step explanation:

The y-value changes by a factor of 240/130 = 24/13 for a unit change in the x-value. This means we can write the function as though it had an initial value of 130 and a growth factor of 24/13, translated 10 units to the right.

y = 130(24/13)^(x -10)

_____

Additional comment

This can also be written in the form ...

y = a·e^(kx)

where a=130·(24/13)^(-10) ≈ 0.28266, and k=ln(24/13) ≈ 0.61310

7 0

3 years ago