For the function f(x)=x^2-12 find (f^-1)(4)

Answers

Answer 1

Answer: f(x) = x^2 - 12
y = x^2 - 12
y + 12 = x^2
x = sqrt(y + 12)
(f^-1)(x) = sqrt(x + 12)

(f^-1)(4) = sqrt(4 + 12) = sqrt(16) = 4
(f^-1)(4) = 4

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A city council consists of six democrats and seven republicans. if a committee of five people is selected, find the probability of selecting three democrats and two republicans.

Answers

Given that a city council consists of six democrats and seven republicans, the probability of selecting three democrats and two republicans if a committee of five people is to be selected is given by

$( ^6C_3* ^7C_2)/( ^(13)C_5) = (20*21)/(1,287) \n \n = (420)/(1,287) =0.3263$

Help me please! I don't know where to start!

Answers

week 4 = 8miles
week 16 = 26 miles
constant increase
16 - 4 = 12 weeks
26 - 8 = 18 miles
so...
in 12 weeks she increased 18 miles
12x=18
x= 18/12
x=1.5 per week

Widget wonders produces widgets. they have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.....the company also discovered that it costs $103. to produce 3 widgets, $163 to produce 7 widgets, and $328 to produce 12 find the total cost of producing 2 widgets

Answers

$c(x)=ax^2+bx+c \n \nc(3)=103 \nc(7)=163 \n c(12)=328 \n \na * 3^2+b * 3 + c=103 \na * 7^2 + b * 7 + c= 163 \na * 12^2 + b * 12 + c =328 \n \n9a+3b+c=103 \n49a+7b+c=163 \n144a+12b+c=328$

$\hbox{the first two equations:} \n9a+3b+c=103 \ \ \ \ \ |* (-1) \n49a+7b+c=163 \n \n-9a-3b-c=-103 \n\underline{49a+7b+c=163 \ \ \ \ \ } \n40a+4b=60 \ \ \ \ \ \ \ \ \ \ \ |/ 4 \n10a+b=15$

$\hbox{the second and third equation:} \n49a+7b+c=163 \ \ \ \ \ \ \ |* (-1) \n 144a+12b+c=328 \n \n-49a-7b-c=-163 \n\underline{144a+12b+c=328 \ \ } \n95a+5b=165 \ \ \ \ \ \ \ \ \ \ \ \ |/ 5 \n19a+b=33$

$\hbox{set up a new system of equations:} \n10a+b=15 \ \ \ \ \ \ \ \ |* (-1) \n19a+b=33 \n \n-10a-b=-15 \n\underline{19a+b=33 \ \ \ \ \ \ } \n9a=18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ 9 \na=2 \n \n10a+b=15 \n10 * 2+b=15 \n20+b=15 \ \ \ \ \ \ \ \ \ \ |-20 \nb=-5$

$49a+7b+c=163 \n49 * 2+7 * (-5)+c=163 \n98-35+c=163 \n63+c=163 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |-63 \nc=100 \n \n\hbox{the equation for the cost of maxing x widgets:} \nc(x)=2x^2-5x+100 \n \nc(2)=2 * 2^2-5 * 2+100=8-10+100=98$

The cost of producing 2 widgets is $98.

The diagram shows two parallel lines a andb cut by transversal lines.
Part A
What is an equation that can be used to
solve for x?
Part B
What is the value of x?

Answers

Answer:

y = 180 - (36 + 65)

x = 69

Step-by-step explanation:

Final answer:

To solve for x in the given diagram of parallel lines cut by a transversal, use the concept of corresponding angles. The value of x is 60°.

Explanation:

Part A: To solve for x, we can use the corresponding angles formed by the transversal and the parallel lines. One of the corresponding angles is x + 60°. Since the other corresponding angle is 120°, we can set up the equation x + 60° = 120°. Solving for x, we find that x = 60°.

Part B: The value of x is 60°.

Learn more about parallel lines here:

brainly.com/question/32035102

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one person can paint a room in 5 hours and the other takes 8 hours working together how long will it take the two of them if they're working together please work the problem out and explain it to me

Answers

ok so find how much work each can do per hour

irst person is 5 hours to do all room
therefor
1 hour=1/5 room

2nd person takes 8 hours to do all room
therefor
1 hour=1/8 room

since working together, add times

1 hour=1/5+1/8
make denoms same
1hour=8/40+5/40=13/40

13/40 room times x hours=1 whole room
multiply both sides by 40/13 to cleaf raction (13/40 times 40/13=520/520=1)

xhours=40/13hours
xhours=3 and 1/13 hours

What multiplies to be -18 and adds to be -9?

Answers

IMPORTANT:
If you're trying to factor a quadratic in Algebra I:
There are no two integers that can solve this problem!
Your quadratic is prime!

If you're trying to solve a quadratic (find x):
The factoring approach will not work for the same reasons listed above.
Try using splitting the middle or the quadratic formula instead.

Here's how you would solve it from a more advanced approach.
If you don't know what this stuff is, just ignore it.
ab = -18, a + b = -9
Find a in terms of b.
a = -9-b
Substitute this for a in the first equation.
(-9-b)b = -18
-9b-b² = -18
Multiply everything by -1 to get rid of all these negative signs.
b² + 9b = 18
Bring over that 18.
b² + 9b - 18 = 0
Apply the quadratic formula.
(a = 1, b = 9, c = -18)
$(-b\pm√(b^2-4ac))/(2a)=(-9\pm√(9^2-4(1)(-18)))/(1*2)=(-9\pm√(81+72))/(2)=(-9\pm√(153))/(2)=\boxed{(-9\pm3√(17))/(2)}$
If you need to write two distinct numbers, just write out one with a + and one with a - in place of the plus-minus sign.

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