Answer:
f
−
1
(
x
)
=
x
−
12
5
Step-by-step explanation:
HELP PLS +10 BRAINLY POINTS (SHOW WORK PLS)
Hi there!
[tex]\large\boxed{\text{System G.}}[/tex]
For a system to have an infinite number of solutions, both expressions must be equal. We can go through each system and determine this:
F:
x + 2 = y
4 = 2y - x
If we rearrange so that both are in the same format, we get:
x + 2 = y
x + 4 = 2y
These cannot be equal, so they do not have infinite solutions.
G:
2y + 6 = 4x
-3 = y - 2x
Rearrange:
2y + 6 = 4x
-y - 3 = -2x
We can try to make the bottom equation look like the top equation by multiplying all terms by -2. We get:
2y + 6 = 4x. This is the same as the top, so G has infinite solutions.
Just to be sure, we can go through the others:
H:
y + 3 = 2x
4x = 2y - 3
Rearrange:
y + 3 = 2x
2y - 3 = 4x. Cannot be equal to the other equation.
J:
y = 2x - 5
y = 2x - 2. Not equal.
The correct answer is G.
Cedar Point has 17 roller coasters. If you want to ride at least 15 of them, how many different combinations of roller coasters can you ride? NO LINKS!!!
================================================
Explanation:
I'll be using the formula
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
which is the nCr combination formula. We use nCr instead of nPr because the order of coasters doesn't matter. The whole time, the value of n stays fixed at n = 17 which is the total number of coasters to pick from.
While n is constant, the value of r will vary. It ranges from r = 15 to r = 17 inclusive of both endpoints. In other words, r will take on values from the set {15,16,17}. So we have three cases to consider. The r value is how many coasters we select. This is due to the "at least 15" which means "15 or more".
-----------------------
If you ride r = 15 coasters, then we have the following number of combinations
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{17} C _{15} = \frac{17!}{15!*(17-15)!}\\\\_{17} C _{15} = \frac{17!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16*15!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16}{2!}\\\\_{17} C _{15} = \frac{17*16}{2*1}\\\\_{17} C _{15} = \frac{272}{2}\\\\_{17} C _{15} = 136\\\\[/tex]
There are 136 ways to ride exactly 15 coasters (when selecting from a pool of 17 total). The order doesn't matter.
We'll use this result later, so let x = 136.
-----------------------
If r = 16, then we follow the same steps as above. You should get 17C16 = 17
There are 17 ways to ride 16 coasters where order doesn't matter. Effectively this is the same as saying "there are 17 ways of picking a coaster that you won't ride"
Let y = 17 so we can use it later
-----------------------
Lastly, if r = 17, then nCr = 17C17 = 1 represents one way to ride all 17 coasters where order doesn't matter.
Let z = 1
-----------------------
Add up the values of x, y, and z to get the final answer
x+y+z = 136+17+1 = 154
Elam can wire a light in 40
minutes. Michael can wire a
light in 60 minutes. How long
would it take them to wire the
light together?
Answer:
24 minutes
Step-by-step explanation:
We use 1/a + 1/b = 1/c
where a and b are the individual times and c is the time together
1/40 + 1/60 = 1/c
Multiply each side by 120c
120c( 1/40 + 1/60 = 1/c)
3c + 2c = 120
5c = 120
Divide each side by 5
5c/5 = 120/5
c = 24
Answer: 24 minutes
Step-by-step explanation: To solve this kind of a problem which is called a work problem, it's important to understand the following idea.
Since Elam can wire a light in 40 minutes, we know that in 1 minute,
Elam can wire 1/40 of the light and in 2 minutes, Elam can wire 2/40 of it.
Therefore, in t hours, Elam can wire t/40 of the light.
The same applies for Michael, in t hours, he can wire t/60 of the light.
So to solve the problem, we use the following formula:
Part of job done by Elam + part of job done Michael = 1 job done
The part of the job done by Elam is t/40 and t/60 for Michael.
So we have t/40 + t/60 = 1.
Now multiply both sides by 120 to get 3t + 2t = 120
or 5t = 120 so t = 24.
So it takes 24 minutes if they work together.
Uhm does anyone know what 8x is as an coefficient?
Answer:
yes 8x is a coefficient
Step-by-step explanation:
because I know but if I'm wrong than sry
i need help ive been stuck on these questions
Which choices are equivalent to the fraction below? Check all that apply.
Answer:
Step-by-step explanation:
It's A and B happy learning
Evaluate the expression when x=7 and y=-3. 5y2-x
Leia needs to make at least 40 necklaces to sell at a craft show. So far, she has made 7. Which inequality shows the
number of necklaces, n, that she still needs to make?
A). n - 7 less than or equal to 40
B) n - 7 greater than or equal to 40
C). n + 7 less than or equal to 40
D). n + 7 greater than or equal to 40
Answer:
The answer is D
Hope this helps!
Brainliest??
Answer:
D
Step-by-step explanation:
the answer is D because if she already made 7 she need to add n to 7 to get 40 or greater
34. find the square root of 298116 by
using long division method *
Answer:
hope it is helpfulto you
Answer:
Step-by-step explanation:
The answer is 546
hup meh please........
Answer:
the answer is
A..0.248 HOPE IT HELPEDWhich problem can be solved using the equation below?
Answer:
Mr. peter puts 24 students into groups of 8. How many groups are there?
Step-by-step explanation:
Whenever the word "groups" is used, it typically means to divide. Because we see the word "groups", it would be reasonable to assume that you will be dividing something.
What times 4 gives me 1/5
Answer:
0.05
Step-by-step explanation:
Because 1/5 divided by 4 gives you 0.05 or 1/20
what is the sum in the simplest from , 4 1/2 + 1 3/5
Answer:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form:
61 / 10
Decimal Form:
6.1
Mixed Number Form:
6 1/10
The nth term of sequence is n2 + 20
Work out the first three times of sequence
How many times in the sequence are less than 50
Answer:
First three terms:
22,24,26
There are 15 terms in the sequence that are 50 or less, yet only 14 if its just less than 50.
Answers:
The first three terms are 21, 24, 29
5 terms of the sequence less than 50.
======================================================
Explanation:
Plug in n = 1 to find that n^2+20 = 1^2+20 = 1+20 = 21. The first term is 21.
Repeat for n = 2 and you should get 2^2+20 = 24 as the second term.
The third term is 29 through similar steps, but this time you use n = 3 of course.
The first three terms are 21, 24, 29
It's effectively the first three perfect squares 1, 4, 9 but we have a tens digit of 2 stuck to the left of each value.
--------------------
We want to find when n^2+20 is less than 50. We could keep plugging values of n into that expression and record if the result is less than 50 or not, then tally those occurrences. You should record 5 such occurrences.
Or we could do a bit of algebra like so
n^2+20 < 50
n^2 < 50-20
n^2 < 30
sqrt(n^2) < sqrt(30)
n < sqrt(30)
On a calculator, sqrt(30) is roughly 5.4772 which means n < 5.4772. If n is a a natural number, then the largest it can get is n = 5 to ensure n^2+20 is less than 50.
We can see that,
n^2+20 = 5^2+20 = 45 when n = 5n^2+20 = 6^2+20 = 56 when n = 6This helps show that n = 5 is the largest n to make n^2+20 < 50 a true statement. This means that there are 5 terms of the sequence less than 50.
A system of equations is shown below: y = 8x − 2 y = 9x − 7 What is the solution to the system of equations? (1 point) (−5, 38) (−5, −38) (5, 38) (5, −38)
Answer:
(5,38)
Step-by-step explanation:
Use graphing calculator and the answer should be the point where the line crosses each other.
Answer:
5,38
Step-by-step explanation:
its correct!
how to find the vat on 14% of 1800
Answer:
[tex]14 \ 100 \1800[/tex]
Your company is planning to air a number of television commercials during a television network's presentation of the an awards show. The network is charging your company $1.9 million per 30-second spot. Additional fixed costs (development and personnel costs) amount to $500,000, and the network has agreed to provide a discount of $160,000 x for x television spots.
Required:
Write down the cost function C, marginal cost function C’, and average cost function
This question is incomplete, the complete question is;
Your company is planning to air a number of television commercials during a television network's presentation of the an awards show. The network is charging your company $1.9 million per 30-second spot. Additional fixed costs (development and personnel costs) amount to $500,000, and the network has agreed to provide a discount of $160,000√x for x television spots.
Required:
Write down the cost function C, marginal cost function C’, and average cost function
Answer:
- The the cost function is 500,000 + 1,900,000x - 160,000√x
- the marginal cost function is 1,900,000 - (80000 /√x )
- The average cost function is 1,900,000 + [ 500,000 / x ] - [ 160,000 / √x ]
Step-by-step explanation:
Given the data in the question;
cost per spot = $1.9 million
Additional cost = $500,000
discount = $160,000√x
Let C(x) represent the cost ;
Cost x television spot = cost per spot × Number pf spots
Cost x television spot = $1.9 million × x
Cost x television spot = $1,900,000x
Now, the television set total cost will be;
C(x) = television cost + additional cost - discount
C(x) = 500,000 + 1,900,000x - 160,000√x
Therefore, The the cost function is 500,000 + 1,900,000x - 160,000√x
Marginal Cost Function;
Cost function C(x) = 500,000 + 1,900,000x - 160,000√x
we differentiate with respect to x
C'(x) = d/dx( 500,000 + 1,900,000x - 160,000√x )
= d/dx( 500000 ) + 1,900,000d/dx -160,000 d/d( √x )
= 0+ 1,900,000(1) -160,000( 1 / 2√x )
= 1,900,000 - (160,000 / 2√x )
= 1,900,000 - (80000 /√x )
Therefore, the marginal cost function is 1,900,000 - (80000 /√x )
Average cost function;
Average cost function = C(x) / x
we substitute
Average cost function = [500,000 + 1,900,000x - 160,000√x] / x
= [500,000 / x ] + [1,900,000x / x ] - [ 160,000√x / x ]
= [ 500,000 / x ] + 1,900,000 - [ 160,000√x / x ]
= 1,900,000 + [ 500,000 / x ] - [ 160,000 / √x ]
Therefore, The average cost function is 1,900,000 + [ 500,000 / x ] - [ 160,000 / √x ]
Determine the area for the figure below.
Answer:
Area = 18
Step-by-step explanation:
Trapezoid formula is Area = (a + b) * h/2
Area = 5 + 7 * 3/2
Area = 18
Enter the coordinates of the vertex of the graph of y = 2(x + 5)2 − 4.
Vertex: (
,
)
9514 1404 393
Answer:
(-5, -4)
Step-by-step explanation:
Compare the given equation to vertex form:
y = a(x -h)² +k
You see that a=2, h=-5, k=-4.
The vertex is (h, k) = (-5, -4).
What is the value of N in this proportion 16/40= 8/n
Answer:
n = 20
Step-by-step explanation:
[tex]\frac{16}{40} = \frac{8}{n}[/tex]
Cross multiplication would result in:
16 * n = 8 * 40
16n = 320
n = 320 / 16
n = 20
Therefore the value of "n" in this proportion is 20.
Hope this helps!
Hi! Kan someone fill in the blanks with either addition, subtraction, multiplication, or division?
I had some trouble finding the answer :/
Goldilocks needs to find at least 12 lbs gold and 18 lbs silver to pay monthly rent. Each day in Mine 1 she finds 2 lbs gold and 2 lbs silver. Each day in Mine 2, she finds 1 lb gold and 3 lbs silver. Set up and solve using either LPsolve or on-line solver How many total days in the mines
Answer:
Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days
Step-by-step explanation:
Requirement : 12 Ibs gold and 18 Ibs silver to pay monthly rent
Mine 1 ; 2 Ibs of gold , 2Ibs of silver.
Mine 2; 1 Ib of gold , 3 Ibs of silver
using LP
Gold : aX1 + bX2 ≥ 12 ---------- ( 1 )
Silver: cX1 + dX2 ≥ 18 --------- ( 2 )
where; X1 = days spent in Mine 1
X2 = days spent in Mine 2
Total days spent in mines : X1 + X2 =
a = Gold found in mine 1 = 2
b = Gold found in mine 2 = 1
c = silver found in mine 1 = 2
d = silver found in mine 2 = 3
Back to equations 1 and 2
2X1 + X2 ≥ 12 ----------- ( 3 )
2X1 + 3X2 ≥ 18 ------------ ( 4 )
solving equations 3 and 4
= 0 + 2X2 ≥ 6 ∴ X2 ≥ 3 days ( days spent in mine 2 )
Input value into ( 3)
2X1 ≥ 12 - 3 = 9
∴ X1 ≥ 4.5 days ( days spent in mine 1 )
Total number of days in the mines = 4.5 days + 3 days ≥ 7.5 days
If g(x)= x+1/x-2 and h(x)= 4-x, what is the value of (g•h)(-3)?
Answer:
8/5
Step-by-step explanation:
First find h(-3)
h(-3)= 4-(-3) = 4+3 = 7
Then take this result and find g(h(-3)) = g(7)
g(7) = (7+1)/( 7-2) = 8/5
find a value of (2power-1*4power-1)
2^( - 1 ) × 4^( -1 ) =
2^( -1 ) × 2^( 2 × ( - 1) ) =
2^( - 1 ) × 2^( - 2 ) =
2^( - 1 - 2 ) =
2^( - 3 ) =
1/ 2^( 3 ) =
1/8
find the product of 5/8 by the reciprocalof -3/8
Answer:
-5/3
Step-By-Step-Solution:
Reciprocal of-3/8 = -8/3
Product = 5/8 × -8/3 = -5/3
Hope that this helps!
Please help! And hurry
Answer:
the answer is b
Step-by-step explanation:
Answer:
b: 78.5cm²
Step-by-step explanation:
answer is b my friend
3 to the fourth power +9
Answer:
81
Step-by-step explanation:
3*3=9
9*3=27
27*3=81
Answer: 90
Step-by-step explanation:
3 to the fourth power = 81
81 + 9 = 90
Is 3.24538 rational
Answer:
yes
Step-by-step explanation:
3.24538 is rational
Huilan is 13 years younger than Thomas. The sum of their ages is 33. What is Thomas's age?
Answer:
Thomas is 20 years old
Step-by-step explanation:
33 - 13 = 20
PLEASE HELP ASAP/ SOON
THANK YOU
Find the sum, if it exists, of the infinite geometric series that is related to the infinite geometric sequence {1,521, ; 1,369 ; 1,232; ...}. Round the value of r to the nearest hundredth, if needed
S = 16,643
S = 15,210
The infinite geometric series diverges.
S = 12,560
9514 1404 393
Answer:
(b) S = 15,210
Step-by-step explanation:
The common ratio is ...
r = 1369/1521 ≈ 0.90
So, the sum is ...
S = 1521/(1 -r) = 1521/0.10 = 15,210 . . . . . sum of the series
9514 1404 393
Answer:
(b) S = 15,210
Step-by-step explanation:
The common ratio is ...
r = 1369/1521 ≈ 0.90
So, the sum is ...
S = 1521/(1 -r) = 1521/0.10 = 15,210 . . . . . sum of the series