Answer:
(u o w) (7) = 22
(w o u) 7) = 8
Step-by-step explanation:
We are given:
[tex]u(x)= x^2+6\\w(x)= \sqrt{x+9}[/tex]
We need to find:
a) (u o w) (7)
First we will find (u o w) (x) and then we will find (u o w) (7)
We know that (u o w) (x) = u(w(x))
Put value of w(x) into u(x)
we have:
[tex]u(x)=x^2+6\\Put\: x =\sqrt{x+9}\\u(w(x))=(\sqrt{x+9})^2+6\\u(w(x))=x+9+6\\ u(w(x))=x+15[/tex]
Now finding (u o w) (7)
We know that: (u o w) (7) = u(w(7))
[tex]u(w(x))=x+15\\Put\:x=7\\u(w(7))=7+15\\u(w(7))=22[/tex]
So, (u o w) (7) = 22
b) (w o u) (7)
First we will find (w o u) (x) and then we will find (w o u) (7)
We know that (w o u) (x) = w(u(x))
Put value of u(x) into w(x)
we have:
[tex]w(x)= \sqrt{x+9}\\Put\:x=x^2+6\\w(u(x))= \sqrt{(x^2+6)+9}\\w(u(x))= \sqrt{x^2+6+9}\\w(u(x))= \sqrt{x^2+15}[/tex]
Now finding (w o u) (7)
We know that (w o u) (7) = w(u(7))
[tex]w(u(x))= \sqrt{x^2+15}\\Put\:x=7\\w(u(7))= \sqrt{(7)^2+15}\\w(u(7))= \sqrt{49+15}\\w(u(7))= \sqrt{64}\\w(u(7))= 8[/tex]
So, (w o u) (7) = 8
There are five boys to every nine girls in an introductory engineering course .if there are 364 students enrolled in the course , how many are boys ?
Answer:
234
Step-by-step explanation:
So what we know is that
5x+9x= students
This equation is saying that for every 5 boys there are 9 girls
we can then plug in 364 for the number of students and add like terms
This means that 14x=364
this means that x=26
This means that there are 26 sets of 5 boys and 9 girls
this means that there are
130 boys
234 girls
Simplify the rational expression by rationalizing the denominator √15/√6x
Answer:
√10/2x
Step-by-step explanation:
Multiply by √6 on the top and bottom to rationalize the denominator.
(√15×√6)/(√6x×√6) = √90/6x = (√9×√10)/6x = 3√10/6x = √10/2x
The table below shows the cube roots of different numbers: Number (x) 8 27 64 125 Cube root (y) 2 3 4 5 Part A: Does the table represent y as a function of x? Justify your answer. (5 points) Part B: The total cost f(x), in dollars, for renting a bike for x hours is shown below: f(x) = 15 + 20x What is the value of f(80), and what does f(80) represent?
Phil bought two hamburgers and a milk shake
for $10.30. Janice bought three hamburgers and
a milk shake for $14.80. What is the cost of the
two milk shakes?
A. $1.30
B. $1.45
C. $2.60
D. $4.50
Answer:
C.
Step-by-step explanation:
[tex]\left \{ {{2x+y=10,3} \atop {3x+y=14,8}} \right.[/tex]
[tex]\left \{ {{y=10,3-2x} \atop {y=14,8-3x}} \right.[/tex]
10,3-2x=14,8-3x
x=4,5 - one hamburger
y=1,3 - one milk shake
OR:
$14,8-$10,3=$4,5 - one hamburger
2*4,5+y=10,3
y=1,3 - one milk shake
2y=2,6
x^3 + 5x^2 + 2x + 10 = 0
Let's solve your equation step-by-step.
x3+5x2+2x+10=0
Step 1: Factor left side of equation.
(x+5)(x2+2)=0
Step 2: Set factors equal to 0.
x+5=0 or x2+2=0
x=−5
Answer:
x=−5
What percent of 25 is 50
Answer:
50 is 200% of 25
Step-by-step explanation:
50 is 200 percent of 25.
To find the percentage of one number in relation to another, we can use the following formula:
(Percentage / 100) * Base = Amount
In this case, we want to find what percentage of 25 is 50.
Let's use x to represent the percentage:
(x / 100) * 25 = 50
To solve for x, we can divide both sides of the equation by 25:
(x / 100) = 50 / 25
Simplifying:
(x / 100) = 2
Next, we can cross-multiply:
x = 100 * 2
Simplifying:
x = 200
Therefore, 50 is 200% of 25.
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What are the like terms in the expression 8 + x squared minus 4 x cubed + 5 x + 2 x squared?
8, 5 x
x squared, 2 x squared
8, 5 x 2 x squared
x squared, Negative 4 x cubed, 2 x squared
Answer:
B; x squared, 2x squared
Step-by-step explanation:
I took the test :))
Answer:
B; x squared, 2x squared
Step-by-step explanation:
hopefully this helped you
30 points! Need help ASAP!
2. If Mr. Escobar had an initial investment of $50,000 and
the annual interest rate was 4%, how long would it take
to double his initial investment?
A)16 year
B)17
C)18
None of the above
Answer:
None of the above
Step-by-step explanation:
The correct answer to the given question is None of the above
Assuming simple rate
The calculation is shown below
$50,000 * 4% = $2,000
this makes an interest of $2,000 per year.
$2,000 / $50,000 = 25 years
It will take 25 years to double Mr. Escobars initial investment so the answer is none of the above.
Esma and Hunter were trying to solve the equation:
x2 + 8x = 2x - 8
They both agreed they should first subtract 2x and add 8 to both sides and rewrite the equation as
22 + 6x + 8 = 0.
Then Esma said, "I can complete the square. I can add 1 to both sides to rewrite this equation as
22 + 6x + 9 = 1, factor, and solve using square roots."
Hunter said, "I'll factor the left-hand side of the equation as (x + 2)(x + 4) and solve using the zero
product property."
Whose solution strategy would work?
Answer:
Both
Step-by-step explanation:
Khan
Both of their strategies completing the square and factoring the left-hand side would work.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given a quadratic equation x² + 8x = 2x - 8.
They both agreed that first subtract 2x and add 8 to both sides and rewrite the equation as
x² + 6x + 8 = 0.
Both of their strategies would work.
As x² + 6x + 9 = 1
(x + 3)² = 1.
x + 3 = ± 1
x = ± 1 - 3.
x = - 2 or - 4.
x² + 6x + 8 = 0.
x² + 4x + 2x + 8 = 0.
x(x + 4) + 2(x + 4) = 0.
(x + 4)(x + 2) = 0.
x = - 4 or x = - 2.
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Fifteen hungry kittens found a bucket of sausages. Each time they cut a sausage or a part of a sausage, they cut it into exactly two new pieces. They made 20 cuts in all and each kitten got 2 (maybe unequal) pieces of sausage. How many sausages were in the bucket?
Answer:
There is a total of 10 sausages. I am 100% sure.
Step-by-step explanation:
A bucket of sausages fed 15 hungry kittens. Each sausage or half of a sausage is sliced into two pieces. They chopped 20 sausages and gave each kitten two (perhaps unequal) portions. Therefore, there were 34,952 sausages in the bucket.
At the start, there is one sausage bucket, and the 15 kittens want to share it.
The first cut divides the sausage into two pieces.
After the second cut, there are four pieces of sausage.
After the third cut, there are eight pieces.
After the fourth cut, there are 16 pieces.
As we can observe, the number of pieces of sausage doubles with each cut. After 20 cuts, there will be 2²⁰ (2 raised to the power of 20) pieces of sausage.
Now, since each kitten received two pieces of sausage, the total number of sausages in the bucket can be calculated by dividing the total number of pieces by 2 × 15 (since there are 15 kittens).
Total sausages = (2²⁰) / (2 × 15)
Let's simplify this:
Total sausages = 2¹⁹ / 15
Now, let's calculate the value:
Total sausages = 524,288 / 15
Total sausages = 34,952.53
Since you can't have a fraction of a sausage, we need to round down to the nearest whole number.
Therefore, there were 34,952 sausages in the bucket.
To know more about number
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87 cities were surveyed to determine sports teams. 22 had baseball, 23 had football, 19 had basketball, 12 had baseball and football, 10 had baseball and basketball. 13 had football and basketball. 5 had all three. How many had only basketball?
Answer:
1 had only basketball hope that helps
Step-by-step explanation:
Someone please help me with this one, I don't want to get it wrong!
The Oliver Company plans to market a new dish washing detergent. The selling price will be $4
per container. Variable costs are estimated to be 46% of the selling price. Fixed costs are
estimated to be $6,115. What is the break-even point? That is, how many containers of the
detergent the company must sell in order to end up with no loss and no profit in its operations?
(Round your final answer to the nearest whole number).
Answer: 2,831 containers
Step-by-step explanation:
To find the breakeven point, use the following formula:
= Fixed cost / Contribution margin
Fixed cost = $6,115
Contribution margin = Selling price - Variable cost
= 4 - (4 * 46%)
= $2.16
Breakeven point = 6,115/2.16
= 2,831 containers
On a lake, Carol rowed a boat for mile. Then Luke rowed
8
3
the boat for mile. How far did Carol and Luke row in all?
8
Simplify the answer if possible.
A А
5
mile
8
B
3
mile
64
1
mile
4
D
1
mile
2.
Answer:
4/10
Step-by-step explanation:
add the miles up so you can find it out
Given f(x)=14(5−x)2 what is the value of f(11)?
Answer:
f(x)=14(5−x)2
f(11)=14(5-11)2
f(11)=14*-6*2
f(11)=-84*2
f(11)= -168
Step-by-step explanation:
Answer:
it would be -82
Step-by-step explanation:
Howard buys a new comforter set for 15% off the original price of 54$.What is the sale price?
Answer:
$45.90
Step-by-step explanation:
What 15% off means is 85% of the original price ($54). 85% is the same as 17/20. Multiply 17/20 by 54 (or multiply 3/20 by 54 and subtract that from 54) to get the sale price.
(17 * 54)/20 (Multiply 17 by 54)
918/20 (Reduce if needed)
459/10 (Divide 459 by 10)
45.9
The sale price of the comforter is $45.90.
Aisha has a smart phone data plan that costs $25 per month that includes 4 GB of
data, but will charge an extra $15 per GB over the included amount. How much
would Aisha have to pay in a month where she used 3 GB over the limit? How much
would Aisha have to pay in a month where she used went over by x GB?
Answer:
20
Step-by-step explanation:
15 POINTS!!!IF YOU HELP ME!!!
1. A shopper bought a 10-pound bag of apples for $12.50. What was the unit price? Show your work. A $0.63 C $6.25 B $1.25 D $12.50
160% of 30
I’ve been stuck on this question for hours I REALLY need help
Answer:
The answer is 48
Step-by-step explanation:
160% is the same as 1.60
A percent of something means you have to multiply them together
1.60 times 30=48
Hope this helps!!
The train station clock runs too fast and gains 5 minutes every 3 days.
How many minutes and seconds will it have gained at the end of 7 days?
9514 1404 393
Answer:
mm:ss = 11:40
Step-by-step explanation:
We assume the amount of gain is proportional to the time that passes.
g/7 = 5/3
g = 7(5/3) = 35/3 = 11 2/3 . . . . minutes
The clock will have gained 11 minutes and 40 seconds after 7 days.
Pls help me with math ASAP
Answer:
Its c
Step-by-step explanation:
4 1/3 times 6
2 3/5 times 3 1/3
Answer:
8
8 2/3
Step-by-step explanation:
Mrs. Lenny is putting up a fence around her garden to keep the bunnies
out. The length of the garden is 8 feet more than the width. If the perimeter
of the garden is 308 feet, what is the length and the width?
Answer:
Length= 81 feet
width = 73 feet
Step-by-step explanation:
P=2{(8+W)+W}
308=2(8+2W)
308=16+4W
308-16=4W
292=4W
W=73
And length = 8+W
8+73=81
Nelson and 3 friends rent a bounce house. It cost $50 for setup and $30 per hour. If they all split the cost, how much will each pay if they rent the bounce house for 5 hours? (HOW DID YOU GET THE ANSWER?)
A. 50
B. 3 25/5
C. 3
D. 22
Answer:50
explanation:
30x5 is 150 and 150 plus 50 is 200 200 divided by 4 is 50
Please someone help me do number 9
Answer:
j=-15
Step-by-step explanation:
Since it it just the exponent of x, we will only see what x's exponent will be:
[tex]x^{6} +x^{-21}[/tex]
Add 6 and -21:
6-21= -15
j=-15
Click the picture
Giving brainlist
Answer:
5
The value of y is also 5!
The value of pair (x,y) is (5,5)
Hopefully this helped! :D
-LavenderVye
The cost of hiring a taxi consists of a fixed cost of $3 plus $0.5 per kilometer distance travelled.
Write an expression in terms of y for hiring a taxi for y kilometers.
Can someone please help and thank you
Answer:
F
Step-by-step explanation:
Thomas is saving up to buy the new Xbox One. He needs to save at least $500. For his birthday he received $275.
He also makes $30 a week working at McDonalds. What is the least number of weeks it will take him to have the
money?
please help me right now i need it
Answer:
8 weeks
Step-by-step explanation:
Which expressions are equivalent to 3 (62)?
Select each correct answer.
3(60 + 20)
3(6+2)
3(6+56)
03 (60+2)
Answer:
3(6 + 52)
Step-by-step explanation:
3(60 +20) = 3(80) ❌
3(6+2) = 3(8) ❌
3(6+56) = 2(62) ✅
