Answer:
x=20
Step-by-step explanation:
Add like terms:
4x + 12x = 16x
16x = 320
320/16 = 20
Vanity Fair was having a blow out sale on shorts and t-shirts. Trevor bought 12 shorts and t-shirts. The shorts were on sale for $12 each and t-shirts were $6 each. Trevor spent $102. how many shorts and t-shirts did Trevor buy? Let x= shorts and y= t-shirts.
Answer:
shorts = 5and
t-shirts 7
Step-by-step explanation:
step one:
given
Let x= shorts and y= t-shirts
Trevor bought 12 shorts and t-shirts.
x+y=12----------1
sale for $12 each and
t-shirts were $6 each
12x+6y=102---------2
the sytems of equation is
x+y=12----------1
12x+6y=102---------2
Step two:
from 1, x=12-y
put x=12-y in 2
12(12-y)+6y=102---------2
144-12y+6y=102
144-6y=102
144-102=6y
42=6y
y=42/6
y=7
put y=7 in 1
x+7=12----------1
x=12-7
x=5
shorts = 5and
t-shirts y
The profit function P(x), revenue function, R(x), and cost function, C(x), are related by the equation P(x) = R(x) – C(x). Andrew has determined that the revenue and cost functions for a new product line at his business are given by these functions. R(x)=8x and C(x)=100+3x What is the profit function for Andrew's new product line?
Answer: 8x - 1200
Step-by-step explanation: Because I did the problem
The profit function for Andrew's new product line is P(x) = 5x - 100.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, The profit function P(x), revenue function, R(x), and cost function, C(x), are related by the equation P(x) = R(x) - C(x).
The revenue and cost functions for a new product line at his business are given by these functions. R(x) = 8x and C(x) = 100 + 3x.
Therefore, P(x) = 8x - (100 + 3x).
P(x) = 8x - 100 - 3x.
P(x) = 5x - 100.
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Bacteria of species A and species B are kept in a single environment, where they are fed two nutrients. Each day the environment is supplied with 10,560 units of the first nutrient and 31,510 units of the second nutrient. Each bacterium of species A requires 2 units of the first nutrient and 5 units of the second, and each bacterium of species B requires 1 unit of the first nutrient and 6 units of the second. What populations of each species can coexist in the environment so that all the nutrients are consumed each day? Incorrect: Your answer is incorrect. Of species A
Answer:
We require 4,550 of species A and 1,460 of species B that can coexist in the environment so that all the nutrients are consumed each day
Step-by-step explanation:
Let n₁ be the population of A required and n₂ be the population of B required.
Now we require 2 units of the first nutrient for species A and one unit of the first nutrient for species B. The total nutrients required by species A is 2n₁ and that by species B is 1n₂ = n₂. So, the total nutrients required by both species A and B is 2n₁ + n₂. Since this equals the quantity of the first nutrient which is 10,560, then 2n₁ + n₂ = 10,560 (1)
Now we require 5 units of the second nutrient for species A and 6 units of the second nutrient for species B. The total nutrients required by species A is 5n₁ and that by species B is 6n₂. So, the total nutrients required by both species A and B is 5n₁ + 6n₂. Since this equals the quantity of the first nutrient which is 31,510, then 5n₁ + 6n₂ = 31,510 (2).
So, we have two simultaneous equations which we would solve to find the populations of A and B which satisfy both equations.
2n₁ + n₂ = 10,560 (1)
5n₁ + 6n₂ = 31,510 (2)
From (1) n₂ = 10,560 - 2n₁ (3)
Substituting equation (3) into (2), we have
5n₁ + 6(10,560 - 2n₁) = 31,510
expanding the brackets, we have
5n₁ + 63,360 - 12n₁ = 31,510
collecting like terms, we have
5n₁ - 12n₁ = 31,510 - 63,360
simplifying, we have
- 7n₁ = -31,850
dividing both sides by -7, we have
n₁ = -31,850/-7
n₁ = 4,550
Substituting n₁ = 4,550 into (3), we have
n₂ = 10,560 - 2(4,550)
n₂ = 10,560 - 9,100
n₂ = 1,460
So, we require 4,550 of species A and 1,460 of species B that can coexist in the environment so that all the nutrients are consumed each day
Number of Bacteria A and Bacteria B = 4550 and 1460 respectively,
Let the number of bacterias of Specie A and Specie B be = x and y respectively.
Given : 2 Nutrient Requirements of both species of Bacteria A and B , Total Nutrients available
To find : Number of Bacteria 1 and Bacteria 2
Nutrient 1 Constraint Equation : 2x + y = 10560
Nutrient 2 Constraint Equation : 5x + 6y = 31510
Putting the value of y from 1st equation in 2nd equation ;
5x + 6 (10560 - 2x) = 31510
5x + 63360 - 12x = 31510
63360 - 31510 = 7x
7x = 31850
x = 31850 / 7 = 4550 { Bacteria A}
Putting the value of x in 1st equation,
2 (4550) + y = 10560
9100 + y = 10560
y = 10560 - 9100 = 1460 {Bacteria B}
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Cora and Cecilia each use chalk to make their own number patterns on the
sidewalk. They make each of their patterns 10 boxes long and line their patterns
up so they are next to each other.
Cora puts o in her first box and decides that she will add 3 every time to
get to the next number.
Cecilia puts o in her first box and decides that she will add 9 every time to
get the next number.
How many times greater is Cecilia's number in the 5th box than Cora's number in
the 5th box? What about the 8th? What predictions can you make about the
relationship between the values in the rest of the pattern?
Answer:
5th box has 45 for Cecilia and 15 for Cora
8th box has 72 for Cecilia and 24 for Cora
Cecilia's boxes numbers are 3 times of Cora's boxes numbers.
Step-by-step explanation:
This can be completed as follows .
0 1 2 3 4 5 6 7 8 9 10
Cora's boxes 0 3 6 9 12 15 18 21 24 27 30
Cecilia's boxes 0 9 18 27 36 45 54 63 72 81 90
The 5th box has 45 for Cecilia and 15 for Cora which means Cecilia's number is 3 times bigger than Cora's number in the 5th box.
The 8th box has 72 for Cecilia and 24 for Cora which means Cecilia's number is 3 times bigger than Cora's number in the 8th box.
As we see that the difference in numbers is of three times from the beginning to the end. Therefore we conclude that Cecilia's boxes numbers are 3 times of Cora's boxes numbers.
In this diagram where is the line of reflection?
The line of reflection is the vertical line x = 1.
What is a reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.
The line of reflection is the vertical line passing through the midpoint of segment AA'.
Since A'(2,5) and A(-4,5) have the same y-coordinate, their midpoint is on the line y = 5.
Therefore, the line of reflection is the vertical line x = 1.
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Pythagorean theorem: Manuel purchases a rectangular picture
frame that has a diagonal measure of
17 inches and a height of 8 Inches. What is
the width of the picture frame?
Answer:
width = 15
Step-by-step explanation:
a² + b² = c² This the the formula
(PLUG IN)
8² + b² = 17²
64 + b² = 289 (subtract 64 on both sides)
b² = 225 (square root)
b = 15
Hope this helps ya!!
A recipe calls for 1 1/2 cups of mayonnaise and 3/8 cups of pecans. How much mayonnaise should be used if 1 cup of pecans is used?
Answer:
4 cups of mayonnaise.
Step-by-step explanation:
The ratio of the amount of pecans comparing reality and the recipe is:
1 : 3/8
= 1/(3/8)
= 8/3
Hence, to find the amount of mayonnaise that should be added:
8/3 * 3/2
= 8/2
= 4 cups
Hope this helped!
How long is 50% of 60 minutes?
Answer:
30 minutes
Step-by-step explanation:
60 divided by 2 = 30
lable min
Find the scale length of 15cm and 3cm.
Please help if you can thank youuu
Answer: 5
the scale length of 15cm and 3cm is 15/3 = 5
Step-by-step explanation:
10 Theo earned £16520 last year and spent 13% of his money on making home improvements.
Find how much money Theo spent on home improvements last year.
Give your answer to the nearest penny.
f
(2)
Answer:
2147.60
Step-by-step explanation:
What inequality is shown in the graph below?
Answer:
1/2
Step-by-step explanation:
Let f be the function with derivative given by f'(x)=cos(2x^2 -1). How many relative extrema does f have on the interval 2 < x < 4?
Please help
Side -side -angles
Angles-side-angels
Angle -angle -side
Angle-angle-angel
Side-angel-side
Side-side-side
Hypotenuse-leg
Congruent or not ?
Answer:
it's congruent
side-side -side
Answer:
not congruent because all the sides a different .
HELP ME ASAP PLEASE ?!?!Find the value of x.
Answer:
38 degree
Step-by-step explanation:
all the angles of a triangle are 180 . a supplementary angle is 105 degree... first subtract 180 - 105 (A), because it is a supplementary angle , so 75 degrees then do 180 - ( 67 + 75 ) that is 38 = x
A model with 1 shaded part and 3 unshaded parts.
Write the unit fraction depicted in the model as a percent.
One-fourth =
%
Answer:
he is wrong it is 25 %
Step-by-step explanation:
I just did it
Solve the equation 3/4x + 3 -2x = -1/4+1/2x+5
If necessary: Combine Terms
Apply Properties: Add, Subtract, Multiply, Divide
Answer:
x = -1
Step-by-step explanation:
3/4x + 3 -2x = -1/4 + 1/2x + 5
3/4x + 3 -2x = 19/4 + 1/2x
3x + 12 - 8x = 19 + 2x
-5x + 12 = 19 + 2x
-5x - 2x + 12 = 19
-7x = 19 - 12
-7x = 7
x = -1
By solving the algebraic equation [tex]\frac{3}{4}x+3-2x = -\frac{1}{4}+ \frac{1}{2}x + 5[/tex], x = -1.
What is algebraic equation?Algebraic equation is statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
[tex]\frac{3}{4}x+3-2x = -\frac{1}{4}+ \frac{1}{2}x + 5\\\\\frac{3}{4}x-2x-\frac{1}{2}x = -\frac{1}{4}+5-3\\\\\frac{3x-8x-2x}{4} = \frac{-1+20 - 12}{4} \\\\-\frac{7x}{4} = \frac{7}{4}\\ \\ x = -1[/tex]
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The boundry of a park is shaped like a circle
Answer:
what is the question? a circle is 360 degrees if that is what you're asking.
john’s dog eats 4/5 tin of mince meat added in his meal every day . if dog eats 35 full tins of meat in one week(7 days) then how much does it eat every day.
Answer:
it eats five mince meat everyday
Complete this sentence In a triangle, the angle with the greatest measure is
always opposite the______
O A. shortest side
B. longest side
C. second-longest side
D. angle with the smallest measure
Answer: B. Longest side.
Step-by-step explanation:
Solve for x and explain how I show work
Answer:
x = 100
Step-by-step explanation:
(x - 20) + x = 180
2x - 20 = 180
+ 20 +20
2x = 200
x = 200/2
x = 100
someone help me with this question please.
Answer:
Andre scored 14 points.
Equation: x = 14
Step-by-step explanation:
Let the number of points Andre scored be x.
Diego's points = x-9
Noah's points = (x-9) × 2
= 2x-18
Now, you know the exact value of Noah's points which is 10.
2x-18 = 10
Isolate the 2x.
2x = 10+18
= 28
x = 28÷2
= 14
Answer:
noah = 10 pts.
diego = 5pts. half as many as noah.
diego is 9pts less than andre.
if diego scored 5 and is 9 less than andre. andre scored 5+9
Andre scored 14pts
Step-by-step explanation:
Malik had 54 yards rushing. James had -12 yards rushing. How many more yards
does Malik have than James?
The probability that a new fridge has a fault is 0.015
What is the probability that a new fridge does not have a fault?
Answer:
I will assume you mean 0.015 out of 1.
It is 0.985
Step-by-step explanation:
Answer:
0.985
Step-by-step explanation:
The probability that a new fridge does not have a fault = 1 - 0.015
= 0.985
What is the percent change from 9,000 to 900?
Answer:
-90%
Step-by-step explanation:
Change/ original x 100
9000-900= 8100
8100/9000= 0.9
0.9 x 100 = 90
I need help! Please
Answer:
The two trangle's relation by S.AS
Step-by-step explanation:
Idono thes ansar gdau gdddhd hjkdbss hhfc
penny reads 10 pages in 1/3 of an hour. What is the unit rate for pages per hour? For hours per page?
Answer: 42 pages
Because
How can parentheses be added to the following equation to make it true?
[tex]8-3*2-1+1=0[/tex]
Step-by-step explanation:
Add parentheses around 1 + 1.
8 - 3 × 2 - (1 + 1) = 0
8 - 6 - 2 = 0
0 = 0
Answer: The answer is 0.
Step-by-step explanation: You'll need to add the parentheses around 1+1.
The solution:
[tex]8-3*2-(1+1)[/tex] 2. [tex]8-6-2[/tex] 3. [tex]0[/tex]3pq-6hk,-3pq+14kh
Find the sum
Answer:
ANSWER
3pq−6hk+(−3qp+14kh)
⇒(3pq−3pq)+(14kh−6kh)[∴pq=qp]and
⇒0+8kh[kh=hk]
∴8khAns
The formula A = Pe^rt calculates the amount an investment earning a nominal rate of r compounded continuously is worth. Show that the amount of time it takes for the investment to double in value is given by the expression ln2/r.
Answer:
t = In2/ r
Step-by-step explanation:
Given the formula : A = Pe^rt
For investment to double ;
Final amount (A) = 2 * initial investment (p)
A = 2p
Hence,
2p = pe^rt
2 = e^rt
Take the In of both sides
In2 = rt
Divide both sides by r
In2 /r = rt /r
In2/ r = t
t = In2/ r ; Hence, the proof
The formula for obtaining the time taken when the amount is double the principal is ln2/r.
Given that;
A = Pe^rt
A = amount
P = principal
r = rate
t = time
Now we are told that;
A = 2P
Hence;
2P = Pe^rt
2 = e^rt
ln 2 = rt
t = ln2/r (QED)
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What is the value of c in the equation 3/4 x + 2= 5/4 x -6
Answer:
c isn't in the equation so I'm assuming you're solving for x
x=16
Step-by-step explanation:
3/4x+2=5/4x-6 start by subtracting 3/4x on both sides
2=2/4x-6 now add 6 to both sides
8=2/4x at this point you can simplify 2/4 to 1/2 just to make it easier to divide
8=1/2x divide 1/2 or 0.5 by 8
x=16