Answer:
y = x + 20
Step-by-step explanation:
Isolate the variable you are solving for, y. Note the equal sign, what you do to one side, you do to the other. Add 20 to both sides
x (+20) = y - 20 (+20)
y = x + 20
y = x + 20 is your answer
Answer: Y= x+20
Step-by-step explanation: x = y-20, you must first add 20 to both sides to get Y on its own. So x+20 = y - 20 + 20, the twenties cancel each other out giving us x+20 = y or y=x+20
A model for a company's revenue from selling a software package is R(p) = -2.5p² + 500p, where p is the price in dollars of the software. What price will maximize revenue? Find the maximum revenue.
The price $_____ maximizes the revenue.
The maximum revenue is $_____.
Answer: p = $100, R = $25,000
Step-by-step explanation:
The maximum is the y-value of the Vertex.
Step 1: Use the Axis-Of-Symmetry (AOS) formula to find x: [tex]x=\dfrac{-b}{2a}[/tex]
R(p) = -2.5p² + 500p
a=-2.5 b=500
[tex]p=\dfrac{-(500)}{2(-2.5)}[/tex]
[tex]=\dfrac{-500}{-5}[/tex]
[tex]=100[/tex]
Step 2: Find the maximum by plugging the p-value (above) into the given equation.
R(100) = -2.5(100)² + 500(100)
= -25,000 + 50,000
= 25,000
The price that maximizes revenue for the software package is $100, and the maximum revenue attainable is $25,000 based on the given revenue function R(p).
To find the price that maximizes revenue and the maximum revenue itself, we can use the given revenue function R(p) = -2.5p² + 500p.
To find the price that maximizes revenue, we need to find the vertex of the quadratic function, as the vertex represents the maximum point. The formula for the x-coordinate (price in this case) of the vertex of a quadratic function in the form of ax² + bx + c is given by:
x_vertex = -b / (2a)
In our case, a = -2.5 and b = 500:
x_vertex = -500 / (2 * (-2.5))
x_vertex = -500 / (-5)
x_vertex = 100
So, the price that maximizes revenue is $100.
To find the maximum revenue, we need to substitute this price back into the revenue function:
R(100) = -2.5(100)² + 500(100)
R(100) = -2.5 * 10000 + 50000
R(100) = -25000 + 50000
R(100) = 25000
Therefore, the maximum revenue is $25,000.
So, the price that maximizes revenue is $100, and the maximum revenue is $25,000.
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Geometry help needed, please?
Answer:
A quadrilateral has 4 right angles
Step-by-step explanation:
In a conditional statement
If hypothesis, then conclusion
OR
Conclusion, if hypothesis.
The hypothesis goes with the if part.
At the county fair, the operator of a game guesses a contestant’s weight. For each pound the operator’s guess differs from the contestant’s weight, the contestant will receive \$3$3. A contestant weighing xx pounds received \$15$15 when the operator guessed 120120 pounds. Which of the following equations could be used to solve for the weight of the contestant? Choose 1 answer: 3 | x - 15 | = 120
Answer: [tex]| x - \frac{15}{3} | = 120[/tex] or [tex]\frac{1}{3}| 3 x - 15|= 120[/tex] or [tex]| 3x - 15| = 360[/tex] or [tex]| x - 5 | = 120[/tex]
Step-by-step explanation:
Since, According to the question,
For each pound the operator’s guess differs from the contestant’s weight, the contestant will receive $3.
And, If a contestant weighing x pounds received $15
Then the guessed weight of contestant = [tex]| x - \frac{15}{3} |[/tex]
But, Again according to the question,
The guessed weight is 120 pounds,
Thus, [tex]| x - \frac{15}{3}|= 120[/tex]
⇒ [tex]\frac{1}{3}| 3 x - 15|= 120[/tex]
⇒ [tex]| 3x - 15|= 3\times 120[/tex] (by multiplying 3 on both sides)
⇒ [tex]| 3x - 15|= 360[/tex]
⇒ [tex]3| x - 5|= 360[/tex]
⇒ [tex]| x - 5|= 120[/tex] ( On dividing both sides by 3 )
Answer:
3|x-120|=15
Step-by-step explanation:
what's that?
your welcome ;)
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what is the slope of the line that passes through the pair of points -6,8 2,3
a.-3/8
b.-8/1
c.-7/8
d.-5/8
Answer:
The answer is D
Step-by-step explanation:
Answer:
d. -5/8
Step-by-step explanation:
To find slope, use the following equation
slope (m) = (y₂ - y₁)/(x₂ - x₁)
First, set each coordinate. Let:
(x₁ , y₁) = (-6 , 8)
(x₂ , y₂) = (2 , 3)
Plug in the corresponding numbers for the corresponding variables.
m = (y₂ - y₁)/(x₂ - x₁)
m = (3 - 8)/(2 - (-6))
Simplify. Note that two negative signs would result in a positive sign.
m = (3 - 8)/(2 + 6)
m = -5/8
d. -5/8 is your answer
~
Give the starting value a, the growth factor b, and the growth rate r if Q = abt = a(1 + r)t . Write r as a percent.
Answer:
Option a:
a=79
b=1.002
r=0.2%
Step-by-step explanation:
Q = 79 (1.002)^t
Q = a b^t = a (1+r)^t
Comparing with the formulas:
a=79
b=1.002
1+r=1.002
Solving for r: Subtrating 1 both sides of the equation:
1+r-1 = 1.002 - 1
r = 0.002
Writting r as percent:
r = (0.002) 100%
r = 0.2%
The points ?( 21 21?, 24 24?) and ?( 49 49?, 56 56?) form a proportional relationship. Find the slope of the line through the points.
Answer:
80
Step-by-step explanation:
Answer:
Step-by-step explanation:
Vint is testing ceiling fans in a factory. For one of the tests, he switches the fan on, and after it attains a maximum speed of 500 rotations per minute (rpm), he switches the fan back off, recording the amount of time it takes for the fan to completely stop spinning. The given equation models Vint's test, where x represents time in seconds and y represents the speed in rotations per minute. The equation has been graphed as shown.
Assuming that the test was complete when the fan stopped spinning completely, how long was the test?
A. 100 seconds
B. 10 seconds
C. 20 seconds
D. 500 seconds
Answer:
C. 20 seconds
Step-by-step explanation:
We want to know when y=0.
We are finding the x intercepts.
The first y is when it started and the second y=0 is when it stops.
Looking at the graph y=0 at x=0 and y=0 at x=20
The fan started at time 0 and stopped at 20 seconds.
The difference is the length of the test.
20-0 = 20
20 seconds
Answer:
20 seconds
Step-by-step explanation:
Given :
[tex]y=-5x^2+100x[/tex]
Where x represents time in seconds and y represents the speed in rotations per minute.
To Find : Assuming that the test was complete when the fan stopped spinning completely, how long was the test?
Solution:
Since we are supposed to find how long will it take to stop the fan completely
We assumed that test was complete when the fan stopped spinning completely
i.e. y = Speed = 0
So, Substitute y = 0 in the equation [tex]y=-5x^2+100x[/tex]
⇒[tex]0=-5x^2+100x[/tex]
⇒[tex]5x^2=100x[/tex]
⇒[tex]5x=100[/tex]
⇒[tex]x=\frac{100}{5}[/tex]
⇒[tex]x=20[/tex]
Thus it took 20 seconds to stop the fan
Hence the test was 20 seconds long.
Which of the following polynomials is the expansion of (1/2x-y)^4
Answer:
1/16 x^4 - 1/2x^3y +3/2 x^2y ^ - 2 xy^3 + y^4
Corey used the regression equation y = 1.505x − 88.21, where x is the temperature and y is the number of swimmers, to determine a possible outside temperature when 80 swimmers are at City Pool.
1. y = 1.505(80) − 88.21
2. y = 120.4 − 88.21
3. y = 32.19
4. If there are 80 swimmers at the pool, the temperature is likely to be 32.2°F.
Analyze Corey’s work to find his error. What is Corey’s mistake?
Answer: Corey substituted the number of swimmers into the variable (x) representing the temperature. Then he didn't wonder if the polar bear club really has 80 members.
Step-by-step explanation:
Answer:
A. He substituted 80 for x instead of y.
Step-by-step explanation:
Three times one number minus another number equals 34. If the sum of the numbers is 22, what are the two numbers?
Answer:
8 and 14
Step-by-step explanation:
let the 2 numbers be x and y with x > y
We can model the situation using the following 2 equations
x + y = 22 → (1)
3x - y = 34 → (2)
adding the equations term by term will eliminate the term in y
(x + 3x) + (y - y) = (22 + 34)
4x = 56 ( divide both sides by 4 )
x = 14
substitute x = 14 into (1)
14 + y = 22 ⇒ y = 22 - 14 = 8
what are the real and imaginary parts of the complex number? -11+3i
Answer:
-11 is real and 3i is
Step-by-step explanation:
i is a imaginary number is equals to rad(-1) which doesn't exist
The real part of the complex expression is - 11 and the imaginary part of the complex number will be 3i.
What is a complex number?The complex number is the combination of the real part and the imaginary part. Then the complex number is given as a+bi where the value of i is √(-1) and the value of i² is -1.
The complex number is given below.
⇒ - 11 + 3i
The term that has iota is known as imaginary part and the term that does not have iota is known as real part.
The real part of the complex expression is - 11 and the imaginary part of the complex number will be 3i.
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Margo purchases bulk teas from a warehouse and marks up those prices by 40% for retail sale. When teas go unsold for more than two months, Margo marks down the retail price by 40%. She says that she is breaking Even that is, she is getting the same price for the tea that she paid for it. Is she correct? Complete the explanation.
Answer:
Margo is incorrect.She is selling tea in loss.
Step-by-step explanation:
Let the cost price of teas when purchased from the warehouse = $ x
Then Margo marks retail price of teas a = x + 0.40 x
a = x (1 +0.40)
a = 1.4 x
After 2 months she marks down the retail price by 40% then retail price becomes b = 1.4 x - 40% of 1.4 x
b = 1.4 x - 0.4 x 1.4 x
b = 1.4 x - 0.56 x
b = 0.84 x
Difference between cost price and selling price b is = x - .84 x
= 0.16 x
which shows now Margo is selling under the cost price so Margo is incorrect.
Margo is not correct in saying that she is breaking even by marking down the retail price by 40% when teas go unsold for more than two months. In fact, she is losing money on those teas.
Explanation:Margo is not correct in saying that she is breaking even by marking down the retail price by 40% when teas go unsold for more than two months. In fact, she is losing money on those teas. Let's break it down:
When Margo purchases bulk teas from the warehouse, she marks up the prices by 40% for retail sale. This means if she buys a tea for $10, she sells it for $14.However, when the teas go unsold for more than two months, Margo marks down the retail price by 40%. So if she initially sold the tea for $14, she now sells it for $8.40.This means that for every tea that goes unsold for more than two months, Margo is losing $1.60 ($10 - $8.40).Therefore, Margo is not breaking even, she is actually making a loss by marking down the price of unsold teas.
A rectangle has a perimeter 86 cm and length 36 cm what is its width
Answer: w = 7cm
Step-by-step explanation:
Perimeter = 2 x length + 2 x width = 2L + 2w
Width is 4 cm less than the length, so w = L-4
36 = 2L + 2(L-4)
36 = 2L + 2L - 8
36 = 4L - 8
44 = 4L
L = 11
w = 7
2(11) + 2(7) = 22 + 14 = 36
Length is 11, width is 7
Answer:
7cm
Step-by-step explanation:
36x2= 72
86-72= 14
14/2= 7
Jim has 15 apples, Susie has 7 oranges, Greg has 3 strawberries, Michelle has 1 banana, Carrie has 5 limes, and Tim has 9 pineapples. If you were to add each individual number in AT&T's address together (2401 W. Grace Street), what would that total be? *
Answer:
We are given the following information:
The number of apples Jim has [tex]=15[/tex]
The number of oranges Susie has [tex]=7[/tex]
The number of strawberries Greg has [tex]=3[/tex]
The number of banana Michelle has [tex]=1[/tex]
The number of limes Carrie has [tex]=5[/tex]
The number of pineapples Tim has [tex]=9[/tex]
Therefore, the total would be the sum of the above numbers. Therefore, we have:
[tex]Total=15+7+3+1+5+9=40[/tex]
Hence, the total would be 40.
A middle school keeps track of its population. In 2011, the school population was 1500 students. In 2012, the student population had increased by 10%. In 2013, the student population had decreased by 10%. Andy believes that the 2013 student population is the same as the 2011 student population since the population both increased and decreased by the same percentage. Identify and explain the flaw in Andy's reasoning. Determine the percent change in the number of students from 2011 to 2013.
Answer:
-1%
Step-by-step explanation:
The population will not be the same unless the starting value is the same. Percent is a portion of the total 100%. If the total in 2011 and 2012 was different, then the change in population will be different.
In 2011, the population was 1500 students.In 2012, the population was 10% more than 1500. 1500+1500(0.10)=1500+150=1650In 2013, the population decreased by 10% from 1650. 1650-1650(0.10)=1650-165=1485.To find the percent change,
To calculate the percent increase or decrease, we:
Find the difference between the new value and the original Divide the number by the original Multiply by 100 and the % symbol.The population originally in 2011 was 1500. In 12013, the population is 1485.
1485-1500=-15
-15/1500=-0.01
100(-0.01)=-1%
0.75(100)=75%
The towns population increase by 75%
Andy's reasoning is flawed because the percentage increase and percentage decrease do not result in the same net change in population. The percent change in the number of students from 2011 to 2013 is a 1% decrease.
Explanation:Andy's reasoning is flawed because the percentage increase and percentage decrease do not result in the same net change in population. Let's calculate the population in 2012 after a 10% increase. 10% of 1500 students is 150 students. So the population in 2012 would be 1500 + 150 = 1650 students.
Now, let's calculate the population in 2013 after a 10% decrease from 1650 students. 10% of 1650 students is 165 students. So the population in 2013 would be 1650 - 165 = 1485 students.
To determine the percent change in the number of students from 2011 to 2013, we calculate the difference between the initial population (1500 students) and the final population (1485 students) and divide it by the initial population. (1500 - 1485) / 1500 = 15 / 1500 = 0.01 or 1%. Therefore, there was a 1% decrease in the number of students from 2011 to 2013.
Factor the trinomial below
4x^2+19x-5
A: x+5
B: 4x-1
C: 2x-5
D: x-5
E: 2x+1
Answer:
A: x+5
B: 4x-1
Step-by-step explanation:
4x^2+19x-5
(4x ) ( x )
We know that 1 will be positive and 1 will be negative.
Our choices for the numbers are 5 and 1
4*5 -1 = 19
(4 x - 1) (x + 5)
Math Help:
Which two answers are correct?
Answer:
see below
Step-by-step explanation:
The odd degree (7) tells you the end behaviors are in opposite directions. The negative leading coefficient (-4) tells you the sign of y will be opposite the sign of x.
For x going toward negative infinity, y goes toward positive infinity.
For x going toward positive infinity, y goes toward negative infinity.
A ticket cost $4.80 the new ticket price will be 1.25 times the old price what will the new ticket be
The new ticket price after a 25% increase from the original price of $4.80 will be $6.00.
Explanation:The question asks about the new cost of a ticket if its current price is $4.80 and a 25% (or 1.25 times) increase is applied, so we perform a simple multiplication. To find out the new ticket price, we need to calculate 1.25 times the original price. Therefore, the new ticket price will be 1.25 times $4.80, which can be calculated as follows:
1.25 * $4.80 = $6.00
Hence, the new ticket price after the 25% increase will be $6.00.
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Belkis is pulling a toy by exerting a force of 1.5 newtons on a string attached to the toy. The string makes an angle of 52 degrees with the floor. What could be the vertical and horizontal components of the force? a. ≈ 1.18N; ≈ 0.92 E
b. ≈ 1.07N; ≈ 0.09 E
c. ≈ 1.18N; ≈ 0.09 E
d. ≈ 1.07N; ≈ 0.92 E
Answer: (A) 1.18 North, 0.92 East
Step-by-step explanation:
The vertical component is sin 52° times the Force of 1.5 newtons
⇒ 1.5 sin 52° = 1.18
The horizontal component is cos 52° times the Force of 1.5 newtons
⇒ 1.5 cos 52° = 0.92
Answer:
a. ≈ 1.18N; ≈ 0.92 E
Cody wants to watch a new movie that is 3 hours long. He has watched 1/6 of the movie so far. What fraction of one hour did Cody spend watching the new movie? 5th grade math
Brian Steve and Rita invested a total of $24,000 in a business each person invested the same amount unfortunately in the first quarter they suffered a loss of $4500 which they shared equally by what amount as each individual investment change due to the loss
Answer:
Each individual investment changed by $2250 due to the loss.
Step-by-step explanation:
It is given that Brian Steve and Rita invested a total of $24,000 in a business.
Each person invested the same amount. So amount invested by each person is
[tex]\frac{24000}{2}=12000[/tex]
Therefore invested by each person is $12000.
They suffered a loss of $4500, which they shared equally. Each individual suffered a loss of
[tex]\frac{4500}{2}=2250[/tex]
Therefore Brian Steve and Rita suffered a loss of $2250 each. So, each individual investment changed by $2250 due to the loss.
Answer:
1500
Step-by-step explanation:
please helppppppppppppppppppppppppppppppppp 11/12 - 7/9
11/12 - 7/9
=>taking L.C.M of the denominator
=>11/36 - 7/36
=>4/36
=>2/18=>1/9
Answer:
it is 5 36
heres why
Step-by-step explanation:
Here's how to subtract 7/9 from 11/12:
11
12
−
7
9
Step 1
We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.
So we multiply 11 by 9, and get 99.
Then we multiply 7 by 12, and get 84.
Next we give both terms new denominators -- 12 × 9 = 108.
So now our fractions look like this:
99
108
−
84
108
Step 2
Since our denominators match, we can subtract the numerators.
99 − 84 = 15
So the answer is:
15
108
Step 3
Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?
To find out, we try dividing it by 2...
Nope! So now we try the next greatest prime number, 3...
Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:
15
108
÷ 3 =
5
36
Let's try dividing by 3 again...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
No good. 7 is larger than 5. So we're done reducing.
There you have it! The final answer is:
11
12
−
7
9
=
5
36
Where can the perpendicular bisectors of an acute triangle intersect?
I. Inside the triangle
II. On the triangle
III. Outside the triangle
A. I only
B. III only
C. I or III only
D. I, II, or III
Answer:
D
Step-by-step explanation:
Answer:
I and II
Step-by-step explanation:
Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.
Statement 1 is true because the perpendicular bisectors intersect at the center of the circumcircle.
Since the two triangles have the same circumcircle, therefore, their perpendicular bisectors intersect at the same point. So statement I is true.
Statement II: The distance from C to D is the same as the distance from D to E.
Since they both, that is distance from C to D and the distance from D to E represent the radius of the circle therefore, they both are equal in length.
Therefore, only I and II are correct.
pErIoD
Approximately how many time greater is the amount of earth surface that is covered by water compared to the amount of earth of earth surface that is covered by land?
Answer:
The amount of the earth’s surface covered by water is 2.12*10^8 greater than the amount of the earth’s surface covered by land.
Step-by-step explanation:
(Subtraction of scientific notation)
Earth’s surface covered by water- 3.61*10^8
Earth’s surface covered by land- 1.49*10^8
(3.61*10^8) - (1.49*10^8)
(3.61-1.49) *10^8
2.12*10^8
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Problem 1
Answer: Choice A
Vertically stretching it by a factor of 2 is the same as compressing it horizontally by a factor of 2
====================================================
Problem 2
Answer: choice B
Add up the functions to get
M(s) + L(s) = (225+0.65s) + (54 + 1.15s)
M(s) + L(s) = (225+54) + (0.65s+1.15s)
M(s) + L(s) = 279 + 1.80s
describe the difference between parallel and perpendicular lines, their slopes and graphs
Parallel lines have the same slopes (but different y intercepts). Parallel lines never cross. Parallel lines are the same distance from each other no matter where you are on either line. Think of it like a pair of perfectly straight railroad tracks.
-------------------------------------------------------------------------------------
Perpendicular lines cross at one point. The two lines form a 90 degree angle. The two slopes multiply to -1, which is another way of saying that the slopes are negative reciprocals of one another. For example, a line with a slope of 2/3 and another line with a slope of -3/2 has these two values multiply to -1; therefore showing they are perpendicular lines.
To provide a short definition,
Parallel lines are lines as the word suggests "parallel" which means they will stay side by side and never cross.
Perpendicular lines are lines that cross, usually to determine perpendicular lines you would take a slope and negatively reciprocate it.
Perpendicular:
1/2 -> -2
Parallel:
1x + 3
1x
Matthew and his brother Shawn play pool basketball. Each basket was worth 3 points, Matthews scores 9 points, shawn scores 6 points. What's the total number of baskets made during this game
Answer:
Step-by-step explanation:9÷3=3 +6÷3=2 for a total of 5 baskets
Plz help....................
Look at the picture.
common part, then "and"
Answer: x ≥ -6 and x ≤ 5PLEASE HELP ASAP WILL MARK BRAINLIST 10PTS
The population of a city is 35,400. The population is expected to grow at a rate of 2% each year.
Which function equation represents the population of the city after t years?
f(t)=35,400(1.02)t
f(t)=35,400(2)t
f(t)=35,400(0.02)t
f(t)=35,400(1.2)t
Answer:
f(t)=35,400(1.02)t
Step-by-step explanation:Exponential Growth Function:
y=b(1+r)^t
where:
b is the initial amountr is the rate of changet is timef(t) = 35,400(1 + 0.02)^t
f(t)=35,400(1.02)^t
Answer:
f(t)=35,400(1.02)t
Step-by-step explanation:
im taking the test i gotchu i just finished it and this was the correct answer
If you want to know how many shirts and pairs of pants he bought, what matrix equation could you write to solve?
Answer:
A
Step-by-step explanation:
The equations are ...
... s + p = 15
... 3s + 10p = 94
Matrix equation A is equivalent.