The sum of two numbers:
x + y = 108
The difference of the same two numbers:
x - y = 78
We can use substitution to figure out x and y:
x - y = 78 can be changed to x = 78 + y
We can plug this into the first equation:
78 + y + y = 108
78 + 2y = 108
2y = 30
y = 15
Now solve for x using any of the two equations. I'll use the first equation since it's easier:
x + 15 = 108
x = 93
Owen and his friend kayden are going to a carnival that has games and rides . Owen played 5 games and went on 6 rides and spent a total of 28.75 kayden played 4 games and went on 3 rides and spent a total of 16.25. Determine the cost of each game and the cost of each ride
Each game costs 1.25 and each ride costs 3.75
Step-by-step explanation:
Let,
Cost of each game = x
Cost of each ride = y
According to given statement;
5x+6y=28.75 Eqn 1
4x+3y=16.25 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(4x+3y=16.25)\\8x+6y=32.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 1 from Eqn 3
[tex](8x+6y)-(5x+6y)=32.50-28.75\\8x+6y-5x-6y=3.75\\3x=3.75[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{3.75}{3}\\x=1.25[/tex]
Putting x=1.25 in Eqn 1
[tex]5(1.25)+6y=28.75\\6.25+6y=28.75\\6y=28.75-6.25\\6y=22.50[/tex]
Dividing both sides by 6
[tex]\frac{6y}{6}=\frac{22.50}{6}\\y=3.75[/tex]
Each game costs 1.25 and each ride costs 3.75
Keywords: linear equation, elimination method
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Final answer:
The cost of one game is 1.25 dollars and the cost of one ride is 3.75 dollars at the carnival. This was determined by setting up and solving a system of equations based on the expenses of Owen and Kayden.
Explanation:
To determine the cost of each game and each ride at the carnival, we can set up a system of equations based on Owen and Kayden's expenses. Let x represent the cost of one game and y represent the cost of one ride.
Owen played 5 games and went on 6 rides for a total cost of 28.75 dollars. This can be represented by the equation:
5x + 6y = 28.75
Kayden played 4 games and went on 3 rides for a total cost of 16.25 dollars. This can be represented by the equation:
4x + 3y = 16.25
We now have a system of linear equations:
5x + 6y = 28.75
4x + 3y = 16.25
To solve the system, we can multiply the second equation by 2 to align the y-terms:
5x + 6y = 28.75
8x + 6y = 32.50
Subtracting the first equation from the multiplied second equation, we get:
3x = 3.75
Dividing both sides by 3, we find that x = 1.25, which is the cost of one game.
To find the cost of one ride, we substitute x = 1.25 into either of the original equations. If we use the second equation 4(1.25) + 3y = 16.25, we get:
3y = 16.25 - 5
3y = 11.25
y = 3.75
Therefore, the cost of one ride is 3.75 dollars.
Match Each Equation to the situation it represents.
the first situation goes with the first equation
the second situation goes with the third equation
the third situation goes with the third equation
The equation for Statement 1 is 4+5x=16, the equation for Statement 2 is (5-4)x=16 and the equation for Statement 3 is 16-4x=5.
For the given statements we need to match the given equations.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Statement 1: An adults and 5 children rent skates. It costs $4 per adult for stakes and a total of $16.
Let the cost of 5 children rent skates be 5x.
Now, 4+5x=16
Statement 2: It costs Mikael $4 to make a bike bag, and he sells each for $5. He has made a profit of $16 so far.
Profit=Selling Price-Cost Price
⇒Profit=5-4
⇒(5-4)x=16
Statement 3: It was 16° C. It began falling 4° C per hour until it reached 5° C.
It began falling 4° C per hour, which can be written as 4x.
Now, 16-4x=5
Therefore, the equation for Statement 1 is 4+5x=16, the equation for Statement 2 is (5-4)x=16 and the equation for Statement 3 is 16-4x=5.
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Hey I need help adding rational numbers
Answer:
wat number
Step-by-step explanation:
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A school district has a student population of $6,734 students. If the maximum class size is 25 students. How many more teacher must the district have to supplement their staff of 217 teachers?
Answer:
53 teachers
Step-by-step explanation:
Basically, what we need to do here is to find how many teachers there need to be, first. If there are 6,734 students in the school district and if maximum class size is 25, then the number of teachers needed is:
6,734 / 25 = 269.36
Of course, it's obvious that we can't have a decimal number of teachers, so we need to find integer (269 or 270).
If we take 269 teachers and 25 students per class, we get:
269 • 25 = 6,725 students, which is not enough, since there are 6,734 students.
That means that the number of teachers needed is 270.
It is given that there are already 217 teachers, meaning that 270-217=53 teachers have to be supplemented.
52 more teachers must the district have to supplement their staff of 217 teachers.
Given that,
A school district has a student population of 6,734 students.
If the maximum class size is 25 students.
We have to determine,
How many more teachers must the district have to supplement their staff of 217 teachers?
According to the question,
Total number of students = 6,734
Maximum class size = 25 students
Then,
The number of teachers needed is,
[tex]= \dfrac{6734}{25}\\\\= 269.36[/tex]
Here, 269 teachers are needed for each group of 25 students.
Therefore,
The number of more teacher must the district have to supplement their staff of 217 teachers is,
269 - 217 = 52
Hence, 52 more teachers must the district have to supplement their staff of 217 teachers.
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Use the grouping method to factor the polynomial below completely.
3x3 + 9x2 + 5x + 15
O A. (3x2 + 3)(x+5)
O B. (3x2 + 5)(x + 5)
O C. (3x2 + 3)(x+3)
O D. (3x2 + 5)(x + 3)
The correct answer is D. (3x2 + 5)(x + 3). Here’s how you can use the grouping method to factor the polynomial completely:
Group the first two terms and the last two terms: (3x3 + 9x2) + (5x + 15)
Factor out the greatest common factor from each group: 3x2(x + 3) + 5(x + 3)
Factor out the common binomial factor: (3x2 + 5)(x + 3)
So, the polynomial 3x3 + 9x2 + 5x + 15 can be factored completely as (3x2 + 5)(x + 3).
Hope it helps.
Mr. Walker, the contest sponsor, bought toy Wheels in a package of six dozen for $81. what was the unit cost of each wheel?
Answer:
1.125
Step-by-step explanation:
the unit cost is how much it cost per wheel
dozen is 12
so 12 times 6 is 72
so then you do 81/72 to get your answer
and you are probably wondering how i got the divison from was because i'm supposed to divide to find a unit cost.
the 81 was the total for the 72 packages of toy wheels
Answer:
first find how much a dozen of 6 is, so 6*12=72
next to get the cost of one divide 81/72=$1.125
$1.13
Step-by-step explanation:
Please help ASAP!!!!
The simplified answer is [tex]5\frac{2}{9}[/tex].
Option: C.
Step-by-step explanation:
To simply [tex]-3\frac{1}{9} - (-8\frac{1}{3} )[/tex]:
First convert this improper fraction into normal fraction.
[tex]-3\frac{1}{9}[/tex] = [tex]\frac{-28}{9}[/tex].
[tex]-8\frac{1}{3}[/tex] = [tex]\frac{-25}{3}[/tex].
Now we have to simplify [tex]-\frac{28}{9} - (-\frac{25}{3} )[/tex].
= [tex]-\frac{28}{9} + \frac{25}{3}[/tex].
After applying LCM to the denominators, Multiply the second term with 3 in both numerator and denominator.
= [tex]-\frac{28}{9} + \frac{75}{9}[/tex].
=[tex]\frac{-28+75}{9}[/tex].
=[tex]\frac{47}{9}[/tex].
Convert the answer in improper fraction form.
[tex]\frac{47}{9}[/tex] = [tex]5\frac{2}{9}[/tex].
Thus the simplified answer is [tex]5\frac{2}{9}[/tex].
Algebra 1 WILL BE MARKED BRAINLIEST :)
(04.05 MC) Which of the following is a solution to this inequality?
y>1/2 x + 2
(1, 4)
(−1, 1)
(2, 3)
(0, 2)
What is 3x + 4 = x + 8
Answer:
x is equal to 2
Step-by-step explanation:
2x+4=8
2x=4
x=2
Answer:
x = 2
Step-by-step explanation:
First you must subtract x to both sides leaving you with 2x + 4=8 and you subtract 4 to both sides giving you 2x=4 and lastly to get the x by itself you divide both sides by 2 leaving you with x=2
Write a recursive rule for the sequence.
243, 81, 27, 9, 3, ..
Final answer:
A recursive rule for the sequence 243, 81, 27, 9, 3, ... is to multiply each term by one-third (⅓) of the previous term. The first term is 243, and the rule can be expressed as an = ⅓ × an-1 for n >= 2.
Explanation:
To write a recursive rule for the sequence 243, 81, 27, 9, 3, ... we must first identify the pattern. Observing the sequence, we see that each term is one-third of the previous term. Therefore, to get from one term to the next, we multiply by ⅓ (which is the same as dividing by 3).
The recursive formula for this sequence can be written as follows:
Let the first term a1 = 243. Then for each n >= 2, an = ⅓ × an-1, where an represents the nth term of the sequence.
This recursive rule clearly indicates that every term is a fraction of the preceding term, which is consistent with the pattern of division by three observed in the original sequence.
Describe when you use a solid line or a broken line when graphing inequalities. What does each type of line mean?
Answer:
Graphing Linear Inequalities differs from graphing regular linear equations. That is it has certain rules to be followed to draw the graph.
First, rearrange the equation as y in the left and other terms in the opposite side.Check for the line: y= , y≤ and y≥ comes with straight line where as y< and y> comes with a dotted (broken) line.Shading: If y> greater than or y≥ greater than or equal is present then the space above the line has to be shaded. If y< less than or y≤ less than or equal is present then the space below the line has to be shaded.Thus if the equation has y < or y > then we use broken line and y= , y≤ and y≥ then we use solid line.
LOTS OF POINTS please help
Answer:
C
Step-by-step explanation:
Let's call the middle M. If we take triangle PMQ we see that is has a 90 degrees angle. Also both of the other corners are equal so 180=90-2x. x=45 degrees. In a triangle with two 45 degrees angles and a 90 degrees angle the following applies: Both straigth sides are 1:square root of 2 to the oblique side. That means that if say PM=4 that PQ=4sqrt2. Now we'll that to determine PM. PQ=5x so PM=5xsqrt2. The area of parallelogram PQRS then equals to 5xsqrt2×5xsqrt2=25x^2×2=50x^2. So that is C.
Kendra’s work is shown in the table. Where, if anywhere, did Kendra first make a mistake? Steps Kendra’s Work Step 1 Negative 3 x + 7 y = negative 15. Negative 2 x minus 7 y = 5. Negative 5 x = negative 10. Step 2 Negative 5 x = negative 10. x = 2. Step 3 Negative 3 (2) + 7 y = negative 15. Negative 6 + 7 y = negative 15. 7 y = negative 9. y = Negative StartFraction 9 Over 7 EndFraction = negative 1 and StartFraction 2 Over 7 EndFraction
Answer:
Step 3 because when dividing 7y=-9, you divide by 7, not 9. Kendra divided the whole thing by 9, which is incorrect. You want to get the Y by itself(as in y, not a fraction of y) to solve the rest of the problem.
Step-by-step explanation:
Step 1.
-3x+7y=-15
-2x-7y=5
-5x=10 and x=2
Step 2.
-5x =-10. x = 2.
Step 3.
-3 (2) + 7 y = - 15. - 6 + 7 y = - 15. 7 y = - 9. y = -9/7 = - 1 2/7
- 2X +3Y=7
5x+8y=-2
Solution=(_,_)
Answer:
The solution is the point (-2,1)
Step-by-step explanation:
we have
[tex]-2x+3y=7[/tex] ----> equation A
[tex]5x+8y=-2[/tex] ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system is the intersection point both lines
using a graphing tool
The solution is the point (-2,1)
see the attached figure
area of irregular shapes
Answer:
To find area of irregular shapes you need to divide the irregular shape to get a new shape (for instance: rectangle); then you have to find the area of that particular shape using its formula (for instance: area of square = side*side)
Simplify (12x + 5) + (3x + 7)
Answer:
Your final answer is 15x+12
Step-by-step explanation:
Remove parathenes ( ) group like terms add similar elements add the numbers 5 + 7 = 12
55% of 20 pages is___pages.
Answer:
11 pages
Step-by-step explanation:
55% of 20 is 11. I'm sure! Please give be brainliest.!
Answer:
11
Step-by-step explanation:
It's just 55℅ of 20 pages so 20×55℅ will give u 11
what is the standart dievation of 63 and 37 and what is the standart dievation of 88 and 112 this is a sample not a population
hello that is a hard question but the answer is your face
Answer:
im so sorry about the kid that said that. that was mean
Step-by-step explanation:
Camille shaded 18/30 of a model. Write the decimal that represents the unshaded portion of the model
Answer:
The decimal that represents the unshaded portion of the model is 0.4
Step-by-step explanation:
we know that
Camille shaded 18/30 of a model
That means
The total parts of the model is equal to 30
The shaded parts of the model is 18
To find out the unshaded parts of the model subtract the shaded parts from the total parts
[tex]30-18=12[/tex]
To find out the decimal that represents the unshaded portion of the model, divide the unshaded parts of the model by the total parts of the model
so
[tex]\frac{12}{30}=0.4[/tex]
During the election for class president,40% of the students voted for Gerardo,35% of the students voted for Leonardo, and 25% of the students voted for juju.70 students voted for Leonard.how many more students voted for Gerardo than for juju
Answer:
80 students
Step-by-step explanation:
Let the number of voters in the election for class president is x.
So, given that 40% of the voters voted for Gerardo,35% of the voters voted for Leonardo, and 25% of the voters voted for Juju.
So, the number of voters for Leonardo was [tex]x \times \frac{35}{100} = 0.35x[/tex]
Given that, 0.35x = 70
⇒ x = 200
Now, the number of voters for Gerardo was [tex](x \times \frac{40}{100}) = 0.4x = 0.4(200) = 80[/tex].
(Answer)
What is 25% of 200?
I need help pleaseeeeeeeeeeeeeee!
Answer: 50
Step-by-step explanation: 25% of 100 is equal to 25, so if we multiply that by 2, we would get 50. To fact-check your answer, always make sure that when you multiply (only for 25% problems) by 4, and you should get the whole number. 50x4=200. Or, just 200 divided by 4. It helps!
2m+4s=16
What are the values for M and S?
For this case we have the following equation:
[tex]2m + 4s = 16[/tex]
We solve for each of the variables:
For m:
We subtract 4s from both sides of the equation:
[tex]2m = 16-4s[/tex]
We divide by 2 on both sides of the equation:
[tex]m = \frac {16-4s} {2}\\m = \frac {16} {2} - \frac {4s} {2}\\m = 8-2s[/tex]
For s:
We subtract 2m from both sides of the equation:
[tex]4s = 16-2m[/tex]
We divide between 4 on both sides of the equation:
[tex]s = \frac {16} {4} - \frac {2m} {4}\\s = 4- \frac {m} {2}[/tex]
Answer:
[tex]m = 8-2s\\s = 4- \frac {m} {2}[/tex]
Without additional information or a second equation, the values for 'm' and 's' cannot be specifically determined from the equation 2m+4s=16 due to the infinite number of solutions.
Explanation:The question 2m+4s=16 asks us to find the values of m and s. However, with a single equation and two variables, there are infinite solutions. This is because without additional information or constraints, each variable can take on many different values as long as the equation balances out to 16. Therefore, we cannot determine specific values for m and s without additional equations or information.
To find the values of M and S in the equation 2M + 4S = 16, we can use algebraic methods to solve for the variables.
Step 1: Start by isolating M in the equation. Subtract 4S from both sides of the equation: 2M = 16 - 4S.
Step 2: Divide both sides by 2 to solve for M: M = (16 - 4S)/2.
Now you have an equation that expresses M in terms of S. You can substitute different values for S to find the corresponding values for M. For example, if S = 2, then M = (16 - 4(2))/2 = 4. So, when S = 2, M = 4. Repeat this process for different values of S to find the corresponding values of M.
9 times a number of 390
Answer:
5667
Step-by-step explanation:
Answer:
3510
Step-by-step explanation:
because you have 390 and you multiply it my 9 so you would get 3510 by 9 times
Multiply the polynomials.
* (x + 4)(x2 - 5x + 3)
O
O
O
A. x2 - 5x2 - 17x+ 12
B. x3 – x2 + 3x + 12
c. x2 - 5x2 + 3x + 12
2 2 17 10
Answer:
x^3-x^2-17x+12
Step-by-step explanation:
(x+4)(x^2-5x+3)
x^3-5x^2+3x+4x^2-20x+12
x^3-5x^2+4x^2+3x-20x+12
x^3-x^2-17x+12
Will make brainliest if answered right
Answer:
d 10x=-3
Step-by-step explanation:
please help!
Simplify 5 + 2{x - 4[3x + 7(2 - x)]}.
A -34x - 107
B 34x - 107
C 34x + 107
Answer:
Should be B
Step-by-step explanation:
5 + 2 ( x-4[3x+7(2-x)]
5+2 (x-4[ 4x + 14])
5+2 (17x - 56)
5 + 34x - 112
34x - 107
Which term names FDR‘s plan for ending the Great Depression
Answer:
New Deal
Explanation:
In order to bring an end to the Great Depression, Franklin Delano Roosevelt (the 32nd President of the United States) proposed the "New Deal."
The "New Deal" was a set of programs which allowed the government to have a direct role in making the American lives easier. This mainly supported the poor people, especially the farmers and those who lost their jobs or who were unemployed.
The programs started with the First New Deal, followed by the Second New Deal. The First New Deal focused on reformation while the second one was directed towards protecting the people.
Thus, this explains the answer.
What symbols can make 8 2 6 3 equal to 14
Answer:
The closest you would get is (8*2)-6+3=13
Step-by-step explanation:
Please help!!!!! Math is very confusing and this makes no sense
A running track has the shape of a rectangle capped with a semicircle on each end, as shown below. If the track is 80 feet wide, and the rectangular portion of the track is 90 feet tall, estimate the length around the outside of the track.
The missing figure is attached down
The length around the outside of the track is about 431 feet
Step-by-step explanation:
A running track has the shape of a rectangle capped with a semicircle on each end
The track is 80 feet wideThe rectangular portion of the track is 90 feet tallWe need to estimate the length around the outside of the track
The length of the outside the track is the length of two semi-circle and two straight lengths of the rectangle
∵ The track is 80 feet wide
- From the figure the width of the track is the diameter of the
semi-circles
∴ The diameter of each semi-circle = 80 feet
∵ The radius of a circle is half its diameter
∴ The radius of each semi-circle = [tex]\frac{1}{2}[/tex] × 80 = 40 feet
∵ The length of a circle = 2πr
∴ The length of a semi-circle = πr
∴ The length of two semi-circle = 2 × πr
- Substitute r by 40
∴ The length of two semi-circle = 2 × π(40) = 80π feet
∵ The rectangular portion of the track is 90 feet tall
∴ The length of the rectangle = 90 feet
∴ The two straight parts of the track = 2 × 90 = 180 feet
- Add the length of the two semi-circles and the two straight
parts to find the length of the track
∵ Length of the track = 80π + 180
- Substitute π by 3.141
∴ Length of the track = 80(3.141) + 180
∴ Length of the track = 431.28 ≅ 431 feet
The length around the outside of the track is about 431 feet
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A rectangular painting is 24 inches wide and 20 inches tall without the frame. With the frame, it is 28 inches wide and 24 inches tall. What is the area of the frame not covered by the painting? Show your work.
The area of the frame not covered by the painting is 192 square inches
Solution:
Given that, A rectangular painting is 24 inches wide and 20 inches tall without the frame
The area of rectangle is given as:
[tex]Area = length \times width[/tex]
Find the area of painting without frame:
Length = 20 inches
Width = 24 inches
[tex]Area\ Without\ Frame = 20 \times 24 = 480[/tex]
Thus area of painting without frame is 480 square inches
With the frame, it is 28 inches wide and 24 inches tall
Find the area of painting with frame:
Length = 24 inches
Width = 28 inches
[tex]Area\ with\ frame = 24 \times 28 = 672[/tex]
Thus area of painting with frame is 672 square inches
What is the area of the frame not covered by the painting
Area of the frame not covered by the painting = Area with farme - Area without frame
Area of the frame not covered by the painting = 672 - 480 = 192
Thus the area of the frame not covered by the painting is 192 square inches