Solve the systems of equations:
5x−2y−4=0
3x+16y−54=0
What is x?
What is y?
At silver Gym, membership is $45 per month, and personal training sessions are $25 each. At fit factor, membership is $75 per month, and personal training sessions are $15 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Final answer:
By setting up and solving an equation based on the monthly membership and per-session training costs at both Silver Gym and Fit Factor, it's determined that Sarah would need to buy 3 personal training sessions for the total cost at the two gyms to be equal.
Explanation:
To find how many personal training sessions Sarah would have to buy to make the total cost at Silver Gym and Fit Factor equal, we'll set up an equation. Let x be the number of personal training sessions.
At Silver Gym, the total cost is $45 (membership) + $25x (personal training sessions).
At Fit Factor, the total cost is $75 (membership) + $15x (personal training sessions).
Setting these two expressions equal to each other gives us the equation:
45 + 25x = 75 + 15x.
To solve for x, first subtract 15x from both sides, giving: 10x = 30. Then divide both sides by 10 to isolate x, resulting in x = 3.
Therefore, Sarah would have to buy 3 personal training sessions in one month for the total costs at both gyms to be equal.
Answer:
3 sessions
Step-by-step explanation:
You want to know the number of personal training sessions Sarah would have to buy to make the total costs the same at Silver Gym and Fit Factor. Silver Gym costs $45 per month and $25 per session, while Fit Factor costs $75 per month and $15 per session.
DifferencesSilver Gym costs $25 -15 = $10 more per personal training session, but $75 -45 = $30 less for the monthly fee. This means it takes $30/$10 = 3 sessions for the difference in fees to be made up by the difference in session costs.
Sarah would have to buy 3 sessions for the total cost to be the same.
EquationsIf you need to see this using equations, we can write the cost equations as ...
S = 45 +25x . . . . . . . . cost for x sessions at Silver Gym
F = 75 +15x . . . . . . . . . cost for x sessions at Fit Factor
Setting these equal, we have ...
S = F
45 +25x = 75 +15x
25x -15x = 75 -45 . . . . . . . subtract 45+15x from both sides
10x = 30
x = 30/10 = 3 . . . . sessions for equal cost
Sarah would have to buy 3 sessions for the total cost to be the same.
__
Additional comment
These "break even" problems usually have a higher fixed cost associated with a lower per use cost, and vice versa. The costs are the same when the number of uses, multiplied by the difference in use cost, comes to the same amount as the difference in fixed costs. Here, the $10 difference in session cost, times 3 sessions, is equal to the $30 difference in monthly membership fee.
What is the gcf of 18 and 14
What is the approximate circumference of a circle that has a diameter of 20 Centimeters
Find the unit rate. 6 2/5 revolutions in 2 2/3 seconds
A sporting goods store sells right-handed baseball gloves and left handed baseball gloves. In 1 month 12 gloves were sold for a total revenue of $561. Right-handed gloves cost $45 and left-handed gloves cost $52. How many of each type of gloves did they sell?
They sold 3 left handed gloves and 9 right handed gloves.
To solve this problem, we have to write a system of equations.
Data given;
total number of gloves = 12revenue for 12 gloves = $561right handed gloves (x) = 45left handed gloves (y) = 52Equations[tex]x + y = 12...equation (i)\\ 45x + 52y = 561 equation (ii)[/tex]
From equation (i)
[tex]x + y = 12\\ x = 12 - y...equation (iii)[/tex]
Substitute equation (iii) into equation (ii)
[tex]45x + 52y = 561\\ x = 12 - y\\ 45(12- y) + 52y = 561\\ 540 - 45y +52y = 561\\ 540 + 7y = 561\\ 7y = 21\\ y = 3[/tex]
Put y = 3 in equation (i)
[tex]x + y = 12\\ x + 3 = 12\\ x = 9[/tex]
From the calculations above, they sold 9 right handed gloves and 3 left handed gloves
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CAN ANYONE HELP ME WITH THIS PLSSSSSSSSSSSSSSS
-3x+2(4x-8)-16
Help me solve this
Using front end estimation find a reasonable estimate of: 719 · 26
Answer:
C
Step-by-step explanation:
find the sum of 23 and 87
Answer: 110
Step-by-step explanation: I would start by adding 3 from 23 to 87 which is 90. Then I would add 20 to 90 after that, 110. Hopefully this will help.
WARNING ITS TIMED PLEASSEEE HURRY! Each product represents a fraction of a circle that is shaded.
Drag the pictures to the table that match the products in each column.
Answer:
1/9, 1/8 and 1/4
Step-by-step explanation:
multiply the both given numerators (top numbers) and both given denominators (bottom numbers) given bellow
1/3 x 1/3 = 1/9 because 1 x 1 = 1 and 3 x 3 = 9
1/4 x 1/2 = 1/8 because 1 x 1 = 1 and 4 x 2 = 8
3/4 x 1/3 = 3/12 or 1/4 simplified because 3 x 1 = 3 and 4 x 3 = 12. when you simplify you divide the denominator by the numerator and 12 divided by 3 is 4 and you the 4 stays as the denominator and make the numerator of 1
Choose the fraction that goes in the blank 1/2< <4/5
Jade is painting a rectangular wall. The wall is 414 yards long and 223 yards high. The formula for the area of a rectangle is A=bh. What is the area of the wall? Enter your answer as a mixed number in simplest form in the box. $$ yd2
Answer:
Its actually 11 1/3
Step-by-step explanation:
What is the difference in kilowatt hours of monthly energy production between an average local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour?
1.01<0.99 true,4.5=4.50 true, 3.5<3.39 true?, lastly is 1.51>1.15 true?
what is 7.5% greater than 840.76
Fair Race UNIT NAME: FUNCTIONS
Directions: Follow the instructions below to design a fair race for the new video game Animal Tracks. 1. Choose two animals with different speeds. You can choose from the chart that starts at the bottom of this page or do research to choose your own. 2. Design a fair race in which the two animals have an equal chance of winning if they race at their top speed. Here are a few tips for your design: a. The race is fair if the two animals could finish the race in the same amount of time. b. You can give the slower animal a shorter distance to race. c. Since this is a video game, the race does not need to be realistic—it can be any length, and the animals can run at a constant speed. 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. 4. Graph the system to prove that the two animals have an equal chance of winning the race. Explain how the graph proves the race is fair. Your equations, graph, and explanation for your race design will be submitted as your portfolio assessment.
Animal Speed (mph) cheetah 70 lion 50 coyote 43 rabbit 35 kangaroo 30 squirrel 12 chicken 9 antelope 61 elk 45 ostrich 40 giraffe 32
Animal Speed (mph) elephant 25 pig 11 mouse 8
I need help wiith 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. I choose The mouse and squirrel ....can i get help on the equuations? Can someone explain it to me?
The linear equation for squirrel y = 12x.
The linear equation for mouse y = 8x
The distance covered by the squirrel is 36km at time 3hours.
The distance covered by the squirrel is 24km at time 3hours.
What is linear equation?A linear equation is an "algebraic equation is of the form y=mx + b where 'm' is the slope of the line and 'b' is the y - intercept".
According to the question,
Animal Mouse Squirrel
Speed(mph) 8 12
"x" the time goes along with x-axis and "y" is the distance covered by the animal.
The mouse time and distance would plot the graph (1,8)(2,16)(3,24)....
The squirrel time and distance would plot the graph (1,12)(2,24)(3,36)....
Let us consider the track is straight line and shorter distance is 50 meters.
Formula for straight line equation y = mx + b where 'b' is the base value, 'x' is the time and 'y' is the distance.
The linear equation for squirrel y = 12x+b and the squirrel starts at 0 meters per hour. so the equation becomes y = 12x.
The linear equation for mouse y = 8x + b and the mouse starts at 0 meters. so the equation becomes y = 8x.
Distance covered by the mouse and the squirrel at time x = 3 we can find the distance covered by mouse and the squirrel.
y =12x
y = 12(3)
y = 36.
The distance covered by the squirrel is 36km at time 3hours.
For mouse, at time x = 3 hours.
y = 8(3)
y=24.
The distance covered by the squirrel is 24km at time 3hours.
Hence, The linear equation for squirrel y = 12x.
The linear equation for mouse y = 8x
The distance covered by the squirrel is 36km at time 3hours.
The distance covered by the squirrel is 24km at time 3hours.
Learn more about Linear equation here
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I need this right to pass please helpp
A nickel and a dime are flipped. What is the probability both coins will land tails up
multiply the number of legs on a snake by the number of hours in day .What's the product
Vicki has 210 baseball cards and buys an additional 15 cards every week. Jeb has 275 baseball cards and buys an additional 10 cards every week. After how many weeks will Vicki and Jeb have the same number of baseball cards?
Answer:
After 13 weeks, Vicki and Jeb will have the same number of baseball cards.
Step-by-step explanation:
Let n be the required number of weeks after which Vicki and Jeb have the same number of baseball cards.
The number of cards Vicki will buy after n weeks = 210 + 15n
The number of cards Jeb will buy after n weeks = 275 + 10n
Since, these are equal,
210 + 15n = 275 + 10n
15n - 10n = 275 - 210
5n = 65
Divide both sides by 5.
n = 13.
Hence, after 13 weeks, Vicki and Jeb will have the same number of baseball cards.
shane works at an electronics store. He earns 13% commission on his sales. Shane's commission this month is $780. What are his total sales for the month
Answer:
Shane's total sales is $6000.
Step-by-step explanation:
It is given that the Shane earns 13% commission on his sales and the Shane's commission this month is $780.
Let the Shane's total sales be x. So, 13% of x is $780.
[tex]x\times \frac{13}{100}=780[/tex]
Solve the above equation to find the value of x.
[tex]x=780\times \frac{100}{13}[/tex]
[tex]x=6000[/tex]
The value of x is 6000, therefore Shane's total sales is $6000.
If x < 5 and x > c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions
Final answer:
To ensure there are no solutions to the compound inequality x < 5 and x > c, we can choose c to be 5 or larger, such as c = 6, making the inequality impossible.
Explanation:
To determine a value of c such that the compound inequality x < 5 and x > c has no solutions, we need to choose a value of c that makes the inequality impossible to satisfy.
One way to ensure there are no solutions is to choose c so that it is greater than or equal to 5.
If c is 5 or any number larger than 5, then there is no real number x that can be both greater than c and at the same time less than 5.
For example, if we choose c = 6, then the set of values greater than 6 (x > 6) does not intersect with the set of values less than 5 (x < 5).
Therefore, c = 6 would ensure that there are no solutions to the compound inequality.
∠2 and ∠3 form a linear pair. ∠3 and ∠1 are vertical angles. m∠1= 62 ∘ . What is m∠3?
Help please I will be answering your questions too ;)
At the school carnival, the sixth graders are making directional arrows, as shown below.
Each arrow is to be painted red. How much area needs to be painted for 1 arrow?
26 square inches
29 square inches
32 square inches
44 square inches
Now that you have converted a terminating decimal number into a fraction, try converting a repeating decimal number into a fraction. Repeating decimal numbers are more difficult to convert into fractions. The first step is to assign the given decimal number to be equal to a variable, . For the decimal number , that means . If , what does 10x equal?
Answer:
0.3 repeating
Step-by-step explanation:
from edmentum
re are 5 short rows of chairs, each with an equal number of chairs. On a crowded day, the ushers added 2 chairs to each long row and 3 chairs to each short row.
Bens mom wants to buy carpet for the family room the measures 12 feet by 11 feet she can purchase the carpet on sale for $6 how much will bens mom spend to carpet the family room
Show three ways to make $20 .Use tally marks to record the bills.