The work of a student to solve a set of equations is shown:Equation 1: m = 8 + 2n
Equation 2: 3m = 4 + 4n
Step 1:
−3(m) = −3(8 + 2n) [Equation 1 is multiplied by −3.]
3m = 4 + 4n [Equation 2]
Step 2:
−3m = −24 − 6n [Equation 1 in Step 1 is simplified.]
3m = 4 + 4n [Equation 2]
Step 3:
−3m + 3m = −24 − 6n + 4n [Equations in Step 2 are added.]
Step 4:
0 = −24 − 2n
Step 5:
n = −12
In which step did the student first make an error?
Step 4
Step 3
Step 2
Step 1
Answers
The student first makes an error in the Step 3 where he addsequations in Step 2 to use the elimination method.
What is the elimination method?
To create an equation in one variable using the elimination method, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
How to solve this problem?
Notice that the student uses the elimination method to solve the equations. In Step 1, he makes the coefficients of m equal in both equations. In Step 2, he simplifies the previous step. In Step 3, he wants to add both equations to create an equation in one variable. But He forgot to add 4 of Equation 2. It's a mistake.
Therefore the student first makes an error in the Step 3 where he addsequations in Step 2 to use the elimination method.
Know more about the elimination method here -
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Answers
It takes Franklin 14 hours to make a 200-square-foot cement patio thus his rate is 1/14 patios per hour
It takes Scott 10 hours to make the same size patio thus his rate is 1/10 patios per hour
let x = the hours they need to make the patio together
the together rate is 1/x patios per hour
now we have
1/14 + 1/10 = 1/x ( equation )
by solving we find:
x = 35/6 hr
x = 5 5/6 hr
x = 5 hr (5/6)*60 min
x = 5 hr 50 min
Franklin and Scott will need 5 hours and 50 minutes to make the patio together.
Answers
The current when the resistance is 10 ohms is 24 amps
What are variations?
Variations are simply data that change in values (i.e. not constant)
Types of variation
The types of variations are:
- Direct variation
- Inverse variation
- Joint variation
- Combine variation
From the complete question (see attachment), we have the following highlights
- The variation is an inverse variation
- When current (I) is 30 amps, the resistance (R) is 8 ohms
An inverse variation is represented as:
Where k represents the constant of variation.
The above equation can be rewritten as:
So, we have:
When the resistance is 10 ohms, we have:
Divide both sides by 10
Rewrite the above equation as:
Hence, the current when the resistance is 10 ohms is 24 amps
Read more about inverse variation at:
A. x + 7y = 320
y = 7x
B. x + y = 7
y = 320x
C. x + y = 320
y = 7x
D. x−y=320
y = 7x
2. Nancy bought 360 tropical fish for a museum display. She bought 8 times as many goldfish as angelfish.
How many of each type of fish did she buy?
A. 40 angelfish, 320 goldfish
B. 160 angelfish, 200 goldfish
C. 20 angelfish, 160 goldfish
D. 320 angelfish, 40 goldfish
3. Michael and Kathryn bowl together and their combined total score for one game was 425 points. Michael’s score was 70 less than twice Kathryn’s. What were their scores?
Which is a system of equations to model the problem if x represents Kathryn’s score and y represents Michael’s score?
A. x + y = 70
y = 2x – 425
B. x + y = 425
y = 2x – 70
C. x – y = 425
y = 2x – 70
D. x + y = 425
y = 2x + 70
4. Michael and Kathryn bowl together and their combined total score for one game was 425 points. Michael’s score was 70 less than twice Kathryn’s.
What were their scores?
A. Kathryn: 260, Michael: 165
B. Kathryn: 150, Michael: 275
C. Kathryn: 275, Michael: 150
D. Kathryn: 165, Michael: 260
5. A collection of nickels and dimes is worth $6.10. There are 67 coins in all.
How many nickels are there?
A. 12
B. 18
C. 49
D. 55
Answers
Answer:
D
Step-by-step explanation:
If im wrong, please correct me in the comments.
Answer:
5. D, Let d represent the number of dimes and n represent the number of nickel. We have been given that a collection of coins has 67 coins in all. This means that total number of nickels and dimes is 67. We can represent this information in an equation as:
Since we know that a dime is worth $0.10, so d dimes will be worth 0.10d.
A nickel is worth $0.05, so n nickels will be worth 0.05n. We are also told that the collection is worth $6.10. We can represent this information in an equation as:
We will use substitution method to solve system of linear equations. From equation (1) we will get, upon substituting in equation (2) we will get, Let us divide both sides of our equation by .
Answers
(3xy) (7xy^2)
= 21(x^2)(y^3) is the simplified expression represents the number of colored tiles
y=-3x+5 5x - 4y= -3 solvining systems of equations by substitution
Answers
Answers
=(54 cos 69 degrees , 54 sin 69 degrees)
= (19.4 , 50.4)
hope it helps