Hurry When solving a system of equations, Jared found y = x 10 for one equation and substituted x 10 for y in the other equation. Nicole found x = y – 10 for the same equation and substituted y – 10 for x in the other equation. Who is correct? Explain.

Answers

Answer 1

I can say that Jared and Nicole are correct because they manipulated the equation right. They can either write the equation as y as a function of x then substitute it to the y in the other equation and solve for x. They can also write the equation as x as a function of y and substitute it to x in the other equation and solve for y. For both solution, they will still obtain the same answers.

Answer 2

Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

Given information:

Jared found that [tex]y = \dfrac{x} {10}[/tex] for one equation and substituted [tex]\dfrac{x}{10}[/tex] for y in the other equation.

Nicole found [tex]x = y -10[/tex] for the one equation and substituted [tex]y -10[/tex] for x in the other equation.

So, there are two equations. Based on the question, the equation should be,

[tex]x=10y[/tex] and [tex]y-x=10[/tex].

Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.

This method is the substitution method which is used to find the solution of the system of equations.

Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

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Related Questions

The sides of a triangular lot are represented by x, 3x, and 3x + 2. Find each side if the perimeter is 632 feet.

Answers

Perimeter of triangle is adding all three sides.
For example a triangle with sides 3, 5, and 7 would have a perimeter of 15

Now we use your values.

632 = (x) + (3x) + (3x + 2)
632 = 7X + 2
630 = 7x
90 = X

So side 1 is 90
Side 2 is 3(90) or 270
Side 3 is 3(90) + 2 or 272
Add all those up and you get (you guessed it) 632

Kirk traded New Zealand dollars for Mexican pesos at an exchange rate of 1 New Zealand dollar = 8.8352 Mexican pesos. He gave the exchanger a total of 2600 New Zealand dollars and was charged a flat fee of 65 New Zealand dollars. Approximately how many Mexican pesos does Kirk have?

Answers

The Correct Answer is. 22,397.23

Answer: 22,397.23

Step-by-step explanation:

confirmed

This year, a hardware store has a profit of -$6.0 million. This profit is 3/4 of last year's profit. What is last year's profit?

Answers

4.5Million dollars Bam Boom

The metric system is easy to use because it is based on units of ten. how many centimeters are there in 100 meters?

Answers

The answer is: " 10,000 cm " .
_________________________________________________
Note: 100 cm = 1 m (exact measurement); in which:

"cm" = centimeter(s) ;
"m" = meter(s) ;
_________________________________________________
100 m = ? cm ?

100 m * (100 cm / 1 m) = __?__ cm ;

The units of "m" cancel out; and we have:

(100)* (100 cm) = 10,000 cm .
_______________________________________

What method would you choose to solve the equation 2x^2-7=9

Answers

Here is one way to solve for x.

Step 1) 2x^2-7=9

Step 2) 2x^2-7+7=9+7

Step 3) 2x^2=16

Step 4) (2x^2)/2=16/2

Step 5) x^2=8

Step 6) sqrt(x^2)=sqrt(8)

Step 7) |x|=sqrt(8)

Step 8) x=sqrt(8) or x=-sqrt(8)

-------------------------------------

Below are explanations/reasons to each of the steps above.

Step 1) Original equation

Step 2) Add 7 to both sides

Step 3) Combine like terms

Step 4) Divide both sides by 2

Step 5) Simplify

Step 6) Apply the square root to both sides. The notation "sqrt" is shorthand for "square root"

Step 7) Use the rule that sqrt(x^2) = |x| for all real numbers x

Step 8) Use the rule that if |x| = k then x = k or x = -k for some fixed number k.

-------------------------------------

The two solutions are
x = sqrt(8) or x = -sqrt(8)

According to the number line, what is the distance between points A and B?

6 units
7 units
12 units
14 units

Answers

Answer:

D)14 units

Step-by-step explanation:

Just counts how many numbers you get from point A to B. Its pretty simple.

Answer:

The answer is D. 14 units

from -2 add 2 so you can get to 0 which gives you the 12 left add twelve on top of the two you already added and you get 14 units.

Step-by-step explanation:

With nothing but nick and pennies in his pocket , Rupert can afford 77 cents worth of candy. If he has 21 coins in his pocket how many coins does he have of each type

Answers

14 nickles and 7 pennies

He has 14 nickles and 7 pennies

Lakshmi has had a checking account for over twenty years and has always gotten money from her bank by cashing a check. She would like a more convenient method of getting cash, without having to visit the bank each time she needs to withdraw money. What type of card would she get. A. Cash card. B. Credit card. C. Debit card. D. Store gift card

Answers

b. debit card a debit card is a combination of and ATM and a checkbook and it is tied to a bank with access to an ATM to access funding..

Lakshi wants a new way of banking. She has been cashing a check at the bank for 20 years to get cash but she wants a more convenient, and modern, way of doing things. The perfect thing for her would be to get a debit card. Since she does not seem to like credit, a debit card would give her access to cash just like her old method. She can continue doing what she did before but in a more convenient manner.

Is this function even, odd, or neither?

Answers

when a function is even, they have symmetry with respect to the y-axis, what does that mean? well, the graph to the right-side of the y-axis is just a mirror image of the graph to the left-side of the y-axis.

when a function is odd, the symmetry is with respect to the origin, meaning, the graph to the right-side of the y-axis, is a mirror image of the one on the left-bottom-upside-down. So, you take a photo of the right-side graph,flip it over the x-axis, and then flip it again over the y-axis.

this one, doesn't show that either.

Generally speaking, using a ______ year's history of cash receipts and disbursements will be a satisfactory basis for projecting the future. Part of a year or full year

Answers

the answer is FULL
By collecting full year's history of cash, we could determine the amount of expense that company might need to continue the operation in the future.
This projection is made on the assumption that the company won't make any major change on its way of operation in next year's period.

Generally speaking, using a FULL year's history of cash receipts and disbursements will be a satisfactory basis for projecting the future.

Explanation:

Though a rough projection can be made in half year's data as well, but a good and solid projection can be made using full year's data. Almost all business run for a full year, so its good to project on an yearly basis. Like in this particular year the profits are this much, so we can project that in the next year we can see a higher profit.

Terry wants to tip 15% to the waiter at a restaurant this means he will multiply the cost by 0.15 if this meal costs 18.10 how much did he tip the waiter

Answers

just as the problem states, multiply the cost (18.10) by 0.15

18.10 * 0.15 = 2.72

the tip was $2.72

Is this the correct way to fill out this deposit slip? (For an assignment) I have yet to put my name and date

Answers

Just make sure to put 1600 in the "Total" area and you're all set!

Edna brought 4 pies to a party. At the end of the evening 1 and 5/8 pie was left over. How much pie did the guest eat?

Answers

3 and 3/8 ..I think... if I'm wrong please correct me.

what is 13n-6p-11n=2p solve for n

Answers

13n - 6p - 11n = 2p

2n - 6p (+6p) = 2p (+ 6p)

2n/2 = 8p/2

n = 8p/2

hope this helps

What is the vertex form of f(x)=x^2+24x+138

Answers

f(x) = x^2 + 24x + 138
f(x) = x^2 + 24x + (24/2)^2 + 138 - (24/2)^2
f(x) = (x+12)^2 - 6

Answer:

(x +12)^2 - 6

Step-by-step explanation:

d/dx x^2 + 24x + 138 = 2x + 24

when 2x + 24 = 0, the gradient = 0

x = -12

f(-12) = -6

therefore we have (x +12)^2 - 6.

55.25 divided by 0.85

Answers

55.25 divided by 0.85 would give you the answer of 65. Please give brainliest dude, I'm super close to virtuoso.

Which linear system of equations does the matrix represent?

I think it's B

Answers

-3x+5y=15
2x+3y=-10

third one

i believed the answer is C.
-3x + 5y = 15
2x + 3y = 10

Bryan is buying notebooks and pens at an office
supply store. Notebooks cost $3.59 each and pens
cost $1.49 each. Bryan spent a total of $13.

Let x represent the number of notebooks and let y
represent the number of pens.

Write an equation that represents this situation.

Answers

3.59x + 1.49y = 13 would be an equation to represent this situation

An investor wants to complain that the stock market continues to drop. What might they do to the graph shown to try to convince an audience that this is true?
A:) use a smaller range on the vertical scale
B:) use a larger range on the vertical scale
C:) omit numbers on the horizontal scale

Answers

The answer would be B because the taller one graph may seem, the more the drop looks worse.

Answer:

omit numbers on the horizontal scale

What is the measure of angle a

Answers

Review the meaning of "straight angles."

Here 110 and A are "straight angles," and so 110 + A = 180 (degrees).

Then A = 70 degrees.

Answer:

m∠A = 70°

Step-by-step explanation:

The given figure is nothing but parallel lines cut by a transversal.

We use property of transversal to find the value of angle A.

Here ∠A and 110° are pair of interior angles on the same side.

The pair of interior angles on the same side add upto 180 degrees.

Therefore, ∠A + 110 = 180

Subtract 110 from both sides, we get

∠A + 110 - 110 = 180 -110

∠A = 70°

m∠A = 70°

The 24 students in Mr. Brown’s homeroom sold 72 magazine subscriptions. The 28 students in Mrs. Garcia‘s homeroom sold 98 magazine subscriptions. Whose homeroom sold more magazine subscriptions per student? Explain your reasoning.

Answers

Mr. brown students sold 3 magazines each while Mrs. Garcia students sold 3.5 magazines each. Mrs. Garcia sold more magazines per student

Compare 7/8 with 14/16 using (<,>,=)

Answers

The correct answer is 7/8=14/16

7/8 already reduced to lowest terms, numerator and denominator have no common prime factors, So if you reduce 14/16 it simplifies to 7/8.

The required 7/8 is equal to 14/16, or we can write 7/8 = 14/16.

What is simplification?

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

Here,
To compare 7/8 and 14/16, we can first convert both fractions to a common denominator. The least common multiple of 8 and 16 is 16, so we can convert 7/8 to 14/16 by multiplying both the numerator and denominator of 7/8 by 2,

7/8 = (7 × 2) / (8 × 2) = 14/16

Now we can see that both fractions have the same denominator, so we can compare their numerators directly:

7/8 = 14/16

Therefore, 7/8 is equal to 14/16, or we can write 7/8 = 14/16.

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1. A recipe calls for cups of flour, cup of white sugar, and cup of brown sugar. The recipe makes 6 servings.

(a) How many cups of flour are there per serving? Show your work.
(b) How many total cups of sugar (white and brown) are there per serving? Show your work.
(c) Suppose you modify the recipe so that it makes 9 servings. How much more flour do you need for the modified recipe than you need for the original recipe? Show your work.

2. Your bank account has in it. You deposit $5 per day.

(a) How much money is in your account after 5 days? Show your work.
(b) After you have made all of your deposits, you withdraw $2 a day until your account balance is $0. How many days will you withdraw $2? Show your work.

3. A scuba diver was exploring a reef 32.12 m below sea level. The diver ascended to the surface at a rate of 8.8 m/min.

(a) Write an equation to model the situation. Use the formula d = RT.
(b) Explain why it is reasonable to write the distance, d, as a positive number.
(c) How long did it take the diver to reach the surface?

Need the answer A.S.A.P!

Answers

1. This problem lacks given values, where are the numbers? Just fill-in the numbers I will variables in this case.

Let us say that:

x = number of cups of flour

y = number of cups of white sugar

z = number of cups of brown sugar

(a) Just divide x by 6 to get cups of flour per serving

x / 6

(b) Simply add y and z and divide the sum by 6

(y + z)/6

(c) From (a) we know that there are x / 6 flours per serving, so simply multiply that by 9 then subtract the original x to know how much more you need:

[(x / 6) * 9] – x

(a) We know that we deposit $5 per day, so after 5 days we got:

total deposit = ($5 / day) * 5 days = $25

(b) The total deposit is 25 dollars, so removing $2 a day we need:

25 / 2 = 12.5 days

(a) d is distance, R is rate, T is time

32.12 = 8.8 T

(b) It is rightful to write distance d as a positive number since the scuba diver was ascending towards the surface. If this is to be plotted on a Cartesian plane, we are moving towards the positive y axis

32.12 = 8.8 T

T = 32.12 / 8.8

T = 3.65 minutes

What is the area of trapezoid ABCD? Enter your answer as a decimal or whole number in the box. Do not round at any steps

Answers

The side length AB is √(3²+4²) = 5.

Let's split up the shape in a square and a triangle.

If you introduce point E at (5,1) you see a square ABED with area 5*5=25.
What remains is a triangle with straight sides 5 and √((11-5)² + (1--7)²) = 10. So the triangle's area is 5*10/2 = 25.

This means the total area is 25+25=50.

What is the solution of the system? Use elimination.
-12x - y = 6
17x + y = 4

A. (-30, 2)
B. (-2, 30)
C. (2, -30)
D. (30, -2)

Answers

Note that if we add each side of the 2 equations, y will cancel out:

-12x-y+(17x+y)=6+4

5x=10

x=2

Substituting x=2 in either of the equations, we find the value of y.

Let's use the first equation:

-12x-y=6

-24-y=6

-y=24+6

-y=30, so y=-30.

Thus, the solution is (2, -30)

Answer: C

Answer:

C: (2, -30)

Step-by-step explanation:

Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you explain this to your classmate?

Answers

1) Equilateral Triangles: These triangles have the same side length and same angle for all sides. Knowing this, if the side lengths given are all the same, the triangle will be classified as an equilateral triangle.

2) Isosceles Triangles: These triangles have two sides that have the same side length and one that is not the same. Given this, if the side lengths are all given, the triangle with two same sides are classified as isosceles triangle.

3) Scalene Triangles: These triangles have all sides associated with a different value. If all side lengths are given and they have different values, this triangle would classify as a scalene triangle.

Hope I helped :)

Answer:

First, look at the side lengths a, b, and c, where c is the longest. Then take the sum of a squared and b squared and compare it to c squared. If they are equal, the triangle is a right triangle. If c squared is less than a squared plus b squared, the triangle is acute. If c squared is greater than a squared plus b squared, the triangle is obtuse.

Haresh is writing a coordinate proof involving an isosceles triangle. Haresh places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis.

What coordinates should he assign to this third vertex of the isoceles triangle?

(2a, b)

(a/2, b/2)

(a/2, b)

(b, 2b)

Answers

(a/2,b)

Hope this helps!

Answer:- (a/2, b) is coordinates should he assign to the third vertex of the isosceles triangle.

Explanation:-

As the given triangle is isosceles then the median of the triangle divides it into two equal triangles such that the base of the new triangles becomes half of the original triangle[tex]=\frac{1}{2}a[/tex]

[where a is the base of the original isosceles triangle]

Since the median of the given triangle join the third vertex and the mid point of the base thus the x coordinate of the points remains same[tex]=\frac{1}{2}a[/tex] and from the graph it is clear that y coordinate of third point is b .

Thus the coordinates for the third vertex must be [tex](\frac{a}{2},b)[/tex].

You can get some great new space for $23/square foot per year. You will be leasing 3,200 square feet. What will your MONTHLY rent be? a) $139 b) $3,200
c) $6,133 d) $73,600

Answers

since it is by square foot, and you are paying by square foot, just multiply the two numbers together

23 x 3200 = 73600

your answer is D) 73600

hope this helps

Final answer:

The calculation for the monthly rent involves firstly finding the annual rent by multiplying the cost per square foot per year with the total square footage, and then dividing this annual cost by 12 to get the monthly cost. The correct answer is c) $6,133.

Explanation:

To calculate the monthly rent, we first need to find out the annual rent and then divide it by 12 months. The annual rent can be found by multiplying the cost per square foot per year with the total number of square feet. So if the cost is $23/square foot per year and you are leasing 3,200 square feet, the calculation becomes: $23 * 3,200 = $73,600 for the annual rent. To calculate the monthly rent, we divide the annual rent by 12: $73,600 / 12 = $6,133.33. Therefore the monthly rent is closest to option c) $6,133.

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Find quadratic equation from 3 points calculator

Answers

Given the points P(-2, 7), Q(6, 8) and R(-1, -3), we find the quadratic equation of the form [tex]y=ax^2+bx+c[/tex] as follows:

Step 1:
We check to make sure that no pair of points is colinear (i.e. lie on the same line) by making that the slopes of the combinations of the line are not equal.

Slope of PQ = [tex] \frac{8-7}{6-(-2)} = \frac{1}{8} [/tex]
Slope of PR = [tex] \frac{-3-7}{-1-(-2)} = \frac{-10}{1} =-10[/tex]
Slope of QR = [tex] \frac{-3-8}{-1-6} = \frac{-11}{-7} = \frac{11}{7} [/tex]

Since, the slope of the lines are not equal, thus the points are not colinear nor parallel.

Step 2:
Substitute the x-values and the y-values of the given points into the quadratic equation formular to have three system of equations as follows:

[tex]a(-2)^2+b(-2)+c=7\Rightarrow 4a-2b+c=7 \ .\ .\ .\ (1) \\ \\ a(6)^2+b(6)+c=8\Rightarrow36a+6b+c=8\ .\ .\ .\ (2) \\ \\ a(-1)^2+b(-1)+c=-3\Rightarrow a-b+c=-3\ .\ .\ .\ (3)[/tex]

Step 3:
We solve the system of equations as follows:
[tex]\left[\begin{array}{ccccc}4&-2&1&|&7\\36&6&1&|&8\\1&-1&1&|&-3\end{array}\right] \ \ \ R_1\leftrightarrow R_3 \\ \\ \left[\begin{array}{ccccc}1&-1&1&|&-3\\36&6&1&|&8\\4&-2&1&|&7\end{array}\right] \ \ \ {{-36R_1+R_2\rightarrow R_2} \atop {-4R_1+R_3\rightarrow R_3}} \\ \\ \left[\begin{array}{ccccc}1&-1&1&|&-3\\0&42&-35&|&116\\0&2&-3&|&19\end{array}\right] \ \ \ R_2\leftrightarrow R_3[/tex]

[tex]\left[\begin{array}{ccccc}1&-1&1&|&-3\\0&2&-3&|&19\\0&42&-35&|&116\end{array}\right] \ \ \ \frac{1}{2} R_2\leftrightarrow R_2 \\ \\ \left[\begin{array}{ccccc}1&-1&1&|&-3\\0&1&\frac{-3}{2}&|&\frac{19}{2}\\0&42&-35&|&116\end{array}\right] \ \ \ {{R_1+R_2\rightarrow R_1} \atop {-42R_2+R_3\rightarrow R_3}} \\ \\ \left[\begin{array}{ccccc}1&0&\frac{-1}{2}&|&\frac{13}{2}\\0&1&\frac{-3}{2}&|&\frac{19}{2}\\0&0&28&|&-283\end{array}\right] \ \ \ \frac{1}{28} R_3\leftrightarrow R_3[/tex]

[tex]\left[\begin{array}{ccccc}1&0&\frac{-1}{2}&|&\frac{13}{2}\\0&1&\frac{-3}{2}&|&\frac{19}{2}\\0&0&1&|&\frac{-283}{28}\end{array}\right] \ \ \ {{\frac{1}{2}R_3+R_1\rightarrow R_1} \atop {\frac{3}{2}R_3+R_2\rightarrow R_2}} \\ \\ \left[\begin{array}{ccccc}1&0&0&|&\frac{81}{56}\\0&1&0&|&\frac{-317}{56}\\0&0&1&|&\frac{-283}{28}\end{array}\right][/tex]

Thus,

[tex]a=\frac{81}{56}; \ \ \ b=\frac{-317}{56}; \ \ \ c=\frac{-283}{28}[/tex]

Therefore, the quadratic equation with the three given points is

[tex]y=\frac{81}{56}x^2-\frac{317}{56}x-\frac{283}{28}[/tex]

Final answer:

To find the quadratic equation from 3 points, use the method of substitution and solve the system of equations. Substituting the given points into the general quadratic equation will result in a system of equations that can be solved for the quadratic equation.

Explanation:

To find the quadratic equation from 3 points, we can use the method of substitution. Let's say the three points are (x1, y1), (x2, y2), and (x3, y3). We can substitute these points into the general quadratic equation, y = ax^2 + bx + c, to get three equations. Solving this system of equations will give us the values of a, b, and c, and thus the quadratic equation.

For example, let's say the three points are (1, 3), (2, 6), and (3, 11). Substituting these points into the general quadratic equation, we get the following equations:

3 = a(1^2) + b(1) + c

6 = a(2^2) + b(2) + c

11 = a(3^2) + b(3) + c

Solving this system of equations will give us the values of a, b, and c, and thus the quadratic equation.

What is the y-intercept of y= -5/6x-7

Answers

The y intercept is at (0,-7)
When view the equation y = mx + b as with the equation of y= -5/6x-7
the b is the y intercept and in the equation of y= -5/6x-7 the -7 is in the b spot.

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