Mathematics Middle School

Two lines, C and D, are represented by the equations given below: Line C: y = x + 14 Line D: y = 3x + 2 Which of the following shows the solution to the system of equations and explains why?

Answers

Answer 1

Answer:

(6, 20), because both lines pass through this point

Step-by-step explanation:

We see that both equations are equal to y.  This means we can set the two equations equal to each other:

x+14 = 3x+2

Subtract x from each side:

x+14-x = 3x+2-x

14 = 2x+2

Subtract 2 from each side:

14-2 = 2x+2-2

12 = 2x

Divide both sides by 2:

12/2 = 2x/2

6 = x

Substitute this into the first equation:

y = x+14

y = 6+14

y = 20

This makes the solution (6, 20).

Answer 2

The solution for the given system of equations are (6, 20).

What is a linear system of equations?

A system of linear equations is a set of two or more equations involving two or more variables. All of the equations must be considered at once in order to find the solution, which is any pair of values that makes each equation true independently.

The given system of linear equations are y=x+14 -----(i) and y=3x+2 -----(ii).

From equation (i) and (ii), we get

x+14=3x+2

3x-x=14-2

2x=12

x=6

Substitute x=6 equation (i), we get

y=20

Therefore, the solution for the given system of equations are (6, 20).

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Related Questions

Determine which function has the greatest rate of change over the interval [0, 2].

Answers

Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: [tex]m= \frac{y_{2}-y_{1}}{x_2-x_1} [/tex]

Rate of change of [tex]a[/tex]:
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of [tex]a[/tex]:
[tex]m= \frac{y_{2}-y_{1}}{x_2-x_1} [/tex]
[tex]m= \frac{4-1}{2-0} [/tex]
[tex]m= \frac{3}{2} [/tex]
[tex]m=1.5[/tex]
The average rate of change of the function [tex]a[/tex] over the interval [0,2] is 1.5

Rate of change of [tex]b[/tex]:
Here the end points are (0,0) and (2,2)
[tex]m= \frac{2-0}{2-0}[/tex]
[tex]m= \frac{2}{2} [/tex]
[tex]m=1[/tex]
The average rate of change of the function [tex]b[/tex] over the interval [0,2] is 1

Rate of change of [tex]c[/tex]:
Here the end points are (0,-1) and (2,0)
[tex]m= \frac{0-(-1)}{2-0}[/tex]
[tex]m= \frac{1}{2} [/tex]
[tex]m=0.5[/tex]
The average rate of change of the function [tex]c[/tex] over the interval [0,2] is 0.5

Rate of change of [tex]d[/tex]:
Here the end points are (0,0.5) and (2,2.5)
[tex]m= \frac{2.5-0.5}{2-0} [/tex]
[tex]m= \frac{2}{2} [/tex]
[tex]m=1[/tex]
The average rate of change of the function [tex]d[/tex] over the interval [0,2] is 1

We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.

Answer:

what the other guy said

Step-by-step explanation:

what number must you add to complete the square? x2-20x=17
A. 100
B. -10
C.-100
D. 10

Answers

Answer:

The number is 100

A is correct

Step-by-step explanation:

Given: [tex]x^2-20x=17[/tex]

We need to make completing square at left side.

Rule: We add a number " take half of the coefficient of x and then square it"

Coefficient of x = 20

Half of 20 = 10

Square of 10 = 100

So, we will add 100 both sides make completing square.

Now we make completing square to add 100

[tex]x^2-20x=17[/tex]

Add 100 both sides

[tex]x^2-20x+100=17+100[/tex]

Now we will factor left side perfect square

[tex]a^2-2ab+b^2=(a-b)^2[/tex]

[tex](x-10)^2=117[/tex]

[tex](x-10)^2[/tex] is completing square or perfect square.

Hence, The number is 100

What is the size of the angle in the shaded triangle marked by the arrow

Answers

looks like 128 because it not 130  and it seems not like 129 so 128

which is a ABBC pattern?

Answers

The third choice down is an ABBC pattern. 

Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Step-by-step explanation:

Which of the following is a statistical question?

A.
How much money is in Althea's pocket?
B.
How tall is the tallest building in the United States?
C.
What is the temperature in the refrigerator?
D.
What were the grades on the history final exam?

Answers

I think D because you can get a lot of different answers and that's what a statistical question is.
The answer is D. What were the grades on the history final exam because it requires collecting data. A statistical question is a question that requires the collection of data to answer.

The diameter of a circular placemat is 15 inches. Devon wants to sew a border of lace around the placemat. If the lace he wants is sold by the foot, how many feet of lace will he need to purchase?

Answers

Circumference = πD = π(15) = 47 feet (Nearest feet)


Answer: 47 feet

a window cleaner charges a call out fee of £3 plus 25p per square metre of glass cleaned. a front window in a butcher's shop measures 3.5 m by 6 m. how much does it cost to get 2 of these windows cleaned?

Answers

Pretty sure it's £16.50

Two numbers multiply to be -15 and adds to be 2 what are the numbers?

Answers

Assuming x and y are the two numbers,
[tex]x + y = 2 \\ x \times y = - 15[/tex]

[tex]x + y = 2 \\ x = 2 - y[/tex]

Substitute that into
[tex](2 - y) \times y = - 15 \\ 2y - {y}^{2} = - 15 \\ {y}^{2} - 2y - 15 = 0 \\ (y - 5)(y + 3) = 0 \\ y = 5[/tex]

Substitute that into
[tex]x = 2 - 5 \\ x = - 3[/tex]

Answer : The two numbers are 5 and - 3.

Hope this helps. - M

The median and interquartile range of a set of data is shown. Write a set of data consisting of seven values for the pair of measures.
Median: 5 Interquartile Range: 5

Answers

If there are 7 data points (an odd number), then the median, 5, is right in the middle of the 7 points:  x y z 5 q r s.

If the IQR is 5, we then know that the difference between y and r is 5.

Let's find the 1st and 3rd quartiles.  Focusing on the 1st 3 numbers, we see that the 1st quadrant is y; focusing on the last 3 numbers, we see that the 3rd quadrant is r.  The IQR is r-y = 5.  Just supposing that y were 4, r would be 9:

x 4 y 5 q 9 s

We could arbitrarily let x = 3, y = 4, q = 5 and s = 9:  3 4 4 5 5 9 9.

We must check this!  
What is the median?  Since there are 7 numbers here, we take the middle number (5) as the median.  This agrees with the problem statement.
Next, we find Q1 and Q3.  Q1 is the number between 3 and the 2nd 4, and is 4.  Q3 is 4+5, or 9, because the IQR is 5.  This agrees with the problem statement.

find the value of this expression if x= -6 and y=1. xy^2/-7

Answers

(-6)(1)∧⁽2/-7⁾= -6 is the answer
Hope it's right
Let:
x=-6
y=1

xy^2/-7

substitute the values;

-6*1/-7 = 6/7 = 0.857

which expression is equivalent 121x^2-64y^2 ?

Answers

Would this be the correct answer? If not, can you further explain the question?(11x+8y)(11x-8y) 

Of the 3,558 people impaired drivers killed in 2009 (not counting the drivers themselves) death were preventable

Answers

Final answer:

The preventable nature of deaths caused by impaired driving, emphasizing the impact of alcohol and other risky behaviors on driving safety.

Explanation:

Each day in the United States, over 8 people are killed and 1,161 injured in crashes reported to involve a distracted driver, highlighting a significant public health concern. There is a noted problem with young drivers getting into serious automobile accidents, contributing to many preventable deaths.

It has been estimated that 35 percent of all U.S. early deaths in 2000 could have been avoided by changing just three behaviors, with alcohol being a significant contributing factor to risky behavior on the roads.

In 2014, alcohol-impaired driving fatalities accounted for 9,967 deaths, which is 31% of overall driving fatalities, underscoring the critical need for improved driving safety measures and individual behavior changes to reduce these numbers.

triangle ABC is similar to Triangle XYZ. 

 

AB=9.7, BC=9.6, AC=15.1

YZ=118.8, Find XZ

triangle ABC is similar to Triangle XYZ. 

 

AB=9.7, BC=9.6, AC=15.1

YZ=118.8, Find XZ

Answers

XZ = 186.8625.

Since the triangles are similar, the ratio of their angles is the same.  This means the ratio of BC to YZ will be the same as the ratio of AC to XZ; using this to set up a proportion,

9.6/118.8 = 15.1/x

Cross multiply:
9.6*x = 118.8(15.1)
9.6x = 1793.88

Divide both sides by 9.6:
9.6x/9.6 = 1793.88/9.6
x = 186.8625

A student attempted to generate an equivalent expression using the distributive property, as shown below:

6(m + 3) = 6m + 3

What was the mistake made?

A. 6 was not multiplied by m
B. Incorrect sign was used for the first term
C. Incorrect sign was used for the second term
D. 6 was not multiplied by 3

Answers

Short Answer: D
Look at them one at a time

Choice A
The result of multiplying 6 and m together (which is what you are supposed to do is 6m). This step is correct.

Choice B
There are no minus signs anywhere, either outside or inside the brackets, B is incorrect. Minus signs cannot be manufactured out of thin air. You need a reason.

Choice C
Same as B.

D is the correct answer. Both sides of a plus or minus sign have to be multiplied by what is outside the brackets. The plus sign cannot be destroyed unless you started out with something like

6 ( 4m + 3m) which = 24m + 18m = 42m But you could have combined like terms in the beginning.
6 * 7m = 42m 

.

What conclusions can you make about numbers in scientific notation with negative exponents?

Answers

A conclusion that you can make about numbers in scientific notation with negative exponents that the answer is going to be negative!

PLEASE HELP ASAP WILL GIVE BRAINLIEST!!!!!!
Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following data table.
Weight of elk antler pairs at Mount St Helens NVM:
{34, 34, 30, 30, 30, 28, 28, 26}
Weight of elk antler pairs at Rocky Mountain NP:
{40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the mean and MAD for each area of collection.
(c) Calculate the means-to-MAD ratio for the two areas of collection.
(d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain

Answers

A) The two line plots are attached.

B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8 
              = 240 ÷ 8
              = 30

m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
           = 288 ÷ 8
           = 36

In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
        = {4, 4, 0, 0, 0, 2, 2, 4}

RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
     = {4, 2, 0, 0, 0, 0, 2, 4}

Therefore,
MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
                   = 16 ÷ 8
                   = 2

MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
                = 12 ÷ 8
                = 1.5

C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15

r(RM) = 36 ÷ 1.5 = 24

D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).

A) The two line plots are attached.


B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:

m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8 

             = 240 ÷ 8

             = 30


m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8

          = 288 ÷ 8

          = 36


In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:

MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}

       = {4, 4, 0, 0, 0, 2, 2, 4}


RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}

    = {4, 2, 0, 0, 0, 0, 2, 4}


Therefore,

MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8

                  = 16 ÷ 8

                  = 2


MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8

               = 12 ÷ 8

               = 1.5


C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:

r(MSH) = 30 ÷ 2 = 15


r(RM) = 36 ÷ 1.5 = 24


D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).


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Which system of equation can represent the equation?

Answers

According to the logarithmic property of the base change, the corrected answer is option one or the first.
 The logarithmic property of base change given that
 logx (b) = logc (b) / logc (x)
 Therefore, the same property applies to this problem and the correct expression for this question is:
 y1 = log (x + 3) / log 4
 y2 = log (2 + x) / log2

A motorboat covers the distance from one pier to the other pier in 4 hours and the way back in 5 hours. What is the speed of the boat in still water, if it covers 70 km with the current in 3.5 hours?
(its not 20 i tried)

Answers

r = speed in still water
r + c = speed with current
r - c = speed against current

3.5(r + c) = 70
r + c = 20
c = 20 - r

4(r + c) = distance from pier to pier
5(r - c) = distance from pier to pier
4(r + c) = 5(r - c)
4(r + 20 - r) = 5(r - 20 + r)
80 = 10r - 100
180 = 10r
18 = r
The speed in still water is 18 km/hour

Mrs. Sloan is purchasing 3.4 pounds of trail mix that costs $4.25 per pound. How much change will Mrs. Sloan receive if she gives the cashier $20.00.

a. $14.45 b. $5.55 c. $12.55 d. $7.45

Answers

STEP 1:
multiply number of pounds purchased by price per pound

= 3.4 pounds * $4.25 per pound
= $14.45 total cost


STEP 2:
subtract total cost of purchase (step 1) from amount she gave cashier ($20.00)

= $20.00 - $14.45
= $5.55 amount received back from cashier


ANSWER: (B) $5.55 received back

Hope this helps! :)

Plzz help me

Match the system of the equation to the number of solutions.

y = 5
2x - 2/3y = 10


1. No solutions
2. One solution
3. Infinite solutions

Answers

One solution. 

They have different slopes and therefore must have one solution.

Need Help ASAP..GIVING 15 POINTS TO WHO ANSWERS.IF YOU COPY AND NOT ANSWER YOU WILL GET REPORTED
The original price for a clothes washer and dryer is $999. Which coupon is a better deal? A) SAVE 20% ON ANY WASHER/DRYER COMBO B) SAVE $200 ON ANY WASHER/DRYER COMBO C) SAVE $75 PLUS 5% OFF ON ANY WASHER/DRYER COMBO D) SAVE $50 PLUS 20% OFF ON ANY WASHER/DRYER COMBO

Answers

Its D. It equals out to 749.2 after you do 20% of 999 which is 199.8 while also subtracting the additional 50$ you save on it.

A small Learning Center holds 24 less students than the larger Learning Center. Together the learning centers hold seventy-two students. How many students does each Learning Center hold?

Answers

s=small
L=Large


72=(L-24)+s
48=L+s
By this point, the “-24” no longer affects the equation. L=s for the purpose of division.
48/2
24=s
Now we know s=24.
The “-24” is now important in finding the value of L. We find the inverse of “-24”, +24.
s+24=48


s= 24 students
L= 48 students
Final answer:

The larger Learning Center can hold 48 students and the smaller Learning Center can hold 24 students.

Explanation:

The key to solving this problem is to first express it as two linear equations. Let's denote the number of students the small Learning Center holds as S and the number of students the larger Learning Center holds as L.

The problem provides us with two facts:

The small Learning Center holds 24 less students than the larger one, we can express this as: S = L - 24.Together, both Learning Centers hold seventy-two students, so we can express this as: S + L = 72.

Now, we can solve these two equations simultaneously.

Substitute S from the first equation into the second: (L - 24) + L = 72, simplify to: 2L = 96

Thus, L = 48. This means the larger Learning Center can hold 48 students. Substitute L=48 into our first equation to find S: S = 48 - 24 = 24. So, the small Learning Center can hold 24 students.

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triangle ABC is similar to Triangle d e f if the perimeter of a triangle ABC is 24 in what is the perimeter of triangle d e f a b c has one length of 9 inches and d e f has one length of 6 in

Answers

9/6 = 1.5
24/1.5 = 16
triangle DEF has a primeter of 16 inches

the number of people who attended the spring festival is 799 more than 8 thousands. how many people attended the festival?

Answers

8×1000 +799 = 8,799 people attended the festival.

In this question, we are given the information about total number of people but in word equation.

We are given that, 799 more from 8 thousand attend the festival.

When we are given more, we add the number to the number from which it is more.

Here, we will add 799 to 8,000 in order to calculate total number of people who attended the festival

Thus, total number of people who attended the festival = 8,000 people + 799 people = 8,799 people.


find the missing dimension. use the scale factor 5:8

Answers

Question 14
5 : 8
1.5 : x
[tex]5x = 12 \\ x = 2.4[/tex]
Answer : Actual length = 2.4m

Question 15
5 : 8
x : 20
[tex]8x = 100 \\ x = 12.5[/tex]
Answer : Actual length = 12.5m

Hope this helps. - M

What best describes the expression y over 3?

A. 3 more than some number
B. Some number times 3
C. Some number divided by 3
D. 3 less than some number

Answers

The answer would be C, some number divided by 3.

A represents addition, y + 3
B represents multiplication, y * 3
D represents subtraction, y - 3

Jess is building a skateboarding ramp in the shape of a triangular prism with the dimensions shown. If Jess wants to cover all faces of the ramp with plywood, how much plywood will he need?

96 square feet
144 square feet
156 square feet
168 square feet

Answers

we know that
surface area of the triangular prism=2*area of the base+perimeter of base*height

area of the base=b*h/2
b=3 ft
h=4 ft
area of the base=3*4/2----> 6 ft²

perimeter of the base=3+4+5-----> 12 ft
height of the prism=12 ft

surface area of the triangular prism=2*6+12*12-----> 12+144---> 156 ft²

the answer is
156 ft²

Answer:

C) 156

Step-by-step explanation:

0.16+0.45 eaqkesbnnn

Answers

Sorry, but I have no idea what your "eaqkesbnnn" means.

If you were supposed to add 0.16 and 0.45, the correct answer would be 0.61.
Hello there, and thank you for asking your question here on brainly.

Short answer: 0.61 || 61/100

Why?

When you're adding two decimals, as long as it doesn't have a whole number, you can just add down like so.
      1
   0.16
+ 0.45
_______
   0.61
In fraction form, it is 61/100, because we have the decimal number, and put it to how long it is. (hundred[th])

Hope this helped you! ♥

Below are the data collected from two random samples of 100 members of a large travel club regarding the type of vacation they prefer: Sample Adventure Beach Cruise Ski A 73 4 18 3 B 71 6 22 1 Which of the following inferences can be made based on the data?

Most members prefer a beach vacation.
Most members prefer a cruise vacation.
More members prefer a cruise vacation and a ski vacation than a beach vacation.
More members prefer a beach vacation and a cruise vacation than an adventure vacation.

Answers

The correct answer is C.

There are a total of 18+3+22+1=44 people that prefer a cruise or ski vacation, while 4+6=10 people that prefer a beach vacation.

Answer:

More members prefer a cruise vacation and a ski vacation than a beach vacation.

Step-by-step explanation:

THIS IS SUPER EASY I NEED HELP

Answers

[tex]\left(\dfrac{1}{2}\right)^5=\dfrac{1^5}{2^5}=\dfrac{1}{32}[/tex]

[tex]2^5=2\cdot2\cdot2\cdot2\cdot2=32[/tex]

Answer: [tex]\left(\dfrac{1}{2}\right)^5=\dfrac{1}{32}[/tex]
(1/2)^5 is equivalent to 

(1/2) x (1/2) x (1/2) x (1/2) x (1/2)

The answer is .03125 or 1/32
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