Answer:
x=-7
Step-by-step explanation:
Subtract 33 from -30 (because subtraction is the opposite of addition.
that's leaves 9x=-63
you want to isolate the variable so divide -63 by 9 (since division is the opposite of multiplication)
x=-7
Which image shows a counter-clockwise rotation of the blue quadrilateral PQRS 90° around the origin?
The missing figure is attached below.
Answer:
The first image from left.
Step-by-step explanation:
Given:
Rotation of the quadrilateral PQRS by 90 degree counterclockwise around the origin.
We know that, for a 90 degree counterclockwise rotation, the transformation rule for the coordinates is given as:
[tex](x,y)\to (-y,x)[/tex]
So, the 'x' and 'y' interchange their values after rotation and the 'y' value sign is reversed.
Now, let us check each option.
Option 1:
Coordinates of the original quadrilateral are:
P(5, 2.5), Q(1, 4), R(2, 2.5), and S(1, 1)
Now, after rotation by 90 degree counterclockwise, the coordinates of the transformed figure will be:
[tex](x,y)\to (-y,x)[/tex]. So,
P(5, 2.5) → P'(-2.5, 5)
Q(1, 4) → Q'(-4, 1)
R(2, 2.5) → R'(-2.5, 2)
S(1, 1) → S'(-1, 1)
Now, if we check the coordinates of P', Q', R' and S' on the first option, we see that they are same as calculated above. So, the correct option is option 1.
Option 2:
Coordinates of P are (5, 2.5) and coordinates of P' are (2.5, -5) which doesn't match with the transformation rule. So, this option is incorrect.
Option 3:
Coordinates of P are (5, 2.5) and coordinates of P' are (-5, 2.5) which doesn't match with the transformation rule. So, this option is incorrect.
Mike wants a job as car salesmen. He receives two job offers.
• Hudson cars dealership offers Mike a salary of $2500 per month, plus a commission of
$200 on every car he sells.
• Kennedy used cars dealership offers Mike a salary of $2000 per month, plus a
commission of $250 on every car he sells.
Let T represent the total monthly earning, in dollars, and let n represent the number of cars sold in a
month. For each company, write an equation that represents the relationship between T and n.
Hudson: T = 200n + 2500
Kennedy: T = 250n + 2000
im no math teacher but i do a ton of questions like these, hope this helps
The equation for Mike job which represents the relationship between T and n for Hudson cars is $2500+$200n and for Kennedy used cars is $2000+$250n.
What is linear equation?A linear equation is the equation in which the highest power of the unknown variable is one.
Mike wants a job as car salesmen. He receives two job offers.Let T represent the total monthly earning, in dollars, and let n represent the number of cars sold in a month.
Hudson's cars dealership offers Mike a salary of $2500 per month, plus a commission of $200 on every car he sells. Then the equation for this company is,
[tex]T=2500+200n[/tex]
Kennedy used cars dealership offers Mike a salary of $2000 per month, plus a commission of $250 on every car he sells. Thus, he equation for this company is,
[tex]T=2000+250n[/tex]
Hence, the equation for Mike job which represents the relationship between T and n for Hudson cars is $2500+$200n and for Kennedy used cars is $2000+$250n.
Learn more about the linear equation here;
https://brainly.com/question/14323743
The histogram represents the distributions of essay scores for high school sophomores and juniors in a contest. Which statements are true about the data used to create the histogram? Select three options.
The mean is the best comparison of the measures of center.
The juniors tended to have higher essay scores than the sophomores.
The medians of both data sets are equal.
The interquartile range is the best comparison of the measure of variability.
A histogram is the best way to show that both distributions are nearly symmetric.
Answer:
B,C, and E
Step-by-step explanation:
A histogram is a graphical illustration of information in bars of diverse heights. A histogram displays the shape and spread of continuous sample data. The true statements about the data essay scores for high school sophomores and juniors in a contest are; the juniors tended to have higher essay scores than the sophomores, the medians of both data sets are equal and the histogram is the best way to show that both distributions are nearly symmetric.
Answer:
bce
Step-by-step explanation:
Factor the polynomial.
x²+6x+5
Answer: (x + 1 )(x+5)
Step-by-step explanation:
Given :
[tex]x^{2}[/tex] + 6x + 5
Compare with the general quadratic equation:
a[tex]x^{2}[/tex] + bx + c
To factorize , you are to find two numbers that multiply to give ac , and add to give b.
After which you will re - write the middle number with those numbers.
From the given question , ac = 5[tex]x^{2}[/tex] , we are to find two numbers that will multiply to give 5[tex]x^{2}[/tex] and add to give 6x.
The numbers are 1x and 5x.
We will then replace the middle number by the two numbers , that is
[tex]x^{2}[/tex] + x + 5x + 5
x(x+1) +5( x +1)
(x+1)(x+5)
1) a, = an-1-9
a, = 25
Answer:
an-1-9
25n-1-9
25n-10=0
25n=0+10
25n=10
divide both sides by 25
25n/25 =10/25
n=2/5
Step-by-step explanation:
Answer:
n=1.4
Step-by-step explanation:
given a=25
a=an-1-9..............(1)
put a=25 in equ (1)
25=25n-1-9
25=25n-10
25n=25+10=35
n=[tex]\frac{35}{25}[/tex]=1.4
n=1.4 answer
A fitness club has two options, one for members and one for nonmembers. Members pay a one-time registration fee of $12 plus $8 per gym visit. Nonmembers pay $10 per gym visit.
Upload a graph
Type the system of equations you used to graph the solutions. Use C for the cost of the two payment options and n for number of visits.
After how many gym visits is the payment for the member option more beneficial than the payment for the nonmember option? Explain how you determined your answer.
Answer:
Part 1) The system of equations is
[tex]C=8n+12[/tex] ----> equation 1
[tex]C=10n[/tex] ----> equation 2
Part 2) The graph in the attached figure
Part 3) The number of gym visits must be greater than 6
Step-by-step explanation:
step 1
Find the system of equations that represent the situation
Let
C ----> the total cost in dollars
n ---> the number of gym visits
we know that
The linear equation in slope intercept form is equal to
[tex]C=m(n)+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the C-intercept or initial value of the linear equation
First payment option ---> For Members
we have that
The slope or unit rate is equal to [tex]m=\$8\ per\ gym\ visit[/tex]
The C-intercept or initial value is [tex]b=\$12[/tex] --->one-time registration fee
substitute
[tex]C=8n+12[/tex]
Second payment option ---> For Non-Members
we have that
The slope or unit rate is equal to [tex]m=\$10\ per\ gym\ visit[/tex]
The C-intercept or initial value is [tex]b=\$0[/tex]
substitute
[tex]C=10n[/tex]
we have
[tex]C=8n+12[/tex] ----> equation 1
[tex]C=10n[/tex] ----> equation 2
Part 2) Upload a graph
using a graphing tool
The graph in the attached figure
Part 3) After how many gym visits is the payment for the member option more beneficial than the payment for the nonmember option?
we know that
If the payment for the member option is more beneficial than the payment for the nonmember option, then the cost for the member option is less than the cost for the nonmember option
so
The inequality that represent this situation is
[tex]8n+12 < 10n[/tex]
solve for n
subtract 8n both sides
[tex]12 < 10n-8n[/tex]
[tex]12 < 2n[/tex]
Divide by 2 both sides
[tex]6 < n[/tex]
Rewrite
[tex]n > 6[/tex]
therefore
The number of gym visits must be greater than 6
Plz plz plz plz plz help
Ok, so 27 is >, 30 is <, 13/5 is 2 3/5, 5 2/7 is 37/7, 9 3/4 is 39/4, and 23/3 is 7 2/3
I did not do #27 and #30, just did the table.
What are the intercepts of the graphed function?
x-intercept = (-1,0)
y-intercept = (-3,0)
x-intercept = (0, -1)
y-intercept = (0, -3)
x-intercept = (0, -1)
y-intercept = (-3,0)
x-intercept = (-1, 0)
y-intercept = (0, -3)
Answer:
x-intercept = (-1,0)
y-intercept = (0,-3)
Explanation:
x-intercepts are points where the line crosses the x-axis.
y-intercepts are points where the line crosses the y-axis.
Answer:
D
Step-by-step explanation:
Two linear functions are shown below which function has the greater rate of change
Answer:
On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.
Step-by-step explanation:
Assuming the following two functions:
Function 1: y = 4x + 8
Function 2:
x y
2 20
4 10
6 0
We can find the slope for the second function like this:
[tex]m =\frac{10-20}{4-2}=-5[/tex]
And in order to find the intercept we can use any point for example (2,20) and we got:
[tex]20 =-5(2) +b[/tex]
And then [tex] b=30[/tex]
So our function 2 is given by: [tex] y =-5x +30[/tex]
On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.
How do u add 2 3/4 + 3 3/8
Answer:
change to improper fractions first
6/8 + 6/24
make so there is a common denominator
6/8 × 3/3 = 18/24
now add
18/24 + 6/24 = 24/24 = 1
You need to buy fertilizer for a circular flower bed with a diameter
of 13 feet. If one bag will fertilize 10 square feet, how many bags
do you need to buy?
14 bags of fertilizer are needed
Solution:
Given that You need to buy fertilizer for a circular flower bed with a diameter
of 13 feet
Diameter = 13 feet
[tex]radius = \frac{diameter}{2}[/tex]
[tex]radius = \frac{13}{2} = 6.5[/tex]
Therefore radius of circular flower bed is 6.5 feet
Area of circle is given as:
[tex]\text{ area of circle } = \pi r^2[/tex]
Substitute r = 6.5
[tex]\text{ area of circle } = 3.14 \times 6.5^2 = 132.665[/tex]
Given that one bag will fertilize 10 square feet
1 bag = 10 square feet
Then number of bags needed are:
[tex]\rightarrow \frac{132.665}{10} = 13.2665[/tex]
Thus approximately 14 bags of fertilizer are needed
Pat bounces a basketball 25 times in 30 seconds. At that rate approximately how many times will pat bounce the ball in 150 seconds?
Pat will bounce the ball 125 times in 150 seconds
Solution:
Given that,
Pat bounces a basketball 25 times in 30 seconds
To find: Number of times Pat will bounce the ball in 150 seconds
From given information,
30 seconds = 25 times
Therefore number of times ball bounces in 1 second is:
[tex]\text{1 second } = \frac{25}{30} \text{ times }[/tex]
So to find for 150 seconds, multiply both the sides by 150
[tex]150 \text{ seconds } = \frac{25}{30} \times 150 = 125 \text{ times }[/tex]
Therefore Pat will bounce the ball 125 times in 150 seconds
Answer:
125
Step-by-step explanation:
Help please,
I had a question like this before but got it wrong, can somebody please explain how to get the answer?
Answer:
-4,5
Step-by-step explanation:
I need to know the answers for a, b, and c for 23.
Answer:
Step-by-step explanation:
m∠1 = 50°
m∠2 = 88°
Step-by-step explanation:
Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.
Answer:
m∠1 = 50°
m∠2 = 88°
Step-by-step explanation:
Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.
Mr. Edwards hired a new employee to work in his bakeshop. In one hour, this
employee burned 439 chocolate chip cookies, which represented 25% of all the
cookies the employee burned in that day. How many cookies did the new employee
burn in the course of the day?
To find the total number of cookies burnt in the day, which is the whole, we would use the formula 'whole = part / percentage', or 'whole = 439 / 0.25', which gives us 1756 cookies.
Explanation:The subject of this question is Mathematics, specifically it's a problem on percent. The problem states that 439 cookies represented 25% of all the cookies the employee burnt that day. The question asks us to find the total number of cookies burnt by using this information.
When trying to find the whole from a percent, you can use the formula: whole = part / percentage. In this case, 'part' refers to the 439 cookies, and 'percentage' is 25% expressed as a decimal (0.25).
Using the formula, we find that the total (whole) number of cookies burnt is: whole = 439 / 0.25 = 1756 cookies. So, the new employee burnt 1756 cookies in the course of the day.
Learn more about Percentage here:https://brainly.com/question/30697911
#SPJ12
Writing an equation of the form A/x+B)C to solve a word probl...
Trey has a part-time job and gets pald the same amount each hour. For each hour he works, he puts $2 aside for his mom. Trey works 7 hours a day and the
total amount he keeps each day is $56. How much does he get paid each hour?
(a) Write an equation that could be used to answer the
question above. First, choose the appropriate form. Then,
fill in the blanks with the numbers 2, 7, and 56. Leth
represent the amount (in dollars) Trey gets paid each hour.
(b) Solve the equation in part (a) to find the amount (in
dollars) Trey gets paid each hour.
h =
Answer:
(a) The equation is [tex]7h-2=56[/tex].
(b) Trey gets approximately $8.29 for each hour of work.
Step-by-step explanation:
Given:
Number of hours Trey works = 7
Amount of money he put aside for mom = $2
Total Amount he keeps each day = $56
We need to find the amount he gets for each hour.
Let 'h' represent the amount (in dollars) Trey gets paid each hour.
Solving for part (a).
We need to write the equation to find the amount he gets paid for each hour.
Now we can say that;
Total Amount he keeps each day is equal to Number of hours Trey works multiplied by the amount he gets paid for each hour minus Amount of money he put aside for mom.
framing in equation form we get;
[tex]7h-2=56[/tex]
Hence the equation is [tex]7h-2=56[/tex].
Solving for part (b).
we need to solve the above equation to find the amount he gets paid for each hour.
On solving the equation we get;
Adding both side by 2 we get
[tex]7h-2+2=56+2\\\\7h=58[/tex]
Now Dividing both side by 7 using Division Property we get;
[tex]\frac{7h}{7} = \frac{58}{7}\\\\h \approx \$8.29[/tex]
Hence Trey gets approximately $8.29 for each hour of work.
Karli and her friend can paint 6/7 of a picture in 3/14 of an hour. How many pictures can they paint in a full hour?
Answer:
4 pictures
Step-by-step explanation:
(6/7)/(3/14)=x/1
cross product
3/14*x=6/7*1
3/14x=6/7
x=(6/7)/(3/14)
x=(6/7)(14/3)
x=(6/1)(2/3)
x=12/3
x=4
The number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
It is given that Karli and her friend can paint 6/7 of a picture in 3/14 of an hour.
Let's assume they can paint x number of pictures in a full hour.
So , the fraction by dividing 6/7 by 3/14 can be written equal to x .
i.e.,
[tex]\frac{6/7}{3/14}[/tex] = x
We need to do the cross product here :
[tex]\frac{3}{14}[/tex] × x = [tex]\frac{6}{7}[/tex]
or
x = ([tex]\frac{6}{7}[/tex]) ÷ ([tex]\frac{3}{14}[/tex])
We know that when dividing two fractions we need to change the division sign to multiplication sign by inverse the fraction value right to the division sign i.e.,
x = ([tex]\frac{6}{7}[/tex]) × ([tex]\frac{14}{3}[/tex])
x = 84 / 21
x = 4
Therefore , the number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.
Learn more about algebra here :
brainly.com/question/12377332
#SPJ2
Factor completely 6xv^2-18xv
Answer: 6xv( v - 3 )
Step-by-step explanation:
6xv² - 18xv
Looking into the equation critically, we could see that 6xv is common to the expression.
Therefore, the expression now becomes
6xv( v - 3 ).
How are the two angles related?
Answer:
They are supplementary
Step-by-step explanation:
Two Angles are Supplementary when they add up to 180 degrees.
A spinner is divided into three equal parts that are colored different. The colors are red white and blue
What is the period of the function?
Identify the period of a periodic function from its graph. π 2π 4π 8π
PLEASE HURRY
Answer:
4π
Step-by-step explanation:
Period is whenever a wave repeats itself. I highlighted the period.
The Period of the given function is 0 to 4π.
What is Period of Function?The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.
Here, graph starts from 0 and goes down. After π our graph starts increasing and acheive maximum at 3π and then start coming down to y = 0 at 4π.
It means that from 0 to 4π graph complete its one cycle and in the same trend it start repeating again.
Thus, the Period of the given function is 0 to 4π.
Learn more about Periodic Function from:
https://brainly.com/question/26369761
#SPJ2
Earl Pumpernickel owns and operates The Earl of Sandwiches, a profitable catering business in Logic Town. Recently, Earl was lucky enough to land a lucrative contract that will enable him to supply food for the Big Corporation for an entire month of lunch conferences. For the upcoming week, for example, he knows that Friday’s meeting will require 12 more sandwiches than Tuesday’s meeting, which will require six fewer sandwiches than Monday’s, which will require 20 more sandwiches than Wednesday’s, which will require five fewer sandwiches than Thursday’s. If the number of sandwiches ordered for the conference that calls for the fewest is 50, how many sandwiches will Earl need to make for the Big Corporation each day next week?
Answer:
Monday: 70
Tuesday: 64
Wednesday: 50
Thursday: 55
Friday: 76
Step-by-step explanation:
Equations
Let's call x to the number of sandwiches ordered for Thursday's meeting. We know that for Wednesday’s, we'll need x-5 sandwiches, for Monday's, we'll need 20 more, i.e. (x-5+20)=x+15 sandwiches. For Tuesday's it will be 6 fewer than x+15, or x+9. Finally, for Friday's, it will be 12 more than x+9 or x+21. Summarizing:
Monday: x+15
Tuesday: x+9
Wednesday: x-5
Thursday: x
Friday: x+21
The fewest of them all is x-5 and is must be equal to 50
[tex]x-5=50[/tex]
[tex]x=55[/tex]
The number of sandwiches per day is
Monday: x+15=70
Tuesday: x+9=64
Wednesday: x-5=50
Thursday: x=55
Friday: x+21=76
pls help fast 25 points! 60% of 45 =
Answer:
27
Step-by-step explanation:
1. Jada measured the height of a plant in a science experiment and finds that, to the 1/4 nearest of an inch, it is 3/4 inches.
a. What is the largest the actual height the plant could be?
b. What is the smallest the actual height the plant could be?
c. How large could the percent error in Jada's measurement be?
The largest possible height of the plant is 1 inch, the smallest possible height is 0 inches, and the largest possible percent error in Jada's measurement is -25%.
Explanation:To find the largest possible height of the plant, we need to round up the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 1 inch. Therefore, the largest the actual height of the plant could be is 1 inch.
To find the smallest possible height of the plant, we need to round down the measurement of 3/4 inch to the nearest whole inch. In this case, that would be 0 inches. Therefore, the smallest the actual height of the plant could be is 0 inches.
The percent error in Jada's measurement can be found by calculating the difference between the approximate measurement and the actual measurement, dividing it by the actual measurement, and then multiplying by 100. In this case, the approximate measurement is 3/4 inch and the actual measurement could be between 0 and 1 inch. So, the largest possible percent error would be (3/4 - 1) / 1 * 100 = -25%, and the smallest possible percent error would be (3/4 - 0) / 1 * 100 = 75%.
Learn more about Measurement here:https://brainly.com/question/2384956
#SPJ12
Consider the graph of the line y = .5x- 4 and the point
(-4,2).
The slope of a line parallel to the given line is
(1/
24
A point on the line parallel to the given line, passing
through (-4, 2), is (0,4) 4.
The slope of a line perpendicular to the given line is
-2
A point on the line perpendicular to the given line,
passing through (-4,2), is
Answer:
slope of parallel line and perpendicular line are 5 and -1/5 espectively
equation of parallel and perpendicular line are y = 5x + 22 [tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex] respectively
Step-by-step explanation:
y = 5x - 4 is in the form
y = mx + c
where m is the slope of the line and c is the y intercept of thr line
therefore slope of the line = 5 and y intercept = -4
when an another line is parallel to the given line then the slope of both the lines are equal
therefore the slope the parallel line = 5
equation of a line passing through a given point [tex](x_{1} ,y_{1})[/tex] with slope m is given by [tex]y-y_{1} = m(x-x_{1} )[/tex]
given [tex](x_{1} ,y_{1})[/tex]= (-4,2)
therefore equation of line y-2 = 5(x+4)
therefore y = 2+ 5x+20
y = 5x + 22is the eqaution of required line.
when two lines are perpendiculer then
[tex]m_{1} m_{2}=-1[/tex]
where [tex]m_{1} and m_{2}[/tex] are slope of the lines therefore
m×5=-1
therefore m= [tex]\frac{-1}{5}[/tex]
therefore eqaution of line passing through (-4,2) and with slope m= [tex]\frac{-1}{5}[/tex] is given by [tex]y - 2= \frac{-1}{5} (x+4)[/tex]
[tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex]
We can see here that the line perpendicular to the given line, passing through (-4, 2), is (0, -6).
How we arrived at the solution?Let's first verify the given information and then find the point on the line perpendicular to the given line passing through (-4, 2).
Given line: y = 0.5x - 4
Slope of a line parallel to the given line:
The slope of the given line is 0.5. Parallel lines have the same slope. Therefore, the slope of a line parallel to the given line is also 0.5.
A point on the line parallel to the given line, passing through (-4, 2):
Since the slope of the parallel line is 0.5, and we know a point (-4, 2) that lies on it, we can find the equation of the parallel line using the point-slope form of a line.
Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Substitute the values: y - 2 = 0.5(x + 4)
Now, let's find a point on the line perpendicular to the given line, passing through (-4, 2):
Slope of a line perpendicular to the given line:
Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is 0.5, so the slope of the line perpendicular to it is -1/0.5 = -2.
A point on the line perpendicular to the given line, passing through (-4, 2):
Using the point-slope form again, we can find the equation of the perpendicular line passing through (-4, 2).
Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Substitute the values: y - 2 = -2(x + 4)
Now, we can find another point on the perpendicular line by setting x = 0:
y - 2 = -2(0 + 4)
y - 2 = -8
y = -6
So, another point on the line perpendicular to the given line, passing through (-4, 2), is (0, -6).
Learn more about slope on https://brainly.com/question/3493733
#SPJ6
Two burgers and one hotdog cost $4.82. At the same price, one burger and two hotdogs cost &3.70. How much does a hotdog cost?
Answer:
Step-by-step explanation:
Price of a hotdog = $0.86
What is an equation?An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
For example, 2x – 5 = 13.
Here,
2x – 5 and 13 are expressions.
The sign that connects these two expressions is “=”.
Given,
2 burgers and 1 hotdog cost = $4.82
1 burger and 2 hotdogs cost = $ 3.70
The price is same
Let the price of burger be x and price of hotdog be y
then,
2x + y = 4.82 ---------(a)
x + 2y = 3.70
Multiplying 2 in above equation
2x + 4y = 7. 40 -----------(b)
Subtracting equation (a) from equation (b)
2x + 4y - (2x+y) = 7.40 - 4.82
2x + 4y -2x -y = 2.58
3y = 2.58
y = 2.58/3
y = 0.86
Price of hotdog = $0.86
Hence, a hotdog costs $0.86.
Learn more about equation here:
brainly.com/question/29657983
#SPJ2
A student is solving a system of equations by substitution and comes up with the solution -3=2. Assuming that she solved the problem correctly, which of the following can be said about this system of equations?
A) the system has exactly 1 solution.
B) the system has exactly 2 solutions.
C) the system has infinitely many solutions.
D) the system has no solution.
HELLLP PLZZZZZ
Answer:
D) the system has no solution.
Step-by-step explanation:
A student is solving a system of equations by substitution and comes up with the solution -3=2.
So, the unknown variables are canceled out and there are only numbers in the equation but -3 ≠ 2.
If we assume that she solved the problem correctly, then there will be no solution for that system of equations because there is no variable remaining in the final equation to solve for. (Answer)
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions
The question is incomplete, here is the complete question:
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions. Write a system of linear equations that represents this situation.
The system of linear equations that represents this situation is:
x + y = 42
x - y = 8
Step-by-step explanation:
To solve the problem assume that
x represent the number of magazine subscriptions that your friend selly represents the number of magazine subscriptions that you sell∵ Your friend sells x magazine subscriptions
∵ You sell y magazine subscriptions
∵ Together you sell 42 magazine subscriptions
∴ x + y = 42 ⇒ (1)
∵ You sell 8 fewer magazine subscriptions than your friend
∵ Your friend sells x magazine subscriptions
∵ You sell y magazine subscriptions
- That means y = x - 8
∴ y = x - 8
- Add 8 for both sides
∴ 8 + y = x
- Subtract y from both sides
∴ 8 = x - y
- Switch the two sides
∴ x - y = 8 ⇒ (2)
The system of linear equations that represents this situation is:
x + y = 42
x - y = 8
Learn more:
You can learn more about the system of linear equations in brainly.com/question/6075514
#LearnwithBrainly
Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven. Pick a U.S. city and research the rates of two
different cab companies in that city. Find companies that charge different amounts per mile and have different flat fees. If you have trouble finding this information for two companies, you can make up what you think would be reasonable prices for a cab's flat rate and a cab's rate per mile.
Answer:
1. New York City: The initial charge is $ 2.50 plus $ 0.50 per 1/5 mile when traveling above 12 mph or per 60 seconds in slow traffic or when the vehicle is stopped. There are other surcharges for overnight, rush hour or congestion.
2. Boston: First 1/7 Mile: $2.60 and each 1/7 Mile thereafter: $0.40.
3. Houston: First 1/11 mile $2.80 , each additional 1/11 mile $0.20 . Rate per mile after first mile $2.20 and wait time per minute $0.40.
Step-by-step explanation:
Normally, there's a standard fare for each city, so for answering the question we picked three well-known cities for comparing the fares.
1. New York City: The initial charge is $ 2.50 plus $ 0.50 per 1/5 mile when traveling above 12 mph or per 60 seconds in slow traffic or when the vehicle is stopped. There are other surcharges for overnight, rush hour or congestion.
2. Boston: First 1/7 Mile: $2.60 and each 1/7 Mile thereafter: $0.40.
3. Houston: First 1/11 mile $2.80 , each additional 1/11 mile $0.20 . Rate per mile after first mile $2.20 and wait time per minute $0.40.
Line 1 thru (3,2) and (5,-1)
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slopw and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, - 1)
m = [tex]\frac{-1-2}{5-3}[/tex] = - [tex]\frac{3}{2}[/tex], thus
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 2), then
2 = - [tex]\frac{9}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{9}{2}[/tex] = [tex]\frac{13}{2}[/tex]
y = - [tex]\frac{3}{2}[/tex] x + [tex]\frac{13}{2}[/tex] ← equation of line
Answer:
The equation of the line passing through the given points is
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]
Step-by-step explanation:
GIven two points are (3,2) and (5,-1)
To find the equation of the line passing through these two points
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the two points (3,2) and (5,-1) respectively
Using the two points formula for finding slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-1-2}{5-3}[/tex]
[tex]m=\frac{-3}{2}[/tex]
Therefore [tex]m=-\frac{3}{2}[/tex]
By using formula:
[tex]y=mx+c[/tex]
Here Let (x,y) be (3,2)
[tex]y=mx+c[/tex]
[tex]2=-{\frac{3}{2}}\times 3+c[/tex]
[tex]2=\frac{-9}{2}+c[/tex]
[tex]c=\frac{9}{2}+2[/tex]
[tex]c=\frac{9+4}{2}[/tex]
[tex]c=\frac{13}{2}[/tex]
Therefore substitute values of m and c in
[tex]y=mx+c[/tex]
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]
Therefore the equation of the line passing through the given points is
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]