how do you solve this system , y=1/2x-4 and y=-2x+1 by graphing
Answers
Answer:
x=2
y=-3
Step-by-step explanation:
we have
[tex]y=\frac{1}{2}x-4[/tex] ----> equation A
[tex]y=-2x+1[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system of equations by graphing is the intersection point both lines.
using a graphing tool
The intersection point is (2,-3)
therefore
The solution is
x=2
y=-3
Related Questions
Find the equation of the line with slope m = 3/2 that contains the points (2,1).
Answers
Answer:
y=3/2x-2
Step-by-step explanation:
m=3/2 A(2,1)=A(x1, y1) ... x1=2,y1 =1
y-y1=m(x-x1)
y-1=3/2(x-2)
y-1=3/2x-3/2*2
y-1=3/2x-3
y=3/2x-3+1
y=3/2x-2
A function is given:
f(x) = 3x + 12
a. Determine the inverse of this function and name it g(x).
b. Use composite functions to show that these functions are inverses.
c. Evaluate f(g(–2)). Explain: What is the domain?
WILL GIVE BRAINLIEST PLEASE EXPLAIN WELL
100 POINTS
Answers
Answer:
Step-by-step explanation:
hello :
a)
let f(x) = y so : x = g(y)
in expression = f(x) =3x+12
means : y = 3x +12 calculate : x
3x = y -12
x = (1/3)y - 4
the inverse is : g(x) = (1/3)x - 4
b)f(g(-2) = f(-14/3)
because: g(-2) = (1/3)(-2)-4 = -2/3-4 = -14/3
so : f(g(-2) = f(-14/3)=3(-14/3)+12 = - 2
1. The inverse of the function is g(x) = (1/3)x - 4.
3. The value of f(g(–2)) is -2.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x)= 3x+ 12
1. let f(x) = y then x = g(y)
y = 3x+ 12
y- 12 = 3x
x= y/3 + 4
So, the inverse of the function is g(x) = (1/3)x - 4.
2. For showing the function are inverse we have to that
(fog)(x) = f(g(x)) =x and (gof)(x) =g(f(x)) = x
Take (fog)(x) = f(g(x))
= f( (1/3)x - 4.)
= 3 ((1/3)x - 4) 12
= x - 12 + 12
= x
Now, (gof)(x)
=g(f(x))
= g(3x+ 12)
= (1/3) ( 3x+ 12) -4
= x + 4 - 4
= x
3. f(g(-2))
So, g(-2)
= (1/3)(-2)-4
= -2/3-4
= -14/3
Then, f(g(-2)) = f(-14/3)
=3(-14/3)+12
= - 2
Learn more about function here:
https://brainly.com/question/12431044
#SPJ2
Ashley is deciding between two jobs. Job A pays $2000 per month with a monthly raise of $85. Job B pays $2000 per month with a monthly raise of 4%. Write a function to represent the monthly salary for Job B after x months.
Answers
The monthly salary for Job B after x months, which includes a 4% monthly raise, can be represented by the exponential function S(x) = 2000 * (1 + 0.04)^x, where S(x) is the salary and x is the number of months.
Explanation:To represent the monthly salary for Job B after x months, we need to account for the 4% raise each month. Since the starting salary is $2000, and the raise is 4% (or 0.04 in decimal form) of the previous month's salary, the function to represent the monthly salary can be written using a geometric sequence formula.
Let S(x) be the salary at month x. The function will be an exponential function in the form:
S(x) = 2000 * (1 + 0.04)^x
Here, 2000 is the initial salary, 0.04 represents the 4% raise, and x is the number of months that have passed.
A balance scale was in perfect balance when Jane placed a box of candy on one pane of the balance and 3/4 of the same sized candy box together with 3/4 pound weight on the other pane. How much did the full box of candy weight.
Answers
Answer:
Step-by-step explanation:
i'm pretty sure that you will have to add it.
so, when we add two fractions such as 3/4 + 3/4, we make sure that the denominators (the bottom numbers) are the same and then we simply add the numerators (the top numbers).
in this problem, the denominators are the same so we will simply add 3+3 which equals to 6/4. the denominator will remain the same.
answer:
3/4 + 3/4 = 6/4
i hope this is helpful.
The required weight of the candy box is 3 pounds.
Given that,
A balance scale was in perfect balance when Jane placed a box of candy on one pane of the balance and 3/4 of the same-sized candy box together with 3/4 pound weight on the other pane.
To determine how much the full box of candy weighs.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the weight of the candy box be x,
3/4 of the same-sized candy box
weight = 3/4 pound
x = 3/4x + 3/4
x / 4 = 3/4
x = 3
Thus, the required weight of the candy box is 3 pounds.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Kevin and Marcus were comparing their ages. The same of their ages was at least 9 years but was at most 24 years. If Kevin is 6 years old, which of the following inequalities represents all possible values for Marcus age, m?
Answers
The inequality that represent age of marcus is:
[tex]24\geq 6+m\geq 9[/tex]
The possible values for age of Marcus is:
m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Solution:
Given that,
The sum of ages of Kevin and Marcus was at least 9 years but was at most 24 years
Kevin is 6 years old
Let "m" be the age of Marcus
Thus we frame a inequality as:
[tex]24\geq \text{ sum of ages } \geq 9[/tex]
at least 9 years means that "greater than or equal to 9"
at most 24 years means "less than or equal to" 24
From given,
Sum of ages = kevin age + marcus age
Sum of ages = 6 + m
Thus the inequality is:
[tex]24\geq 6+m\geq 9[/tex]
Solve the inequality
[tex]\mathrm{If}\:a\ge \:u\ge \:b\:\mathrm{then}\:a\ge \:u\quad \mathrm{and}\quad \:u\ge \:b\\\\24\ge \:6+m\quad \mathrm{and}\quad \:6+m\ge \:9\\\\Solve\ them\ separately[/tex]
[tex]24\ge \:6+m\\\\\mathrm{Switch\:sides}\\\\6+m\le \:24\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\le \:24-6\\\\\mathrm{Simplify}\\\\m\le \:18[/tex]
Now solve another inequality
[tex]6+m\ge \:9\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\ge \:9-6\\\\\mathrm{Simplify}\\\\m\ge \:3\\\\\mathrm{Combine\:the\:intervals}\\\\m\le \:18\quad \mathrm{and}\quad \:m\ge \:3\\\\\mathrm{Merge\:Overlapping\:Intervals}\\\\3\le \:m\le \:18[/tex]
[tex]24\ge \:6+m\ge \:9\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:3\le \:m\le \:18\:\\ \:\mathrm{Interval\:Notation:}&\:\left[3,\:18\right]\end{bmatrix}[/tex]
Thus possible values for age of Marcus is:
m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
I am a fraction that is greater than 1 but less than 2 the sum of my numerator and denominator is 11 my denominator subtracted from my numerator is 1 what fraction am I
Answers
Answer:
that fraction is an improper fraction I think.
Using the values from the graph, compute the values for the terms given in the problem. Choose the correct answer.
Percentage of
Market Value
of Car
(solid line)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Maintenance and Repair Costs
as Percentage of Car's Value
(dashed line)
-
-
-
0
1st
yr.
2nd
yr.
3rd
yr.
4th
yr.
5th
yr.
6th
yr.
7th
yr.
8th
YT.
9th
yr.
10th
yr.
Age of car = 6 years.
Original cost = $12,995.
The current market value is $
Answers
Answer:
$1299.50
Step-by-step explanation:
It appears that the graph shows the percentage of market value of a 6-year-old car is about 10%. So the value of such a car with an original value of $12,995 would be ...
$12,995 × 0.10 = $1299.50
The current market value is $1299.50.
The current market value of the car is $1299.50
How to determine the current market valueThe original cost is given as:
Original = $12,995.
From the graph, the worth of the car after 6 years is
Rate = 10%
So, the current market value of the car is:
Value = $12,995 * 10%
Evaluate the product
Value = $1299.50
Hence, the current market value of the car is $1299.50
Read more about depreciation at:
https://brainly.com/question/843074
PLEASE HELP ME FAST. WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER
The following data set is graphed on a coordinate plane: (10,45), (25,70), (46,105). If the y-intecept of the line of best fit is at 28.5 ,what would be the most reasonable slope of line: 1/3, 5/3, or -4/3? Show/explain how you know.
Answers
Slope is the change in Y over the change in. X
Using two of the given points:
Slope = 70-45 / 25-10
Slope= 25/ 15
Slope = 5/3
$239 television; 10% discount
Answers
answer: $215.10
the TV's original price is $239, but with 10% off, it is now 90% of the original price. therefore we have to find 90% of 239:
0.90*239=215.10
Answer:
215.10 here ya go
How many different triangles can you make if you’re giving the measurements for two sides and the angle between those sides
Answers
Answer:
1
Step-by-step explanation:
When is a zero not significant?
O
A. When it comes after the decimal point, as in 4.000
O
B. When it is included in scientific notation, as in 3.04 x 10-2
O
C. When it precedes a non-zero digit but falls after a decimal point,
as in 0.0004
O
D. When it falls between two non-zero digits, as in 4.09
Answers
Answer: A. When it comes after the decimal point, as in 4.000
Step-by-step explanation: If there are no other numbers after the zeros, there is no reason for them to be place holders. Zeros in decimals act as place holders such as in 4.09 or 4.0009. This actually does change the value of the decimal but 4.000 is just the same as a regular old 4. Hope this helps!
Given the point (-5,6), what is the value of the y-coordinate?
The y-coordinate of the point is
(Type an integer or a decimal.)
Answers
Answer:
6
Step-by-step explanation:
The numbers in an ordered pair are usually (x, y). That is, the y-value comes second in the pair.
The second number in your ordered pair is 6. The y-coordinate is 6.
Find the slope of the following and then write the equation
Answers
Answer:
See explanation
Step-by-step explanation:
Assuming we want to find the slope and equation of the line going through:
(0,1) and (1,2).
Then the slope is given by:
[tex]m = \frac{2 - 1}{1 - 0} [/tex]
This implies that:
[tex]m = 1[/tex]
The equation is given by:
[tex]y = mx + b[/tex]
Where b=1 is the y-intercept since the line passes through (0,1).
Hence the equation is:
[tex]y = x + 1[/tex]
There are 95 students who have applied for a scholarship.
If there are 41 men and 36 minorities, 19 of whom are
women, how many women applied for the scholarship?
Answers
Answer:
37
Step-by-step explanation:
Students who applied or a scholarship=95
Of that:
Men= 41
Minorities= 36
Minorities who are women= 19
Minorities who are men = 36-19=17
Women+ Minorities who are women=Students who applied or a scholarship-(Men+Minorities who are men)
x + 19=95-(41+17)
x+19=95-58
x+19=37
x= 37-19
x=18
Women who are NOT minority=18
Total women=Minorities who are women+Women who are NOT minority
Total women=18+19
Total women=37
By understanding the problem as a basic arithmetic problem, we determine there are 54 women who applied for the scholarship by subtracting the number of men (41) from the total number of students (95).
Explanation:To resolve the question, 'how many women applied for the scholarship', it's essential to understand the problem as a basic addition and subtraction problem. The numbers provided in the question give us initial points. It's stated that there are 41 men who applied, and if there are 95 students in total, we can calculate the total women by subtracting the number of men from the total. So, 95 total students - 41 men = 54 women. This calculation gives us the number of women that applied for the scholarship.
Learn more about addition and subtraction problemhttps://brainly.com/question/25421984
#SPJ12
a line with a slope of -3 and an x-intercept of 15 passes through wich of the following points
A. (0,30)
B. (5,15)
C. (10,10)
D. (−5,60)
Answers
The Answer is D) because it is
A jar contains 12 caramels, 7 mints and 16
dark chocolates. What is the probability of
selecting a mint expressed as a fraction?
Answers
Answer:
Step-by-step explanation:
Add the three digits together:
12+7+16=35
7/35, or 1/5.
Kelsey solved the following equation:
7x − one over two (8x + 2) = 6
Step Work Justification
1 7x − 4x − 1 = 6
2 3x − 1 = 6
3 3x = 7
4 x = 7 over 3
Which of the following has all of the correct justifications Kelsey used to solve this equation?
Answers
1. distributive property
2. combine like terms
3. addition property of equality
4. division property of equality
Solution:Given that,
Kelsey solved the following equation:
[tex]7x - \frac{1}{2}(8x+2) = 6[/tex]
Step 1:By distributive property,
a(b + c) = ab + bc
Therefore,
[tex]7x - (\frac{1}{2} \times 8x)+( \frac{-1}{2} \times 2)= 6\\\\7x - 4x - 1 = 6[/tex]
Step 2:Combine the like terms
7x - 4x - 1 = 6
3x - 1 = 6
Step 3:Addition property of equality
The property means that when we add the same number to both sides of an equation, the sides remain equal
3x - 1 = 6
Add 1 on both sides
3x - 1 + 1 = 6 + 1
3x = 7
Step 4:Division property of equality
The Division Property of Equality means that when we divide both sides of an equation by the same non zero number, the sides remain equal
3x = 7
Divide both sides by 3
[tex]\frac{3x}{3} = \frac{7}{3}\\\\x = \frac{7}{3}[/tex]
Thus the correct justifications Kelsey used to solve this equation is:
1. distributive property. 2. combine like terms. 3. addition property of equality. 4. division property of equality
Answer:
I took the test it is 1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality
Write the equation y-2=6x+3 in y=mx+b form
Answers
Answer:
y=6x+5
Step-by-step explanation:
y-2=6x+3
y=6x+3+2
y=6x+5
What situation can be represented by the expression-3 + 3?
A. Nancy owes $3 on an account and then withdraws another $3.
B. Jason pays $3 on the $3 he owes in fines.
C. There is a change in temperature from -3 degrees F to 0 degrees F.
D. A toy car travels at a rate of 3 meters per minute for 3 minutes.
E. Teri’s score in a word game is 0 after scoring 3 points.
My son has chosen C and E as the answers. Correct?
Answers
Answer:
Step-by-step explanation: It B
-3 + 3 = 0
How do you write nine and two hundred thirty five thousandths?
Answers
Answer:
9.235
Step-by-step explanation: There you g. Hope it helps!
WILL GIVE BRAINLIEST You can draw a quadrilateral with no parallel lines and at least one right angle. True/ False
Answers
Answer:
True because a right angle can't exist with any parallel lines.
Answer:
true hope this helped.
Step-by-step explanation:
Solve the system of linear equations below.
2х + Зу = 2
х+ 6у = 4
А. x = 0, y=2/3
Bх = 2, y = -2/3
C. х = 4/3, у=2/9
D. x = 4, y = -2
Answers
Multiply the 2nd equation by -2
-2x -12y = -8
Then add it to the 1st equation
-9y = -6
y = 2/3
By substituting in the 1st equation
2x + 3(2/3) = 2
2x = 0
x=0
Find the sum of 8 + 11 + 14 + ... + 602 + 605.
Answers
Answer:
61300
Step-by-step explanation:
Y=5x+39
Y=3.5x+60
Solve the following system
Answers
x=14 and y=109
Step-by-step explanation:
Given
y= 5x +39
y= 3.5x +60
5x+39 = 3.5 x+60
5x-3.5x = 60-39
1.5x =21
x= 21/1.5 = 14
Use the value of x = 14 in equation y=5x+39
y=5*14 +39
y=109
Hence, x=14 and y=109
Learn More
Simultaneous equations:https://brainly.com/question/12318095
Keywords : solve, system , equations
#LearnwithBrainly
Final answer:
To solve the given system of linear equations, we use the elimination method to find the intersection point (14, 109), which is where the two lines represented by the equations meet.
Explanation:
To solve the system of equations:
y = 5x + 39
y = 3.5x + 60
We can use the method of substitution or elimination. In this case, elimination is the straight-forward choice. Since both equations are already solved for y, set them equal to each other and solve for x:
5x + 39 = 3.5x + 60
Now, subtract 3.5x from both sides:
1.5x + 39 = 60
Subtract 39 from both sides:
1.5x = 21
Divide both sides by 1.5:
x = 14
Now, plug the value of x into one of the original equations to solve for y:
y = 5(14) + 39
y = 70 + 39
y = 109
The solution to the system is (14, 109). This represents the point where the two lines intersect on a graph.
6,000(1-(1+0.06)‐³²)/0.06(1+0.06)
Answers
Answer:
79716.98
Step-by-step explanation:
Woahhhhhh numbers
Step-by-step explanation:
I don’t know.
URGENT WILL GIVE BRAINLIEST IF CORRECT!
Finley's pumpkin had a mass of 6.5 (kg) before he carved it. After carving it, the pumpkin had a mass of 3.9 kg
What was the percent decrease in the mass of the pumpkin?
Answers
Answer:
40% decrease
Step-by-step explanation:
6.5*40%=2.6
6.5-2.6=3.9
Answer:
40%
Step-by-step explanation:
Original Mass of the pumpkin = 6.5kg
After carving, the mass of the pumpkin became = 3.9 kg
Decrease in mass = 6.5 — 3.9 = 2.6kg
Therefore, the percentage decrease in mass of the pumpkin = (2.6/6.5)x100 = 40%
Check your answer for 3(p+2)=18
Answers
3(p + 2) = 18
3p + 6 = 18
3p = 12
p = 4
Check:
3(p + 2) = 18
3(4 + 2) = 18
3(6) = 18
18 = 18
This proves that p = 4.
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Answer: p = +4
Step-by-step explanation: To solve this equation for p, our first step is to distribute the 3 through the parentheses on the left side.
3 times p is 3p and 3 times 2 is 6.
So we have 3p + 6 = 18.
Next, we need to isolate the p term by subtracting 6 from both sides of the equation to get 3p = 12.
Finally, we divide both sides of the equation by 3 to get p = +4.
3(p-3) – 5p>-3p- 6
How do u solve?
Answers
Answer:
p>3
Step-by-step explanation:
<=> 3p - 9 - 5p > -3p - 6
<=> -2p + 3p > -6 + 9
<=> p > 3
To solve the inequality 3(p-3) - 5p > -3p - 6:
Simplify and combine like terms to get p > 3 as the solution.
An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.
The given expression is:
3(p-3) – 5p>-3p- 6
Distribute the 3 to the terms inside the parentheses:
3p - 9 - 5p > -3p - 6
Combine like terms on both sides of the inequality:
-2p - 9 > -3p - 6
Move all the terms containing p to one side by adding 3p to both sides: -2p + 3p - 9 > -6
Simplify:
p - 9 > -6
Move the constant term to the other side by adding 9 to both sides:
p - 9 + 9 > -6 + 9
Simplify: p > 3
Hence,
The solution of the given inequality is p > 3.
To learn more about inequality visit:
https://brainly.com/question/30231190
#SPJ6
Evaluate the expression 1/3(4+18) -2 squared
Answers
Answer:
Evaluate the expression 1/3(4+18) -2 squared
Step-by-step explanation:
First of all we will add brackets to understand the question as:
= ((1/3) * (4+18) - (2 squared))
= ((1/3) * ( 22) - 2² )
According to Math's rule that Multiplication and division must be completed before addition and subtraction.
= (( 1/3 * 22) - 4 )
= (( 7.33) - 4 )
= ( 7.33 - 4 )
= 3.33
3.33 is the correct answer.
What was the origin of the territorial dispute over Taiwan
Answers
Answer:
The territorial dispute over Taiwan originated in 1949 when the Chinese people fled to Taiwan due to the complete control of Communists in Mainland China.
Explanation:
The event happened after the "Chinese Civil War," a war between the Kuomintang and the Communist Party of China (CPR). This resulted to many Chinese people fleeing from Southern China to Taiwan in order to prevent the advances of the Communist Party. This was also a sign of retreat from the war.
Moving to Taiwan from China took 4 months and this was meant to be a temporary solution rather than being permanent. However, the plan could not be realized thus, resulting to many Chinese people living in Taiwan until today.
So, this led to the controversial issue that Taiwan is, somehow, part of China. In connection with this, territorial disputes arose whether Taiwan should be unified with Mainland China.