A pair of equations is shown below:
y = 6x − 4
y = 5x − 3
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
Answers
Linear equations are written in the format y = mx+b, where m represents the slope/slope intercept and b represents the y-intercept.
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Part A
the slope and y-intercept
y = mx +b
m - the slope; b- y-intercept
therefore;
y = 6x - 4
m = 6; b = -4
y = 5x - 3
m = 5; b = -3
The coordinates of the point where the lines are crossed are the solution to the system of linear equations.
How to graph the lines:
y = 6x - 4
y-intercept (0; -4)
for x = 1 ⇒ y = 6 · 1 - 4 = 6 - 4 = 2 ⇒ (1; 2)
y = 5x - 3
y-intercept (0; -3)
for x=1 ⇒ y = 5 · 1 - 3 = 5 - 3 = 2 ⇒ (1; 2)
***look at the img for graph reference***
Part B: x = 1; y = 2
Related Questions
Brenda needs $40 to buy a large box of chocolate. She has saved $12 and plans to work as a babysitter to earn $7 per hour. Which inequality shows the minimum number of hours, n, that Brenda should work as a babysitter to earn enough to buy the large box of chocolate?
Answers
If n = number of hours Brenda works then her baby sitter earning = 7n
12 + 7n ≥ 40 , so n≥4
So answer is c
By definition, a rational number is a number q that can be written as a fraction in the form q=a/b where a and b are integers and b≠0. So, 1/3 is rational because it is exactly what you get when you divide one integer by another.Sep 22, 2015
Answers
A 1:35 scale model of a fishing hut is 17 cm tall, 18 cm wide, and 19.7 cm long. What are the dimensions of the actual ice fishing hut?
Answers
17*35 = 595 cm
18*35 = 630 cm
19.7 * 35 = 689.5 cm
in meters the dimensions are L = 6.895 m, W = 6.3 m and H = 5.95 m
To determine the actual size of an ice fishing hut from a 1:35 scale model, multiply each model dimension by 35, resulting in a real hut approximately 5.95 meters tall, 6.3 meters wide, and 6.895 meters long.
The dimensions of the actual ice fishing hut, based on the 1:35 scale model, can be found by multiplying each dimension of the model by 35. To find the height, multiply 17 cm by 35, which gives 595 cm or 5.95 meters. To find the width, multiply 18 cm by 35, which gives 630 cm or 6.3 meters. Finally, to find the length, multiply 19.7 cm by 35, resulting in 689.5 cm or 6.895 meters. Therefore, the actual dimensions of the ice fishing hut are approximately 5.95 meters tall, 6.3 meters wide, and 6.895 meters long.
how do you solve for the variable ?? help
Answers
2(3x - 4) + 10 = 5(x + 4)
First, let's distribute 2 to 3x and -4, then 5 to x and 4.
2(3x) + 2(-4) + 10
6x - 8 + 10
6x + 2 is our first half of the equation simplified. Now let's do the other.
5(x + 4)
5(x) + 5(4)
5x + 20 is our second half of the equation simplified. Now let's put them back in their original spots.
6x + 2 = 5x + 20
Get x on one side - subtract 5x from both sides.
x + 2 = 20
Isolate x by adding 8 to both sides.
x = 18 is our answer.
I hope this helps!
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 3θ. PLEASE HELP ME SOLVE RN I NEED THIS, ALSO INCLUDE THE PROVING PART.
Answers
If
f(r, θ) = f(r,-θ), symmetric to the polar axis or the x-axis
f(r, θ) = f(-r,θ), symmetric to the y-axis
f(r, θ) = f(-r,-θ), symmetric to the pole or the origin
Test for symmetry about the x-axis
f(r,θ): r=4 cos3θ
f(r,-θ): r = 4 cos3(-θ) ⇒ r = 4 cos3θ
∴The graph is symmetric about the x-axis.
Test for symmetry about the y-axis
f(r,θ): r=4 cos3θ
f(-r,θ): -r = 4 cos3θ
∴The graph is not symmetric about the y-axis.
Test for symmetry about the origin
f(r,θ): r=4 cos3θ
f(-r,-θ): -r = 4 cos3(-θ) ⇒ r = -4 cos3θ
∴The graph is not symmetric about the origin.
Martina purchased a prepaid phone card for $15.00. Calls cost 5 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for x minutes of calls is given by the following function.
C (x) = 15.00 -0.05x
How much credit is left on the card after Martina uses it for 20 minutes of calls?
Answers
C(x) = 15.00 - 0.05x
C is how many dollars are left after
x minutes.
So if she uses it for 20 minutes, input that into the x.
C(20) = 15.00 - 0.05(20)
C(20) = 15.00 - 1
C(20) = 14.00
After 20 minutes, there are $14.00 left on the card.
find the value of x below if necessary round to the nearest tenth.
NEED ANSWER PLEASE HELP
Answers
x = 20 x sin(27)
= 9.0798
rounded to nearest tenth = 9.1
Anton bought a picnic cooler. His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without tax? The cost of an item is 100% of its price. What number goes in the ? Of the additional problem
Answers
1.00-0.06 = 0.94
7.95 x 0.94 = 7.473, round to 7.47 without the tax
Help me with the first question
Answers
Part B) The discount here is 10%. So far, discount A is better
Part C) The discount here is 15%. Discount A is also better because 15.798% is larger than 15%
Part D) Convert 1/4 to decimal form to get 0.25 and then move the decimal point 2 spots to the right to get 25%. So 1/4 = 25%. The discount here is 25%. This discount (of 25%) is much better than discount A.
Store 5 has the best discount since 25% is the largest among all the percentages.
Answer: Choice D)
Which statement is true about the circumference of a circle?
It is about three times the diameter.
It is about three times the radius.
It is about twice the radius.
It is about half the diameter.
Answers
C = pi*d
where
C = circumference
pi = 3.14 approximately
d = diameter
So saying "the circumference is roughly 3 times the diameter" is appropriate because pi = 3.14 is roughly 3 if you round to the nearest whole number.
Answer: Choice A) three times the diameter
If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second. A. True B. False
Answers
We have P(Day 1 ∩ Day 2) = 0.1 and P(Day 1) = 0.4
We can deduce that 30% of the group ONLY had sandwiches on Day 1 and there's 60% of the group ONLY had sandwiches on Day 2.
We obtain the value 60% = 0.6 from 100%-(10%+30%)=60%
We also can deduce that there 70% of the group that had sandwiches on Day 2
The proportion of people who ate sandwiches on Day 2 GIVEN that they ate sandwiches on Day 1 is given by
P(Day 1 ∩ Day 2)÷P(Day 2) = 0.1÷0.4 = 0.25 = 25%
The statement is TRUE
I can't seem to figure it out can someone please help me??
Answers
We know that line DC = 16, that means line AD also 16
Line AE = ED = 8
Line EF = FD = 4
Line FG = GD = 2
Line DB = 16+32 = 48
Line DH = 48/2 = 24
Line GH = 2+24 = 26
Complete the equation and tell what property you used 16+31=31+16
Answers
In your day-to-day routines, you use math when you go to the grocery store, bank, mall and when cooking. How do you imagine that you will use math in your healthcare career?
Answers
Which property of real numbers is illustrated by the following statement?
6(7x) = (6 ∙ 7)x
Answers
answer
Associative Property of Multiplication
Which of these is the algebraic expression for "some number to the power of 4?"
x4
4x
4x
x + 4
Answers
Answer:
They deserve brainliest!
Step-by-step explanation:
In this exercise we have to identify the formula that is being treated in a written way, so correlating correctly we have:
Letter A
What is power number?The power is a simplified notation of representing the multiplication of a number, which we call the base, repeatedly by the value of a power that determines how many times we must multiply this number.
So the only one that corresponds to "some number to the power of 4" is:
[tex]x^4[/tex]
See more about power at brainly.com/question/1618040
In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of m?
A. m = 2
B. m = 3
C. m = 19
D. m = 35
Which is the correct answer???
Answers
Answer: The correct option is (C) 19.
Step-by-step explanation: We are given to find the value of m so that the data the table to represent a linear function with a rate of change of –8.
We know that
the rate of change for a linear function with two points (a, b) and (c, d) is given by
[tex]R=\dfrac{d-b}{c-a}.[/tex]
From the table, we note that the points (10, 27) and (11, m) satisfy the given linear function.
So, the rate of change of the linear function will be
[tex]R=\dfrac{m-27}{11-10}\\\\\\\Rightarrow -8=\dfrac{m-27}{1}\\\\\Rightarrow -8=m-27\\\\\Rightarrow m=27-8\\\\\Rightarrow m=19.[/tex]
Thus, the required value of m is 19.
Option (C) is CORRECT.
Create a scenario that leads to an inequality of the form ax + b > c.
Answers
Answer:
Ben needs more than 200 points to unlock the next level in the game
He already has 45 points
For every win, he receives 5 points
No. of wins required: x
5x + 45 > 200
solve for w.
7w=11.2
Answers
To solve for w, all you have to do is divide both sides of the equation by 7. This will get rid of the coefficient on the variable, w, allowing you find out what it equals. 11.2/7 = 1.6, and 7w/7 = w, so w = 1.6.
1/12 as a decimal. Long division.
Answers
NEED HELP FAST!!!
2.
Two lines, C and D, are represented by the equations given below:
Line C: y = x + 10
Line D: y = 3x + 2
Which of the following shows the solution to the system of equations and explains why? (5 points)
(5, 17), because one of the lines passes through this point
(5, 17), because the point lies between the two axes
(4, 14), because the point does not lie on any axis
(4, 14), because both lines pass through this point
Answers
[tex]x+10 = 3x+2 \\ x+8=3x \\ 8=2x \\ x=4\\[/tex]
To find the value of y, just plug x back into one of the equations:
[tex]y=4+10 \\ y=14[/tex]
The answer to the system is (4,14), but there are two choices corresponding to that. Because this system has a solution that satisfies both x and y, they intersect at a certain point (4,14)
Your answer is (4, 14), because both lines pass through this point
Answer:
answer D
Step-by-step explanation:
What is 1 3/4 - 5/6r =8/3
Answers
-5/6r + 7/4 = 8/3
-5/6r +7/4 - 7/4 = 8/3 -7/4
-5/6r = 11/12
(6/-5)*(-5/6r)=(6/-5)*(11/12)
=-11/10
r = -1 1/10
What is the circumference of a circle with a 7 foot diameter
Answers
Answer: 21.98 feet
given that diameter=7ft
circumfernece=7ft times pi
circumfernce=7π ft or aprox 21.98ft
Grandma baked 96 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received 5 fewer cookies than she would have received had all of the cookies been evenly divided among the h grandchildren.
How many cookies did Cindy receive?
Write your answer as an expression.
Answers
So Cindy received (96/h) - 5 cookies
even number= 96/n, Cindy gets 96/n-5, the rest receive the rest of the cookies:
96 - (96/n-5) = 96*(1-1/n) + 5 = 96*(n-1)/n + 5.
Then each of them (n-1) receive the previous number divided by (n-1) -Cindy is not there:
each of the other grandchildren receives:
96/n + 5/(n-1), and Cindy receives 96/n-5, it just needs to be positive.
So any number 'n' which divides 96 and 'n-1' divides 5 works.
Indeed ONLY n=6, makes 5/(6-1) possible.
So there are 6 grandchildren:
5 receive 17 cookies, and Cindy gets 11.
If it were evenly distributed, all would have got 96/6 = 16 cookies.
Now 5 get one more cookie, and Cindy 5 less.
WOW. Very nice problem!! Gonna share it :)
simplify (4x-4)-3 , pleas help
Answers
unless it asks you to factorise again
12(x+1)
hope this helps! Dont forget to put it as the brainliest answer to help me out too xD
[tex](4x-4)-3[/tex]
Add like terms
[tex]4x-7[/tex]
This is the furthest you can simplify this expression.
Hope this helps.
-Benjamin
A watering can dispenses water at a rate of 0.15 gallon per minute. The original volume of water in the can was 5 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y) as a function of time in minutes (x) from the first minute after the can starts dispensing water?
Answers
The initial volume of water in the can at time = 0 is 5 gallons
The function will be a linear function in the form of [tex]y=ax+b[/tex] where
[tex]y[/tex] is the volume of water in the can after [tex]x[/tex] minutes
[tex]a[/tex] is the changing rate
[tex]b[/tex] is the initial volume when time is 0
Substitute all the values into the form we have
[tex]y=0.15x+5[/tex]
Answer:
The changing rate of the amount of water in the watering can is a constant rate of 0.15 gallon per minute.
The initial volume of water in the can at time = 0 is 5 gallons
The function will be a linear function in the form of where
is the volume of water in the can after minutes
is the changing rate
is the initial volume when time is 0
Substitute all the values into the form we have
Step-by-step explanation:
y=0.15x +5
solve
18x^2 -3x -10
What is the smallest solution
Answers
x^2-3x-180
(x-15)(x+12)
(6x-5)(3x+2)
Using ZPP
6x-5=0
6x=5
x=5/6 <=== one of the roots
3x+2=0
3x=-2
x=-2/3 <==== another root
Final answer: -2/3
the height of an object dropped from the top of a 320-meter building is given by h(t)= -5t^2+320. how long will it take the object to hit the ground
Answers
320=5t^2
t^2=64
t^2=8^2
t=8
if x=2 , y=3 , and z=4 , what Is xyz?
Answers
2*3*4
6*4
24
Final answer: 24
If F(x)=8x, which of the following is the inverse of F(x)
Answers
[tex]f(x) = 8x[/tex]
let : [tex]y=8x[/tex]
so : [tex]x= \frac{1}{8} y[/tex]
the inverse of [tex]f(x)[/tex] is : [tex]g(x) = \frac{1}{8} x[/tex]
Answer: answer is F^1(x) = x/8
Step-by-step explanation: