3. (05.06 MC)
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > 3x + 10
y<-
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically. (4 points)
(10 points)
Answers
Answer:
Step-by-step explanation:
y > 3x + 10
y < -3x - 1
Part A:You'd graph the given systems of linear inequalities the same way as you graph the linear equations.
To graph y > 3x + 10, plot the y-intercept, (0, 10), then use the slope, m = 3 (rise 3, run 1), to plot other points on the graph. Use a dashed line (because of the ">" symbol).
Follow the same steps for the other linear inequality. Plot the y-intercept, (0, -1), then use the slope, m = -3 (down 3, run 1) to plot other points. Use a dashed line (because of the "<" symbol).
Pick a test point on either side of the boundary line and plug it into the original problem. This will help determine which side of the boundary line is the solution. Plug in a test point that is not on the boundary line.
Use the point of origin, (0, 0) as the test point. Plug in these values into the given systems of linear inequalities to see whether it will provide a true statement.
y > 3x + 10
0 > 3(0) + 10
0 > 0 + 10
0 > 10 (False statement).
y < -3x - 1
0 < -3(0) - 1
0 < 0 - 1
0 < -1 (false statement).
Since the point of origin provided a false statement to the given systems of linear inequalities, you must shade the half-plane region where it doesn't contain the test point.
Part B:
You'll do the same process as what I've done for the test point. Plug in the values of (8, 10) into the given systems of linear inequalities. If it provides a false statement, then it means that it is not a solution to the system.
y > 3x + 10
10 > 3(8) + 10
10 > 24 + 10
10 > 34 (False statement).
y < -3x - 1
10 < -3(8) - 1
10 < -24 - 1
10 < -25 (false statement).
Therefore, (8, 10) is not a solution to the system.
Related Questions
Help please!!!!!!!!!!!! I need help
Answers
Slope of second graph = 4
Slope of Function A is less than that of Function B
Answer:
The slope of Function A is less than the slope of Function B.
Step-by-step explanation:
Using the slope formula:
m = (y2 - y1)/(x2 - x1)
and the following ordered pairs from Function A:
(x1, y1) = (-5, -3)
(x2, y2) = (-10, -8)
m = (y2 - y1)/(x2 - x1)
[tex]m = \frac{-8 - (-3)}{-10 - (-5)} = \frac{-8 +3}{-10+5} = \frac{-5}{-5} = 1[/tex]
Since Function A's slope = 1, and Function B's slope = 4, then it means that the slope of Function A is lesser than the slope of Function B.
Help please.............................................................
Answers
Answer:
the third one
Step-by-step explanation:
The line passes through the point
- y int is -6
[tex]x/6=7/2x=[/tex]
Answers
Answer:
x = √21, x = -√21
Please help me solve this!! I will give brainliest and this is due in 10 minutes
There's a big soccer game next month, and Juan has purchased 3 tickets for himself and his siblings. He spent 53 dollars.
Rosie wants to take her family also, but knows her parents and some cousins will want to attend as well. She knows she will have to purchase 9 tickets. Estimate approximately how much money Rosie will likely have to spend on the tickets. Explain your reasoning below.
Answers
Answer:
53 divided by 3 would be $17.66
so 17.66 times 9 would be $158.94
Answer:
158.4 dollars
Step-by-step explanation:
so first of all the three tickets were 53 dollars so we divide the dollars and the no of tickets like this 53÷3 = 17.6 dollars
so since each ticket is 17.6 dollars now we know that Rosie wants to purchase 9 tickets so we will multiply the no of tickets by dollars per ticket like this
9×17.6= 158.4 dollars
and 158.4 is your answer
Compute the average rate of change of f(x)=(x+4)/(x-3) over the interval [5,7].
A)4/3
B)7/8
C)-7/8
D)-4/3
(Image attached below)
Answers
Answer:
C) - 7/8Step-by-step explanation:
Average rate of change is:
[f(7) - f(5)]/(7 - 5)Find the values and substitute into expression:
f(7) = (7 + 4)/(7 - 3) = 11/4f(5) = (5 + 4)/(5 - 3) = 9/2 = 18/4Find the rate of change:
(11/4 - 18/4)/2 = (-7/4)/2 = - 7/8Correct choice is C
What is the slope of a line perpendicular to the line whose equation is x-3y=12x−3y=12. Fully simplify your answer.
Answers
Answer:
(2+3y=12) that is the simplify form
9sin(2x) sin (x) = 9cos(x)
Answers
Answer:
[tex] \sin(2x) = 2 \sin(x) \cos(x) \\ 9( 2 \sin(x) \cos(x) ) \sin(x) = 9 \cos(x) \\ 18 { \sin}^{2} (x)9 \cos(x) - 9 \cos(x) = 0 \\ 9 \cos(x) (2{ \sin}^{2} (x) - 1) = 0 \\ 9 \cos(x) = 0 \: or \: 2{ \sin}^{2} (x) - 1 = 0 \\ \sin(x) = \pm \frac{1}{ \sqrt{2} } \\ \cos(x) = 0 \\ x = { \cos}^{ - 1} (0) \\ x = \frac{ \pi}{2} = 90 \degree \\ x = \frac{ \pi}{2} + 2\pi \: n \: \forall \: n \: \in \: \Z \\ = 90 \degree + 360\degree\: n \: \forall \: n \: \in \: \Z \\ = \pm\frac{ \pi}{4} \pm2\pi \: n \: \forall \: n \: \in \: \Z \\ x = \pm45\degree \pm 360\degree\: n \: \forall \: n \: \in \: \Z[/tex]
i need help ahhahahhahahwvwvvee
Answers
Answer:
C.
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Say we had 2 fractions:
2/4 & 3/6
and we were trying to find out if they were proportional.
An easy way to do this is to divide the numerator of the second fraction by the numerator of the first fraction, then multiply what you get by the denominator of the first fraction. If your final number equals the denominator of the second fraction, then the two fractions are proportional.
Let me demonstrate:
2/4 and 3/6
1. 3 ÷ 2 = 1.5
2. 1.5 × 4 = 6
3. 6 = 6
Therefore, these fractions are proportional.
Let's try another problem:
4/5 and 10/19
1. 10 ÷ 4 = 2.5
2. 2.5 × 5 = 12.5
3. 12.5 ≠ 19
Therefore, these fractions are not proportional.
Hope this helps!
Simplify 2x2 + 3x2 + 3x
Answers
Answer:
10+3x
Step-by-step explanation:
2(2) = 4
3(2) = 6
4+6 = 10
10+3x
Answer:
Step-by-step explanation:
what is 9x² -4 in factored form. i just need more help understanding how to do this.
Answers
Answer:
the factored form of 9x²-4 is (3x-2)(3x+2)
A basketball player made 12 out of 15 free throws she attempted.She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85%. Write an equation to represent this situation.
Answers
Answer:
(12 + x)/(15 + x) = 85/100
Step-by-step explanation:
12/15 = 0.8
She currently has an 80% rate.
To raise it, she needs to make x shots. Since she makes all x shots, we add x to both the number of shots made and attempts.
She will make 12 + x shots in 15 + x attempts.
We want that rate to be 0.85 which is the same as 85%.
(12 + x)/(15 + x) = 85/100
(12 + x)/(15 + x) = 17/20
20(12 + x) = 17(15 + x)
240 + 20x = 255 + 17x
3x = 15
x = 5
Answer:
The equation is (12 + x)/(15 + x) = 85/100.
Question
The formula for simple interest is I=Prt.
Solve the formula for t.
Answers
We can solve for t by making it the subject of the equation.
since I = Prt [divide both sides by Pr]
∴ I = t PrWhich expression is equivalent to 6m + (m – 2)(m + 7) + 3?
Answers
Answer:
m^2 + 11m - 11
Step-by-step explanation:
Step 1: Distribute.
[tex]6m + (m)(m) + (m)(7) + (-2)(m) + (-2)(7) + 3[/tex] [tex]6m + m^2 + 7m -2m -14 + 3[/tex]Step 2: Combine like terms.
[tex](m^2)+(6m+7m-2m)+(-14+3)[/tex] [tex]m^2 + 11m - 11[/tex]Therefore, the answer is [tex]m^2 + 11m - 11[/tex].
Work out the sum of 2/9 and 5/9 Give your answer in its simplest form.
Answers
Answer:
5 4/9
Step-by-step explanation:
Convert a mixed number 2 19
to a improper fraction: 2 1/9 = 2 19 = 2 · 9 + 19 = 18 + 19 = 199
Answer:
7 / 9
Step-by-step explanation:
You cannot simplify this fraction any more. The two fractions have the same denominator you can just add the numerators.
Identify the center and radius of the circle with equation x2 + y2 - 8x - 4y - 5=0.
center:
radius:
Answers
The radius is 5
Hope this helps
(x^2 - 8x + 16) + (y^2 - 4y + 4) = 5 + 16 + 4
(x - 4)^2 + (y - 2)^2 = 25 = 5^2
Centre at (4, 2) with radius = 5
Can someone tell me the answer to this please?
Answers
Answer:
B
Step-by-step explanation:
total cents is $4. there are 20 more nickels than quarters. how many nickels and how many quarters.
Answers
Answer:
Step-by-step explanation:
- 4х +4y +z= 24
2x – 4у +z= 0
- 3х + 6z =- 12
Answers
Answer:
here's the answer it's :
x=-28
y=-18
z=-16
-4(50x-20)=10x+15+23
Answers
Answer:
0.2 or 1/5
Step-by-step explanation:
-4(50x - 20) = 10x + 15 + 23
-200x + 80 = 10x + 38
80 = 210x + 38
42 = 210x
0.2 = x
Hope this helps! Pls give brainliest!
Answer: x = 1/5 or 0.2
Step-by-step explanation:
-4(50x-20)=10x+15+23
-200x +80=10x+38
-80 -80
-200x=10x-42
-10x. -10x
-210x = -42
/-42. /-42
= 5
PRE- CALC MATH HELP
100 Points and Brainlist.
if PDF doesn't work Follow the link in my comments
Follow the link for question
Answers
i cant see the pdf???????????????
Find the range of the function f (x) = 2x - 1 with the given domain -1, 0, 1, 2
I will give Brainliest!
Answers
Answer:2x-1
Step-by-step explanation:
Solve and graph x - 2 > -5 and x - 2 < 4 on a number line
Answers
Answer:
dont take my word for it but
Step-by-step explanation:
x<-7
Multi step problem 4/7w = 4.2
Answers
Answer:
7.35
Step-by-step explanation:
4/7w=4.2
multiply both sides by 7
24/7w=29.4
simplify
4w=29.4
divide both sides by 4
w=7.35
Answer:
w equals 7.35
Step-by-step explanation:
7 times 4/7w = 4.2 times 7
4w = 29.4
Divide: 4w/4 = 29.4/4
w = 7.35
The following graph shows how many gallons of water leaves a bucket every hour.
- right the slope intercept equation. Find the constant rate of change and the vertical intercept of the line. Explain how they are related to this situation
Answers
Answer:
thanks for your points and the time
A paint store sells exterior
paint for $35.75 a gallon and paint rollers for $6.00 each. Write an equation in
standard form for the number of gallons x of paint and rollers y that a customer could buy with $190.
Answers
3x + y - 8 3y + 1 Simplified?
Answers
__________
[tex] \: [/tex]
(3x + y - 8)(3y + 1) = ...
= 9xy + 3x + (y.3y) + 1y + (-24 - 8)
= 9xy + 3x + 3y² + y - 32✔
may. be the ans is 3x +2y =9
Need answer asappppp
Answers
Answer:
y=4x+3
=)4x=y-3
=)x=(y-3)/4
Answer:
[tex]\frac{y - 3}{4}[/tex]
Step-by-step explanation:
To make x the subject, first, subtract 3 from both sides:
y = 4x + 3 → y - 3 = 4x
Next, divide both sides by 4 to get x on its own:
y - 3 = 4x → (y - 3)/4 = x
Hope this helps
How far is it from Harrisburg, PA to Trenton, NJ?
milea
O 184 mi
O 158 mi
O 133 mi
O 96 mi
Answers
Based on the data, it can be inferred that Harrisburg, PA is 158 miles from Trento, NJ.
How to calculate the distance between Harrisburg and Trento?To calculate the distance between Harrisburg and Trento we must carry out the following procedure. First we look at the entire table to see the different distance values between the cities. As we can see, the values for Trento, NJ are not there, so we will have to look elsewhere for additional information.
In this case, we must take as a reference the closest city to Trento that is on the list, this would be Filadeldia. Now, we must find the distance between Philadelphia and Trento and add this value to the distance between Philadelphia and Harrisburg.
According to the above, Philadelphia is 114 miles from Harrisburg and 44 miles from Trneto.
114 - 44 = 158Based on the above, the total distance between Trento and Harrisburg is 158 miles.
Learn more about miles in: https://brainly.com/question/23245414
#SPJ1
please solve this fast
Answers
Step-by-step explanation:
shape BCD is an isosceles triangle meaning the base angles will be the same.
CA is a straight line meaning that it is 180
the sum of angles in a triangle always is 180
so
180-36= 144
to find x you need to half 144 as it is the sum of the base angles of the isosceles triangle.
144/2= 72
x=72
the angle just below y is also 72.
as CA is a straight line,
180-72= 108 giving you the answer for y
y= 108
so to make the answer clear
x= 72
y= 108
hope that helped! :)
if you would like to give me a brainliest feel free as im nearly to the end of my goal.
Solve by multiplying
digits of value and filling
in zeros:
700 x 102
Х
HELP PLEASE