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)
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.
Find the measures of the angles of a right triangle with one angle whose measure is 10
Answer:
10, 80 and 90 degrees.
Step-by-step explanation:
The third angle will 90 - 10 = 80 degrees.
Work out the area of a rectangle with base,b= 32mm and perimeter,P= 78mm.
Answer:
224
Step-by-step explanation:
b = 32, h = 7 is the solution to P = 78. Hence, 7*32 = 224 is the answer
Which graph shows y=x^2+3x-4
Answer:
Third graph in the photo
Step-by-step explanation:
x^2+3x-4 can be factored as (x+4)(x-1). When y=0, x must be -4 or 1 to satisfy the equations, and thus the roots of the graph are at x=-4 and x=1. When x=0, y=(4)(-1)=-4. The only graph that satisfies both of these requirements is the third/last one.
Can someone please help me w/ this I need to plot the points on the graph (picture provied) then the answer is where ever the points met on the graph. ( please draw a line were they met u can screen shot the photo)
THE ANSWER IS SUPOSE TO LOOK LIKE THIS ( ___,___) IXL cc.2 8th grade
Answer:
-6,-6 because -7x-1 would be -6x
Step-by-step explanation:
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (-2,3), (5, 5)
There isn't any graph example but I need help!!! i will award 10 brainiest
Answer:
Slope: 2/7
Step-by-step explanation:
y2 - y1/ x2 - x1 = 2/7
The sum of half of a number and 8 less
than the number is 25. Find the number.
Answer:
The number is 22
Step-by-step explanation:
let x = the number
[tex] \frac{1}{2} x + x - 8 = 25 \\ \frac{1}{2} x + x - 8 + 8 = 25 + 8 \\ \frac{1}{2} x + x = 33 \\ factor \: out\: x \: on \: the \: left \\ x( \frac{1}{2} + 1) = 33 \\ divide \: both \: sides \: by \: \frac{1}{2} + 1 \\ \frac{x( \frac{1}{2} + 1) }{ \frac{1}{2} + 1} = \frac{33}{ \frac{1}{2} + 1} \\ x = \frac{33}{ \frac{3}{2} } \\ x = \frac{66}{3} \\ x = 22[/tex]
let's factor out x from the left hand sid
Find last year's salary if, after a 5% pay raise, this year's salary is 35,175
Answer:
Step-by-step explanation:
x + 0.05x = 36225
x(1 + 0.05) = 36225
x*1.05 = 36225
by solving we find:
x = $34,500
Express 0.1345345... using bar notation
Answer:
0.1345
Step-by-step explanation:
The bolded numbers are what is barred
345 is constantly repeated so that is what would be barred as that repeats for ever
Answer:
3/1345
Step-by-step explanation:
9/6 × 4/5
1
) 36/11
) 6/5
) 32/30
) 13/15
Answer:
6/5
Step-by-step explanation:
9×4=36
6×5=30
36/30÷2
18/15÷3
6/5
let (3x+24) represent the measure of a right angle. what are the possible values of x?
Answer:
x=22
Step-by-step explanation:
because 3x+24=90
3x=90-24
3x=66
x=22
brainlist please
If 10 litres of paint cost £45 find the cost of 13litres
Answer:
£58.50
Step-by-step explanation:
Ratio of Paint : Cost
10 : 45
13 : x
10x : 585
[tex] \frac{10x}{10} = \frac{585}{10} \\ x = 58.5 [/tex]
Can someone help me with this
Answer:
4/5, 3/4, 5/7, 2/7, 1/7
Step-by-step explanation:
Answer:
I am here to help you like a hero
Step-by-step explanation:
so the order is 4/5,3/4,5/7,2/7,1/7
A laboratory is testing a product by heating or cooling it at different rates. The table shows the results of four tests. Drag a number to each empty cell to complete the table.
ill give brainliest
Answer:Cell content
Started at 20° and dropped 4° each minute -4
Cell content
Started at −20° and rose 1° each minute 1
Cell content
Started at 20° and dropped 1° each minute -1
Cell content
Started at −20° and rose 4° each minute 1
Step-by-step explanation:
Answer:
Cell content
Started at 20° and dropped 4° each minute -4
Cell content
Started at −20° and rose 1° each minute 1
Cell content
Started at 20° and dropped 1° each minute -1
Cell content
Started at −20° and rose 4° each minute 1
Step-by-step explanation:
What is the easiest way to solve 5-x=10 whilst showing working out
What are the y-intercept and the slope of the graph of the
following equation?
-2x + 4y = 8
Answer:
slope=2/4 or 1/2
Y-Intercept=8
Step-by-step explanation:
-2x+4y=8
+2x both sides
4y=2x+8 /4
y=2/4x+8
Slope=2/4 or 1/2
Y-Intercept=8
Mel bought pizza and soda for her End of Summer party. If she spent $12.57 on the sodas and $10.95 for each pizza, how many pizzas did she buy if she spent $89.22? Which equation models this scenari
The equation that models the situation is: 89.22 = $10.95p + $12.57.
The cost of one pizza is $10.95. The cost of 2 pizzas would be equivalent to the multiplication of $10.95 by 2. Since we are not provided with the information on the total amount of pizza she bought, the total number of pizza bought would be represented with p.
Thus the total cost of p boxes of pizza = $10.95 x p = $10.95p
The total amount spent on sodas is $12.57.
The total amount spent is $89.22.
The equation that models the situation is: 89.22 = $10.95p + $12.57.
A similar question was answered here: https://brainly.com/question/20063434?referrer=searchResults
Suppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.
Answer:
letter A
Step-by-step explanation:
because that's my favorite letter
Find the slope of the line through each pair of point
Answer:
what are the pair of points?
3. Write the explicit definition for the sequence given
Answer: You did not give a sequence so I cannot help you.
Step-by-step explanation: try to copy and paste the entire sequence.
Tìm hàm số bậc nhất,biết đồ thị đi qua điểm (3;−2), song song với đường thẳng
′:3−2+1=0
20234555446698382636
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
7/8 divided by 2 1/4
Answer:
7/18
Step-by-step explanation:
Several students form a circle by standing next to each other. Samantha and Aaron are directly across from each other and are approximately 30 feet apart. If each student takes about about 4 ft of the circle. How many students are in the circle?
pls help
Answer:
about 24 people in the circle
Step-by-step explanation:
find circumfrence using pi r squared which is 94 and divide by 4 which is the distance between students
HELP HELP HELP HELP HELP HELP
Problem 1
I'm assuming your teacher means "list all the possible rational roots".
If so, then we use the rational root theorem. This is the idea where we'll divide the factors of the last term over the factors of the first coefficient.
Factors of 5: 1, 5Factors of 3: 1, 3If we divide said factors in the order mentioned, then we get this list of possible positive rational roots:
1/1, 1/3, 5/1, 5/3
That list simplifies to
1, 1/3, 5, 5/3
That takes care of the positive possible rational roots. We double the list to incorporate the negative possible rational roots as well
-1, -1/3, -5, -5/3
Answer: 1, -1, 1/3, -1/3, 5, -5, 5/3, -5/3Note: We can rewrite that list in bold into [tex]\pm 1, \pm\frac{1}{3}, \pm 5, \pm \frac{5}{3}[/tex] to shorten it.
============================================================
Problem 2
We'll follow the same idea as the previous problem
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 4: 1, 2, 4
To keep track of everything, I made a spreadsheet table. Refer to the diagram below. The factors of 36 are laid across the top while the factors of 4 are along the left side. Each inner cell represents dividing the headers.
For example, 36/4 = 9 is in the bottom right corner. The first table is before the fractions are reduced, and the second table after the fractions are reduced.
As the second table shows, we have a few repeats. The unique items here are:
1,2,3,4,6,9,12,18,36,1/2,3/2,9/2,1/4,3/4,9/4
We'll then mirror this set to include negative values as well to write the full list of all possible rational roots.
Answer: 1,2,3,4,6,9,12,18,36,1/2,3/2,9/2,1/4,3/4,9/4-1,-2,-3,-4,-6,-9,-12,-18,-36,-1/2,-3/2,-9/2,-1/4,-3/4,-9/4============================================================
Problem 3
Factors of 15: 1, 3, 5, 15Factors of 5: 1, 5Divide the factors of 15 over the factors of 5 to get
1/1, 1/5, 3/1, 3/5, 5/1, 5/5, 15/1, 15/5
That list reduces to
1, 1/5, 3, 3/5, 5, 1, 15, 3
we can then toss out the duplicates to get
1, 3, 5, 15, 1/5, 3/5
Don't forget to include the negative values as well
Answer: 1, 3, 5, 15, 1/5, 3/5-1, -3, -5, -15, -1/5, -3/5============================================================
Problem 4
The steps will be effectively the same as before. You can write out the factors like done in problem 3, or make a table like done in problem 2. I'll skip the steps shown here unless you need me to go over them.
Answer: 1, 3, 9, 1/2, 3/2, 9/2-1, -3, -9, -1/2, -3/2, -9/2============================================================
Problem 5
There's not really much new here, except for the fact that the first term has coefficient of 1. This is a special case where all we have to do is list the factors of the last term -40 to generate all the roots we need. This is because each time we're dividing over +1 or -1 which doesn't really change the overall result (except for the sign part).
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Don't forget the negative values as well
Answer:1, 2, 4, 5, 8, 10, 20, 40-1, -2, -4, -5, -8, -10, -20, -40Rewrite each of the following expressions using either a generic rectangle or the Distributive Property
Answer:
a) -8yx-20y
b) -6x ² - 3xy - 16x -2y - 8
Step-by-step explanation:
a) -4y(2x+5) apply multiplicative distribution law
-4y × 2x - 4y × 5 multiply the monomials
-8yx - 20y
b) kinda the same steps like a
:) distributive property btw
hope it helps if you need the steps for b I'll send them in the comment
Help With this Math Problem!
Answer:
84
Step-by-step explanation:
1110 = 150 + (15 * 64)
150 is 20 cameras, so we get 64 + 20 = 84 cameras
Answer:
93 cameras
Step-by-step explanation:
it's actually 92.6666666667 but i rounded
Identify if the given statement is true or false.
The incenter is the point of concurrency of the altitudes of a triangle.
True or False
Answer:
false, true, false
Step-by-step explanation:
PLS HELP I GOTTA TURN THIS INNN
Answer:
Lauren
Step-by-step explanation:
1/2 is Erin
3/4 is Lauren
Answer:
1/2 for Eric and 6/8 for lauren
Eric: 1/2 = 4/8
Lauren: 6/8
Lauren was more succesful
Step-by-step explanation:
___1.which of the following illustrate the union of two sets
___2.which of the following represent the intersection of two sets
___3.which of the following is the factored form x³ + 4x²+4x+16
Answer:
I am going to say 3. but not 100% if it right let me know
