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
Azim wants to order school spirit t-shirts for the fundraising club. Company R charges a $70 screen setup fee plus $11.25 per t-shirt. Company S charges a $35 screen setup fee plus $14.75 per t-shirt. What equation can determine the number of t-shirts, x, that need to be ordered for the total cost of Company R to equal the total cost of Company S?
Answers
Answer:
10 t shirts
Step-by-step explanation:
70 + 11.25x = 35 + 14.75x
35 + 11.25x = 14.75x
35 = 3.5x
10 = x
helppppppppppppppppppppppppppppppppppppppp
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Answer:
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST NO RANDOM ANSWERS
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Answer:
2 is the correct answer
Tiffany is filling her daughter's pool with water from a hose. She can fill the pool at a rate of 1/10 gallons per second.
Create at least three equivalent ratios that are associated with the rate. Use a double number line to show your work.
Answers
Final answer: 1/10 gallons / second = 6 gallons / minute = 1/40% 3D quarts / second = 3/2 quarts / minute Hope I helped :)
The three equivalent ratios are 6/1 gallons/minute, 1/40 quarts/second and 360/1 gallons/hour.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, Tiffany can fill the pool at a rate of 1/10 gallons per second.
Equivalent ratios are the ratios that are the same when we compare them.
We know that, 60 seconds =1 minute
1/10 × 60 = 6 gallons/minute
1 gallon = 4 quarts
1/10 = 1/10×4 = 1/40 quarts/second
1 hour =60 minute
So, 6 gallons/minute =6×60
= 360 gallons/hour
Here, 6 gallons/minute = 1/40 quarts/second = 360 gallons/hour
Therefore, the three equivalent ratios are 6/1 gallons/minute, 1/40 quarts/second and 360/1 gallons/hour.
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A farmer has a grain bin with 4,000 cubic feet of barley in it. He uses 800 cubic feet to feed his herd of cows. The next day, he buys 800 cubic feet of barley and puts it into the grain bin. How many cubic feet of barley are in the grain bin now?
A) 2,400
B) 4,000
C) 4,800
D) 5,600
Answers
Answer:b- 4,000
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
It is B because
4000-800=3200
then
3200+800=4000
so he answer is B.4000
please help me to solve problems
Answers
Step-by-step explanation:
4a)
the principle of similar triangles : they have the same angles.
and we do not forget : the sum of all angles in a triangle is always 180 degrees.
a = 180 - 65 - 45 = 70 degrees
b = 65 degrees
c = 70 degrees
b)
same principles.
x = 58 degrees
y = 52 degrees
z = 180 - 58 - 52 = 70 degrees
c)
same principles.
plus the fact that complementary angles around a point on one side of a line are also together 180 degrees.
x = 85 degrees
y = 180 - 40 - 85 = 55 degrees
z = 180 - 85 = 95 degrees
d)
again same principles.
y = 2x (as these 2 angles correspond to each other among the 2 similar triangles).
the angle POQ is again complementary with 87 degrees,
POQ = 180 - 87 = 93 degrees
x + y + 93 = x + 2x + 93 = 180
3x = 87
x = 29 degrees
y = 2x = 2×29 = 58 degrees
george is building a fence at a consent rate of 1/3 section of fence every 1/2 hour at the rate. what fraction represents the section iof fence george can build per hour
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PLEASE PLEASE PLEASE HELP
Answers
10- 9
11- 5
12- 1
13- 10
14- 3
15- 7
16- 3
17- 3
18- 6
Find the vaule of x. then classify each triangle as acute, right, or obtuse
Answers
Answer:
1) = 90=acute angle 2)103=acute angle
Step-by-step explanation:
Answer:
1.) x = 90 (Right angle)
2.) x = 103 (Obtuse angle)
Step-by-step explanation:
All triangles' angles have a sum of 180°.<90° = Acute, 90° = Right, >90° = Obtuse[tex]1.)\\x+48+42=180\\x+90=180\\x=90\\\\2.)\\x+45+32=180\\x+77=180\\x=103[/tex]
How much will you pay in all for the $78 lunch bill with a 15% tip ?
Answers
→ You will pay $ 89.7.
The tip value is based on the bill value. Hence, to find the total payment you have to multiply 78 by 1.15 (this includes the tip, 1.15).
[tex]\Large \text {$Total = 78 \times 1.15 = 89.7 $}[/tex]
Or you can first find how many 15% is from $78:
[tex]\Large \text {$0.15 \times 78 = 11.7$}[/tex]
And then add this to $78:
[tex]\Large \text {$78 +11.7 = 89.7$}[/tex]
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Answer:
$89.70
Step-by-step explanation:
15/100=0.15
78 * 0.15 =89.70
-54/87 simplified to a fraction
Answers
Answer:
-18/29
Step-by-step explanation:
54 ÷ 3 = 18 - numerator
84 ÷ 3 = 29 - denominator
-54/84 = -18/29
Andrea drove 20 1/2 miles in 1/3 of an hour at constant speed what was that speed
Answers
Answer:
423
Step-by-step explanation:
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The constant speed for the given distance and time is 123/2 miles/hour.
Given that, Andrea drove [tex]20\frac{1}{2}[/tex] miles in 1/3 of an hour at constant speed.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Here, [tex]20\frac{1}{2} = \frac{41}{2}[/tex]
Now, speed = Distance ÷ Time
= 41/2 ÷ 1/3
Change division to multiplication and reciprocal the fraction
That is, 41/2 × 3/1
= 123/2 miles/hour
Therefore, the constant speed for the given distance and time is 123/2 miles/hour.
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How many milligrams are in a 2 tsp dose of liquid medication if there are 2.5 g in 2 fl oz?
Answers
Alexis is selling team cards for her volleyball fundraiser. She expects to sell 4 cards for every 5 houses that she visits. If she wants to sell 20 cards total, how many houses should she expect to visit?
Answers
Answer:
5 houses
Step-by-step explanation:
She needs to visit 5 houses as 20 divided by 4 is 5
Please help me as soon as you can.I will give you 30points and who answers the quickest will be the brainiliest
Answers
100 mm in a cm so divide by 100
4500 divided by 100 is 4.5 cause you move the decimal to the left two times
Determine the value of x for which r || s. then find m<1 and m<2.
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Answer:
thx you so much
have a nice day
Which angles are vertical angles?
<8 and <6
<8 and <7
<8 and <5
Answers
Angle 8 and angle 5 are vertical angles
Find the distance between points (1, 3) and (9, 18) on the coordinate plane.
Answers
which strategy would not solve the rational equation?
Answers
Answer:
This may occur when you decide to determine a function as well as a graph.
Step-by-step explanation:
Hope this helps! :D
The fuel tank of a certain airplane can hold up to gallons of fuel. Let be the total weight of the airplane (in pounds). Let be the total amount of fuel in its tank (in gallons). Suppose that gives as a function of .
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Where W is the weight of the plane and F is the number of gallons of fuel.
The domain is the set of possible values for F. That is from 0 (empty tank) to 400 (full tank).
So the domain is F = [0,400], or what is equivalente 0 ≤ F ≤ 400.
The range is the set of values of W.
The minimum value of W is when F = 0 => W = 7(0) + 5000 = 5,000.
The maximum value of W is when F = 400 => W = 7(400) + 5000 = 7,800
So the range is W = [5,000 ; 7,800], pr 5000 ≤ W ≤ 7,800.
For how many shoe strings will Toby and Marie have the same amount of money in the account? Must show your work by making a table or solving algebraically by setting the equations equal to each other.
Answers
Answer:
we need more information to solve your problem.
Step-by-step explanation:
PLEASE HELP ASAP I WILL GIVE U A LOT OF POINTS AND BRAINLIEST :D
Answers
Multiply to get the answer:
4×10⁷ * 3.65×10² = (4*3.65)×10⁷⁺² = 14.6×10⁹ = 1.46×10¹⁰ krill#2Convert to scientific notation and find the ratio of the second number by the first:
26000000000 = 2.6×10¹⁰Divide:
4.94×10¹³ ÷ 2.6×10¹⁰ = (4.94/2.6)×10¹³⁻¹⁰ = 1.9×10³ = 1900 timeswhat is the value of Y
Answers
Answer:
y = 150º
Step-by-step explanation:
The sum of internal angles of a triangle must be 180º and the sum of y + (x-20) forms a straight line which is also 180º, so:
2x + x + (x - 20) = 180
4x - 20 = 180
4x = 200
x = 50
x - 20 = 50 - 20
x - 20 = 30
y = 180 - 30
y = 150º
Put the following equation of a one into a slope -intercept form, simplifying all fractions.
8x+6y=-54
Answers
Answer:
y = -4/3x -9
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
8x+6y = -54
Subtract 8x from each side
8x+6y-8x = -8x-54
6y = -8x-54
Divide each side by 6
6y/6 = -8x/6 -54/6
y = -4/3x -9
Answer:
y = -4/3x - 9
Step-by-step explanation:
Putting this into 'y=mx+c' form:
i) Firstly, make it only y on the LHS:
6y = -8x-54
ii) Secondly, making the 'y' have a co-efficient of 1. This can be done by dividing both sides by 6:
6y/6 = -8x/6 - 54/6
y = -4/3x - 9
Hence,
y = -4/3x - 9
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
Which is the correct simplified version of the expression 32x+8-34x? *
1 point
66x+8
74x
-2x+8
6x
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Bc 32 minus 34 is -2 then just add the 8
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Answers
Answer:
hsoabajakahaknanaKambaKla
the function is expressed by the formula f(x)=x^3 - 1. Find the value of the function if the independent variable is equal to -1
Please answer quick
Answers
The value of the function if the independent variable is equal to -1 is -2
Given the function p(x) = x^3 - 1
The input variable "x" is the independent variable. If the independent variable is equal to -1, the value of the function will be expressed as:
P(-1) = (-1)^3 - 1
P(-2) = -1 -1
P(-2) = -2
Hence the value of the function if the independent variable is equal to -1 is -2
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The value of 10^4 is 10,000. Use this fact to change 5.2 x 10^4 to standard notation. 5.2 x 10^4 = 5.2 x ____ =?
Answers
Step-by-step explanation:
5.2 × 10000
yep that is the answer
Answer:10,000. i think
Step-by-step explanation: Example: 104 = 10 × 10 × 10 × 10 = 10,000.
Will give brainliest to the correct answer
Write each function in slope-intercept form
:9.4y=−8x−10
10. −5x+ 2y=−10
Answers
Step-by-step explanation:
9) y= -2x - (5/2)
10) y = -5 + (5/2)
The area of a square is 25/36 in ^2. What is the length of its side
Answers
Answer:
5/6 inches
Step-by-step explanation:
An area of a square is basically length * width but the length and width are the same length so we can simply do the square root of (25/36)
5/6 is your final answer