Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < x + 2
y > x + 2
Answers
Answer: The graph is represented by the inequality y>3x+2
Step-by-step explanation:
Linear inequality is like linear equation just we have inequality signs (<,>,≤,≥) instead of equal sign(=).
In the given question we have the linear inequality represented by graph
We can see the line in the graph passing through the point (-3,-7)
Let's check which option satisfy the point
1) y<3x+2 for this the line should be y=3x+2
⇒ -7=3(-3)+2
⇒-7= -9+2⇒-7=-7,which is true.
2) y>3x+2 which similar as first.
3) y<x+2 for this the line should be y=x+2
⇒ -7= -3+2
⇒-7=-1 which is not true.
4) y > x + 2 is similar to third.
Option 3) and 4) cannot be the required linear inequality.
Now from 1) and 2) , 2) should be the required linear inequality as the graph is shaded above the line and that must be for y (>) greater than inequality. [ for y (<) less than inequality the graph must be shaded below the line]
Therefore, 2) y > 3x + 2 is the required linear inequality which is represented by the graph.
The linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex] .
Further explanation:
It is given that a line passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex] as shown below in Figure 1.
The slope of a line passes through points [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left( {{x_2},{y_2}}\right)[/tex]is calculated as follows:
[tex]m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}[/tex] ........(1)
Here, the slope of a line is denoted as [tex]m[/tex] and points are [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex].
Substitute [tex]0[/tex] for [tex]{x_1}[/tex] , [tex]2[/tex] for [tex]{y_1}[/tex] , [tex]-3[/tex] for [tex]{x_2}[/tex] and [tex]-7[/tex] for [tex]{y_2}[/tex] in equation (1) to obtain the slope of a line that passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex] .
[tex]\begin{aligned}m&=\frac{{-7-2}}{{-3-0}}\\&=\frac{{-9}}{{-3}}\\&=3\\\end{aligned}[/tex]
Therefore, the slope is [tex]3[/tex] .
The point-slope form of the equation of a line with slope [tex]m[/tex] passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:
[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex] .......(2)
Substitute [tex]0[/tex] for [tex]{x_1}[/tex] , [tex]2[/tex] for [tex]{y_1}[/tex] and [tex]3[/tex] for [tex]m[/tex] in equation (2) to obtain the equation of line.
[tex]\begin{aligned}y-2&=3\left({x-0}\right)\\y-2&=3x\\y&=3x+2\\\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]3x+2[/tex] .
Since the shaded part in Figure 1 is above the equation of line [tex]y=3x+2[/tex], therefore, greater than sign is used instead of is equal to.
Thus, the linear inequality is [tex]y>3x+2[/tex] as shown below in Figure 2.
Now, the four options are given below.
[tex]\begin{aligned}{\text{OPTION A}}\to &y<3x+2\hfill\\{\text{OPTION B}}\to &y>3x+2\hfill\\{\text{OPTION C}}\to &y<x+2\hfill\\{\text{OPTION D}}\to &y>x+2\hfill\\\end{aligned}[/tex]
Since OPTION B matches the obtained equation that is [tex]y>3x+2[/tex] .
Thus, the linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex].
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Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, inequality
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Step-by-step explanation:
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Answers
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Collect the like terms.
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=====
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Answers
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k=yx
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c.2
d.4
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Hey !!
Check the attachment.
Hope it helps you :)
Answer:
2 so your answer would be C.
$10.00 divided by $1.49
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Answers
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(1):
x - 3y = 9
x = 9 + 3y ----------- (1a)
(2):
1/5x - 2y = -1
x - 10y = -5 --------- (2a)
Sub (1a) into (2a):
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Answer:
B
Step-by-step explanation:
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12 boxes are needed in all.
Last box will contain only 20 kernels.
Step-by-step explanation:Given is :
The popped corn is put into small popcorn boxes that each hold 130 popped kernels.
There are 1450 kernels in a pound of un popped popcorn.
If all the boxes are filled except for the last box, then how many boxes are needed?
Number of boxes = Total number of kernels/Number of kernel in each box
=> [tex]\frac{1450}{130}= 11.15[/tex]
Therefore, a total of 11+1 = 12 boxes are needed as 11.15 is more than 11.
And the last box will contain = [tex]1450-1430=20[/tex] kernels.
Therefore, the last box will have 20 kernels.
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Answers
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Explanation:
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attached is the graph please have a look at it
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Answers
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Answer:
(6,7)
Step-by-step explanation:
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Thus [tex](x_2,y_2)=(6,7)/tex]
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Answers
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Answer:
The answer on edgenuity for dividing fractions is -3 on the assignment good luck!
Step-by-step explanation:
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A. 3
B. 4
C. 5
D. 2
Answers
A 4th degree polynomial will have at most 3 extreme values. Since the degree is even, there will be one global extreme, with possible multiplicity. The remainder, if any, will be local extremes that may be coincident with each other and/or the global extreme.
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A class contains 3 female and 9 male students. Find the probability that a student chosen at random is a male, and then a second student chosen at random from the remaining students is also male.
a). 9/16
b). none
c). 1/2
d).6/11
e).3/4
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Answers
9 are male
1st = 9/12 = 3/4
2nd = 8/11
3/4 * 8/11 = 6/11
Answer = D) 6/11
The probability that two student chosen at random is a male is 6/11.
What is the Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Here, Class contains 3 females and 9 males it means total 12 students.
Probability for having 1st student male = 9/12 = 3/4
Probability for having 2nd student is also male = 8/11
Overall Probability = [tex]\frac{3}{4} X \frac{8}{11}[/tex]
= 6/11
Thus, the probability that two student chosen at random is a male is 6/11.
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Solve the equation
Answers
We want to solve for x. Start by getting x by itself on one side.
We can do this by adding 64 to both sides of the equation.
x^3 = 64
Now, to get rid of the 3rd power that x is raised to, we can raise both sides to the 1/3 power
(x^3)^1/3 = 64^1/3
(x^3)^1/3 is the same as x
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How many pounds of mozzarella cheese did Mama Mia start with?
Answers
Mama Mia restaurant used start fraction, 1, divided by, 2, end fraction of their mozzarella cheese making pizza and the remaining 64 ounces making pasta.
How many pounds of mozzarella cheese did Mama Mia start with?
Let
x---------------> total ounces of mozzarella
we know that
making pizza-----------> (1/2)*x------> x/2
therefore
making pasta-------> [x-x/2]--------> (2x-x)/2-----> x/2
making pizza=making pasta=x/2
(x/2)=64---------------> x=64*2-----------> x=128 ounces
remember that
1 ounces----------------> 0.0625 pounds
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the answer is 8 pounds
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a. |-15| + |-26|
15 + 26
41
b. -|-40|
-40
c. |0.5| + |-1 1/2|
0.5 + 1 1/2
0.5 = 1/2
1/2 + 1 1/2
2
write an expression that is equivalent to 5 cubed
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5^3 is three 5s multiplied together.
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Since the diameter given is 16 inches, the radius is 8 inches.
Using the formula, we find that the area is pi*(8 inches)^2 = 64pi inches^2
A cruise boat travels 48 miles Downstream in 2 hours and returns Upstream in 3 hours. Find the speed of the boat in still water and the rate of the Stream.
Answers
The downstream speed will be x+y, the upstream speed will be x-y.
but:
distance=speed*time
therefore; as the boat travels in 2 hours downstream we shall have:
2(x+y)=48......i
and as the boat travels upstream we shall have:
3(x-y)=48........ii
simplifying i and ii we get:
x+y=24....iii
x-y=16....iv
adding the above iii and iv we get
2x=40
x=40/2=20
substituting x=20 into iii we obtain:
20+y=24
y=24-20
y=4
so the speed of the boat in still waters is 20 miles per hour
the rate of the stream is 4 miles per hour
Final answer:
The speed of the cruise boat in still water is 20 mph and the rate of the stream is 4 mph.
Explanation:
The student is asking about a problem related to the rate of the boat in still water and the rate of the stream, given the times it takes to travel downstream and upstream. To solve this, we can use the following steps:
Let the speed of the boat in still water be b mph and the rate of the stream be s mph.Downstream, the effective speed is b + s and upstream it's b - s.Using the formula distance = speed imes time, we have two equations based on the given information: 48 miles = (b + s) imes 2 hours for downstream and 48 miles = (b - s) imes 3 hours for upstream.Solve the two equations simultaneously to find the values of b and s.Let's solve the equations:
48 = 2(b + s) => 24 = b + s48 = 3(b - s) => 16 = b - sAdding both equations:
24 + 16 = (b + s) + (b - s) => 40 = 2b => b = 20 mph (boat speed in still water)Subtracting the upstream equation from the downstream equation:24 - 16 = (b + s) - (b - s) => 8 = 2s => s = 4 mph (rate of the stream)Therefore, the speed of the boat in still water is 20 mph and the rate of the stream is 4 mph.
Elliot buys a 5 pound package of ground beef for 12.50. At the same unit price, how much would 8 pounds of ground beef cost
Answers
So 8*2.5=20
It should be 20 dollars
2.5 x 8 = 20
8 pounds of ground beef would cost $20.
In the Chang family's budget, 0.6% of the expenses are for internet service. What is the fraction of the family's expenses is for internet service? Write the fraction in the simplest form.
Answers
You probably know intuitively that 100% is one whole, for example. But it's also the same as saying [tex] \frac{100}{100} [/tex]. Likewise, 67%, for instance, is actually [tex] \frac{67}{100} [/tex].
In this case, you can write [tex] \dfrac{0.6}{100}[/tex]. But you may realize that you shouldn't have a decimal in a fraction. For every number after the decimal, you multiply the whole thing by a corresponding power of ten. Here, you write [tex] \dfrac{0.6}{100} * \dfrac{10}{10} = \dfrac{6}{1,000} [/tex]. Since 10/10 is equal to 1, we aren't changing anything (Identity Property). If you had 0.06/100, you would multiply by 100/100, and so on...
So, now we have [tex] \dfrac{6}{1000} [/tex]. Our next step is to simplify. The greatest common factor of these two numbers is 2, we rewrite as [tex] \dfrac{3}{500} [/tex] to put it into simplest form. And that's all there is to it.
NEED HELP ASAP PLEASE!
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5x + 25 < 85
5x < 85 - 25
5x < 60
x < 60 ÷ 5
x < 12
x < 12
Explanation:
To solve this, we will need to isolate the x on one side of the inequality as follows:
5(x+5) < 85
x+5 < 85/5
x+5 < 17
x+5-5 < 17-5
x < 12
Hope this helps :)
You bought the meat for Saturdays cookout. A package of hot dogs cost $1.60 and a package of hamburgers cost $5. You bought a total of 8 packages of meat and you spent $23. How many packages of hamburger meat did you buy?
Answers
The number of hamburger meat he bought is 3.
How to find the number of hamburger meat bought?A package of hot dogs cost $1.60 and a package of hamburgers cost $5.
You bought a total of 8 packages of meat and you spent $23.
Therefore,
let
x = number of package of hot dogs
y = number of package of hamburger
Hence,
x + y = 8
1.60x + 5y = 23
multiply equation(i) by 5
5x + 5y = 40
1.60x + 5y = 23
Subtract equation(ii) from equation(i)
3.4x = 17
x = 17 / 3.4
x = 5
y = 8 - 5
y = 3
Therefore, the number of hamburger meat he bought is 3.
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