Four students, Amanda, Briana, Courtney, and Diana were given an assignment in their math class to create inequalities with the sme solution set as shown on the graph below.
Answers
The graph of the inequality is drawn by placing a shaded circle at 4 as the starting point of ray pointing towards negative infinity
The students that created inequalities with appropriate solution set are;
A. Amanda
D. Diana
Reasons:
Question: The table of the question is presented as follows, and the graph of the inequality is attached
[tex]\begin{array}{|l|l|}\mathbf{\underlie{Amanda}}&-3\cdot x + 5 > -7\\&\\\mathbf{\undrline{Briana}}& \dfrac{1}{2} \cdot (2\cdot x - 4) >2 \\&\\\mathbf{\undrline{Courtney}}&-7\cdot x + 8 > -3 \cdot x +24\\&\\\mathbf{\undrline{Diana}}&9\cdot x - 6 <3 \cdot x+18\end{array}\right][/tex]
Solution:
The inequality with the same solution as the given graph is x < 4
The inequalities created by the students are;
Amanda;
-3·x + 5 > -7
Rearranging the above inequality gives;
-3·x + 5 - 5 > -7 - 5
-3·x > -12
Dividing both sides by (-1) and reversing the inequality sign gives;
[tex]\dfrac{-3 \cdot x}{-3} = x < \dfrac{-12}{-3} = 4[/tex]
x < 4
Therefore;
The solution of the inequality created by Amanda is x < 4, which is the same as the solution set of the graph, and therefore, is appropriateBriana;
The solution set created by Briana is [tex]\dfrac{1}{2} \cdot (2\cdot x - 4) >2[/tex]
Multiplying both expressions on either side of the equality by 2 gives;
[tex]2\times \dfrac{1}{2} \cdot (2\cdot x - 4) >2\times 2[/tex]
(2·x - 4) > 4
2·x > 4 + 4 = 8
[tex]x > \dfrac{8}{2}[/tex]
Therefore
x > 4
The solution of the inequality created by Briana is x > 4 which is not appropriate for the given graphCourtney;
The inequality created by Courtney is -7·x + 8 > -3·x + 24
Rearranging gives;
8 - 24 > -3·x + 7·x
-16 > 4·x
4·x < -16
[tex]x < \dfrac{-16}{4}[/tex]
x < -4
Courtney's solution is x < -4, which is not an appropriate solution to the given graphDiana;
Diana's solution is 9·x - 6 < 3·x + 18
Rearranging, we get;
9·x - 3·x < 18 + 6
6·x < 24
[tex]x < \dfrac{24}{6}[/tex]
x < 4
Therefor;
Diana's solution is an appropriate solution to the given graphTherefore, the students that created inequalities with appropriate solution set are;
A. Amanda
D. Diana
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Answer:
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OA.
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>
<
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>
<
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a. >
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Answer:
here is your aneswer
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A line passes through the point (0, 1) and has a positive slope. Which of these points could that line NOT pass through? Check all that apply.
(12, 3)
(–2, –5)
(–3, 1)
(1, 15)
(5, –2)
Answers
We have to find slopes one by one.
#1
(0,1)
(12,3)
Line passes through this.
#2
(-2,-5)
Line passes through this
#3
(-3,1)
Not possible (Line passes through y axis as one co-ordinate is (0,1))
#4
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Line passes through this
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(g + 4) – 3g = 1 + g
Answers
Answer:
4-2g=1+g
4-1=g+2g
3=3g
G=1
Step-by-step explanation:
This rectangle has a perimeter of 40 meters and a length of 12 meters what is its area
Answers
Answer:
The answer is 84
Step-by-step explanation:
What is the geometric mean of 7 and 56 ?
Answers
Answer:
14[tex]\sqrt{2}[/tex]
Step-by-step explanation:
7 x 56 = 392
[tex]\sqrt{392}[/tex] = [tex]\sqrt{2^{3} x 7^{2} }[/tex] = 14[tex]\sqrt{2}[/tex]
:)
Your Aunt Yvonne is shopping for flower pots at the local
garden store.
2 pots = 24 cm
4 pots = 32 cm
Answers
The equation which relates the height of the flower pot based on the number of pots is 4a + 16
Creating a system of linear equations based on the information given :
a = number of flower pots b = height of base4a + b = 32 - - - - - (1)
2a + b = 24 - - - - - (2)
From (2)
2a + b = 24
Make b the subject ;
b = 24 - 2a - - - - (3)
Put b = 24 - 2a in (1)
4a + 24 - 2a = 32
4a - 2a + 24 = 32
2a = 32 - 24
2a = 8
a = 8/2
a = 4
From (3) :
b = 24 - 2(4)
b = 24 - 8
b = 16
The equation which relates the height of a flower pot is 4a + 16
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2. Find the value of x and y.
62°
(4x+2)°
(12y)
144°
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Ox= 14, y= 11
Ox=14, y = 12
Ox= 15, y= 11
Answers
Answer:
x=15,y=12
Step-by-step explanation:
Alternate angles are those angles that are on the opposite side of the parallel lines transverse with a line touching both parallel lines.
The value of x and y are 15 and 12.
x = 15
y = 12
Option A is the correct answer.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The figure contains four angles.
62 and (4x + 2) are alternate angles.
12y and 144 are alternate angles.
We know that alternate angles are equal.
So,
62 = 4x + 2 ____(1)
12y = 144 _____(2)
From (1) we get,
62 = 4x + 2
Subtract 2 on both sides.
62 - 2 = 4x + 2 - 2
60 = 4x
Divide both sides by 4.
4x = 60
x = 60/4
x = 15
From (2)
12y = 144
Divide both sides by 12.
y = 144/12
y = 12
Thus,
The value of x and y are 15 and 12.
x = 15
y = 12
Option A is the correct answer.
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Here is the histogram of a data distribution.
4
3
2
1
5 6 7 8
9
10
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A. Bimodal symmetric
B. Bimodal skewed
Ο Ο Ο Ο Ο
C. Unimodal symmetric
D. Unimodal skewed
E. Uniform
Answers
Answer:
Uniform
Step-by-step explanation:
The shape of the given histogram is uniform.
Option E is the correct answer.
We have,
A uniform histogram is a type of histogram where all the bars have approximately the same height, indicating that the data is evenly distributed across the range of values.
In other words, the frequency of occurrence for each value or interval is roughly the same.
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Uniform histograms are useful for visualizing data that is evenly distributed or to identify outliers that are not consistent with the rest of the data. However, in some cases, a uniform histogram may not accurately represent the underlying distribution of the data, especially if there are gaps or clusters of data within certain ranges.
In such cases, other types of histograms or statistical methods may be more appropriate.
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The shape of the given histogram is uniform.
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Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The equation f(x) = g(x) has : (in box 1)
[tex]1[/tex]Box - 2 :
[tex]x = 1[/tex]Someone help plz and plz make sure it’s right will mark brainiest:)
Answers
The second one, y= 1/3x + 10/3
25 points
Graph the equation by translating y = |x|
y = |x+2
Please use the graph
Answers
Hope this helps
Slopes, and y-Intercepts: Mastery Test
Here's a graph of a linear function. Write the
equation that describes that function.
8
Express it in slope-intercept form.
6
Enter the correct answer.
OOO
DONE
Clear all
+1?
-8
-6
6
8
6
Answers
Since m/slope = 2/3 and b/y-intercept = -1, the equation would be:
y = 2/3x - 1
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A line is a one-dimensional shape that is straight. The equation of the given line in slope-intercept form can be written as y=(5/6)x -2.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The given line goes through two points, (0, -2) and (6, 3). Therefore, the slope of the given line can be calculated as,
Slope, m = (-2 - 3)/(0 - 6) = -5 / -6 = 5/6
Further, it can be seen that the line intersects the y-axis of the graph at (0, -2), therefore, the y-intercept of the given line is -2.
Since the equation of a line in slope intercept form is written as y=mx+c. Therefore, substituting the slope and the y-intercept in the equation.
y=mx+c
y=(5/6)x -2
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Answer:
x = 11, 10 or 9
Step-by-step explanation:
Simon bought a $48 table on sale at 30% off.
Select from the drop-down menu to correctly complete the sentence.
The best estimate for the discount can be found using the expression
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Answer:
he paid $33.60
Step-by-step explanation:
the expression is 48(.70)
70% is how much is still paid so multiply it and you get the answer.
this applies to any question like this.
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Hey, not quite sure how to help you but I just wanted to say that you've got this! Whatever endeavors or problems you are facing right now I know that you are able to triumph over them. If it means anything at all you have someone rooting for you on my end. Have a great day!
What are the combining like terms plz
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Answer:
-7q and 9q, 2 and 6
Step-by-step explanation:
they are like each other
Answer: Terms that have identical variable parts (same variable(s) and same exponent(s)). So in this case the like terms are -7q and 9q AND 2 and 6 are like terms *REMEMBER: constant (which are numbers with NO variables can also be like terms)
but to solve this:
first group the like terms so:
(-7q+9q) that gives us 2q
(2+6) that gives us 8
*In your FINAL answer ALWAYS put the number(s) with variables first so the final answer is 2q+8
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Answers
Answer:
Step-by-step explanation:
(a) Using Geometry Vocabulary, describe a sequence of transformations that maps
figure X onto figure Y.
(b) Write the Transformation Mapping Rule(s) for the sequence you described in part
(a).
Answers
Answer:
Translate figure X [tex]\left[\begin{array}{ccc}1\\0\\\end{array}\right][/tex], reflect figure X in the y-axis to give figure Y.
Step-by-step explanation:
It is very clear that shape X is being reflected in the y-axis to give shape Y. However, when reflecting shape X, it doesn't perfectly align with Y (it is off by 1 square).
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This leaves us with the column vector [tex]\left[\begin{array}{ccc}1\\0\\\end{array}\right][/tex]. And our final step is to write about the reflection that we identified earlier.
So the final answer is : Translate figure X [tex]\left[\begin{array}{ccc}1\\0\\\end{array}\right][/tex], reflect figure X in the y-axis to give figure Y.
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The third option.
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C
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It's pretty self explanatory. Try looking at the whole number first and then focusing on the fraction!
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here. this should help
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B
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Answers
Line BC is equal to line AD
∴
x + 17 = 3x + 7
x - 3x = 7 - 17
-2x = - 10
-2x / -2 = - 10 / -2
x = 5
AD
3x + 7
3(5) + 7
15 + 7
22
CD
2x - 6
2(5) - 6
10 - 6
4
BC
x + 17
5 + 17
22
AB
Line AB is equal to line CD therefore its length is 4
Answer:
x = 5
AB = 4
BC = 22
CD = 4
AD = 22