11. The test scores of 20 students are shown below.
1 answer:
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Inequalities are used to express unequal expressions.
The inequalities from the word problems are:
.
.
The statements from the inequalities are:
- -4 is not a solution to
- -6 is not a solution to
- -1 is not a solution to
- Graph b represents
<u>1. A number minus 3.5 is less than or equal to -2</u>
The statement can be broken down into the following expressions
So, when the expressions are brought together, we have:
<u>2. Zero is greater than or equal to twice a number x plus 1</u>
The statement can be broken down into the following expressions
So, when the expressions are brought together, we have:
<u />
<u>3. -1/2 is at least twice a number k minus 4</u>
The statement can be broken down into the following expressions
So, when the expressions are brought together, we have:
None of the options is correct
<h3>The solutions</h3><u>4. Tell whether -4 is a solution to x + 8 < -3</u>
We have:
Subtract 8 from both sides
The above inequality means that:
<em>x is less than -11</em>
-4 is not a solution, because -4 is greater than -11
<u>5. Tell whether -6 is a solution to 10 <= 3 - m</u>
We have:
Subtract 3 from both sides
Multiply both sides by -1 (the inequality sign changes)
Make m the subject
The above inequality means that:
<em>m is less than -7</em>
-6 is not a solution, because -6 is greater than -7
<u>6. Tell whether -1 is a solution to -3x <= -12.5</u>
We have:
Divide both sides by -3 (the inequality sign changes)
The above inequality means that:
<em>x is greater than or equal to </em><em />
-1 is not a solution, because -1 is less than <em />
The inequality is given as:
The less than sign (>) means that:
- The graph would use an open circle
- The arrow must point to the right
Only graph b satisfies this condition
Hence, the graph of is graph b
Read more about inequalities at:
Based on the image attached of the graph, the points that show equivalent ratios that would also be on the graph are option A and D which are: (6,18) (1,3).
<h3>What is the graph about?</h3>Note that:
=
= 1/3
So when you use 1/3 to compare all the options given, you will see that only option A and D is equal to the value given.
So if a person can write that we got 1 fish and we needs 3 gallons and when a person make a point on the line, it will be (1,3).
The other equivalent fraction is known to be 6/18. When a person multiply the numerator and denominator by 2, the value that will be obtained is:
= 6/18.
So therefore, Based on the image attached of the graph, the points that show equivalent ratios that would also be on the graph are option A and D which are: (6,18) (1,3).
See full question below
Christina wants to buy some miniature goldfish. She reads that a 9-gallon aquarium is the right size for 3 miniature goldfish. The graph represents this relationship.
Which points show equivalent ratios that would also be on the graph? Select all that apply.
A. (6,18)
B. (6,12)
C. (4,10)
D. (1,3)
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We have from the angle bisector theorem that the sides AC and CD are proportional to AB and BD. Hence, we get the following equality that holds in general when the angles BAD and CAD are equal.
Substituting:
Substituting: