HURRY PLS You are competing in a race. The table shows the times from last year's race. You want your time to be last year's med
1 answer:
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Answer:
Please check the explanation.
Step-by-step explanation:
Given the inequality
-2x < 10
-6 < -2x
<u>Part a) Is x = 0 a solution to both inequalities</u>
FOR -2x < 10
substituting x = 0 in -2x < 10
-2x < 10
-3(0) < 10
0 < 10
TRUE!
Thus, x = 0 satisfies the inequality -2x < 10.
∴ x = 0 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 0 in -6 < -2x
-6 < -2x
-6 < -2(0)
-6 < 0
TRUE!
Thus, x = 0 satisfies the inequality -6 < -2x
∴ x = 0 is the solution to the inequality -6 < -2x
Conclusion:
x = 0 is a solution to both inequalites.
<u>Part b) Is x = 4 a solution to both inequalities</u>
FOR -2x < 10
substituting x = 4 in -2x < 10
-2x < 10
-3(4) < 10
-12 < 10
TRUE!
Thus, x = 4 satisfies the inequality -2x < 10.
∴ x = 4 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 4 in -6 < -2x
-6 < -2x
-6 < -2(4)
-6 < -8
FALSE!
Thus, x = 4 does not satisfiy the inequality -6 < -2x
∴ x = 4 is the NOT a solution to the inequality -6 < -2x.
Conclusion:
x = 4 is NOT a solution to both inequalites.
Part c) Find another value of x that is a solution to both inequalities.
<u>solving -2x < 10</u>
Multiply both sides by -1 (reverses the inequality)
Simplify
Divide both sides by 2
<u>solving -6 < -2x</u>
-6 < -2x
switch sides
Multiply both sides by -1 (reverses the inequality)
Simplify
Divide both sides by 2
Thus, the two intervals:
The intersection of these two intervals would be the solution to both inequalities.
and
As x = 1 is included in both intervals.
so x = 1 would be another solution common to both inequalities.
<h3>SUBSTITUTING x = 1</h3>FOR -2x < 10
substituting x = 1 in -2x < 10
-2x < 10
-3(1) < 10
-3 < 10
TRUE!
Thus, x = 1 satisfies the inequality -2x < 10.
∴ x = 1 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 1 in -6 < -2x
-6 < -2x
-6 < -2(1)
-6 < -2
TRUE!
Thus, x = 1 satisfies the inequality -6 < -2x
∴ x = 1 is the solution to the inequality -6 < -2x.
Conclusion:
x = 1 is a solution common to both inequalites.
<em>Note: Since you missed to add the figure. So, after a little research I am kind of able to find the figure and hence, assuming it as a reference. Hence, I am attaching the figure and solution of that figure is also visible in the same figure.</em> Please check the attached figure (a)
Answer:
Segment B'D' will be parallel to segment BD and will be shorter than segment BD. Please see the attached figure (a) for better understanding.
Step-by-step explanation:
As we know that there are certain rules when a quadrilateral is dilated by a certain scale centered around a certain point.
So,
Let suppose P(a, b) is the point.
The dilation rule by a scale factor of 1 over 3 or (1/3) centered around (1, 2) is
P(a, b) →
Hence,
A(1, 2) → A'(1, 2)
B(2, 3) → B'(4/3, 7/3)
C(4, 2) → C'(2, 2)
D(2, 1) → D'(4/3, 5/3)
The attached figure show that if we draw the all these points in the coordinate plan i.e. A(1, 2), B(2, 3), C(4, 2), D(2, 1) and A'(1, 2), B'(4/3, 7/3), C'(2, 2), D'(4/3, 5/3), we can determine that Segment B'D' will be parallel to segment BD and will be shorter than segment BD.
<em>Keywords: dilation, quadrilateral, segment</em>
<em> Learn more about dilation from brainly.com/question/7569824</em>
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