Option C:
{x: –1 < x < 7}
Solution:
Given expression is (x – 2 < 5) ∩ (x + 7 > 6).
Let us first solve the inequality.
First inequality:
⇒ x – 2 < 5
Add 2 on both sides of the expression.
⇒ x – 2 + 2 < 5 + 2
⇒ x < 7
Second inequality:
⇒ x + 7 > 6
Subtract 7 on both sides of the expression.
⇒ x + 7 – 7 > 6 – 7
⇒ x + 7 – 7 > 6 – 7
⇒ x > –1
Now to find the intersection of these inequalities.
(x – 2 < 5) ∩ (x + 7 > 6) = (x < 7) ∩ (x > –1)
= (x < 7) ∩ (–1 < x)
= –1 < x < 7
Thus, option C is the correct answer.
(x – 2 < 5) ∩ (x + 7 > 6) = {x: –1 < x < 7}
Answer: Choice C
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Reason:
The portion on the left represents because of the open circle at -2 and shading pointing to the left. This represents all numbers smaller than -2.
The portion on the right represents all values that are 4 or larger; hence . Note the use of a closed circle at 4 to include this value.
We connect those two inequalities with the keyword "or" because x can only pick one of those options, but not both at the same time.
Answer:
B (10, 5)
Step-by-step explanation:
We simply set the midpoint equal to each of its respective variable equation in
Step 1: Solve <em>x</em>
4 = (-2 + x)/2
8 = -2 + x
x = 10
Step 2: Solve <em>y</em>
3 = (1 + y)/2
6 = 1 + y
y = 5
Put it in coordinates and we have our final answer!
Answer:
21.66.
Step-by-step explanation:
First convert to improper fractions:
= 55/2 x 192/3 / 325/4
= 10560/6 / 325 / 4
= 10560/ 6 x 4/325
= 10560/ 3 * 2/325
= 21120/ 975
= 21.66.
<span>What will be the cost of the glass to cover the picture?
</span>
D.$21.78