Answer:
x ≥ 7
Step-by-step explanation:
|x - 7| = x - 7
A. For each absolute, find the intervals
x - 7 ≥ 0 x - 7 < 0
x ≥ 7 x < 7
If x ≥ 7, |x - 7| = x - 7 > 0.
If x < 7, |x - 7| = x - 7 < 0. No solution.
B. Solve for x < 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
-x + 14 = x
14 = 2x
x = 7
7 ≮7. No solution
C. Solve for x ≥ 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
True for all x.
D. Merge overlapping intervals
No solution or x ≥ 7
⇒ x ≥ 7
The diagram below shows that the graphs of y = |x - 7| (blue) and of y = x - 7 (dashed red) coincide only when x ≥ 7.
Answer:
a. 3
Step-by-step explanation:
We can get to know if a number is divisible by 3 if after adding all the digits of that number we get a number which is completely divisible by 3 or we can say the number appears in the table of 3.
For example: In the given number if we will add all the digits the we will get 21 and we all know that 21 is divisible by 3.
10,534,341 = 1 + 0 + 5 + 3 + 4 + 3 + 4 + 1 = 21
21 = 21/3 = 7
Other options are incorrect.
Divisibility rule for 2 : A number is said to be divisible by 2 if it's ones place ends in 0, 2, 4, 6 or 8 i.e. an even number. The given number does not satisfy this condition because it ends in 1 which is an odd number.
Divisibility rule for 9 : A number is said to be divisible by 9 if after adding all the digits of that number we get a number which is completely divisible by 9. Since the sum total of the given number is 21 which is not completely divisible by 9 we can easily infer that 9 is not the answer for this question.
To solve the problem shown above, you must follow the proccedure shown below:
1. By definition, Completary angles are those angles whose sum is 90 degrees and Suplementary angles are those angles whose sum is 180 degrees.
2. Keeping the information above on mind, you have:
<span>
(a) An angle measures 43 . What is the measure of its complement?
=90°-43°
=47°
(b) An angle measures 81 . What is the measure of its supplement?
</span>
=180°-81°
=99°
The answers are:
a) 47°
b) 99°
Answer:
See explanation
Step-by-step explanation:
Dinosaur Discovery show = 8 friends
Wild Weather show = 4 friends
Cost of Dinosaur Discovery show = $d
Cost of Wild Weather show = $w
At regular price:
Total cost of his friends' tickets = 8 * d + 4 * w
= 8d + 4w
At half price
Total cost of his friends' tickets =
8 * 1/2d + 4 * 1/2w
= 8/2d + 4/2w
= 4d + 2w
Total cost of his friends' tickets = 4d + 2w
Yes.
It’s a flat figure (2D), and all of its lines are connected with one another. There aren’t any open points/lines. It’s closed to create a shape. This means it’s a polygon.
