Answer:
Danny will watch all of them on the same day again on August 31
Step-by-step explanation:
Here, we have a word problem.
The shows and frequency of watching are;
Show A Every 2 days
Show B Every 3rd day
Show C Every 5th day
Show D Every 10th day
Danny watched all four shows on August 1, therefore, the day he will watch all four shows can be found by finding the Lowest Common Multiple, LCM of the frequency of his watching each of the shows. That is, the LCM of 2, 3, 5 and 10
Therefore we have, since 10 is the highest frequency and 3 is not a factor of 10, then the LCM that applies to 3 and 10 is 3×10 = 30.
Since the other frequencies are also a factor of 30, then the LCM of 2, 3, 5, and 10 is 30
Therefore, Danny will watch all four shows again on the same day again in 30 days after August 1. That is August (1 + 30) = August 31.
Answer:
Step-by-step explanation:
Answer:
A.
3x + 3y = 0
7x − y = 8
Step-by-step explanation:
Given
3x + 3y = 0
-4x + 4y = -8
Required
Find the equivalent
To solve for the equivalent we simply solve for x and y in the given equation.
Subtract 3x from both sides in 3x + 3y = 0
3x - 3x + 3y = 0 - 3x
3y = -3x
Multiply both sides by ⅓
⅓ * 3y = -3x * ⅓
y = -x
Substitute -x for y in -4x + 4y = -8
-4x + 4(-x) = -8
-4x -4x = -8
-8x = -8
Multiply both sides by -⅛
-⅛ * -8x = -⅛ * -8
x = 1
Recall that y = -x
y = -1
So, we have that x = 1 and y = -1
We'll substitute these values in the list of options;
A.
3x + 3y = 0
7x − y = 8
7(1) - -(1) = 8
7 + 1 = 8 ----- This is equivalent
B.
3x + 3y = 0
−7x − y = 8
-7(1) - (-1) = 8
-7 + 1 = 8
-6 ≠ 8 .... This is not an equivalent expression
C.
3x + 3y = 0
−7x + 7y = 8
-7(1) + 7(-1) = 8
-7 -7 = 8
-14 ≠ 8 .... This is also not an equivalent expression
D.
3x + 3y = 0
-4x + 7y = 8
-4(1) + 7(-1) = 8
-4 -7 = 8
-11 ≠ 8 -_- This is also not an equivalent expression
The sum of 14 and 16 is 30.30 times 4 is 120.
<span>(<span>14+16</span>)</span><span>(4)
</span><span>=<span><span>(30)</span><span>(4)</span></span></span><span>=
<span>120</span></span>
Answer:
= 6 items per hour
Explanation:
This is a fraction equal to 18 items ÷ 3 hours
We want a unit rate where 1 is in the denominator, so we divide top and bottom by 3
18 items ÷ 3
3 hours ÷ 3
= 6 items/1 hour
= 6 items/hour
= 6 items per hour
