Answer:
-15/16
Step-by-step explanation:
3/2 x (-5/8) = 12/8 x -5/8 = -60/64 = - 15/16
Answer:
<u>The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.</u>
Step-by-step explanation:
Let's find out the pattern Zack is using to water his garden, this way:
First week = 1 3/8 gallons of water
Second week = 1 3/4 gallons of water = 1 3/8 + 3/8 = 1 6/8 = 1 3/4
Third week = 2 1/8 gallons of water = 1 3/4 + 3/8 = 1 6/8 + 3/8 = 2 1/8
The constant of adding every week is 3/8 gallons, therefore,
Fourth week = 2 1/8 + 3/8 = 2 4/8 = 2 1/2 gallons of water
Fifth week = 2 1/2 + 3/8 = 2 4/8 + 3/8 = 2 7/8 gallons of water
<u>The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.</u>
Answer:
x = {nπ -π/4, (4nπ -π)/16}
Step-by-step explanation:
It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:
cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)
= cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)
= sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))
= (sin(x) +cos(x))·(sin(4x) +cos(4x))
Each of the sums in this product is of the same form, so each can be simplified using the identity ...
sin(x) +cos(x) = √2·sin(x +π/4)
Then the given equation can be rewritten as ...
cos(3x) +sin(5x) = 0
2·sin(x +π/4)·sin(4x +π/4) = 0
Of course sin(x) = 0 for x = n·π, so these factors are zero when ...
sin(x +π/4) = 0 ⇒ x = nπ -π/4
sin(4x +π/4) = 0 ⇒ x = (nπ -π/4)/4 = (4nπ -π)/16
The solutions are ...
x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n
Answer:
Step-by-step explanation:
Given the equation solved by Morgan, Dakota and Taylor expressed as 7x+5x+1=73, to get the value of x, the valid steps are as shown;
7x+5x+1=73
take the sum of 7x and 5x
12x+ 1 = 73
subtract 1 from both sides
12x+1-1 = 73-1
12x = 72
Divide both sides by 12
12x/12 = 72/12
x = 6
Based on the calculation above, the students with invalid first step is Dakota.
<em>Dakota added 5x with 1 to get 6x which is an invalid step because 1 is not attached to a variable x. A function cannot be added to a constant hence making his first step invalid.</em>
Answer:
200/120 = 5/3
5/3 x 3 = 5 oz
<u>you can also do it this way:</u>
3/120 = x/200
x = 600/120 = 5
