Answer:
Options A and C are correct choices.
Step-by-step explanation:
We have been given an expression 
and we are asked to choose all the equivalent expressions from given choices.
Let us simplify our given expression.
Let us see which of our given choices matches with our answer.
A. 
Upon using distributive property 
we will get,
Therefore, option A is a correct choice.
B. 
Upon using distributive property we will get,
Since this expression is not equivalent to our answer, therefore, option B is not a correct choice.
C. 
Upon removing parenthesis we will get,
Upon combining like terms we will get,
Therefore, option C is the correct choice.
Answer:
- reflected across the y-axis
- compressed by a factor of 2
Step-by-step explanation:
Replacing x by -x in f(x) causes it to be reversed horizontally, that is, reflected across the y-axis.
Replacing x by 2x in f(x) causes it to be compressed horizontally by a factor of 2.
Both of these transformations result in g(x) being a horizontally compressed horizontal reflection of f(x).
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See the attachment for an example. The blue curve is g(x); the red curve is f(x).
Answer:
The number is 4.
Step-by-step explanation:
We can answer the above question as follow:
The square of a number, x is written as: x²
Eight times the number is written as: 8x
From the question, we were told that the square of the number, x is 16 less than eight times the number. This can be written as:
x² = 8x – 16
Rearrange
x² – 8x + 16 = 0
Solving by factorisation method:
Multiply the 1st term (i.e x²) and the last term (i.e 16) together. The result is 16x² as shown below:
x² × 16 = 16x².
Next, find two factors of 16x² such that when we add them together, it will result to the 2nd term ( i.e – 8x).
The factors are –4x and –4x.
Next, replace – 8x in the equation with –4x and –4x. This is illustrated below:
x² – 8x + 16 = 0
x² – 4x – 4x + 16 = 0
Factorise
x(x – 4) – 4(x – 4) = 0
(x – 4)(x – 4) = 0
x – 4 = 0 or x – 4 = 0
x = 4 or x = 4
Thus, the number is 4.
***** Check *****
x² = 8x – 16
x = 4
4² = 8(4) – 16
16 = 32 – 16
16 = 16
Answer:
Please find a visual representation of the scenario generated with MS Excel
Step-by-step explanation:
The given data on how Kylo fills up the bathtub with water are;
The time it takes to fill the bathtub with 50 gallons of water = 15 minutes
The time it takes to drain 30 gallons from the bathtub = 5 minutes
The time it takes to add 5 gallons of hot water = 2 minutes
The time it takes for all the water to drain out = 4 minutes
The given scenario can be represented visually on the coordinate plane, as follows;
The y-axis represents the amount of water in the bathtub in gallons
The x-axis represents the time from the when Kylo begins to fill the bathtub
The coordinates of points in the visual representation of the given scenario are therefore;
At the start, the bathtub is empty;
y = 0, x = 0
Then we have;
Plotting the number of gallons and the cumulative time values on MS Excel gives a visual representation of the scenario
It is the multiplying factor for the whole equation if that makes sense.
