Answer:
f(x) = ![\sqrt[3]{x + 6}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%20%2B%206%7D)
+ 1
Step-by-step explanation:
Whenever addition or subtraction occurs within the cube root, it moves horizontally; the opposite is done for the translation, thus if it is addition, which in this case it is, instead of moving the positive direction, the function moves the negative direction.
As opposed to addition or subtraction outside of the cube root, it moves vertically, and in this case, it is translated exactly as stated. Here it states addition, thus the graph moves up in one unit.
The origin of the parent function is at ( 0, 0), in contrast, the origin of the function is at ( -6, 1 )
By using what we know, we can determine that the answer will be f(x) = + 1 since we know that the inside of the cube root should be the opposite of the x value and the outside of the cube root should be the same.
Answer:
$75
Step-by-step explanation:
Joni currently earns $300 per week (given)
To find how much more she will earn each week, write an expression adding the original pay and the raise amount.
$300 + 25%
Find 25 as a decimal for multiplication
25% = 25/100 = 0.25
Write an expression to represent the scenario
Expression example 1:
$300 + 0.25(300)
This expression adds the original pay and the new raise together.
Expression example 2:
$300 (1.25)
This expression already takes the new pay into account by finding 125% of the original pay.
Simplify both expressions
Expression 1:
$300 + 0.25(300)
$300 + $75
$375
Expression 2:
$300 (1.25)
$375
Both expressions represent the same scenario and therefore come out to the same result. Now that we know how much Joni made after the raise, we need to find how much more money she will earn in a week with the following equation.
New amount - original amount = amount increase
Substitute known values into the equation
$375 - $300
Simplify
$75
Joni will earn $75 more each week.
Let me know if you have any questions!
Answer:
If you simplify 2/6, you get 1/3 by dividing the numerator and denominator by 2.
Therefore, 1/3 and 2/6 would be the same point on the number line.
Answer:
y = x^2/ 60 + 15
=>( x - h)^2 = 4a[ (x^2/6 + 15) - k ].
Step-by-step explanation:
Okay, in order to solve this question very well, one thing we must keep at the back of our mind is that the representation for the equation of a parabola is given as ; y = ax^2 + bx + c.
That is to say; y = ax^2 + bx + c is the equation for a parabola. So, we should be expecting our answer to be in this form.
So, from the question above we are given that "the satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground"
We will make an assumption that the point on the ground is (0,0) and the focus is (0,30). Thus, the vertex (h,k) = (0,15).
The equation that best describes the equation of the satellite is given as;
(x - h)^2 = 4a( y - k). ------------------------(1).
[Note that if (h,k) = (0,15), then, a = 15].
Hence, (x - 0)^2 = (4 × 15) (y - 15).
x^2 = 60(y - 15).
x^2 = 60y - 900.
60y = x^2 + 900.
y = x^2/ 60 + 15.
Hence, we will have;
(x - h)^2 = 4a[ (x^2/6 + 15) - k ].
