Answer:
Step-by-step explanation:
We want to find the inverse of the function:
To find the inverse of a function, we will flip the variables and solve for <em>y</em>. So:
Solve for <em>y</em>. Subtract two from both sides:
Divide both sides by two:
And take the principal square root of both sides. Therefore:
Answer:
Shen served 32 orders, Aldo served 16 orders and Heather served 9 orders
Step-by-step explanation:
Let S represent Shen, A, Aldo and H, Heather
Now, let's interpret the question
Shen served 2 times as many as Aldo, this gives:
S = 2A ...eq 1
Aldo served 7 more orders than Heater
A = 7 + H ... eq 2
Slot in the value of A in eq 1
Therefore,
S = 2 (7 + H)
Expand the bracket
S = 14 + 2H
Shen, Heather and Aldo served a total of 57 orders
S + A + H = 57
Slot in the values of S and A
(14 + 2H) + (7 + H) + H = 57
14 + 2H + 7 + H + H = 57
Collect like terms
14 + 7 + 2H + H + H = 57
21 + 4H = 57
4H = 57 - 21
4H = 36
H = 9
Substitute the value of eq 2
A = 7 + H
A = 7 + 9
A = 16
Substitute the value of A in eq 1
S = 2A
S = 2(16)
S = 32
Therefore, Shen served 32 orders, Aldo served 16 orders and Heather served 9 orders
To solve for this, we need to use the Distributive Property, which allows us to multiply the number/variable outside of the parenthesis by all numbers/variables inside of the parenthesis. Once we've done that, we can attempt to simplify the equation.
Our current equation is:
7a + 3(9+5a) = 0
Let's use the Distributive Property.
3(9 + 5a)
3(9) + 3(5a)
27 + 15a
Our current equation now is:
7a + 27 + 15a = 0
Combine like-terms.
15a + 7a = 22a
22a + 27 (If this is not being solved, THIS is your answer as an expression)
Subtract 27 from both sides
22a = -27
Divide both sides by 22 to get a.
a = -27/22.
If we are not solving for a, but getting an expression, your answer is:
22a + 27.
If we are solving for a, our answer is:
a = -27/22.
I hope this helps!
Answer:
Step-by-step explanation:
We can break down this problem by first realizing different parts of the circle.
- The line which is 8 units long is a chord of the circle.
- The line that is 3.6 is <em>almost</em> the radius of the circle
- The line that x sits on is the radius.
With this, we can find out if we find the radius of the circle, we have our answer.
We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.
<em>What we need is a way to find the radius of the circle</em><em>. This will get us x</em>. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.
If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).
We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:
Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!
Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.
The line X does just that. Therefore, the value of x is also 5.4.
Hope this helped!
Answer:
A
Step-by-step explanation:
Substitute 6 into place and solving the answer gives you 4 which is indeed bigger than 3. All the other numbers will give you an answer of something lower than 3 which is not what we're looking for in this case.
