Answer:
0
Step-by-step explanation:
Combine like terms, perform the operations with the coefficients of the variable, then write the variable.
10r - 5r + 3r - 8r
= 5r + 3r - 8r
= 8r - 8r
= 0
Answer: 28 shirts
Step-by-step explanation:
From the question, we are informed that Lisa sold 11 shirts for every 7 shirts Becky sold. This can be expressed in a fraction as:
Lisa = 11/(11 + 7) = 11/18
Becky = 7/(11 + 7) = 7/18
If the girls sold 72 shirts in all, the number of shirts sold by Becky will be:
= 7/18 × 72
= 7 × 4
= 28
The equation of this sinusoidal function is either
f(x) = a sin(bx) + c
or
f(x) = a cos(bx) + c
Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.
If the period is π/2, then
2π/b = π/2 ⇒ b = 4
If the maximum value is 10 and the minimum value is -4, then
-4 ≤ a sin(4x) + c ≤ 10
-4 - c ≤ a sin(4x) ≤ 10 - c
-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a
Recall that sin(x) is bounded between -1 and 1. So we must have
-(4 + c)/a = -1 ⇒ a = c + 4
(10 - c)/a = 1 ⇒ a = -c + 10
Combining these equations and eliminating either variable gives
a + a = (c + 4) + (-c + 10) ⇒ 2a = 14 ⇒ a = 7
a - a = (c + 4) - (-c + 10) ⇒ 0 = 2c - 6 ⇒ c = 3
Finally, we have either
f(x) = a sin(bx) + c ⇒ f(0) = c = 3
or
f(x) = a cos(bx) + c ⇒ f(0) = a + c = 3
but the cosine case is impossible since a = 7.
So, the given function has equation
f(x) = 7 sin(4x) + 3
<u>Answer:</u>
(-1, 5)
<u>Step-by-step explanation:</u>
The center of a circle is the midpoint of the diameter.
So we have to calculate the midpoint of the diameter, using this formula:
midpoint = ( 
, 
)
= (
, 
)
= (-1, 5)
∴ The center of the circle lies at the point (-1, 5).
Answer:
4 + 2i
Step-by-step explanation:
First distribute;
7 - 3 - 4i + 6i
= 4 + 2i
