Answer:
54 cm
Step-by-step explanation:
Perimeter = TZ + TX + RX + RY + SY + SZ
TZ = 5 cm
TX = 13 cm
RY = 9 cm
RX = TX = 13 cm (tangents drawn from and external point)
SY = RY = 9 cm (tangents drawn from and external point)
SZ = TZ = 5 cm (tangents drawn from and external point)
Plug in the values:
Perimeter = 5 + 13 + 13 + 9 + 9 + 5 = 54 cm
<span>a. n/4 ≤ -1
Multiply both sides by 4 => n ≤ - 4, which is all the real numbers less or equal than - 4.
That in the real number line is all the numbers to the left of - 4 (including -4)
The matching graph is the B.
b. -10n ≥ -100
Divide both sides by - 10 => n ≤ 10
That is all the real numbers less or equal than 10.
In the real number line it is all the numbers to the left of 10, including 10.
So, the matching graph is the A.
c. 5x ≥ 20
Divide both sides by 5 => x ≥ 4
That is all the real numbers greater or equal to 4.
In the real number line it is all the numbers to the right of 4, including 4.
The matching graph is C.</span>
Answer:
Nifal received $ 4 for washing the first car.
Nifal received $ 5 for washing the second car.
4 and 5 have a sum of 9.
Step-by-step explanation:
The problem can be rewritten as follows: Find the sum of two consecutive entire numbers equal to 9. That is:


Then, by eliminating y:

Now, let is clear
:


Nifal received $ 4 for washing the first car.
The earning for the second car is: (
)



Nifal received $ 5 for washing the second car.
4 and 5 have a sum of 9.
Answer:
t-shirts: 2790
profit: $12209
Step-by-step explanation:
Given the function:
p(x) = -x³ + 4x² + x
we want to maximize it.
The following criteria must be satisfied at the maximum:
dp/dx = 0
d²p/dx² < 0
dp/dx = -3x² + 8x + 1 = 0
Using quadratic formula:







d²p/dx² = -6x + 8
d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0
d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0
Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.
Replacing into profit equation:
p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209
that is, $12209