Answer:
Part A: 299 + 45A + 30B + 50c
Part B: 569 (or 570 if you round it up)
Step-by-step explanation:
Part A:
Because there is no variable for the number of PlayStation 4s, let's assume that there is only one. That will be 299.
If A is the number of wireless controllers and each wireless controller is worth 45 dollars each, the price for the wireless controller(s) is 45A.
If B is the number of wireless controller charging stations and each wireless controller charging station cost 30 dollars, then the price of the wireless controller charging station(s) is 30B
If C is the number of games and each game cost 50 dollars, then the price of the game(s) is 50C
Put that all together, and we get 299 + 45A + 30B + 50c.
Part B:
Let's plug the numbers into the formula.
A = 2
B = 1
C = 3
<span>y=(4/9)x-2
This is in slope intercept form (y=mx+b), where m is the slope.
A perpendicular line will have the opposite reciprocal of the slope.
So if the slope here is 4/9, then the perpendicular line's slope will be -9/4.
Now that you have the slope (-9/4) and a point (4, 3), you can use the point-slope formula to find the equation.
y - y</span>₁ = m(x - x₁)
y - 3 = (-9/4)(x - 4)
y - 3 = (-9/4)x + 9
y = (-9/4)x + 12
So the answer will be:
C. <span>y= -(9/4)x+12</span>
Answer:
125.6637061 or 125.7
Step-by-step explanation:
V=πr²h
Big: π(3)²(5) = 141.3716694
Hole: π(1)²(5) = 15.70796327
141.3716694
- <u>15.70796327</u>
125.6637061
1) The perimeter is the sum of the lengths of the straight edge (the diameter of the semicircle) and the length of the arc of the semicircle.
The circumference of a 4 ft circle is
π*diameter = π*4 ft ≈ 12.566 ft
The semicircle will have a length that is half that, 6.283 ft. When this length is added to the diameter, the perimeter is found to be
Perimeter = 4 ft + 6.283 ft ≈ 10.3 ft.
2) The area of a circle is given by the formula
A = (π/4)d²
For a diameter of 15 inches, the area is
A = (π/4)(15 in)² = 56.25π in²
A ≈ 176.7146 in²
The area of the circle is about 176.71 in².
Answer:
32√5
Step-by-step explanation:
We have the right triangles PQA and PQB as well as the given right triangle QAB.
cot(PAQ) = 2/5 = QA/PQ
cot(PBQ) = 3/5 = QB/PQ
cot(PAQ) / cot(PBQ) = (2/5) / (3/5) = 2/3
cot(PAQ) / cot(PBQ) = (QA/PQ) / (QB/PQ) = QA / QB
QA / QB = 2/3
QA = (2/3) QB
QB = (3/2) QA
By the Pythagorean Theorem we have:
(QA)² + 32² = (QB)²
(QA)² + 32² = (3/2 QA)²
(QA)² + 1024 = (9/4) (QA)²
(5/4) (QA)² = 1024
(QA)² = (4/5)1024 = 4096/5
QA = 64/√5
Solve for PQ.
cot(PAQ) = QA/PQ
PQ = QA / cot(PAQ)
PQ = (64/√5) / (2/5) = 32√5
The height of the tower is 32√5.
