I think this is what you are looking for:
=−12
a
b
=
−
12
+=4
a
+
b
=
4
(+)2=42
(
a
+
b
)
2
=
4
2
2+2+2=16
a
2
+
b
2
+
2
a
b
=
16
∴2+2=16+2×12=40
∴
a
2
+
b
2
=
16
+
2
×
12
=
40
Now, (−)2=2+2−2=40+2×12=64
(
a
−
b
)
2
=
a
2
+
b
2
−
2
a
b
=
40
+
2
×
12
=
64
∴(−)=64‾‾‾√=±8
∴
(
a
−
b
)
=
64
=
±
8
So, 2−2=(+)(−)
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
2−2=(4)(±8)=±32
a
2
−
b
2
=
(
4
)
(
±
8
)
=
±
32
Hope that helps and sorry if it is confusing!
Answer:
The value of x is 14
Step-by-step explanation:
The value of x is 14 because the smaller triangle was dilated by 3 to get the bigger triangle. I figured this out because
9 ÷ 3 = 3
so this would mean that 5 was dilated by 3 also. So to figure this out, it would be
5 × 3 = 15
1 of that 15 is already there.
So this means that
15-1=14
A=14
I hope this helps you.
Answer:
2.
Step-by-step explanation:
For #2, another way to word this question is: For which of the following trig functions is π/2 a solution? Well, go through them one by one. If you plug π/2 into sinθ, you get 1. This means that when x is π/2, y is 1. Try and visualize that. When y is 1, that means you moved off the x-axis; so y = sinθ is NOT one of those functions that cross the x-axis at θ = π/2. Go through the rest of them. For y = cos(π/2), you get 0. At θ = π/2, this function crosses the x-axis. For y = tanθ, your result is undefined, so that doesn't work. Keep going through them. You should see that y = secθ is undefined, y = cscθ returns 1, and y = cotθ returns 0. If you have a calculator that can handle trig functions, just plug π/2 into every one of them and check off the ones that give you zero. Graphically, if the y-value is 0, the function is touching/crossing the x-axis.
Think about what y = secθ really means. It's actually y = 1/(cosθ), right? So what makes a fraction undefined? A fraction is undefined when the denominator is 0 because in mathematics, you can't divide by zero. Calculators give you an error. So the real question here is, when is cosθ = 0? Again, you can use a calculator here, but a unit circle would be more helpful. cosθ = π/2, like we just saw in the previous problem, and it's zero again 180 degrees later at 3π/2. Now read the answer choices.
All multiples of pi? Well, our answer looked like π/2, so you can skip the first two choices and move to the last two. All multiples of π/2? Imagine there's a constant next to π, say Cπ/2 where C is any number. If we put an even number there, 2 will cut that number in half. Imagine C = 4. Then Cπ/2 = 2π. Our two answers were π/2 and 3π/2, so an even multiple won't work for us; we need the odd multiples only. In our answers, π/2 and 3π/2, C = 1 and C = 3. Those are both odd numbers, and that's how you know you only need the "odd multiples of π/2" for question 3.
Answer:
20.625 dollars or about 20.63 dollars
Step-by-step explanation:
33/8 = 4.125
4.125 times 5 = 20.625
Answer:
Step-by-step explanation:
Given data
Total units = 250
Current occupants = 223
Rent per unit = 892 slips of Gold-Pressed latinum
Current rent = 892 x 223 =198,916 slips of Gold-Pressed latinum
After increase in the rent, then the rent function becomes
Let us conside 'y' is increased in amount of rent
Then occupants left will be [223 - y]
Rent = [892 + 2y][223 - y] = R[y]
To maximize rent =
Since 'y' comes in negative, the owner must decrease his rent to maximixe profit.
Since there are only 250 units available;
![y=-250+223=-27\\\\maximum \,profit =[892+2(-27)][223+27]\\=838 * 250\\=838\,for\,250\,units](https://tex.z-dn.net/?f=y%3D-250%2B223%3D-27%5C%5C%5C%5Cmaximum%20%5C%2Cprofit%20%3D%5B892%2B2%28-27%29%5D%5B223%2B27%5D%5C%5C%3D838%20%2A%20250%5C%5C%3D838%5C%2Cfor%5C%2C250%5C%2Cunits)
Optimal rent - 838 slips of Gold-Pressed latinum
