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NISA [10]
2 years ago
6

Please show your work !!!!!!!!!!!!

Mathematics
1 answer:
dedylja [7]2 years ago
3 0

Answer:

(3.4)

Step-by-step explanation:

  • Our equation is f(x)=-2(x-3)^2+4
  • Now there are 2 ways you can do this, I'll show you the shortcut
  • If you have an equation like this, just take the value in parenthesis and equate it to zero
  • x-3=0.x=3 is the x of the vertex
  • Put this back into the equation
  • f(x)=-2(x-3)^2+4\\x=3\\f(3)=-2(3-3)^2+4\\f(3)=-2(0)^2+4=4 this is the y
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Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).
erma4kov [3.2K]

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

|u|=\sqrt{14^2+9^2} which is \sqrt{277}

|v|=\sqrt{3^2+6^2} which is \sqrt{45}

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

cos\theta=\frac{uv}{|u||v|} where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

cos^{-1}\theta=\frac{96}{111.64676} which returns an angle measure of 30.7. Plugging that all into the dot product formula:

u*v=\sqrt{277}*\sqrt{45}cos(30.7) gives you a dot product of 96

6 0
2 years ago
Ms. Moran has started an investment club at BSS. $8000 is invested, some at 10%
labwork [276]
The answer can be readily calculated using a single variable, x:

Let x = the amount being invested at an annual rate of 10%
Let (8000 - x) = the amount being invested at an annual rate of 12%

The problem is then stated as:

(x * 0.10) + ((8000 - x) * 0.12) = 900
0.10(x) + ((8000 * 0.12) - 0.12(x)) = 900
0.10(x) + 960 - 0.12(x) = 900
0.10(x) - 0.12(x) = 900 - 960
-0.02(x) = -60
-0.02(x) * -100/2 = -60 * -100/2
x = 6000 / 2
x = 3000

Thus, $3,000 is invested at 10% = $300 annually; and $8,000 - $3,000 = $5,000 invested at 12% = $600 annually, which sum to $900 annual investment.
6 0
2 years ago
Is (6, -24) a solution to the equation: y = -7x + 18? ¿Es (6.-24)
KatRina [158]

i think that's the answer

6 0
3 years ago
Find the value of tan(B)<br><br> please help quickly
elena55 [62]

Answer:

it is 4/3

Step-by-step explanation:

because tan(B) = opposite/adjacent

4 0
3 years ago
I need help showing steps to solve 36v-12=12
Ad libitum [116K]
36v - 12 = 12 .....add 12 to both sides
36v - 12 + 12 = 12 + 12...simplify
36v = 24...divide both sides by 36
(36/36)v = 24/36
v = 2/3 <===
8 0
3 years ago
Read 2 more answers
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