Answer:
<11,33>
Step-by-step explanation:
If it is perpendicular to <3,-1> We can use <0,0> as the other point to get the slope
m = (y2-y1)/(x2-x2)
The slope of the vector is
(-1-0)/(3-0)
= -1/3
Then we want a vector perpendicular, so we take the negative reciprocal of the slope
- (-3/1) =3
So the perpendicular slope is 3
Our new vector y/x = 3/1
Using cross products
3x=y
The magnitude has to be 11 sqrt (10)
magnitude = sqrt( ((x)^2 + y^2) = 11sqrt(10)
magnitude = sqrt( ((x^2 + y^2) = 11sqrt(10)
Square both sides
x^2+y^2 = 11^2*10
x^2 + y^2 =1210
We have 2 equations and 2 unknowns
x^2 +y^2 =1210 and
3x=y
Replace y with 3x
x^2 + (3x)^2 =1210
x^2 +9x^2 =1210
10x^2 =1210
Divide both sides by 10
x^2 =121
Take the square root of each side
sqrt(x^2) = sqrt(121)
x=±11
But it problems states it has to be in the first quadrant so x=11
x =11
Now we can find y
y =3x
y =11*3
y =33
The vector is <11, 33>
Answer:
A. -0.70
Step-by-step explanation:
If you type in z score calculator you can just put in the numbers and it will calculate the z score for you.
Answer:
<em>Expected Payoff ⇒ $ 1.50 ; Type in 1.50</em>
Step-by-step explanation:
Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;
<em>Thus, Solution ; Expected Payoff ⇒ $ 1.50</em>
Answer:
x is equal to 40
Step-by-step explanation:
Since the two angles together equal 90, we can add them together and solve for x.
10 + 2x = 90
2x = 80
x = 40
Answer:
(f + g)(x) = x² + 5x - 36
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Terms/Coefficients/Degrees
- Function Notation
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = x² + 4x - 32
g(x) = x - 4
(f + g)(x) is f(x) + g(x)
<u>Step 2: Find</u>
- Substitute: (f + g)(x) = x² + 4x - 32 + (x - 4)
- Combine like terms (x): (f + g)(x) = x² + 5x - 32 - 4
- Combine like terms (Z): (f + g)(x) = x² + 5x - 36