Consider vectors u and v, where u=(1,-1) and v=(1,1). What is the measure of the angle between the vectors? 0° 60° 90° 180°

Answer:

4 + 5i

Step-by-step explanation:

To calculate this you have to combine the like terms until they cannot be combined any further:

7 + 10i + 4 - 10i - (7 - 5i)

11 + 0i - 7 - 5i

7 & 4 are liked terms so add them together + subtract 10i and 10i

4 + 5i  <--- Final answer

Hope this helps!

Answer:

4 + 5i

Step-by-step explanation:

(7 + 10i) + (4 - 10i) - (7 - 5i)

7 + 10i + 4 - 10i - (7 - 5i)

11 - 7 + 5i

4 + 51

Answer:

[tex] \frac{7 + 7 \sqrt{5} }{ - 4} [/tex]

Step-by-step explanation:

We would multiply the fraction by its conjugate

( A conjugate is a expression that has the same integer or number values but have different signs) for example

[tex]5x + 2[/tex]

and

[tex]5x - 2[/tex]

ARE Conjugates.

The conjugate of

[tex]1 - \sqrt{5} [/tex]

is

[tex]1 + \sqrt{5} [/tex]

So this means we will multiply the expression by 1 plus sqr root of 5 on the numerator and denominator.

Our new numerator will be

[tex]7 \times (1 + \sqrt{5} ) = 7 + 7 \sqrt{5} [/tex]

We can apply the difference of squares for the denominator.

[tex](x + y)(x - y) = x {}^{2} - {y}^{2} [/tex]

So our denominator will be

[tex]1 - 5 = - 4[/tex]

So our rationalized fraction will be

[tex] \frac{7 + 7 \sqrt{5} }{ - 4} [/tex]

Answer: About 6.71 units

Step-by-step explanation:

You use the distance formula: [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex].

Assign the the two points to the variables:

[tex](x_{1}, y_{1}) = (1, 3)\\(x_{2}, y_{2}) = (4, -3)[/tex]

Substitute them in the formula:

[tex]\sqrt{(4-1)^{2}+(-3-3)^{2}}[/tex]

And solve it:

[tex]\sqrt{(4-1)^{2}+(-3-3)^{2}}\\=\sqrt{(3)^{2}+(-6)^{2}}\\=\sqrt{9+36}\\=\sqrt{45}\\=6.71[/tex]

Answer:

I got the answer as 6.70 .here's how

Step-by-step explanation:

c= ( 1,3)

d=(4,-3)

Now , formula of distance

√(x2 - x1)^2 +(y2 - y1)^2

or, √(4-1)^2+(-3-3)^2

or, √(3)^2+(-6)^2

or,√9+36

or√45

√45 = 6.70 units approx

Answer:

A. A prediction based on Model 1 is better than a prediction based on Model 2.

Step-by-step explanation:

Given :

Model 1 :

R² = 0.92

s = 1.65

Model 2 :

R² = 0.85

s = 1.91

The Coefficient of determination of the first model is 0.92 which is greater than the coefficient of determination of the Second model, the coefficient of determination gives the proportion of variation in the dependent variable which is caused by the regression line. Hence, we can say a prediction based on Model 1 is better than a prediction based on Model 2 because a larger proportion of the variation in the dependent variable is predictable from the independent variable.

Answer:

0.2305 = 23.05% probability that exactly 2 workers say yes.

Step-by-step explanation:

For each worker, there are only two possible outcomes. Either they say yes, or they say no. The probability of a worker saying yes is independent of any other worker, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

5% of workers in the US use public transportation to get to work.

This means that [tex]p = 0.05[/tex]

You randomly select 25 workers

This means that [tex]n = 25[/tex]

Find the probability that exactly 2 workers say yes.

This is P(X = 2). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{25,2}.(0.05)^{2}.(0.95)^{23} = 0.2305[/tex]

0.2305 = 23.05% probability that exactly 2 workers say yes.

Answer:

Joel wants to find the quotient of a number and 4, minus thirteen

Step-by-step explanation:

Given the expression :

n/4 - 13

The options B and D cannot be possible answers as they are referring to products and sums which is not a part of the operation used in the expression.

However, the most appropriate option would be A because,

13 is subtracted from the quotient of n/4 which is what the first option expresses.

What is meant by option C however is :

13 - n/4

Hence. Option A is the correct choice.

Answer:

Joel wants to find the quotient of a number and 4, minus thirteen

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

180 - 75 = 105

Answer:

Step-by-step explanation:

Total no. of goods, n = 200

no. of defective units in the goods, d = 20

hence the no. of proper units,

g = n-d

g = = 200-20

g = 180

a)

ways in which a vending company buys fifteen of these microwaves and receive no defective units be:

[tex]^{180}C_{15}=\frac{180!}{15!\times (180-15)!}[/tex]

[tex]\approx 2.83\times 10^{21}[/tex]

b)

ways in which a vending company buys fifteen of these microwaves and receive exactly two defective units be:

[tex]^{20}C_2\times ^{180}C_{13}=\frac{20!}{2!\times (20-2)!} \times \frac{180!}{13!\times (180-13)!}[/tex]

[tex]\approx 190\times (2.146\times 10^{19})[/tex]

[tex]\approx 4.076\times 10^{21}[/tex]

c)

ways in which a vending company buys fifteen of these microwaves and receive at least one defective units be:

[tex]^{20}C_{1}\times ^{199}C_{14}=\frac{20!}{1!\times (20-1)!} \times \frac{199!}{13!\times (199-13)!}[/tex]

[tex]\approx 20\times (8.258\times 10^{19})[/tex]

[tex]\approx 1.652\times 10^{21}[/tex]

Answer:

12

Step-by-step explanation:

First lets list all the factors of these numbers

72: 1,2 3,4,6,8,9,12,18,24,36,72

84: 1 , 2 , 3 ,4 , 6 , 7 , 12 , 14 ,  21 , 28 , 42 , 84

Now lets find the biggest number that is a factor of both 84 and 72  

as we can see the highest number that is the factor of both 84 and 72 is 12

12 is the hcf

Answer:

the eq of given line is 2x+y+3=0

Answer:

x = 4

y = 3

Step-by-step explanation:

Given equations :-

Second equation can be written as ,

Adding them :-

Put this in (ii) :-

Answer:

option d is correct one in which value of T lies

Answer:

B. -infinity < x < infinity

Step-by-step explanation:

Since it's linear and kind of horizontal, it stretches to infinity on both sides (indicated by arrows on both sides of the line.

Answer:

10. CD + DE = CE

11. BC + CE = BE

Step-by-step explanation:

10. CD and DE lie on a straight line, therefore, CD + DE = CE based on the segment addition postulate.

11. BC and CE lie on a straight line, therefore, BC + CE = BE based on the segment addition postulate.

Answer:

2

Step-by-step explanation:

Since x=0, and it's not <0, the "else statement" is executed making y=0+2

There is a category called "computer and technology", maybe you can get better answers if you select that instead of "mathematics"

Answer:

-7i or 7i

Step-by-step explanation:

You can't take the square root of a negative number, so the value "i" is automatically taken out. You're now left with i +/- sqrt(35). The square root of 35 now can either be -7 or 7 because of the +/-, so the final answer is -7i or 7i.

Answer:

5

Step-by-step explanation:

I'm going to call x, x1 because I want to use x as a variable.

So we have a ray with points (0,0) and (3x1,5) on it. This equation for this ray would be y=5/(3x1)×x.

We have another ray with points (0,0) and (2,-6). This equation for this ray would be y=-6/2×x or y=-3x.

We want these two lines' slopes to be opposite reciprocals. The opposite reciprocal of -3 is 1/3.

So we want to find x1 such that 5/(3x1)=1/3.

Cross multiply: 15=3x1

Divide both sides by 3: 5=x1

We want x1 to be 5 so that 5/(3×5) and -3 are opposite reciprocals which they are.

Another way:

If two vectors are perpendicular, then their dot product is 0.

The dot product of <3x,5> and <2,-6> is 3x(2)+5(-6).

Let's simplify:

6x-30.

We want this to be 0.

6x-30=0

Add 30 on both sides:

6x=30

Divide both sides by 6:

x=5

Answer:I’m pretty sure ( not 100% thou ) the awnser would be A) 4

Answer:

a = 3

Step-by-step explanation:

(a, -1) is (x, y)

Plug in the value of y into the given equation to solve for a (x):

4x - 3(-1) = 15

4x + 3 = 15

4x = 12

x = 3

(x, y) is (a, -1) so (a, -1) = (3, -1)

Answer: a=3

Step-by-step explanation:

We are given a point and an equation. To see what "a" is, we can plug in the coordinate into the equation and solve for x.

4a-3(-1)=15       [multiply]

4a+3=15           [subtract both sides by 3]

4a=12               [divide both sides by 4]

a=3

Now, we know that a=3.

Answer:

C

Step-by-step explanation:

tracing paper is your friend

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

95°=6r°+47(being vertically opposite angle)

or,48°=6r

or,48=/6=r°

or,r=8°

The tangent to the curve at a point P (x, y) has slope dy/dx at that point. By the chain rule,

dy/dx = (dy/dθ) / (dx/dθ)

We're in polar coordinates, so

y (θ) = r (θ) sin(θ)   ==>   dy/dθ = dr/dθ sin(θ) + r (θ) cos(θ)

x (θ) = r (θ) cos(θ)   ==>   dx/dθ = dr/dθ cos(θ) - r (θ) sin(θ)

We're given r (θ) = 1 - sin(θ), so that

dr/dθ = -cos(θ)

Then the slope of the tangent to the curve at P is

dy/dx = (dr/dθ sin(θ) + r (θ) cos(θ)) / (dr/dθ cos(θ) - r (θ) sin(θ))

dy/dx = (-cos(θ) sin(θ) + (1 - sin(θ)) cos(θ)) / (-cos²(θ) - (1 - sin(θ)) sin(θ))

dy/dx = - (cos(θ) - sin(2θ)) / (sin(θ) + cos(2θ))

The tangent is horizontal if dy/dx = 0 (or when the numerator vanishes):

cos(θ) - sin(2θ) = 0

cos(θ) - 2 sin(θ) cos(θ) = 0

cos(θ) (1 - 2 sin(θ)) = 0

cos(θ) = 0   or   1 - 2 sin(θ) = 0

cos(θ) = 0   or   sin(θ) = 1/2

[θ = π/2 + 2nπ   or   θ = 3π/2 + 2nπ]   or   [θ = π/6 + 2nπ   or   θ = 5π/6 + 2nπ]

where n is any integer.

In the interval 0 ≤ θ ≤ 2π, we get solutions of θ = π/6, θ = 5π/6, and θ = 3π/2. (We omit π/2 because the denominator is zero at that point and makes dy/dx undefined.) So the points where the tangent is horizontal are themselves (√3/4, 1/4), (-√3/4, 1/4), and (0, -2), respectively.

The tangent is vertical if 1/(dy/dx) = 0 (or when the denominator vanishes):

sin(θ) + cos(2θ) = 0

sin(θ) + (1 - 2 sin²(θ)) = 0

2 sin²(θ) - sin(θ) - 1 = 0

(2 sin(θ) + 1) (sin(θ) - 1) = 0

2 sin(θ) + 1 = 0   or   sin(θ) - 1 = 0

sin(θ) = -1/2   or   sin(θ) = 1

[θ = 7π/6 + 2nπ   or   θ = 11π/6 + 2nπ]   or   [θ = π/2 + 2nπ]

Then for 0 ≤ θ ≤ 2π, the tangent will be vertical for θ = 7π/6 and θ = 11π/6, which correspond respectively to the points (-3√3/4, -3/4) and (3√3/4, -3/4). (Again, we omit π/2 because this makes dy/dx non-existent.)

Answer:

(-8,0), (0,-6)

Step-by-step explanation:

Answer - It’s 31.56

Step-by-step explanation: You just do regular multiplication and then add  the decimal point

Answer:

Part A 12 ≤ 6x ≤ 36

Part B 2 ≤ x ≤ 6

Step-by-step explanation: