Instructions: Select the correct answer.

Vector u has a magnitude of 5 units and a direction angle of 30°. Vector v has a magnitude of 7 units and a direction angle of 120°. What is the direction angle of their vector sum?


A.) 82.21°


B.) 84.46°


C.) 85.11°


D.) 86.13°

Answer:

  A.  0.0134

Step-by-step explanation:

This is a question that must be answered using a table or calculator. (Tables are not in general use these days.) See below for a calculator's output.

___

The answer would be 0.0135 if it were properly rounded.

Final answer:

The quadratic expression 3x^2-48 can be completely factored as 3(x-4)(x+4) by first factoring out the common factor and then utilizing the difference of squares.

Explanation:

To factor this expression completely, we first need to look for common factors and any patterns that might help simplify the expression. Both terms in the expression 3x2−48 have a common factor of 3. Factoring out this common factor gives us:

Notice that the expression inside the parenthesis, x2 − 16, is a difference of squares, which can be factored further into (x − 4)(x + 4). Therefore, the fully factored form of the original expression is:

This shows how identifying common factors and utilizing the difference of squares helps in completely factoring the given expression.

Answer:

OPTION B

Step-by-step explanation:

To solve, create a formula.

y= 5(copay)+premium

Using this you get:

Option A: 5(20)+55= $155

Option B: 5(15)+60= $135

Option C: 5(25)+65= $190

Option D: 5(30)+50= $200

Answer:

Option B

Step-by-step explanation:

Option A : 55 + 20(5) = 155

Option B : 60 + 15(5) = 135

Option C : 65 + 25(5) = 190

Option D : 50 + 30(5) = 200

Answer:

-4 ≤ f ([tex]\theta[/tex]) ≤ 4

Step-by-step explanation:

The range of a function is the allowed y-values of the function.

We can simply look at the periodic function below and see that the y-value ranges from a negative 4 to a positive 4. It oscillates betwen -4 and 4. That is the range.

We can say -4 ≤ f ([tex]\theta[/tex]) ≤ 4

Last answer choice is right.

*** NOTE: it is a type, not "0", rather "[tex]\theta[/tex]"

Answer:

480 = x(6)

Step-by-step explanation:

Given in the question that,

distance travelled by the train = 480 miles

time taken by the train to travel 480 miles = 6 hours

Suppose speed of train = x miles/hour

Formula to use to drive the equation

480 = x(6)

x = 480/6

x = 80 miles/hour

Answer:

[tex]x=\frac{5\pi}{4}[/tex]

Step-by-step explanation:

We want to solve;

[tex]\cscx=-\sqrt{2}[/tex] in the 3rd quadrant

Recall that;

[tex]\sin x=\frac{1}{\csc x}[/tex]

We use the reciprocal ratio to get;

[tex]\sin x=-\frac{\sqrt{2}}{2}[/tex]

In the third quadrant the solution is

[tex]x=\pi+\sin^{-1}(\frac{\sqrt{2} }{2} )[/tex]

[tex]x=\pi+\frac{\pi}{4}[/tex]

[tex]x=\frac{5\pi}{4}[/tex]

Answer:

Ratio is it rate. Can you do the rate of numbers.

For example, if we say: If the car was very high to acceleration at least, 1,000 km/h.

If Usain Bolt was won on the Olympics, he has 27 km/h.

Hmm, the ratio isn't rate at all. This method can do the non rate. For example, if we say: If the gas price at BP, there's $100 per year.

Step-by-step explanation:

With this method, you must solve the ratio isn't rate.

For there's the group, this was what do you say, it's GCF, or greatest common factor. With this GCF method, for example: if we say, the European Parliament, and the MPs, are divided by gender, if we divide by male and female. For more examples, see the answer at the above with the picture

With this method of the rate, there are no of speed, price, or something else.

There are some examples like the km/h, representing the Kilometers per hour.

Hopefully with this helpful example

90 degrees

3 ( square root sign) 10

                 10√2

Then b = ------------ = 5√2

                     Answer:

5√2

Step-by-step explanation:

Notice that the sine function links side b, the hypotenuse (10) and the 45° angle:

                 1

sin 45° = ------ = b/10

                √2

Then b = 10√2 / 2  = 5√2

Answer:

From the information, we know that Jamal's mother is 28 years older than Jamal, so his mothers age should be:

x + 28 (years)

Also, we know that his uncle's age is twice as much as Jamal's mother age, so we have the following expression:

(x + 28) · 2 = 2x + 56

*Hope this help you

Jamal's uncle's age can be expressed as 2(x + 28), which simplifies to 2x + 56 years.

Jamal is x years old, and his mother is 28 years older than him. Therefore, his mother's age can be represented by x + 28. Jamal's uncle is two times older than Jamal's mother, which means we need to multiply his mother's age by 2 to get the uncle's age. So, the expression for Jamal's uncle's age is 2(x + 28). Simplifying this expression, we get:

2(x + 28)

2x + 2(28)

2x + 56

Thus, Jamal's uncle's age is represented by the expression 2x + 56 years.

Answer:

Option A. [tex]x=34\°[/tex]

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

[tex]x=\frac{1}{2}(arc\ CD+arc\ AB)[/tex]

substitute the values

[tex]x=\frac{1}{2}(23\°+45\°)[/tex]

[tex]x=34\°[/tex]

Answer:

the answer is A.

Step-by-step explanation:

Answer:

A) distance, in miles, between the cities

Step-by-step explanation:

correct on edge

A) The formula for surface area of a sphere is A = 4*PI*r^2

using 3.14 for PI:

Surface area for Earth = 4 * 3.14 x 3960^2 = 196,960,896 miles^2

Surface area of the moon: 4 * 3.14 * 1080^2 = 14,649,984 miles^2

B)Divide the Surface of the Earth by the moon:

196,960,896 / 14,649,984 = 13.44

The Earths surface is 13.4 times larger than the moon.

C) Multiply the surface of the Earth by 70%:

196,960,896 * 0.70 = 137,872,627.2 million square miles of water.

Calculating surface areas of Earth and the moon, comparing them, and determining the amount of water on Earth's surface.

a. Find the surface area of Earth and the moon:

b. Compare the surface areas of Earth and the moon: Earth's surface area is approximately 13.5 times greater than the Moon's surface area.

c. About 70% of Earth's surface is water: There are approximately 137.9 million square miles of water on Earth's surface.

Answer:

Step-by-step explanation:

Look at the picture.

We must use the tangent.

[tex]tangent=\dfrac{opposite}{adjacent}[/tex]

We have:

[tex]opposite=h\\adjacent=1,500\ ft\\\\\tan10^o\approx0.1763[/tex]

Substitute:

[tex]\dfrac{h}{1,500\ ft}=0.1763[/tex]      multiply both sides by 1,500 ft

[tex]h=264.45\ ft\to h\approx264.49\ ft[/tex]

Caitlin will have 18 and Jeremy will have 6 at first because then 18-6=12 which is how many cards Caitlin have to Jeremy

Answer:

3.5

Step-by-step explanation:

7/2=3.5

Answer:

3.5

Step-by-step explanation:

Ratio of

those who walk : those who ride = 2 : 7

This means that for every 2 students who walk, there are 7 students who ride

Therefore, for every 1 student that walks, (hypothetically) there are 3.5  (7/2) students who ride

Then the number of bus riders is 3.5 times the number of students that walk.

Answer:

The question is incomplete, the complete question is Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 12 ft³ of fluffy material. The base is 3 ft, the height is 2 ft, what is the length of the pillow?

The length of the pillow is 4 feet

Step-by-step explanation:

The formula of the volume of the wedge is [tex]V=\frac{1}{2}bhl[/tex] , where

∵ The pillow in the shape of a wedge

∵ The pillow is filled with 12 ft³ of fluffy material

∴ The volume of the wedge = 12 ft³

∵ The base = 3 feet

∵ The height = 2 feet

- Use the formula of the volume above to find its length

∵ [tex]V=\frac{1}{2}(2)(3)l[/tex]

∴ V = 3 l

∵ V = 12 ft³

- Equate 3 l by 12

∴ 3 l = 12

- Divide both sides by 3

∴ l = 4 feet

∴ The length of the pillow is 4 feet

Answer: C

y=-5cos(x) is the graphed equation. Cos(x) starts at (0,0) and one period is 2pi or 6.28 and by cos(x) multiplied by -5 starts the cosine wave at (0,-5) and thus corresponds to the graphed equation shown.

Any questions please feel free to ask. Thanks

Answer:

a.V=1.57

b. 2786 cubic feet (696.9)

c. 1/12 pie

Step-by-step explanation:

a. I have that the volume of a cylinder can be expressed as [tex]V= \pi r^{2} h[/tex] what would be the base (the area of ​​the circle) by the height, so [tex]V=\pi * (\frac{1}{2}) ^{2} *1 =\frac{\pi }{2} = 1.57[/tex]

b. The volume of a sphere is given by the formula [tex]V=\frac{4}{3} \pi r^{3}[/tex] as the diameter is twice the radius I have to

[tex]V= \frac{4}{3} \pi (\frac{d}{2} )^{3} =\frac{4}{3} \pi (5.5)^{3} = 696.9[/tex]cubic feet the nearest cubic foot be 2786 cubic feet

c. The volume of a cone is given by the formula [tex]V=\frac{1}{3} \pi r^{2} h[/tex] so [tex]V=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \pi (\frac{1}{2} )^{2} *1=\frac{1}{3}\pi \frac{1}{4}=\frac{1}{12}\pi[/tex]

Answer:

[tex]\boxed{7k + 3}[/tex]

Step-by-step explanation:

Average cost = total cost/number of items = (35k² + 29k + 6)/(5k + 2)

Perhaps the best way to solve this problem is to use long division.

                       7k  + 3  

5k + 2)35k² + 29k + 6

          35k² +  14k              

                       15k + 6

                       15k + 6

                                0

Thus,

[tex]\frac{35k^{2}+29k+ 6}{5k + 2} = 7k+3[/tex]

The average cost per item is [tex]\boxed{7k+3}[/tex].

Answer:7k+3

Step-by-step explanation:

Answer:

  A|  12, 3

Step-by-step explanation:

The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...

  y = (x -12)(x -3)

A quick check shows this product is ...

  y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required

The factors are zero when x is either 12 or 3.

The zeros of the equation are 12 and 3.

____

Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).

Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.

I'm not sure what to make of the "h" and "i" in your question, so I'll just ignore them (and the 3). Looks like we have

[tex]\vec f(x,y,z)=(x+y,x-y,x^2+y^2-2z)[/tex]

and a surface parameterzied by

[tex]\varphi(u,v)=(u+2v,u-2v,u^2+2v^2)[/tex]

with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. Then

[tex]\varphi_u\times\varphi_v=(4u+4v,4u-4v,-4)[/tex]

so that the flux is given by the integral

[tex]\displaystyle\iint_S\vec f\cdot\mathrm d\vec S=\int_0^1\int_0^1(2u,4v,4v^2)\cdot(4u+4v,4u-4v,-4)\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle8\int_0^1\int_0^1(u^2+3uv-4v^2)\,\mathrm du\,\mathrm dv=\boxed{-2}[/tex]

To calculate the flux of the given vector field through the surface S, you need to calculate the partial derivatives of the parametrization, then find the cross product of these partial derivatives, and finally evaluate the double integral over the surface using the flux formula.

To calculate the flux of the vector field f(x, y, z) = 3hx + y, x − y, x2 + y2 − 2zi through the surface S parametrized by φ(u, v) = u + 2v, u − 2v, u2 + 2v2 with 0 ≤ u, v ≤ 1 and oriented by φu × φv:

Answer:

C) √5(cos(117°) +i·sin(117°))

Step-by-step explanation:

The rectangular number a+bi can be written in polar form as ...

√(a^2+b^2)×(cos(arctan(b/a)) + i·sin(arctan(b/a)))

Here, we have a=-1, b=2, so the magnitude is ...

√((-1)^2 +2^2) = √(1+4) = √5

and the angle is ...

arctan(2/(-1)) = arctan(-2) ≈ 116.565° . . . . . a 2nd-quadrant angle

Then you have ...

-1 +2i = √5(cos(117°) +i·sin(117°)) . . . . . . customary "polar form"

_____

Comment on the answer

The "polar form" is generally written as ...

(magnitude)·(cos(angle) +i·sin(angle))

You may also see it as ...

(magnitude) cis (angle) . . . . . . . where "cis" is shorthand for "cos + i·sin"

In my engineering courses, we often used the form ...

(magnitude) ∠ (angle)

The form used by my calculator is ...

(magnitude)·e^(i·angle) . . . . . where angle is usually in radians

ANSWER

7

EXPLANATION

The given functions are:

[tex]f(x) = 4 \cos( \theta - 90) [/tex]

and

[tex]f(x) = 2 \cos( \theta - 90) + 1[/tex]

From the question,

[tex]A(x)=f(x)+g(x)[/tex]

[tex]A(x)=4 \cos( \theta - 90) + 2 \cos( \theta - 90) + 1[/tex]

This simplifies to:

[tex]A(x)=6\cos( \theta - 90) + 1[/tex]

The maximum value is 6+1=7

Answer:

45

it is what it is

The cost of basic hokey kit is $45.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the beginners field hockey kit costs $150 it is $15 more than three times the cost of the basic kit.

Let the cost of the basic kit be x.

Now, 3x+15=150

3x=135

x=$45

Therefore, the cost of basic kit is $45.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ5

Answer:

The center is (0,0) and the radius is 5

Step-by-step explanation:

To find the center of a circle, you need to look at the equation

In this case this equation could be written as

[tex](x-0)^2+(y-0)^2=5^2[/tex]

The x value is x=0 for the center and the y values is y=0

The radius can be found by looking at the constant that is squared, so r=5

In the case of an equation like this

[tex](x-1)^2+(y+1)^2=3^2[/tex]

The center point would be (1,-1) and r=3

Answer:

61-25=n

Step-by-step explanation:

Answer:

h

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

Final answer:

Dominique needs to earn $34 per hour to reach her goal of $100, after accounting for her $15 expenses on supplies, for the 2.5 hours she will be working at the carnival.

Explanation:

To calculate how much Dominique needs to earn per hour to reach her goal of $100 after spending $15 on supplies, we first need to subtract the cost of supplies from her earnings goal:

$100 - $15 = $85

This leaves us with $85 that she needs to earn while working for 2.5 hours. By dividing $85 by the 2.5 hours, we can find out her required hourly earning rate.

So, the calculation will be $85 ÷ 2.5 hours = $34 per hour.

Therefore, Dominique will need to earn $34 per hour during her 2.5 hours of work to reach her goal of $100 after spending $15 on supplies.

Answer:

a food container and a bowl

Answer: 5/16

Step-by-step explanation:

First, let's calculate the total number of possible outcomes:

4 options in the first bag      and      4 options in the second bag   = 16

Here is the list:

23   24   25    26

33   34    35   36

43   44    45   46

53   54    55   56

Next, calculate the total number of outcomes which result in the product of 12, 13, 14, or 15.

Here are their products:

6    8     10    12

9   12     15    18

12   16     20   24

15   20    25   30

There are 5 outcomes that include a product of 12, 13, 14, & 15.

Probability is:  (# of satisfactory outcomes)/(total outcomes) = 5/16