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?

Answer:

f(3) = 1

Step-by-step explanation:

f(x) = x² - 2ˣ

You are solving for f(3). Plug in 3 for x in the equation:

f(3) = (3)² - (2)³

Simplify. First, simplify each number by solving the powers, then subtract:

f(3) = (3 * 3) - (2 * 2 * 2)

f(3) = (9) - (8)

f(3) = 9 - 8

f(3) = 1

f(3) = 1 is your answer.

~

Answer:

Step-by-step explanation:

First, we know that the sin function is odd which means:

sin(-x) = -sin(x).

Secondly evaluating an inverse trigonometric function with a normal trigonometric function as the argument can be rewritten as an algebraic expression.

Let [tex]t = \sin(-\frac{11\pi}{4}) = - \sin(\frac{11\pi}{4})[/tex]

We know the certain identity.

[tex]\sin(\theta) = \sin(2\pi + \theta)[/tex]

We use it to evaluate sin(11 pi / 4).

[tex]\sin(\frac{11 \pi}{4}) = \sin({\frac{8\pi}{4} + \frac{3 \pi}{4}}) = \sin(2\pi + \frac{3 \pi}{4}) = \sin(\frac{3\pi}{4})[/tex]

Another helping identity is the following:

[tex]\sin(\theta) = \sin(\pi - \theta)[/tex]

[tex]\sin(\frac{3\pi}{4}) = \sin(\pi - \frac{3\pi}{4}) = \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}[/tex]

But let's not forget that t = -sin(11 pi/4) = - sqrt(2) / 2

Now we end up with the following equation.

[tex]\cos^{-1}(-\frac{\sqrt{2}}{2}) = x\\\cos(x) = -\frac{\sqrt{2}}{2} => x = \frac{3\pi}{4}[/tex]

Answer: B

Step-by-step explanation: If you use inverse sin, then you can take sin^-1(1/7) and get 8.2. To check this, do sin(8.2) and it comes out to 1/7

The sample space encompasses all of the potential outcomes of an event.  The correct option is D, 5H.

The sample space encompasses all of the potential outcomes of an event. Sometimes determining the sample space is simple. For example, if you roll a die, six different outcomes are possible. You may get a 1, 2, 3, 4, 5, or 6 on the dice.

Since the sample space for rolling dice is 1, 2,3, 4, 5, and 6. While the sample space for tossing coins is H and T. Thus, the sample space for first rolling a die and then tossing a coin is,

As it can be seen that the only option that is in the sample space is 5H.

The correct option is 5H.

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Answer:

4 x + 5 = 2 x + 2 x + 5

Step-by-step explanation:

If we simplify the following equation it will be 4 x + 5 = 4 x + 5. This equation has infinitely many solutions because every value for x we substitute in, it will be the same on both sides, for example

Substitute x = 7 into 4 x + 5 = 4 x + 5

4 × ( 7 ) + 5 = 4 × ( 7 ) + 5

28 + 5 = 28 + 5

33 = 33

Every x value that we substitute in will result in the equation having the same result on both sides

Answer:

no

Step-by-step explanation:

it asks if the given value is a solution of the inequality, but I'm pretty sure it's not

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Z(\stackrel{x_2}{7}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{7+x}{2}~~,~~\cfrac{-3+y}{2} \right)~~=~~\stackrel{\stackrel{midpoint}{K}}{(-1,-11)}\implies \begin{cases} \cfrac{7+x}{2}=-1\\[1em] 7+x=-2\\ \boxed{x=-9}\\ \cline{1-1} \cfrac{-3+y}{2}=-11\\[1em] -3+y=-22\\ \boxed{y=-19} \end{cases}[/tex]

Answer:

[tex](-9,-19)[/tex]

Step-by-step explanation:

Givens

[tex]K(-1,-11)\\Z(7,-3)\\Q(x_{1},y_{1})[/tex]

Now, the definition of midpoint is

[tex]K(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2}}{2} )[/tex]

But, we know that [tex]K(-1,-11)[/tex], so we replace each vale, where [tex]x_{2} =7[/tex] and [tex]y_{1}=-3[/tex]

[tex]-1=\frac{x_{1}+7 }{2} \\-2=x_{1}+7\\-2-7=x_{1}\\x_{1}=-9\\[/tex]

[tex]\frac{y_{1}+y_{2}}{2}=-11\\y_{1}-3=-22\\y_{1}=-22+3\\y_{1}=-19[/tex]

Therefore, Q is located at [tex](-9,-19)[/tex]

Answer:

b 44 degrees

Step-by-step explanation:

cos x = adjacent side / hypotenuse

cos x = 15/21

cos x = 5/7

Take the inverse cos of each side

cos ^-1 (cos (x) )= cos ^-1 (5/7)

x =44.4153086

To the nearest degree

x = 44 degrees

Answer:

The correct answer is option(b).  44°

Step-by-step explanation:

From the figure we can see a right angled triangle with one angle is x° and two sides are given.

To find the value of x

From the given figure we get the adjacent side of angle is given

Therefore we can write,

Cos x = Adjacent side/Hypotenuse

 = 15/21

 = 0.7142

x = Cos ⁻¹ (0.7142)

 = 44°

Therefore the value of x = 44°

The correct answer is option(b).  44°

Answer:

Here's what I get    

Step-by-step explanation:

∆PQR is a right triangle.

PR² = PQ² + QR² = 48² + 64² = 2304 + 4096 = 6400

PR = √6400 = 80  

PQ:QR:PR = 48:64:80 = 3:4:5

We can consider ∆PQR as a 3:4:5 triangle.

[tex]\sin \theta = \dfrac{4}{5} \\\\\cos \theta = \dfrac{3}{5}\\\\\tan \theta = \dfrac{4}{3}\\\\\cot \theta = \dfrac{3}{4} \\\\\csc \theta = \dfrac{5}{4}\\\\\sec \theta = \dfrac{5}{3}[/tex]

Answer:

The formula used for Pythagoras Theorem.

(Hypotenuse)² = (Base)² + (Perpendicular)²

We have

PQ = 48, QR = 64 and PR = ?

⇒ (PR)² = (PQ)² + (QR)²

⇒ (PR)² = (48)² + (64)²

⇒ (PR)² = 2304 - 4096 = 64 00

⇒ PR = 80

The six trigonometric functions we have are:

Answer:

5/32.

Step-by-step explanation:

                     1

                  1      1

              1       2      1

           1       3      3       1

      1       4       6      4       1

  1      5      10      10     5       1

As there are 5 lights we need the last row in the above Pascals triangle.

And  there is 1 red and 4 green  ( = 5) and it can happen in 5 ways, so that gives us the second term in the last row . The total  in that last row = 1+5+10+10+5+1 = 32.

so the probability is 5/32.

Answer:

A

Step-by-step explanation:

Given

cx - 4 = 7 ( isolate the term in x by adding 4 to both sides )

cx = 11 ( divide both sides by c )

x = [tex]\frac{11}{c}[/tex] → A

Answer:

the area of a sector is 151.976 cm²....

Step-by-step explanation:

Area of sector(A)is given by:

A=πr².θ/360°

where,

r is the radius and θ is the angle in degree.

As per the statement:

A central angle of 4π/5 radians and a radius of 11 cm.

r=11cm

Use conversion:

1 radian=180/π

then:

4π/5 radians=180/π * 4π/5

=144°

θ=144°

Substitute these given values and use 3.14 for π we have;

A=3.14*(11)²*144/360

A=3.14(121)*144/360

A=379.94*0.4

A=151.976 cm²

Therefore the area of a sector is 151.976 cm²....

The area of a sector with a central angle of 4π/5 radians and a radius of 11 cm is approximately 96.8 cm², calculated using the formula A = (θ/2π) * πr² and rounded to two significant figures.

To find the area of a sector of a circle with a given central angle in radians and a specific radius, you can use the formula:

A = (θ/2π) * πr²

where A is the area of the sector, θ is the central angle in radians, and r is the radius of the circle.

In this case, the central angle is 4π/5 radians and the radius is 11 cm. Substituting the given values into the formula:

A = (4π/5/2π) * π * (11 cm)²
= (2/5) * π * 121 cm²
= (2/5) * 3.1415927 * 121 cm²
= 96.76 cm² to two significant figures, since the radius is given to two significant figures.

Hence, the area of the sector is approximately 96.8 cm².

Answer:

(−29, 7)  CORRECT

(19, 7)  CORRECT

(−21, 7)

(13, 7)

(−5, −17)

(−5, 31)

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

Just got it right

Answer:

26

Step-by-step explanation:

For this case we must find the inverse of the following function:

[tex]y = x ^ 2-2[/tex]

We exchange the variables:

[tex]x = y ^ 2-2[/tex]

We clear the variable "y":

Adding 2 to both sides we have:

[tex]x + 2 = y ^ 2[/tex]

Applying square root on both sides of the equation:

[tex]y = \pm \sqrt {x + 2}[/tex]

We change y by [tex]f ^ {- 1} (x)[/tex]:[tex]f ^ {- 1} (x) =\pm \sqrt {x + 2}[/tex]

Answer:

[tex]f ^ {- 1} (x) = \pm\sqrt {x + 2}[/tex]

Answer: c) 24.9

Step-by-step explanation:

Use the distance formula then add and round to nearest tenth

The perimeter of the triangle ABC will be 24.9. Then the correct option is C.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x – h)² + (y – k)²

The vertices of the triangle are A(1, 3), B(11, 4), and C(7, 9).

The distance between AB will be

AB² = (11 – 1)² + (4 – 3)²

AB² = 101

AB = 10.05

The distance between BC will be

BC² = (11 – 7)² + (4 – 9)²

BC² = 41

BC = 6.40

The distance between AC will be

AC² = (7 – 1)² + (9 – 3)²

AC² = 72

AC = 8.50

Then the perimeter of the triangle ABC will be

Perimeter = AB + BC + CA

Perimeter = 10.05 + 6.40 + 8.50

Perimeter = 24.95 ≈ 24.9

The perimeter of the triangle ABC will be 24.9.

Then the correct option is C.

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Answer:

14-inch pizza

Step-by-step explanation:

The area of a circle (or a pizza) is πr^2, if r is the radius.

For a 14-inch pizza, the radius is 14/2=7 and therefore the area is π*7^2 which is approximately 154 square inches. Therefore, the price per square inch is 12/154, or approximately 0.078 dollars per inch.

Similarly, the area of a 4-inch pizza is π*2^2 which is approximately 12.5 square inches, two 4-inch pizzas are 25, and so the price per square inch is 8/25 which is approximately 0.32 dollars per inch.

So the 14-inch pizza is the better deal.

Answer:

(D) 4m/2

Step-by-step explanation:

took test

Answer:

[tex]\large\boxed{\overline{AC}\ and\ \overline{DF}}[/tex]

Step-by-step explanation:

[tex]\triangle ABC\cong\triangle DE F\\\\\text{Corresponding angles:}\\\\\angle A\to\angle D\\\angle B\to\angle E\\\angle C\to\angle F\\\\\text{Corresponding sides:}\\\\AB\to DA\\AC\to}DF\\BC\to EF[/tex]

Answer:

0.095

Step-by-step explanation:

the probability of getting the word riddle is 0.095.

I'm sorry if the answer is wrong.... I'm not that good at maths either but I wanted to help :)

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have:

[tex]leg=7\ mm,\ leg=a,\ hypotenuse=\sqrt{85}\ mm[/tex]

Substiute:

[tex]7^2+a^2=(\sqrt{85})^2[/tex]       use (√a)² = a for a ≥ 0

[tex]49+a^2=85[/tex]           subtract 49 from both sides

[tex]a^2=36\to a=\sqrt{36}\\\\a=6\ mm[/tex]

Answer:

A. 6mm

Step-by-step explanation:

Using the Pythagorean Theorem, which is a^2 + b^2 = c^2, the c is always the hypotenuse so the problem would be: a^2 + 7^2 = square root of 85 squared. square root of 85 squared is just 85. 7^2 is 49. 85 - 49=36. square root of 36 is 6... If you liked this answer then mark me as brainliest.

Answer:

No intersection

Zero intersections

Step-by-step explanation:

Let's determine the slope first.

If the slopes are different, then there is one solution.

If the slopes are the same, there are 2 possibilities.  The first possibility is that there is no solutions because the lines are parallel.  The second possibility is that there is infinitely many solutions because they are the same line. When I say solution, I'm also referring to intersection.

So I'm going to find the slope by lining up the points and subtracting vertically then putting 2nd difference over 1st difference.

Let's do that for line A:

 (  2  ,   8)

- (  -2 , -4)

---------------

  4        12

So the slope is 12/4 or just 3.

Let's do this for line B now:

  (  4  ,  10)

-  ( -3  ,  -11)

-------------------

    7     21

So the slope is 21/7 or just 3.

So we have more work now. The lines either are the same or parallel.

We are going to use this to determine if they same or parallel, we are going to find the slope-intercept form of the equation for both lines.

That is y=mx+b where m is slope and b is y-intercept.

Let's look at line A:

y=mx+b with m=3 and a point (x,y)=(2,8)

8=3(2)+b

8=6+b

2=b

So the line is y=3x+2

Let's look at line B.

y=mx+b with m=3 and a point (x,y)=(4,10)

10=3(4)+b

10=12+b

-2=b

The equation of this line is y=3x-2

So the lines y=3x+2 and y=3x-2 are not the same, they are parallel which means they intersect zero times.

Answer:

Zero

Step-by-step explanation:

How many points of intersection are there between line A and line B if they contain the points listed?

Line A: (2, 8) and (–2, –4)

Line B: (4, 10) and (–3, –11)

Answer:

The correct option is 24 square units.

Step-by-step explanation:

Given data:

Base= 4units

height = 6 units

Area = ?

Now substitute the values in the formula:

Area= base * height

Area= 4*6

Area= 24 square units

Thus the correct option is 24 square units....

Answer:

I am a little late but its 24

Step-by-step explanation:

4*6 = 24

Answer:

V = 1017.88

Step-by-step explanation:

The volume of a right circular cylinder with a radius of 6 and a height of 9 is 1017.88.

V=πr2h=π·62·9≈1017.87602

Answer:

are perpendicular

Step-by-step explanation:

Two lines that intersect and make a right angles are by definition perpendicular

Answer:

C) are perpendicular

Step-by-step explanation:

Perpendicular: a straight line at an angle of 90° to a given line, plane, or surface.

Answer:

a lot

Step-by-step explanation:

Answer:

192 pieces of tiles will be required.

Step-by-step explanation:

A customer is tiling a shower's back wall which is in the dimensions of 6' by 4'

This area of the wall is = 6 × 4 square feet = 24 feet²

Customer wants to cover this wall with the tiles measuring 3" by 6" or 3 inches by 6 inches.

Now we will convert these dimensions of the tiles in foot.

Since 12 inches = 1 foot

Therefore, 1 inch = [tex]\frac{1}{12}[/tex] foot

Dimensions of one tile in foot will be [tex]\frac{3}{12}[/tex] foot by [tex]\frac{6}{12}[/tex] foot.

In simplified form, dimensions of the tile is [tex]\frac{1}{4}[/tex] foot by [tex]\frac{1}{2}[/tex] foot.

Area of one tile = [tex]\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}[/tex] square feet

Number of tiles = [tex]\frac{\text{Area of the wall}}{\text{Area of one tile}}[/tex]

                          = [tex]\frac{24}{\frac{1}{8}}[/tex]

                          = 24×8

                          = 192 tiles

Therefore, 192 pieces of tiles will be required.

Answer:5 vans   7 cars

Step-by-step explanation:

c=cars         v=vans

c+v= 12

c =( 12-v)

11v + 4(12-v) = 83

11v + 48-4v = 83

7v = 35

v= 5

c = 12-5         c = 7

7 cars x 4 students = 28 students

5 vans x 11 students = 55 students

55+28 = 83 students

Answer:

4

Step-by-step explanation:

The equation is in the form

y= mx+b

where m is the slope and b is the y intercept

y = -3x +4

-3 is the slope and 4 is the y intercept

Answer:

y intercept is 4

Step-by-step explanation:

When you are finding the Y intercept, you need to pretend that x=0. Cover up the x and you would find the y-intercept which is 4

if it is wrong, let me know and I will fix it

hope this helps!

Answer:

D: x = -2, x = 5

Step-by-step explanation:

To solve for a variable, you first have to isolate it on one side of the equation. Remember that whatever you do to one side, you also have to do to the other.

2x² + 2x + 12 = 3x² - x + 2   Subtract 2x² from both sides

2x + 12 = x² - x + 2   Subtract 2x from both sides

12 = x² - 3x + 2   Subtract 12 from both sides

0 = x² - 3x - 10   Using factoring, split this into two expressions

0 = (x - 5) (x + 2)   Set each expression equal to 0

x - 5 = 0 and x + 2 = 0   Solve each expression

x = 5 and x = -2

Now, you can plug in both answers to check your work

2x² + 2x + 12 = 3x² - x + 2   Plug in 5

2(5)² + 2(5) + 12 = 3(5)² - 5 + 2   Simplify

2(25) + 10 + 12 = 3(25) - 5 + 2   Simplify some more

50 + 10 + 12 = 75 - 5 + 2   Simplify one more time

72 = 72   It works!

2x² + 2x + 12 = 3x² - x + 2   Plug in -2

2(-2)² +2(-2) + 12 = 3(-2)² -(-2) + 2   Simplify

2(4) - 4 + 12 = 3(4) + 2 + 2   Simplify again

8 - 4 + 12 = 12 + 2 + 2   Simplify one more time

16 = 16   It also works!

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

If the slope m = 0, then an equation in form y = 0x + b → y = b it's a horizontal line with a slope equal to 0.

Answer:

r = 3

Step-by-step explanation:

x^2 + 6x + y^2 - 8y = - 16

Take half the linear term and square it.

x^2 + 6x + (3)^2 + y^2 - 8y + (-4)^2 = - 16

Add the squared amounts to the right.

x^2 + 6x + 9 + y^2 - 8y + 16 = - 16 + 9 + 16  

Combine on the right.

x^2 + 6x + 9 + y^2 - 8y + 16 = 9

Represent the 2 quadratics as perfect squares.

(x + 3)^2 + y - 4)^2 = 9

The radius is the square root of 9 which is 3

Answer:

radius=3

Step-by-step explanation:

Given:

x^2 +6x +y^2 - 8y=-16

completing the squares

: x^2 +6x +9 = (x+3)^2

:y^2-8y+16 = (y-4)^2

(x+3)^2 + (y-4)^2 -9-16=-16

(x+3)^2 + (y-4)^2=-16+9+16

(x+3)^2 + (y-4)^2=9

Now comparing with standard equation of circle i.e. (x-h)^2 + (y-k)^2=r^2, we get

origin(h,k)= (-3,4)

r=3 !