If v1 = (2,5) and V2 = (4,-3), then the angle between the two vectors is
Round your answer to two decimal places,

Answer:

[tex] s = 14.1 [/tex]

Step-by-step explanation:

Given:

<S = 31°

SQ = r = 9

SR = q = 21

s = ?

To find s, use the Law of Cosines:

s² = r² + q² - 2rs*cos(S)

[tex] s^2 = 9^2 + 21^2 - 2*9*21*cos(31) [/tex]

[tex] s^2 = 81 + 441 - 378*0.8572 [/tex]

[tex] s^2 = 522 - 324.02 [/tex]

[tex] s^2 = 197.98 [/tex]

[tex] s = 14.1 [/tex] (nearest tenth)

Answer:

Explained below.

Step-by-step explanation:

Consider the diagram of a regular octagon is inscribed inside a circle.

Suppose the perimeter if the octagon is 8a.

(a)

Compute the measure of a side of the octagon as follows:

[tex]\text{Perimeter}=8\times side\\\\8\times side=8a\\\\side=a[/tex]

Thus, the side of the octagon is a units.

(b)

The sum of all angles of around a point is 360°.

Consider the point P on the octagon.

The sum of all the angle surrounding P will be 360°.

There are a total of 8 angle surrounding the point P.

Then the measure of central angle is:

[tex]\text{Central Angle}=\frac{360^{o}}{8}=45^{o}[/tex]

Thus, the measure of central angle is 45°.

(c)

The line segment from the center of an octagon to the midpoint of a side, perpendicular to said side, is known as the apothem.

Consider the diagram.

In the diagram the line segment PC is an apothem, that is perpendicular to the AB.

The measure of segment AC = a/2 and the measure of segment PA is r (radius of the circle).

Compute he measure of PC as follows:

[tex]PA^{2}=PC^{2}+AC^{2}\\\\PC^{2}=PA^{2}-AC^{2}\\\\PC=\sqrt{PA^{2}-AC^{2}}[/tex]

      [tex]=\sqrt{r^{2}-\frac{a^{2}}{4}}[/tex]

Thus, the measure of the apothem of the octagon  is[tex]\sqrt{r^{2}-\frac{a^{2}}{4}}[/tex].

(d)

The area of an octagon is:

[tex]\text{Area}=2(1+\sqrt{2})a^{2}[/tex]

Answer:

Domain: 0 [tex]\leq[/tex] t [tex]\leq[/tex] 40      Range: 0 [tex]\leq[/tex] V(t) [tex]\leq[/tex] 200

Step-by-step explanation:

The domain is greater than or equal to 0 and less than or equal to 40 because in 40 months, she will lose all her money ($5 x 40months = $200) since she loses 5 dollars per month. Not to mention, time can't be negative in any situation. For the range, the value has to be greater than or equal to zero and less than or equal to 200 because she only has $200, the more time she spends using the phone, the more money she will lose over the course of the month( limiting her time). I hope this helps!

Answer:

Domain: [tex]0\leq t\leq 40[/tex];   Range: [tex]0\leq V(t)\leq 200[/tex]

Step-by-step explanation:

The price of the cellphone was initially of $200. Each month, its price decreases by $5. Then, you have that for 200/5 = 40 month the price of the cellphone will be of $0.

The price of any object always will have a positive value. If V(t) is a function that describes the price of the cellphone in time t, with t in months, you have that the domain of the function is given by the total amount of months on which the cellphone has some price, that is, for:

[tex]0\leq t\leq 40[/tex]  

The range of the function is the price of the cellphone. Its initial price was $200 (maximum price) and its final price after 40 months is $0 (minimum price). Hence, the range of the function is:

[tex]0\leq V(t)\leq 200[/tex]

Answer:

93.75 cm^2

Step-by-step explanation:

The breadth = x cm

length=x+5 cm

perimeter =2 (l+b) which becomes

2 (x+5+x)=4x+10 cm:

4x+10=40

4x=30

x=30/4=7.5

so, breadth = 7.5 cm

length = 12.5 cm,

area = 12.5*7.5 = 93.75

Step-by-step explanation:

perimeter of the rectangle= 2(length+width)

let the known width be 'x'

length be 5+x

40 = 2(5+x+x)

40 = 10+2x+2x

40-10 = 4x

30/4 = 4x/4

x = 7.5

width=7.5cm

length= 7.5+5 = 12.5cm

area = length×width

area = 12.5×7.5 = 93.75cm²

Answer:

B. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.

Step-by-step explanation:

Translation and reflection are examples of methods of rigid transformation. Translation ensure that each point on a given figure is moved the same distance with respect to the reference plane. Reflection involves the flipping of a given figure across a given line.

From the question, both reflection and transformation would map the triangles into one another. Since the reference line contains AB, then the two triangles are congruent and would share a common side.

Thus, the triangle pairs that can be mapped into each other is that of option B.

Based on the information given, the triangle pairs that can be mapped to each other using both a translation and a reflection across the line containing AB will be A. Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A.

The triangle pair that can be mapped to each other using both translation and reflection across line containing AB is the first triangle pair.

The first figure consists of ΔXYZ and ΔABC that are a reflection of each other across the line AB and a translation.

Learn more about triangles on:

https://brainly.com/question/12261308

Answer:

3/2

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1

m * -2/3  =-1

Multiply by -3/2 to isolate m

m * -2/3 * -3/2 = -1 * -3/2

m = 3/2

The perpendicular line has a slope of 3/2

Answer:

At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.

At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.

Step-by-step explanation:

At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.

At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.

Step-by-step explanation:

Let a be the first interior angle. Since they are in 1:14, the second same side interior angle is b = 14a.

We know that the sum of interior angles equals 180°.

So, a + b = 180°

a + 14a = 180°

15a = 180°

a = 180/15

a = 12°

At alternate angle to the other interior angle, b adjacent to a is c = b = 14a = 14 × 12 = 168°

The angle vertically opposite to a is d = a = 12°

The angle vertically opposite to a is b = e = 168°

At the intersection of the second parallel line and the transversal, the angle alternate to a is f = a = 12°

the angle vertically opposite to angle b is g = b = 168°

the angle vertically opposite to f is h = 12°

Answer:

168 degrees and 12 degrees

Step-by-step explanation:

i cant explain on here but i hope this helps :)

Answer:

29

Step-by-step explanation:

(5+1)^2-(12+3^2)/3      Add 5 and 1 = 6.

6^2-12+3^2/3            Calculate 6 to the power of 2 =  36.

36-12+3^2/3              Calculate 3 to the power of 2  = 9.

36-12+9/3                  Add 12 and 9 =  21.

36-21/3                       Divide 21 by 3 =  7.

36−7                            Subtract 7 from 36 to get 29.

Answer:

93107

Step-by-step explanation:

add all of the numbers together

divide by 5 since there are 5 numbers

you would get 92106.8

so round that up since you cannot have 1/8 of a squirrel

Hope this helps!!

Step-by-step explanation:

The perimer of a traingle is the saum of its sides

P = 2(3x+7) + 2(2x+2)

Answer:

x∈(-∞,3]

Step-by-step explanation:

2x-6<=5*3-5x

2x-6<=15-5x

+5x        +5x

7x-6<=15

+6       +6

7x<=21

:7     :7

x<=3

x∈(-∞,3]

Answer:

Step-by-step explanation:

find the difference between the two angles first:

155-65=90 degrees

d is the distance d:

d^2=a^2+b^2-2ab cos(90)

d^2=10^2+8^2-2(10)(8)cos(90)

d^2=164

d=√164=12.81

the bearing of R from P to the nearest degree:

180-155=35 degrees

Answer: She had $5400

Step-by-step explanation:

We will let x represent the total amount of money in her pocket .

So we know that 1/3 of x has to equal 1800 because 2/3 of the money is already been spent so 1/3 will of the money will be left.

1/3 * x = 1800  solve for x by divide both sides by 2/3

x=5400  

Check.

1/3 * 5400 =1800

Answer:

120 miles

Step-by-step explanation:

Distance = 150 miles

train 1 = 60 mph

train 2 = 90 mph

directions of trains = towards each other

Time to meet = 150/(60+90) = 150 miles / 150 mph = 1 hour

Speed of fly = 120 mph

Since fly has been flying for one hour, it travelled 120 miles.

Answer:

linear

Step-by-step explanation:

We can write this  in the form

y = mx+b

where m is the .75 per mile and b is the 39 dollars

y = .75x + 39

Answer:

The correct answer is "As the x-values go to positive infinity the function's value go to positive infinity".

Step-by-step explanation:

If we start analyzing this function at a value of x that is really small, which would be close to negative infinity and we increase the value of x, we will notice that the y-value will also increase. Therefore if we go far into the left, that is, we apply minus infinity to the function we will receive an output that is equal to minus infinity. When the value of x approach 0, the value of the function also approaches 0. Finally when we go far into the right, to positive infinity the function will also go to infinity. Therefore the correct answer is "As the x-values go to positive infinity the function's value go to positive infinity".

Answer:

2 28ounce cans and 4 15ounce cans

Step-by-step explanation:

28+28=56 and 15+15+15+15=60

56+60=116

Answer:

your answer is the second option

Step-by-step explanation:

Answer:

c.18

Step-by-step explanation:

32/24=1.33333333333

40/30=1.33333333333

24/1.33333333333=18

Side ST correlates to side BC. Let's use these two sides to find the scale factor between the two triangles

[tex]\text{Scale Factor}=\dfrac{30}{40}=\dfrac{3}{4}[/tex]

Triangle ABC has side lengths are the 3/4 smaller than that of RTS. The value of x is the length of side AC, which correlates with side RS

Multiply 24 by 3/4 to find the value of x

[tex]x=\dfrac{3}{4}\times24=18[/tex]

This is answer choice C. Let me know if you need any clarifications, thanks!

Answer:

483,000

Step-by-step explanation:

hope this helps :)

Answer:

The answer is 483,000 as an ordinary number

Step-by-step explanation:

Answer:

Happybday have a graet day miss uad

Step-by-step explanation:

Answer:

Step-by-step explanation:

Dear grandma,

Thank you for your infinite life and wisdom. I hope you have a wonderful birthday this year. You are the best! Although right now isn't the best time of the year, I still wish you a happy birthday and a healthy life.

I think that would work...

Answer:

144 min.

Step-by-step explanation:

y=0.09x+5    ( x is the number of minutes, y is the bill amount)

17.96=0.09x+5

17.96-5=0.09x

x=12.96/0.09=144 minutes

Answer:

  see below

Step-by-step explanation:

You can work this based only on the domain. You don't need to figure the volume, though you can if you want to check the answer further.

x represents the length of the box, which has a restriction that it can be no greater than 6 ft. This tells you x ≤ 6. However, the width is 5 ft shorter than the width, so its value is x-5. But we know the width must be greater than zero:

  0 < x -5

  5 < x

So, the constraints on the domain of x are ...

  5 < x ≤ 6 . . . . . . only matches the last choice, (5, 6]

___

Checking the volume

The height is 3 more than the width, so the volume is ...

  V = LWH = (x)(x -5)(x -5 +3) = x(x -5)(x -2) = x(x^2 -7x +10)

  V = x^3 -7x^2 +10x

Answer:

5 units

Step-by-step explanation:

Image of the trapezoid is attached.

To find the height of the trapezoid (image attached), let's take the formula for area of a trapezoid.

The formula for area of a trapezoid is:

[tex] A = (\frac{a + b}{2}) h [/tex]

Here, a and b represents the bases of the trapezoid.

a = 6

b = 10

h which represents height is unknown.

A = 40

Substitute figures:

[tex] 40 = (\frac{6 + 10}{2}) h [/tex]

[tex] 40 = (\frac{16}{2}) h [/tex]

[tex] 40 = 8 * h [/tex]

Solve for h:

[tex] h = \frac{40}{8} [/tex]

[tex] h = 5 [/tex]

The height of the trapezoid is 5 units

Answer:

5 units

Step-by-step explanation:

Answer:

angle of depression = 38.1°

Step-by-step explanation:

tan x = 29/37

tan x= 0.784

x = tan-¹ 0.784

x = 38.1°

Answer:

She has 158 dollars.

Step-by-step explanation:

This problem tells us that originally Taylor had 147 dollars, but she spent 42 dollars on sneakers, thus she now has [tex]147-42 = 105[/tex] dollars. However, she later won a race wearing those sneakers and earned 53 dollars, therefore she now has [tex]105 + 53 = 158[/tex] dollars.

Thus, Taylor has 158  dollars left now.

Answer:

The answer is

Step-by-step explanation:

5m+8n-2(3m-n)

Expand the terms in the bracket

That's

5m + 8n - 6m + 2n

Group like terms

We have

8n + 2n + 5m - 6m

Simplify

The final answer is

10n - m

Hope this helps you

Answer:

HF is 20 m away from the tower which makes it the base of a triangle

tan 30= opp/adj=PF/HF

PF=tan 30°(20)=11.547

tan 50=T F/20 ⇒ T F=20*tan 50= 23.835

PT= T F-PF= 23.835-11.547=12.288 m

b ) the distance from point H to the power is the hypotenuse

cos 50=adj/hyp

hypo(HT)= 20/cos 50=31.114

(HF at a new angle=40)

tan 40=opp/adj = T F/HF

HF=T F/tan40=23.835/tan 40=28.405

Answer:

1. 40.8 degrees

2. 65.6 degrees

Step-by-step explanation:

1.

sin(x) = opposite / hypotenuse = 17/26

x = arcsin(17/26) = 40.83 degrees

2. tan(x) = opposite / adjacent =  11/5 = 2.2

x = arctan(11/5) = 65.56 degrees

Answer:

Step-by-step explanation:

6s³ + 9s + 10 + 3s³ + 4s - 10

Collect like terms

6s³ + 3s³ + 9s + 4s + 10 - 10

Since, two opposites add up to zero, remove them from the expression

6s³ + 3s³ + 9s + 4s

add the like terms

9s³ + 13s

hope this helps..

best regards!!

Answer:

9s^3+13s

Step-by-step explanation:

Add each term:

9s^3+13s

I hope this helps...

And plz mark me brainliest!!

Answer:

72.96

Step-by-step explanation:

Let the first circle's radius be r and quarter circle's radius be R

Area of circle = π[tex]r^{2}[/tex]

                       = 3.14 × 8 × 8

                       = 200.96 [tex]cm^{2}[/tex]

Area of quarter circle = π[tex]R^{2}[/tex]/4

                                     = 3.14 × 16 × 16

                                     = 803. 84/4

                                     =200.96

Area of shaded portion = (Area of Quarter circle - Area of semi-circle ACD - Area of triangle ABC) + (Area of the circle -  Area of semi-circle ACD - Area of triangle ABC)

Area of Semi-circle =   Area of the circle divided by 2

                                 = 100.48

Area of triangle = [tex]\frac{bh}{2}[/tex]

                           = [tex]\frac{16 * 8}{2}[/tex]

                           = 64

Therefore, The area of shaded portion= (200.96-100.48-64) + (200.96 - 100.48 - 64)

= 36.48 +36.48

=72.96