Round 56.0649702307 to 4 decimal places.

Answer:

The fourth one: [tex]\frac{\sqrt{2+\sqrt{2} } }{2}[/tex]

Step-by-step explanation:

The exact value of sin 112.5° can be found using the half-angle identity formula. Substituting values for sin 45° and cos 90°, we find that the exact value of sin 112.5° is ± √2/2.

We can find the exact value of sin 112.5 using half-angle identity. As we know, 112.5 degrees is equal to 45 degrees/2 + 90 degrees, these values are much simpler to work with. Let's start by understanding the half-angle formula, which is sin(x/2) = ± √[(1 - cos x) / 2] .

The exact value of sin 45 degrees is √2/2 and cos 90 degrees is 0.

Now, let's put these values in our half-angle formula

sin 112.5 = sin(45/2 + 90) = √[(1 - 0) / 2] = ± √[1/2] = ± √2/2

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Answer:

True

Step-by-step explanation:

I did it on ap3x and got it right!

Answer:

190

Step-by-step explanation:

40/100 x 198= 76

40/100 x 198= 114

114-76= 38

Answer:

190.

Step-by-step explanation:

Let x represent total number of votes.

We have been given that Joel got 60% of the votes, which was 38 votes more than Sean.

60% of total votes: [tex]\frac{60}{100}x=0.60x[/tex]  

Since Joel got 60% of total votes, so Sean got 40% of total votes that is [tex]\frac{40}{100}x=0.40x[/tex]  

Since Joel got 38 votes more than Sean, so we can represent this information in an equation as:

[tex]0.60x=0.40x+38[/tex]

[tex]0.60x-0.40x=0.40x-0.40x+38[/tex]

[tex]0.20x=38[/tex]

[tex]\frac{0.20x}{.20}=\frac{38}{.20}[/tex]

[tex]x=190[/tex]

Therefore, the total number of votes cast is 190.

Answer:

C. After gaining independence, territory in both former colonies was divided due to religious conflicts

Step-by-step explanation:

The British had India as their colony, and Palestine as their mandate. Once the World War II ended though, the British saw that they are not in a financial position to be able to keep their colonies and mandates, so they decided to grant them independence. The independence didn't went as desired by the locals though, as both India and Palestine got partitioned because of religious reasons. India was partitioned into Hindu and Muslim part, while Palestine and Muslim and Jewish part. The situation in the Indian subcontinent quickly escalated, as well as in Palestine where the Arabs saw the formation of Israel as stealing of their land.

Answer:  C. After gaining independence, territory in both former colonies was  divided due to religious conflicts.

Answer: [tex]36.1\ units^2[/tex]

Step-by-step explanation:

You need to use the SAS area formula. This is:

[tex]A=\frac{a*b*sin(\alpha)}{2}[/tex]

Given the triangle ABC, you know that:

[tex]a=AC=10\ units\\b=BC=17\ units\\\alpha=\angle ABC=25.1\°[/tex]

 Therefore, substituting these values into the formula, you get that the area of the triangle ABC is:

[tex]A=\frac{(10\ units)(17\ units)*sin(25.1\°)}{2}\\\\A=36.1\ units^2[/tex]

Answer:

x = 5

Step-by-step explanation:

3x + 1 = 16

Subtracting 1 on both sides of the equation,

3x + 1 – 1 = 16 – 1

Summing algebraically (in this case subtracting by having different signs) on both sides,

3x = 15

Isolating x by dividing both sides by 3

3x / 3 = 15 / 3

Dividing,

x = 5

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

We have the following expression:

[tex]3x+1=16[/tex]

and we need to solve for [tex]x[/tex], so the first thing we have to do (in order to leave the x alone on one side of the equation) is move the +1 to the left sife with the opposite sign (-1):

[tex]3x=16-1\\3x=15[/tex]

now we divide each side by 3, and we get:

[tex]\frac{3x}{3}=\frac{15}{3} \\x=5[/tex]

the answer is [tex]x=5[/tex]

Answer: A. 1/5 because it's the actual right answer.

Scale factor of ΔABC to ΔXYZ is [tex]\frac{1}{5}[/tex].

The ratio of corresponding sides are equal, and this ratio is called the scale factor.

We know that

ΔABC and ΔXYZ are similar from the figure

[tex]\frac{XY}{AB}=\frac{YZ}{BC} =\frac{XZ}{AC}[/tex]

Substitute the values

[tex]\frac{9}{45} =\frac{12}{60}=\frac{7}{35} =\frac{1}{5}[/tex]

Therefore, Scale factor of ΔABC to ΔXYZ is [tex]\frac{1}{5}[/tex].

Find out more information about scale factor here

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Answer:

x = ± 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given

12 - x² = 0 ( add x² to both sides )

12 = x² or

x² = 12 ( take the square root of both sides )

x = ±[tex]\sqrt{12}[/tex]

  = ± [tex]\sqrt{4(3)}[/tex] = ± 2[tex]\sqrt{3}[/tex]

Answer:

- 1

Step-by-step explanation:

Using the rules of exponents

[tex]a^{0}[/tex] = 1

[tex](a^n)^{m}[/tex] = [tex]a^{nm}[/tex]

Given

27[tex]a^{0}[/tex][tex](-\frac{1}{3}) ^{3}[/tex]

Note [tex]a^{0}[/tex] = 1 for any value of a, thus

= 27 × 1 × - [tex]\frac{1}{3^{3} }[/tex]

= 27 × 1 × - [tex]\frac{1}{27}[/tex] ← cancel the 27 on numerator/ denominator

= 1 × - 1

= - 1

[tex]X\cup Y=\{0,10,100,1000\}[/tex]

Answer:

21

Step-by-step explanation:

[tex] \frac{v}{7} = 3[/tex]

Multiplying both sides by 7, we get

[tex] \frac{v}{7} \times 7 = 3 \times 7 [/tex]

The two 7s on the left cancel out to give 1, so

[tex]v = 21[/tex]

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Answer:

A

Step-by-step explanation:

Sn=a(n-1) d

this formula for Calculating arithmetic sequence

Answer:  D. [tex]a_n=6+(n-1)(-3)[/tex]

Step-by-step explanation:

Given : An arithmetic sequence has this recursive formula:

[tex]a_1=6 \ \ \; \ a_n=a_{n-1}-3[/tex]

Using the given information, Second term of arithmetic sequence will be :-

[tex]a_2=a_{1}-3=6-3=3[/tex]

That means common difference = [tex]a_2-a_1=3-6=-3[/tex]

The explicit formula for arithmetic sequence is given by :-

[tex]a_n=a+(n-1)d[/tex], where a is the first term and d is the common difference.

Put a= 6 and d= -3, we get

The explicit formula for this sequence :-

[tex]a_n=6+(n-1)(-3)[/tex]

Answer:

[tex]\dfrac{1}{8}[/tex]

Step-by-step explanation:

If the probability of having a boy or a girl is the same, then

the probability of having a boy = a probability of having a girl = 1/2.

Let B denote boy and G denote the girl.

The sample space of having three children is:

BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG.

The probabilities of each of those events is

[tex]Pr(BBB)=Pr(BBG)=Pr(BGB)=Pr(GBB)=\\ \\=Pr(BGG)=Pr(GBG)=Pr(GGB)=Pr(GGG)=\\ \\=\dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}=\dfrac{1}{8}.[/tex]

Answer:

−2x^2−x−8

Step-by-step explanation:

5x^2 - 9 - 7x^2 - x + 1 = −2x^2−x−8

5*x^2-9-7*x^2-x+1 = (-2*x^2)-x-8

Answer:

Three points that are member of the solution set could be (-2,10), (5,5) and (10,13)

The graph in the attached figure

Step-by-step explanation:

we have

[tex]-3x-y < 12[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dashed line [tex]-3x-y=12[/tex]

[tex]2x+3y\geq 9[/tex] -----> inequality B

The solution of the inequality B is the shaded area above the solid line [tex]2x+3y=9[/tex]

The solution of the system of inequalities is the shaded area between the dashed line and the solid line

see the attached figure

A solution to the system of inequalities is any point in the shaded area.

therefore

Three points that are member of the solution set could be (-2,10), (5,5) and (10,13)

Answer:

Last one.

Step-by-step explanation:

Let's look at the fist one

x+1<-1 and x+1<1

Subtract one on both sides for both inequalities:

  x<-2 and x<0

Graph it!  

*********************************o                       x<0

 *************o                                                 x<-2

________(-2)_________(0)____________

So the inequalities do have some common sets of numbers shared so there is a solution and it is any number less than -2.

Let's look at the second one

x+1<=1  and x+1>=1

Subtract one on both sides for both inequalities:

x<=0    and  x>=0

Graph it!

                           @*****************  x>=0

*********************@                         x<=0

-----------------------(0)-------------------

The only number included by both graphs is 0 so it still has a solution. The solution is 0.

Let's look at the third one:

x+1<1   and   x+1>1

Subtract one on both sides for both inequalities:

 x<0    and     x>0

Graph it!

************************O                                   x<0

                               O************************* x>0

---------------------------(0)------------------------------

These inequalities have no overlap.  They don't even both include zero because of the open circle (the lack of equal sign).  This is the compound inequality that has no solution.

Answer:

See attachment

Step-by-step explanation:

The given function is [tex]f(x)=\frac{5x-2}{x+2}[/tex].

This rational function has a vertical asymptote at where the denominator is zero.

The denominator [tex]x+2=0[/tex] when [tex]x=-2[/tex]

There is vertical asymptote at [tex]x=-2[/tex]

The horizontal asymptote for this rational function is given by the ratio of the leading coefficient of the numerator to the leading coefficient of the denominator.

[tex]y=\frac{5}{1}[/tex]

The horizontal asymptote is [tex]y=5[/tex]

The graph of this rational function is shown in the attachment  

Answer:

y = - 2x - 3

Step-by-step explanation:

Given

y - 5 = - 2(x + 4) ← in point- slope form

Distribute the right side

y - 5 = - 2x - 8 ( add 5 to both sides )

y = - 2x - 3 ← in slope- intercept form

Answer:

c. 2

Step-by-step explanation:

if you mix up the numbers you can find that 1998 is 27. then you have to start adding and subtracting numbers. Your digital sum includes a basic three 9's so, you also have 2799.

Answer: D. -3x+9i)(x+3i) i hope this helped :)

Answer: D is the correct answer

Step-by-step explanation:

A P E X

Answer:

Last choice.

Step-by-step explanation:

8, 5, 2, -1, ...​

Make a table

n            |      1            2             3           4          5  

an          |      8           5             2           -1         -4

You really should just think of this as finding the equation of a line.

The slope can be used by using any two points.

How about

(1  ,  8)  and

(2 ,  5)?

------------I really like to find the slope by lining up my points and subtracting vertically and then putting second number on top of first.

That is the same as using the formula directly which is (y2-y1)/(x2-x1)

or (y1-y2)/(x1-x2) which gives you the same thing too.

Subtracting the pairs now:

(1  ,  8)

-(2 ,   5)

-----------

-1       3

So the slope is 3/-1 or -3/1 or -3.

So you can already rule out choice B.

So we have the equation is y=-3x+b

where y really represents an and x really represents n here.

You can use any point that you know is on the line to find b.

How about (1,8)?

Plug it into y=-3x+b.

y=-3x+b

8=-3(1)+b

8=-3+b

11=b

So the line is y=-3x+11

Want to confirm?

No problem:

At x=1 you have y=-3(1)+11=-3+11=8 which is first number in the list.

At x=2 you have y=-3(2)+11=-6+11=5 which is second number in the list.

At x=3 you have y=-3(3)+11=-9+11=2 which is the third number in the list.

At x=4 you have y=-3(4)+11=-12+11=-1 which is the fourth number in the list.

So we have confirmed our solution of y=-3x+11.

So the answer is an=-3n+11

please insert the entire of the question

Answer:

1, 4, 5

Step-by-step explanation:

Answer:

negative, with slope of -5 and the y-intercept is at 1.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The graph of the new function would be the graph of the old one, translated 14 units to the left.

Answer:

$14.40 for 24 markers

Step-by-step explanation:

Lets find the price per marker

$8.04 /12 = .67

$5.60/8 =.70

$14.40 /24 =.60

$10.40/16 =.65

The lowest amount is .60, which is the best deal

$14.40 for 24 markers

Answer:

Part 1) [tex]C=90\°[/tex]

Part 2) [tex]A=63\°[/tex]

Part 3) [tex]b=6.8\ units[/tex]

Part 4) [tex]a=13.4\ units[/tex]

Step-by-step explanation:

step 1

Find the measure of angle C

we know that

The triangle ABC is a right triangle

so

Angle C is a right angle

therefore

[tex]C=90\°[/tex]

step 2

Fin the measure of angle A

we know that

In the right triangle ABC

∠B+∠A=90° -----> by complementary angles

we have

[tex]B=27\°[/tex]

substitute

[tex]27\°+A=90\°[/tex]

[tex]A=63\°[/tex]

step 3

Find the length side b

we know that

In the right triangle ABC

[tex]sin(B)=b/c[/tex]

[tex]b=(c)sin(B)[/tex]

substitute the given values

[tex]b=(15)sin(27\°)=6.8\ units[/tex]

step 4

Find the length side a

we know that

In the right triangle ABC

[tex]sin(A)=a/c[/tex]

[tex]a=(c)sin(A)[/tex]

substitute the given values

[tex]a=(15)sin(63\°)=13.4\ units[/tex]

Answer:

A = 63 , a = 13.4, b = 6.8

Step-by-step explanation:

Answer:

$26

Step-by-step explanation:

Start with $56.

Add $265, obtaining a + balance of $321.

Let x represent the unit price of the backpacks.  Then:

$321 - 3x = $243.

Combining like terms:

3x = $78

Then x, the price of the individual backpack, was $78/3, or $26.

Answer:

(1,9)

Step-by-step explanation:

For this case we must locate the point M in the coordinate system, once we visualize it we count the number of grid that are between the axis "x" and the point M, we have that there are 9 grids, then the coordinate "y" from the point M is 9. Now we count the number of grids between the "y" axis and the point M, we see that there is a grid, so the coordinate "x" of the point M is 1.

Point M: (1,9)

Answer:

Option C

Answer:

The volume of the prototype is [tex]V=250\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a hexagonal prism is equal to

[tex]V=BH[/tex]

where

B is the area of the hexagonal base

H is the length of the rectangular face

we have

[tex]B=25\ in^{2}[/tex]

[tex]H=10\ in[/tex]

substitute

[tex]V=(25)(10)[/tex]

[tex]V=250\ in^{3}[/tex]

Answer:

Volume of the prototype is 250 in.³

Step-by-step explanation:

Given:

Base area of the watch packaging case = 25 in.²

Length of the rectangle on the side = 10 in.

To find: Volume of the packaging prototype.

Prototype of the packaging of the watch is in shape of prism whose base is a hexagon and sides are in shape of rectangle.

So, Volume of the prism = Base Area × Height

Thus, Volume of the Prototype = 25 × 10

                                                   = 250 in.³

Therefore, Volume of the prototype is 250 in.³