( 60 POINTS FOR EVERYTHING )
Need some help on this INTEGERS Worksheet.
Not too difficult, but I don't have much time left.
( Use in this format v )

1.) ??
2.) ??
3.) ??
etc..

Answer:  see proof below

Step-by-step explanation:

Use the following Sum/Difference Identities:

sin(A + B) = sin A · cos B + sin B · cos A

sin(A - B) = sin A · cos B - sin B · cos A

Use the following Half-Angle Identities:

[tex]\sin\bigg(\dfrac{\theta}{2}\bigg)=\dfrac{\sqrt{1-\cos \theta}}{\sqrt2}\\\\\\\cos\bigg(\dfrac{\theta}{2}\bigg)=\dfrac{\sqrt{1+\cos \theta}}{\sqrt2}[/tex]

[tex]\text{Use the Unit circle to evaluate:}\ \cos\dfrac{\pi}{4} = \sin\dfrac{\pi}{4} = \dfrac{\sqrt2}{2}[/tex]

Use the following side work:

[tex]\sin\bigg(\dfrac{\pi}{8}\bigg)=\sin\bigg(\dfrac{\frac{\pi}{4}}{2}\bigg)=\dfrac{\sqrt{1-\cos \frac{\pi}{4}}}{\sqrt2}=\dfrac{\sqrt{2-\sqrt2}}{2}\\\\\\\cos\bigg(\dfrac{\pi}{8}\bigg)=\cos\bigg(\dfrac{\frac{\pi}{4}}{2}\bigg)=\dfrac{\sqrt{1+\cos \frac{\pi}{4}}}{\sqrt2}=\dfrac{\sqrt{2+\sqrt2}}{2}[/tex]

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \qquad \qquad \sin^2\bigg(\dfrac{\pi}{8}+\dfrac{A}{2}\bigg)-\sin^2\bigg(\dfrac{\pi}{8}-\dfrac{A}{2}\bigg)\\\\\text{Sum/Difference Identity:}\qquad \bigg(\sin\dfrac{\pi}{8}\cdot \cos \dfrac{A}{2}+\sin \dfrac{A}{2}\cdot \cos \dfrac{\pi}{8}\bigg)^2\\\\.\qquad \qquad \qquad\qquad \qquad \quad -\bigg(\sin\dfrac{\pi}{8}\cdot \cos \dfrac{A}{2}-\sin \dfrac{A}{2}\cdot \cos \dfrac{\pi}{8}\bigg)^2[/tex]

[tex]\text{Expand and Simplify:}\qquad \quad 4\sin \dfrac{\pi}{8}\cdot \cos\dfrac{A}{2}\cdot \sin \dfrac{A}{2}\cdot \cos \dfrac{A}{2}\\\\\\\text{Substitute:}\qquad \qquad \qquad 4\bigg(\dfrac{\sqrt{2-\sqrt2}}{2}\bigg)\cdot \cos \dfrac{A}{2}\cdot \sin \dfrac{A}{2}\bigg(\dfrac{\sqrt{2+\sqrt2}}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \sqrt2\cos \bigg(\dfrac{A}{2}\bigg)\cdot \sin \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Half-Angle Identity:} \quad \sqrt2\bigg(\dfrac{\sqrt{1+\cos A}}{\sqrt2}\bigg)\bigg(\dfrac{\sqrt{1-\cos A}}{\sqrt2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \dfrac{\sqrt{1-\cos^2 A}}{\sqrt2}\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{\sqrt{\sin^2 A}}{\sqrt2}\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{\sin A}{\sqrt2}[/tex]

[tex]\text{LHS = RHS:}\quad \dfrac{\sin A}{\sqrt2} = \dfrac{\sin A}{\sqrt2}\quad \checkmark[/tex]

Answer:

[tex]U = 4\\W = -6\\V = 5\\Z = 1\\x = 3\\y = 2[/tex]

Step-by-step explanation:

Then given expression is:

[tex]20a^3b^3-24a^5b^2+4a^3b^2[/tex]

To express the given expression in the form:

[tex]Ua^xb^y(Wa^2+Vb+Z)[/tex]

and to find the values of [tex]U, W, V, Z, x, y[/tex].

First of all, let us check the maximum common powers of [tex]a, b[/tex] in each term from the given expression.

The maximum common power of [tex]a[/tex] is 3 and

The maximum common power of [tex]b[/tex]  is 2.

So, we can take [tex]a^3b^2[/tex] common out of each term.

And maximum common coefficient that can be taken out common is 4.

Taking 4[tex]a^3b^2[/tex] common from each term of given expression, we get:

[tex]4a^3b^2(-6a^2+5b+1)[/tex]

Now, let us compare the given term with:

[tex]4a^3b^2(-6a^2+5b+1)[/tex] = [tex]Ua^xb^y(Wa^2+Vb+Z)[/tex]

Now, the values that we get the following values:

[tex]U = 4\\W = -6\\V = 5\\Z = 1\\x = 3\\y = 2[/tex]

which is our answer.

Answer:

(gOh)(x) on edg 2020

Step-by-step explanation:

Answer: 50%

Step-by-step explanation:

10/20×100=50%

Answer:

50

Step-by-step explanation:

Answer:

[tex]248 + 18\sqrt{15}[/tex]

Step-by-step explanation:

[tex](9\sqrt{3}+\sqrt{5} )(9\sqrt{3}+\sqrt{5} )=(9\sqrt{3}+\sqrt{5} )^2[/tex]

[tex]81 \cdot 3 + 2\cdot 9\sqrt{3} \cdot \sqrt{5} + 5[/tex]

[tex]243 + 18\sqrt{15} + 5[/tex]

[tex]248 + 18\sqrt{15}[/tex]

Answer:

3 hours

Step-by-step explanation:

he washed one car in 20 minutes so 9 cars will be 20 x 9=180minutes which is 3 hours

Answer:

8x^2 + 5y + 1

Step-by-step explanation:

1 + x^2 - 3 + 2y + 7x^2 + 3 + 3y

group like terms

= x^2 + 7x^2 + 2y + 3y + 1 - 3 + 3

add similar items

= 8x^2 + 2y + 3y + 1 - 3 + 3

add similar items

= 8x^2 + 5y + 1 - 3 + 3

= 8x^2 + 5y + 1

Answer:

[tex]\Huge \boxed{8x^2 +5y+1}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]1+x^2-3+2y+7x^2+3+3y[/tex]

Grouping like terms.

[tex]7x^2 +x^2+2y +3y +3+1 -3[/tex]

[tex](7x^2 +x^2)+(2y +3y) +(3+1 -3)[/tex]

Combining like terms.

[tex]8x^2 +5y+1[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

The answer is 206.8. But you want me to round to the nearest cent so the real answer is $207.00

Step-by-step explanation:

Answer:

4 hours .  

Step-by-step explanation:

4x8.50=34

34 + 16=50

Answer:

He worked 4 hours i think

Step-by-step explanation:

Take 50 and subtract his tips ($16)

then divide your answer by how much he makes an hour ($8.50)

Answer:

let x be the salary of individual with bachelor degree

Then the average salary of individual with Masters degree is:

(2x-40000)

the combined of two salaries is 110000:

x+(2x-40000)=110000

3x-40000=110000

3x=110000+40000

x=150000/3

Answer:

Negetive

Step-by-step explanation:

It helps to re-write.

-6 + -6 is the same as -6 -6

-6 + -6 = - 12

It would be different if these were multiplied together, but AS WRITTEN, they are subtracted. If it was (-6)(-6) or -6(-6) that would indicate multiplication as well.

The answer is negative.

Answer:

A

Step-by-step explanation:

12.7 meters divided by 3.6 seconds is 3.527 round it up and it stays 3.5 m/s

The average speed of the cart is: 3.5 m/s

The correct option is (A).

The average speed is the total distance traveled by the object in a particular time interval.

Given:

distance = 12.7m, time= 3.6 seconds

Average speed will be,

= Distance/time

=12.7/3.6

=3.522 m/s

Hence, the average speed is 3.522 m/s.

Learn more about average speed here:

https://brainly.com/question/12322912

#SPJ2

Answer:

4x - 2

Step-by-step explanation:

Perimeter of triangle

[tex] =( 2x - 5) + (3x - 2) +( 5 - x) \\ = 2x + 3x - x - 5 - 2 + 5 \\ = 5x - x - 2 \\ = 4x - 2[/tex]

Answer:

Probability of pulling a blue marble is 1/3 about 33% chance

Probability of pulling a red marble is 1/2 = 50% chance

Step-by-step explanation:

Total marbles = 6+2+4 = 12

4 of those 12 are blue

4/12=1/3 when reduced

________________________

Total marbles are still = 12

6 of the 12 are red

6/12=1/2 when reduced

Hope this helps! :)

Answer:

12 + 20d

Step-by-step explanation:

OG fare = 12

Ticket price =d

20 Tickets =20d

Answer:

Mr. Doyle has 460000 bees

Step-by-step explanation:

We are told that Mrs. Zhang's bee farm has a population that is about 1 tenth as large as Mr. Doyle's bee farm.

Thus;

Population size of Mrs. Zhang's bee farm = 1/10 × population size of Mr. Doyle's bee farm

Now, we are given that Mrs. Zhang's bee population is about 46,000.

Thus, from the earlier equation, we have;

46000 = 1/10 × population size of Mr. Doyle's bee farm

Thus, when we multiply both sides by 10,we get;

population size of Mr. Doyle's bee farm = 46000 × 10 = 460000 bees

Answer:

n-58

Step-by-step explanation:

Answer: n - 58

Step-by-step explanation:

The n goes first. You are subtracting 58 to find the missing value once n is determined.

Answer:

Step-by-step explanation:

Given from the problem statement

Melissa has made 20 zebra-printed hats

and Rachel has made h amount of striped hats

and also the total amounts of hats made by both of them is 42 hats

We can write a simple equation for the scenario as

[tex]42= 20 +h[/tex]

We can solve the equation to know the amount of hats made by  Rachel

[tex]42= 20+h\\\\h= 42-20\\\\h= 22[/tex]

Hence Rachel has made 22 hats

Answer:

1

Step-by-step explanation:

1

Answer:

15 bananas

Step-by-step explanation:

If two loaves of bread uses 3 bananas then multiply that by 5 because 10 divided by 2 is 5 and get 15 bananas.

Answer:

Area of square= d²/2

= 4²/2

= 16/2

= 8cm²

Step-by-step explanation:

A=

[tex]a {?}^{2} [/tex]

d=

[tex] \sqrt{2a} [/tex]

we can find A.USE THIS FORMULA

A =1/2 d squared

so 1/2×4 squared=8

8 is the answer

Answer:

39

Step-by-step explanation:

If her bank account is overdrawn, that means that it has a negative balance. This means that without the $60, she has -$21 and once she deposits the $60, twenty one of the 60 will be subtracted

Answer: The answer is 39

Step-by-step explanation: -21+60=49

hope you like it :)

Answer:

Step-by-step explanation:

Hello,

You can list the following ones which are correct for a), b) and c)

[tex]\boxed{\sf \bf \ \ 1, \dfrac{1}{2}, \dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5} \ \ }[/tex]

Thanks

Answer:

1/5

Step-by-step explanation:

Total Question no. 5

Three must be answer correctly so 3/5 to pass

  and 2/5 to fail  

So 1/5 because to pass the test he can answer it  correctly only one time

Answer:

12.

Step-by-step explanation:

3x = 0.5x + 30

2.5x = 30

x = 30 / 2.5

x = 12

Density = Mass / Volume, so you could use that information to solve for each value in the graph.

2. Mass = Density * Volume = 8.07 * 1.04 = 8.59 g

3. Volume = Mass / Density = 8.26 / 8.10 = 1.02 mL

4. Density = Mass / Volume = 7.91 / 0.99 = 7.99 g/mL

5. Mass = Density * Volume = 8.05 * 0.98 = 7.89 g

6. Volume = Mass / Density = 8.53 / 8.05 = 1.06 mL