Abby reads 8 more than twice
as many books than Kristen in
the first quarter. Write an
expression for the number of
books that Abby has read,

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π                    →    A + B = π - C

                                                    →    A + C = π - B

Use the Cofunction Identities:   sin (π - A) = sin A

                                                    sin (A - π/2) = cos A

                                                    cos (π/2 - A) = - sin A

Use the Power Reducing Identity:  sin ² A - sin² B = sin (A + B) · sin (A - B)

Use the Sum to Product Identity:

                                               sin A - sin B = 2 [cos (A + B)/2] · [sin (A - B)/2]

Proof LHS → RHS:

LHS:                                   sin² A - sin² B - sin² C

                                       = (sin² A - sin² B) - sin² C

Power Reducing:           sin (A + B) · sin (A - B) - sin² C

Given:                             sin (π - C) · sin (A - B) - sin² C

Cofunction:                    sin C · sin (A - B) - sin² C

Factor:                            sin C [sin (A - B) - sin C]

[tex]\text{Sum to Product:}\qquad \sin C\bigg[2\cos \bigg(\dfrac{(A-B)+C}{2}\bigg)\cdot \sin \bigg(\dfrac{(A-B)-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad \qquad =2\sin C\bigg[\cos \bigg(\dfrac{(A+C)-B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-(B+C)}{2}\bigg)\bigg][/tex]

[tex]\text{Given:}\qquad \qquad 2\sin C\bigg[\cos \bigg(\dfrac{(\pi - B)-B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-(\pi - A)}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =2\sin C\bigg[\cos \bigg(\dfrac{\pi -2B}{2}\bigg)\cdot \sin \bigg(\dfrac{2A-\pi}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =2\sin C\bigg[\cos \bigg(\dfrac{\pi}{2} -B}\bigg)\cdot \sin \bigg(A-\dfrac{\pi}{2}\bigg)\bigg][/tex]

Cofunction:             2 sin C (-sin B) · (cos A)

                           = -2 sin C · sin B · cos A

                           = -2 cos A · sin B · sin C

LHS = RHS:   -2 cos A · sin B · sin C = -2 cos A · sin B · sin C  [tex]\checkmark[/tex]

Answer:

4 gallons

Step-by-step explanation:

He needs 105 over 3 to fill all the cups. 1 gallon would be 10 and 2 third cups or 32 over 3. 2 gallons would be 21 and 1 third cups or 64 over 3. 3 gallons would be 32 or 96 over 3. 4 gallons would be 42 and 2 third cups or 128 over 3. So 4 gallons would fill up all 35 of his sisters 12 ounces cups. That would leave 7 and 2 third cups that hold the same amount. His sister gets all 35 of her 12 ounces each cups filled and he gets 7 and 2 thirds of new and unused 12 ounces cups. Basically out of the 4 gallons there would be 512 ounces and his sister with all 35 cups that hold 12 ounces each she would get 420 ounces. Which would leave him with 92 ounces of juice for himself. Hope this understandable and helpful.

Answer:

times -6

Explanation... 2 x 10-6 x -6=56

                      6 x 10-4=56      

Hope this helps

Answer:

x= 2.5

Step-by-step explanation:

-7.5 (x-3) = 3.75

(divide both sides of the equation by -7.5)

x-3 = -0.5

(move the constant to the righthand side and change the sign)

x = -0.5+3

(calculate the sum)

x = 2.5

Answer:

w = -4

Step-by-step explanation:

w - 2 + 2w = 6 + 5w

Add 2 to both sides.

w + 2w = 8 + 5w

Subtract w from each side.

2w = 8 + 4w

Subtract 4w from each side.

-2w = 8

Divide.

w = -4

Answer:

Step-by-step explanation:

524-6x3+52-(12÷2)

Multiplique los números

Answer:

12x+10

Step-by-step explanation:

Add up the lengths of all sides to find the perimeter

P = x + 2( x+5) + 6(x-1) + 3(x+2)

Distribute

  = x + 2x+10 +6x-6 + 3x+6

Combine like terms

 =x+ 2x+ 6x+3x    + 10 -6+6

 = 12x+10

Answer:

a,c,d

Step-by-step explanation:

[tex]a. \\4i^9+4i^7\\=4i(i^2)^4+4i(i^2)^3\\=4i(-1)^4+4i(-1)^3\\=4i-4i\\=0\\b.\\2i^{18}-3i^{11}\\=2(i^2)^9-3i(i^2)^5\\=2(-1)^9-3i(-1)^5\\=-2+3i\\c.\\7i^{36}-11i^{11}-11i^9\\=7(i^2)^{18}-11i(i^2)^5-11i(i^2)^4\\=7(-1)^{18}-11i(-1)^5-11i(-1)^4\\=7+11i-11i\\=7\\d.\\8i^{22}-1\\=8(i^2)^{11}-1\\=8(-1)^{11}-1\\=-8-1\\=-9[/tex]

e.

[tex]2i^{27}+4\\=2i(i^2)^{13}+4\\=2i(-1)^{13}+4\\=-2i+4[/tex]

Answer: 114

Step-by-step explanation:

To find the perimeter, you will find the distance around the shape by adding the numbers.

The is one missing side  and to find that side you will subtract  10 from 38.

38 - 10 = 28

Now add the them.

28 + 5 +  10 + 26 + 10 + 35 = 114

Answer:

x=[tex]-\frac{1+2i\sqrt{31} }{5}[/tex]

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

−25=  [tex]\frac{1}{2}[/tex]  (10x−2)+3x

−25=([tex]\frac{1}{2}[/tex])(10x)+( [tex]\frac{1}{2}[/tex] )(−2)+3x(Distribute)

−25=5x+−1+3x

−25=(5x+3x)+(−1)(Combine Like Terms)

−25=8x+−1

−25=8x−1

Step 2: Flip the equation.

8x−1=−25

Step 3: Add 1 to both sides.

8x−1+1=−25+1

8x=−24

Step 4: Divide both sides by 8.

8x  ÷ 8   =   −24  ÷ 8

Answer:

[tex]C = 180 - 3a[/tex]

Step-by-step explanation:

Given

[tex]A = a[/tex]

[tex]B = 2a[/tex]

Required

[tex]Find\ C[/tex]

Since, ABC is a triangle, we have:

[tex]A + B + C = 180[/tex]

Substitute values for A and C

[tex]a + 2a + C = 180[/tex]

[tex]3a + C = 180[/tex]

Subtract 3a from both sides

[tex]C = 180 - 3a[/tex]

Answer:

180°-3α

Step-by-step explanation:

If you forgot to put the degree sign on 180, that's why you got it wrong!

Answer:

d. 20(x)+3(2x)=138

ap3x

The number of gloves she buys is B. 20 (2x) + 3 (x) + 8 = 138, where x = 3.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now it is given that,

Cost of each softball , $3.

Cost of each gloves, $20 .

Total money spend , $138 .

Tax , $8 .

She buys twice as many softballs as gloves.

To Find the number of gloves she buys .

Let , x represent the number of gloves she buys.

So , number of softballs she buys is 2x .

20 (2x) + 3 (x) + 8 = 138

or, 40x + 3x + 8 = 138

or, 43x + 8 = 138

Subtract 8 both the side we get,

43x = 130

or, x = 3.02

0r, x = 3

Hence,the number of gloves she buys is B. 20 (2x) + 3 (x) + 8 = 138, where x = 3

More about linear equation :

https://brainly.com/question/24267899

#SPJ2

Step-by-step explanation:

4(5x-9)=-2(x+7)

4*5x-4*9=-2*x-2*7

20x-36=-2x-14

20x+2x=-14+36

22x=22

x=22/22

x=1

Answer:

3840g

Step-by-step explanation:

... ..... ......

Answer:

n = s/180 +2

Step-by-step explanation:

180(n-2)=s

Distribute

180n - 360 =s

Add 360 to each side

180n -360+360 = s+360

180n = s+360

Divide each side by 180

180n/180 = s/180 + 360/180

n = s/180 +2

132/4 = 33, x = 33 boxes

Answer:

4x=132

you divide by 4 on both side

x should be by it self

x=132/4

x=33

If you want make a harder equations use this

4x+10=142

subtract 10 9n both side

-10+10 +4x= 142-10

4x=132

divide by four on both side

x=132/4

x=33

Answer:

[tex]L = 0.83\ in[/tex]

Step-by-step explanation:

Given

Width = 1.2 in when Length = 1 in

Required

Determine the length when width = 1 in

First, we need to determine the ratio:

[tex]Ratio = \frac{Width}{Length}[/tex]

[tex]Ratio = \frac{1.2}{1}[/tex]

[tex]Ratio = 1.2[/tex] --- (1)

Let the required Length be represented with L

So:

[tex]Ratio = \frac{Width}{Length}[/tex]

[tex]Ratio = \frac{1}{L}[/tex] --- (2)

Equate (1) and (2)

[tex]\frac{1}{L} = 1.2[/tex]

Multiply through by L

[tex]L * \frac{1}{L} = 1.2 * L[/tex]

[tex]1 = 1.2 * L[/tex]

Divide through by 1.2

[tex]L = \frac{1}{1.2}[/tex]

[tex]L = 0.83\ in[/tex] (Approximated)

2 3 5 7 11 13 17 19 23

29 31 37 41 43 47 53 59 61 67

71 73 79 83 89 97 101 103 107 109

113 127 131 137 139 149 151 157 163 167

173 179 181 191 193 197 199 211 223 227

229 233 239 241 251 257 263 269 271 277

281 283 293 307 311 313 317 331 337 347

349 353 359 367 373 379 383 389 397 401

409 419 421 431 433 439 443 449 457 461

463 467 479 487 491 499 503 509 521 523

541 547 557 563 569 571 577 587 593 599

601 607 613 617 619 631 641 643 647 653

659 661 673 677 683 691 701 709 719 727

733 739 743 751 757 761 769 773 787 797

809 811 821 823 827 829 839 853 857 859

863 877 881 883 887 907 911 919 929 937

941 947 953 967 971 977 983 991 997   Thats all the prime numbers between 1 and 1000   Prime numbers can only be multiplied by its self ad one

Answer:

Around 22200 dollars

Step-by-step explanation:

Firstly, it was depreciating 20% per year for 17 years. So, if we were to go back in time, it would be appreciating by 25%. Therefore, after doing the plugging in, it is 500 * 1.25^17. The initial value is around 22200. It is around 22204, to be exact.

Answer:

0.167

Step-by-step explanation:

Converting it to decimal form would be :0.16666667

Rounding it to the nearest thousands would be the 3rd decimal place. Round it up to be 0.167

Answer:

C

Step-by-step explanation:

39*34= 1326 (the area of the full square

8*10=80 (the area of the small square that is cut off)

1326-80= 1246

Answer:

C = 1246 sq. cm.

Step-by-step explanation:

finding the area is simply splitting the area into two (see image)

A1 = 26 x 39 = 1014

A2 = 8 x 29 = 232

total area = 232 + 1014

total area = 1246 sq. cm.

therefore, the answer is C = 1246 sq. cm.

Answer:

the answer is 42

Step-by-step explanation:

12-6+(14-8)^2

12-6(6)^2

12-6+36

=42

Answer:

Step-by-step explanation:

Answer:

22 weeks

Step-by-step explanation:

Equation: 40 + 15w = 370

370 - 40 = 330

330/15 = 22

22 weeks is your answer.

Hopefully this helps you

pls mark brainlest

Answer:

1.) Reflection over y=1

2.) Translation rule: (x-5, y-3)

3.) Reflection over the y axis

4.)Translation rule: (x-4, y+1)

Step-by-step explanation: