3. Prove or disprove. For n> 1, use mathematical induction to establish each of the following divisibik statements: (a) 8|52n + 7. [Hint: 520k+1) + 7 = 5²(5²k + 7) + (7 – 52.7).] (b) 15|24n – 1. %3D F123n+1 on+1

Q: 3.5(0.3x-1.5y)-4(0.2x-1.2y)

A: According to question,Given expression,3.50.3x - 1.5y-40.2x-1.2y

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

Q: 3. 42P 4-2p-1 =

A:

Q: 4x e 3x

A: I = ∫4x e−3x dx

Q: 1. a 2 b 4

A:

Q: 4w2 -324=

A:

Q: 6. -8 3s+5 1. %3D

A:

Q: 4. w/- 4. 2.

A: Given:

Q: 1b+1b

A: Applying  addition operation since terms with same variable  binomial addition

Q: 4. X = 100

A:

Q: x- 5y = 5

A:

Q: Simplify. 54 A_ng 3 6 9v y+15v

A: We have to simplify the expression : 3u5v4 / ( 9v3y6 + 15v5 ).

Q: Solve. 40 8 .2. -16 X-4 x+4

A:

Q: A 2/15 B 30 V35 5 20

A: Given,  A circle with secant and tangent  We have to find the value of x

Q: graph shows the relationship between the volume of the dilated box and the scale factor. diusuon 5.…

A:

Q: Solve. 1.24 15

A: Given1.243=y15

Q: d. 1 3a+18 = 1 - 8 a+6

A:

Q: limx→- f(x) limo+ f(x) limx→ = = =

A:

Q: 4. Find tricingeo. FincX 3.2 2.7

A:

Q: Simplify. 3-5m+mp³ m +7+4mp² 5mp²-6m +10 O None of these 5mp²-4m-4 O 5mp² +6m-4 4mp² + 6m-4

A: To simplify the expression, First we start by combining the like terms ( i.e m, mp2)…

Q: 3 33. 3 .2 3.

A:

Q: 4. 18 у -7 у

A: To solve the equation for y

Q: limx→2 f(x) = lim, ¹x→−1+ f(x) =

A: Given graph of the function fx is   1. Find :  limx→2 fx. 2. Find :limx→-1+ fx.

Q: 5x + 8 = 78

A: We Solve the Equation, Find The value of x.  Given Equation is 5x+8= 78.

Q: 2. Ꮖ2 ds Ꮭ Ꮖ1 Ꮖ

A: The integral is: ∫x1x2dsx. To Do: We have to evaluate this integral.

Q: 0.3x  +  4.6y  =  1 1.6x  +  1.3y  =  2

A: Consider the following system of linear equations: 0.3x+4.6y=1                               ......…