Find a counterexample to show that the following conjecture is false. Conjecture: For all numbers x,(x+4)2=x2+16.

Q: -1- xy(3 + x)-x²y + 10r

A: Given -1-xy(3+x)-x2y+10x

Q: 2x2 – 8 x² – 16 Ax) =

A: We have to draw the graph

Q: L[3t²+ 4t3/2]

A: We have to the Laplace transformation of 3t2+4t32

Q: If m∠2 = 6x + 8 and m∠6 = 8x – 6, find the value of x so that ℓ ║ m.

A: GIVEN, If m∠2 = 6x + 8 and m∠6 = 8x – 6, THEN m∠2 = m∠6 { If lines are parallel slope is same)

Q: Find the quotient of (x/2 - 2/x) and (1 - x2/4). What are the restrictions on the variable?

A: We have to find the quotient of the given two expression.

Q: Let P(x) = ax² + bx³ + x +1 where a and b are real numbers. Find values of a and b such that P(2i) =…

A:

Q: As+B If L(3t5 + 8) = the value of B is

A:

Q: 2.-1 fx(1 + x²³)¯¯¹dx 88

A: Given that ∫-∞∞x(1+x2)-1dx

Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: Evaluate (x2x+Idx

A:

Q: If 3log37=x, find x ?

A: Given,

Q: (d) 2√2-7 = 16 x 22 X

A: given  2x-7=16 if ax=ay,  than x=y

Q: Exl show that 9dx (x²+4)² 97 16 H.W

A: Here we have to show the above integral.

Q: h(x) = [(x2 - 9) / (x - 3) if x ≠ 3 or 6 if x = 3]. Evaluate : a. h(5)           b. h(0)…

A: We have to evaluate the following: a. h5          b. h0        c. h3 Where function is hx=x2-9x-3 if…

Q: Find the product. Assume variables represent positive real numbers. 2) 2x2/5(x11/5-3x) A)2x13/5 -…

A:

Q: Show that (x? + y²)² = (x² – y²)² + (2xy)? for all real numbers x and y.

A: We have to prove algebraically that x2+y22=x2-y22+2xy2 Simplifying both the sides , we get Here ,…

Q: how that Q(√2 + √3) =Q(√2,√3).

A:

Q: If f(x) = x³ + x4 + ax³ + 4x² – : 32x + b is divisible by x² – 36, find the values of a and b.

A: We will find out the required values.

Q: -: Show that -1+i√3 =1 for all combination of signs.

A:

Q: 4. Use the Binomial Theorem to expand and simplify: (2x– 3y)*

A:

Q: 3x3-5x2+5 Different iate with respect to X. x2+1 (x²+1)2 Different iate with respect to x. x2-1

A:

Q: hat are all the real zeros of y=(x-12)3-7?

A: We have to find the real zeros of y=(x-12)3-7.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.