MATHEMATICS HIGH SCHOOL

What values of x will make x^2 = 16 true ?

Answers

Answer 1

Answer:

Answer:

x = 4, x = -4

Step-by-step explanation:

In order to solve this equation, we need to square-root bothsides.

$\sf{x^2=16}$

$√(x^2)=√(16)$

Simplify:

$x=4,x=-4$

Answer 2

Answer:

Answer:

x = -4 or 4

Step-by-step explanation:

⇒ $x^2=16$

⇒ $x = √(16)$

∴ $x =$ ± 4

Therefore, x can be either 4 or -4 such that $x^2=16$ .

Thank You :)

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Which value of a in the exponential function below would cause the function to stretch?

Answers

Answer:

f(x)=a(1/3)x D. 1.5

Step-by-step explanation:

BRAINLIST PLEASE

a would have to be greater than 1 to get a vertical stretch

It's not b please help me

Answers

the answer is C. all you have to do is subtract the exponents

To divide variables, it is subtraction!

So, $a^3 - a^2 = a$

$b^2 - b = b$ . So in conclusion your answer is C. ab. Hope this helped!

Skylar has a smart phone data plan that costs $50 per month that includes 7 GB of data, but will charge an extra $30 per GB over the included amount. How much would Skylar have to pay in a month where she used 5 GB over the limit? How much would Skylar have to pay in a month where she used went over by

Answers

i have concluded the answer is a

it would be 200 if she used 5 over the limit. 30 x 5 = 150 150+50=200

Why is the sum of a rational number and its opposite always equal to 0

Answers

because its like saying what's 4-4=0. -4 and 4 are the same distance away from zero, so if you subtract them (or add them), it'll always end up to be zero

Derivative of R=(100+50/lnx)

Answers

Answer:

$\displaystyle R' = (-50)/(x(\ln x)^2)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle (d)/(dx) [(f(x))/(g(x)) ]=(g(x)f'(x)-g'(x)f(x))/(g^2(x))$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle R = 100 + (50)/(\ln x)$

Step 2: Differentiate

Derivative Property [Addition/Subtraction]: $\displaystyle R' = (d)/(dx)[100] + (d)/(dx) \bigg[ (50)/(\ln x) \bigg]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle R' = (d)/(dx)[100] + 50 (d)/(dx) \bigg[ (1)/(\ln x) \bigg]$
Basic Power Rule: $\displaystyle R' = 50 (d)/(dx) \bigg[ (1)/(\ln x) \bigg]$
Derivative Rule [Quotient Rule]: $\displaystyle R' = 50 \bigg(((1)' \ln x - (\ln x)')/((\ln x)^2) \bigg)$
Basic Power Rule: $\displaystyle R' = 50 \bigg( (-(\ln x)')/((\ln x)^2) \bigg)$
Logarithmic Differentiation: $\displaystyle R' = 50 \bigg( ((-1)/(x))/((\ln x)^2) \bigg)$
Simplify: $\displaystyle R' = (-50)/(x(\ln x)^2)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Find the 60th term of the arithmetic sequence −29,−49,−69,

Answers

Answer: The 60th term of the arithmetic sequence -29, -49, -69, … is -1209.

Step-by-step explanation:

The given arithmetic sequence is -29, -49, -69, …

To find the 60th term of this sequence, we need to use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where a_n is the nth term of the sequence, a_1 is the first term of the sequence, n is the number of terms in the sequence, and d is the common difference between consecutive terms.

In this case, a_1 = -29 and d = -20 (since each term is 20 less than the previous term). We want to find a_60, so we substitute n = 60 into the formula:

a_60 = -29 + (60 - 1)(-20) = -29 + 59(-20) = -29 - 1180 = -1209

Therefore, the 60th term of the arithmetic sequence -29, -49, -69, … is -1209.

Please let me know if you have any other questions!

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