MATHEMATICS HIGH SCHOOL

Can someone explain how to find the answer to this equation in steps?

2^2x = 8^x-1

Answers

Answer 1
Answer: remember
(x^(m))^(n)=x^(mn)
and
if a^x=a^y where a=a, then x=y so
make bases the same



2^(2x)=8^(x-1)
8=2^3
8^(x-1)=(2^3)^(x-1)=2^(3(x-1))
2^(2x)=2^(3(x-1))
threfor
2x=3(x-1)
2x=3x-3
0=x-3
3=x

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Is (2,4) a solution of the equation y=x-2

Answers

4 = 2 - 2
4 = 0
Is it a solution for y = x - 2?
No.

Final answer:

To determine if a point is a solution to an equation, substitute the values of the coordinates into the equation. The point (2,4) was found to not be a solution to the equation y=x-2.

Explanation:

To test if the point (2,4) is a solution to the equation y=x-2, we replace the 'x' with '2' and 'y' with '4' in the equation.

So if y is indeed equal to x - 2, then, replacing x and y should leave you with a true statement. That will be 4 = 2 - 2. But this results in, 4 = 0 which is not true.

So, (2,4) is not a solution to the equation y=x-2.

Learn more about Solving equations here:

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Question b, how would I find K

Answers

So if seven is 7, and its 7+k=blah blah blahAnd the first number there was is 7.5 so k+7=7.5 k is 0.5

Cos3x=4cos^3x-3cosx prove

Answers

\bf cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\n\n\n\textit{also recall that }cos(2\theta)=\begin{cases}cos^2(\theta)-sin^2(\theta)\n1-2sin^2(\theta)\n\boxed{2cos^2(\theta)-1}\end{cases}\n\n\nand\qquad sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\n\n-------------------------------

\bf cos(3x)=4cos^3(x)-3cos(x)\n\n-------------------------------\n\ncos(3x)\implies cos(2x+x)\implies cos(2x)cos(x)-sin(2x)sin(x)\n\n\n\[2cos^2(x)-1]cos(x)-[2sin(x)cos(x)]sin(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2sin^2(x)cos(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2[1-cos^2(x)]cos(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~[2cos(x)-2cos^3(x)]\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2cos(x)+2cos^3(x)\n\n\n4cos^3(x)-3cos(x)

What is the correct answer to 42r - 18

Answers

6• (7r-3) I got this question using my calculator please let me know how you feel have a great day

Answer:

I'm working during the same thing

Which of the following is equiangular and equilateral?A. rhombus
B. square
C. rectangle
D. parallelogram

Answers

I think its B because squares has equal sides and angles
Square is the correct answer

When Frederick was born, his grandparents gave him a gift of 2000, which was invested at an interest rate of 5% per year, compounded yearly. How much money will Frederick have when he collects the money at the age of 18? Give your answer to the nearest hundredth of a dollar.

Answers

Answer:

Frederick collects the an amount of $4813.24 at the age of 18 out of which $2000 was the beginning amount.

Step-by-step explanation:

We are given the following information in the question:

Amount = 2000

Interest rate = 5%

The money is compounded annually or yearly.

Time = 18 years

Compound interest =

A = P\bigg(1+\displaystyle(r)/(n)\bigg)^(nt)

where P is the principal amount, r is the interest rate, t is the time in years and n is the number of compounding in a year.

Since, the money is compounded yearly we put n = 1.

Putting all the values, we get,

A = P\bigg(1+\displaystyle(r)/(n)\bigg)^(nt)\n\nA = 2000\bigg(1+(5)/(100)\bigg)^(18)\n\nA = 4813.24\n\n\text{Interest, I} = \text{Amount - Principal} = A - P\n\nI = 4813.24 - 2000 = 2813.24

Thus, Frederick collects the an amount of $4813.24 at the age of 18 out of which $2000 was the beginning amount.

Answer:

$4813.24

Step-by-step explanation:

Five percent growth corresponds to multiplication by 1+5%=1.05. So, the amount of money Frederick will have in 18 years is 2000(1+.05)^18= $4813.24
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