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3 years ago

How to simplify 3sin^2x + 3(1-sin^2x)

1 answer:

5 0

$\bf \textit{Pythagorean Identities}\\\\sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\[-0.35em]\rule{34em}{0.25pt}\\\\3sin^2(x)+3[1-sin^2(x)]\implies 3sin^2(x)+3cos^2(x)\\\\\\\stackrel{\textit{common factor}}{3[sin^2(x)+cos^2(x)]}\implies 3(1)\implies 3$

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Solve the following system of equations by substitution. Show all steps.

Alinara [238K]

Answer:

Given system of equations:

$\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}$

To solve by substitution, equate the equations and solve for x:

$\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}$

Therefore, the x-values of the solution are $x = 0$ and $x = 4$ .

To find the y-values of the solution, substitute the found values of x into the functions:

$f(0)=-(0)^2+2(0)+3=3$

$g(0)=-2(0)+3=3$

$f(4)=-(4)^2+2(4)+3=-5$

$g(4)=-2(4)+3=-5$

Therefore, the solutions to the given system of equations are:

$(0, 3)$ and $(4, -5)$

4 0

2 years ago

Does doubling the radius of a sphere double the surface area? Explain your reasoning using an example.

Annette [7]

Answer:

yes

Step-by-step explanation:

because area of sphere equals =

$4\pi \: r{2}$

so if we doubled the radius the surface area will be doubled

5 0

3 years ago

The rent for an apartment is represented by R(a) = 2.00a + 50.00, where a is the area of the apartment in square feet. The rent

QveST [7]

Answer:

The correct option is: D) S(a) = 2.00a + 100.00; shift 50 units up

Step-by-step explanation:

The rent for an apartment is represented by $R(a) = 2.00a + 50.00$

Now, the rent increases by $50.00 when the apartment is furnished. So, the rent of a furnished apartment will be: $(2.00a+50.00+50.00) = (2.00a+100.00) dollar$

Thus the new function will be: $S(a)= 2.00a+100.00$

As the output of the original function is increased by 50.00, so the graph of the original function will shift 50 units upward.

8 0

3 years ago

2 questions in one. Help?..

daser333 [38]

Answer:

2. 3

3. 4^45

Step-by-step explanation:

${ ({5}^{4} ) }^{m} = {5}^{12} \\ = > {5}^{4m} = {5}^{12} \\ = > 4m = 12 \\ = > m = \frac{12}{4} \\ = > m = 3 \\ \\ number \: of \: books \: at \: library \\ = {({4}^{9})}^{5} \times {4}^{0} \\ = {4}^{45} \times 1 \\ = {4}^{45}$

4 0

3 years ago

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Please help giving brainlest!! no links no unnecessary comments thank you :)

seraphim [82]

Answer:

Last point is at (7,-3)

Step-by-step explanation:

4 0

3 years ago

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