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2 years ago

If f(t)= 3t^2-2, find f(k-2)

Mathematics

1 answer:

DedPeter [7]2 years ago

7 0

By plugging (k-2) in t, we can write that
$f(k-2)=3(k-2)^{2}-2=3(k^{2}-4k+4)-2=3 k^{2}-12k+12-2=$ $3 k^{2}-12k+10$

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Pentagon ABCDE was enlarged:

enot [183]

Answer/Step-by-step explanation:

The ratio of the enlargement to the original = A'E' to AE = A'E':AE = A'E'/AE

AE = 2.5

A'E' = 4

Ratio of the enlargement to the original = 4:2.5 = 1.6:1

To convert to percentage, divide 4 by 2.5 and multiply by 100.

$= \frac{4}{2.5}*100$

$= 1.6*100$

$= 160 percent$

7 0

2 years ago

In the derivation of the quadratic formula by completing the square, the equation (x+b over 2a)^2=-4ac+b^2 over 4a^2 is created

vredina [299]

Answer:

The result of applying the square root property of equality to this equation is $x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

Step-by-step explanation:

Consider the provided equation.

$\left(x+\dfrac{b}{2a}\right)^2=\dfrac{-4ac+b^2}{4a^2}$

As the above equation is formed by perfect square trinomial so simply applying the square root property as shown:

$\sqrt{(x+\dfrac{b}{2a})^2}=\pm \dfrac{\sqrt{-4ac+b^2}}{\sqrt{4a^2}}\\x+\dfrac{b}{2a}=\pm \dfrac{\sqrt{b^2-4ac}}{2a}$

Isolate the variable x.

$x=-\dfrac{b}{2a}\pm \dfrac{\sqrt{b^2-4ac}}{2a}\\x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Hence, the result of applying the square root property of equality to this equation is $x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

4 0

2 years ago

Read 2 more answers

The graph of g(x) is the graph of f(x)=x+6 reflected across the x-axis. Which equation describes the function g?

nika2105 [10]

ANSWER

The correct answer is $g(x)=-x-6$

EXPLANATION

The mapping for reflection across the x-axis is given by $(x,-y)$

Given $f(x)=x+6$ . We can let $y=x+6$

we can write the ordered pair $(x,y)$ or $(x,x+6)$ as the ordered pair of the preimage of $f$ .

The image function will have the ordered pair $(x,-y)$

or

$(x,-x-6)$ .

That is, we negate all the y-coordinates.

Therefore

$g(x)=-x-6$ .

4 0

2 years ago

Read 2 more answers

Laura owes $18,000 on her student loans. The interest rate on the bank loan is 2.5% and the interest rate on the federal loan is

Llana [10]

Answer:

The principal of the bank loan is $4,000

The principal of the federal lone is $14,000

Step-by-step explanation:

* Lets explain how to solve the problem

- Laura owes $18,000 on her student loans

- The interest rate on the bank loan is 2.5%

- The interest rate on the federal loan is 6.9%

- The total amount of interest she paid last year was $1,066

* Assume that the principle of the bank loan is $x and The principal of

the federal loan is $y

∵ Her loan is 18,000

∴ x + y = 18,000 ⇒ (1)

- The interest is I = PRT, where P is the principal, R is the rate of interest

in decimal ant is the time

# The bank lone

∵ P = $x

∵ R = 2.5/100 = 0.025

∵ T = 1

∴ The interest of the bank lone = x(0.025)(1) = 0.025 x

# The federal lone

∵ P = $y

∵ R = 6.9/100 = 0.069

∵ T = 1

∴ The interest of the federal lone = 9(0.069)(1) = 0.069 y

- The total interest is the sum of the interest of the bank lone and the

interest of the federal loan

∵ The total interest is $1,066

∴ 0.025 x + 0.069 y = 1,066 ⇒ (2)

* We have system of equations

- Multiply equation (1) by -0.025 to eliminate x

∴ -0.025 x - 0.025 y = -450 ⇒ (3)

- Add equations (2) and (3)

∴ 0.044 y = 616

- Divide both sides by 0.044

∴ y = 14,000

- Substitute value of y in equation (1) to find x

∴ x + 14000 = 18000

- Subtract 18000 from both sides

∴ x = 4000

∵ x represents the principal of the bake loan and y represents the

principal of the federal lone

* The principal of the bank loan is $4,000

* The principal of the federal lone is $14,000

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2 years ago

Jordan builds a miniature catapult for the science fair. He documents how far the catapult can throw a small rock for his report

GrogVix [38]

The rate to convert yards to meters is

$1 \text{ yard}=0.9144\text{ meters}$

So, if you multiply both sides by 8, you get

$8 \text{ yards} = 8\times 0.9144 = 7.3152 \text{ meters}$

To round the answer to the nearest tenth, we need to choose between 7.3 and 7.4. Since the hundreths digit is 1, which is less than 5, 7.3 is nearest to 7.3152 than 7.4, so the correct answer is 7.3

3 0

2 years ago

Read 2 more answers