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2 years ago

Need answer asap algebra 2 math

Mathematics

1 answer:

Scorpion4ik [409]2 years ago

4 0

Answer:

Step-by-step explanation:

f(x) = 2x^2 - 4x + 5 Put brackets around the first 2 terms.

f(x) = (2x^2 - 4x) + 5 Take out the common factor of 2

f(x) = 2(x^2 - 2x) + 5 1/2 the second term and square.

f(x) = 2(x^2 -2x + (2/2)^2) + 5 Express brackets as a perfect square.

f(x) = 2(x - 1)^2 + 5 Multiply 2 * 1 (the term without an x. Subtract.

f(x) = 2(x - 1)^2 + 5 - 2 Combine

f(x) = 2(x - 1)^2 + 3

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What is the answer? :D

den301095 [7]

Answer:

6/9, 12/18 (just 6 then 12)

Step-by-step explanation:

Please mark brainlest

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2 years ago

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y=c1e^x+c2e^−x is a two-parameter family of solutions of the second order differential equation y′′−y=0. Find a solution of the

vagabundo [1.1K]

The general form of a solution of the differential equation is already provided for us:

$y(x) = c_1 \textrm{e}^x + c_2\textrm{e}^{-x},$

where $c_1, c_2 \in \mathbb{R}$ . We now want to find a solution $y$ such that $y(-1)=3$ and $y'(-1)=-3$ . Therefore, all we need to do is find the constants $c_1$ and $c_2$ that satisfy the initial conditions. For the first condition, we have: $y(-1)=3 \iff c_1 \textrm{e}^{-1} + c_2 \textrm{e}^{-(-1)} = 3 \iff c_1\textrm{e}^{-1} + c_2\textrm{e} = 3.$

For the second condition, we need to find the derivative $y'$ first. In this case, we have:

$y'(x) = \left(c_1\textrm{e}^x + c_2\textrm{e}^{-x}\right)' = c_1\textrm{e}^x - c_2\textrm{e}^{-x}.$

Therefore:

$y'(-1) = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e}^{-(-1)} = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e} = -3.$

This means that we must solve the following system of equations:

$\begin{cases}c_1\textrm{e}^{-1} + c_2\textrm{e} = 3 \\ c_1\textrm{e}^{-1} - c_2\textrm{e} = -3\end{cases}.$

If we add the equations above, we get:

$\left(c_1\textrm{e}^{-1} + c_2\textrm{e}\right) + \left(c_1\textrm{e}^{-1} - c_2\textrm{e} \right) = 3-3 \iff 2c_1\textrm{e}^{-1} = 0 \iff c_1 = 0.$

If we now substitute $c_1 = 0$ into either of the equations in the system, we get:

$c_2 \textrm{e} = 3 \iff c_2 = \dfrac{3}{\textrm{e}} = 3\textrm{e}^{-1.}$

This means that the solution obeying the initial conditions is:

$\boxed{y(x) = 3\textrm{e}^{-1} \times \textrm{e}^{-x} = 3\textrm{e}^{-x-1}}.$

Indeed, we can see that:

$y(-1) = 3\textrm{e}^{-(-1) -1} = 3\textrm{e}^{1-1} = 3\textrm{e}^0 = 3$

$y'(x) =-3\textrm{e}^{-x-1} \implies y'(-1) = -3\textrm{e}^{-(-1)-1} = -3\textrm{e}^{1-1} = -3\textrm{e}^0 = -3,$

which do correspond to the desired initial conditions.

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2 years ago

The diameters of F and G are 5 and 6 units, respectively. Find each measure.

harkovskaia [24]

Answer:

Part 8) B.F=0.5 units

Part 9) A.B=2 units

Step-by-step explanation:

we have

The diameter of circle F is 5 units

The radius of circle F is r.f=5/2=2.5 units

The diameter of circle G is 6 units

The radius of circle G is r.g=6/2=3 units

Part 8) Find B.F

we know that

B.F=G.B-F.G

we have

G.B=rg=3 units

FG=rf=2.5 units

substitute the values

B.F=3-2.5=0.5 units

Part 9) Find A.B

we know that

A.B=A.F-B.F

we have

A.F=r.f=2.5 units

B.F=0.5 units

substitute the values

A.B=2.5-0.5=2 units

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3 years ago

Find a quadratic function with roots x = 7 and x = -1.

Charra [1.4K]

Answer:

x^2 - 6x - 7

Step-by-step explanation:

Roots, 7 and -1

x = 7 is the same as x - 7 = 0

x = -1 is the same as x + 1 = 0

multiply (x-7) by (x + 1)

x(x -7) +1(x - 7)

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3 years ago

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Select the expression that has a value of 96.45

leonid [27]

Given:

Number is 96.45.

To find:

The expression that has a value of 96.45.

Solution:

In option a,

$0.9645\times 10^2=0.9645\times 100$

$0.9645\times 10^2=96.45$

In option b,

$9.645\div 10^1=\dfrac{9.645}{10}$

$9.645\div 10^1=0.9645\neq 96.45$

In option c,

$964.5\times 10^3=964.5\times 1000$

$964.5\times 10^3=964500\neq 96.45$

In option d,

$9645\div 10^3=\dfrac{9645}{1000}$

$9645\div 10^3=9.645\neq 96.45$

Therefore, the correct option is a.

5 0

2 years ago