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4 years ago

Factor completely x2 − 49.

Mathematics

2 answers:

masya89 [10]4 years ago

4 0

Answer:

The answer is (x + 7)(x − 7).

Step-by-step explanation:

Given the expression

$x^2-49$

we have to factorize the above expression completely.

Given expression is

$x^2-49=x^2-7^2$ → (1)

By the identity $a^2-b^2=(a+b)(a-b)$

Put a=x and b=7, we get

$x^2-7^2=(x+7)(x-7)$

Eq (1) can be written as

$x^2-49=(x+7)(x-7)$

∴ Option 2 is correct.

NeX [460]4 years ago

3 0

(x + 7)(x − 7) should be your final result

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How would you convert 276 yards to inches?

valentinak56 [21]

Answer:

9936 inch.

Step-by-step explanation:

Note the measurements:

1 Yard = 3 Feet

1 Feet = 12 Inch

1 Yard = 3 Feet = (12)(3) Inches = 36 Inches; 1 Yard = 36 Inches

Multiply 276 with 36

276 x 36 = 9936

9936 inches is your answer.

6 0

4 years ago

In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the function with its graph

MA_775_DIABLO [31]

Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

$f(x)=(x-2)^{2}+1$

45)

The function g(x) is given by:

$g(x)=f(x-1)$

using f(x) we can find f(x-1)

$g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1$

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

$g(x)'=2(x-3)$

$2(x-3)=0$

$x=3$

Puting it on g(x) we will get y value.

$y=g(3)=(3-3)^{2}+1$

$y=g(3)=1$

Then, the minimum point of this function is (3,1) and it corresponds to (A)

46)

Let's use the same method here.

$g(x)=f(x+2)$

$g(x)=((x+2)-2)^{2}+1$

$g(x)=(x)^{2}+1$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2x$

$0=2x$

$x=0$

Evaluatinf g(x) at this value of x we have:

$g(0)=(x)^{2}+1$

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Then, the minimum point of this function is (0,1) and it corresponds to (C)

47)

Let's use the same method here.

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$g(x)=(x-2)^{2}+1+2$

$g(x)=(x-2)^{2}+3$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

$0=2(x-2)$

$x=2$

Evaluatinf g(x) at this value of x we have:

$g(2)=(2-2)^{2}+3$

$g(2)=3$

Then, the minimum point of this function is (2,3) and it corresponds to (B)

48)

Let's use the same method here.

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$g(x)=(x-2)^{2}-2$

Let's find the first derivative and equal to zero to find x and y minimum value.

$g'(x)=2(x-2)$

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Evaluatinf g(x) at this value of x we have:

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Then, the minimum point of this function is (2,-2) and it corresponds to (D)

I hope it helps you!

8 0

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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