Express 9-y^2 as the product of two binomial factors.

Answers

Answer 1

Answer: This is the difference of squares. Formula is:
A² - B² = ( A - B ) · ( A + B )
9 - y² = 3² - y² = ( 3 - y ) · ( 3 + y )

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Factor completely x2 − 36.(x + 6)(x − 6)

(x + 6)(x + 6)

(x − 6)(x − 6)

Prime

Answers

(x+6)(x-6) is the corrector factoring if what you meant was x^2-36

Answer:

The answer is (x+6)(x-6)

Step-by-step explanation:

Classify the numbers as prime or composite

Answers

Well what numbers? I would say prime even though I don't know the numbers your talking about.

I am gonna give you classify three numbers as prime numbers and three numbers composite numbers, since you never mentioned about any specific numbers.

Prime numbers

1.3- it is a prime number because they only factors it has, is 1 and itself.

2.11- it is a prime number because you can only multiply by 11 or 1 to get 11.

3.13- it is a prime number because it only has 2 factors.

Composite numbers

1.4- it is a composite number because it has more than 2 factors.

2.8- it is a composite number because it has 1,2,4, and 8 as its factors.

3.14- it is a composite number because it has 1,2,7,and 14 as its factors.

the sum of the interior angles of a polygon is 540. determine and state the number of degrees in one interior angle of the polygon.

Answers

The number of degrees in one interior angle of the polygon is 108 degrees.

What is the polygon?

A polygon is a closed two-dimensional shape having straight line segments. It is not a three-dimensional shape.

Sum of interior angles of a polygon with n sides IS;

$\rm (n-2)* 180$

Sum of interior angles of a polygon = 540°

Equating both we can determine the number of sides

$\rm (n-2)* 180=540\n\nn-2=(540)/(180)\n\n n-2=3\n\nn=3+2\n\nn=5$

There are 5 sides in the polygon and the sum of the interior angles of a polygon is 540.

The number of degrees in one interior angle of the polygon is;

$=(540)/(5)\n\n=108$

Hence, the number of degrees in one interior angle of the polygon is 108 degrees.

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Any polygon with interior angles that add up to 540 must have 5 sides and 5 corners (a pentagon). Assuming it is a regular pentagon, you need to work out what 1/5 of 540 is, which is the same as dividing it by 5. 540/5 = 108. this is the number of degrees in one interior angle of a regular pentagon.

Inverse laplace of [(1/s^2)-(48/s^5)]

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I am not familiar with Laplace transforms, so my explanation probably won't help, but given that for two Laplace transform $F(s)$ and $G(s)$ , then $\mathcal{L}^(-1)\{aF(s)+bG(s)\} = a\mathcal{L}^(-1)\{F(s)\}+b\mathcal{L}^(-1)\{G(s)\}$

Given that $(1)/(s^2) = (1!)/(s^2)$ and $-(48)/(s^5) = -2\cdot(4!)/(s^5)$

So you have $\mathcal{L}^(-1)\left\{(1)/(s^2) - 2\cdot(4!)/(s^5)\right\} = \mathcal{L}^(-1)\left\{(1)/(s^2)\right\} - 2\mathcal{L}^(-1)\left\{(4!)/(s^5)\right\}$

From Table of Laplace Transform, you have $\mathcal{L}\{t^n\} = (n!)/(s^(n+1))$ and hence $\mathcal{L}^(-1)\left\{(n!)/(s^(n+1))\right\} = t^n$

So you have $\mathcal{L}^(-1)\left\{(1)/(s^2)\right\} - 2\mathcal{L}^(-1)\left\{(4!)/(s^5)\right\} = \boxed{t-2t^4}$ .

Hope this helps...

Final answer:

To find the inverse Laplace transform of the given expression, use partial fraction decomposition to simplify it into individual fractions and then find their inverse transforms.

Explanation:

To find the inverse Laplace transform of the given expression, we can use partial fraction decomposition. First, we factor the denominator: s2*(s3-48). The next step is to represent the expression as a sum of simpler fractions:

1/s2 - 48/s5 = A/s + B/s2 + C/(s - 2) + D/(s + 2) + E/(s + 4) + F/(s2 - 4)

Next, we solve for A, B, C, D, E, and F by performing algebraic manipulations and equating the corresponding coefficients. Finally, we can look up the inverse Laplace transform of each individual fraction term in tables or by using known formulas.

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What are the solutions to the quadratic equation 3(x − 4)^2 = 75?a- x = −9 and x = 1
b- x = −5 and x = 5
c- x = −4 and x = 4
d- x = −1 and x = 9

Answers

the answer is (d) where x = -1 & 9

Graph each function. Identify the domain and range of g(x)=|-3|