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3 years ago

What is the expression in factored form? 9x^2-4 please shows steps

2 answers:

5 0

This expression can be factorized using the difference of squares which can be illustrated as follows:
A^2 - B^2 = (A+B)(A-B)

In the given example:
sqrt(9x^2) = 3x
sqrt(4) = 2
and the two squares are separated by a negative sign
Therefore, the difference of squares is applicable

Based on this, factoring the given expression would give us:
9x^2 - 4 = (3x+2)(3x-2)

Andrews [41]3 years ago

3 0

$9x^{2}-4$ given
Use the difference of squares theorom. i.e. $a^{2}-b^{2}=(a+b)(a-b)$ .
In this case, a is 3x (the sqaure root od $9x^{2}$ ) and b is 2(the sqaure root of 4). So we have:
$(3x-2)(3x+2)$

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3 years ago

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Carmen received a gift of $5,000 from her grandmother and decided to invest it. the expression 5000(1.0005)^12t represents the a

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The equivalent expression for the expression that represents the amount Carmen would earn is 5000(1.0005^12)^t.

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Based on the expression given, Carmen's investment is compounded monthly.

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FV = P (1 + r)^nm

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2 years ago

Marys family had to pay 3$ for the car plus 2$ for each number of people in the car.

Gala2k [10]

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y=2x+3

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Y is the total amount that the family pays. 2x represents 2 dollars for every person (so, 2 multiplied by the number of people). Finally, 3 represents the initial amount that they must pay, no matter how many are in the car.

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2 years ago

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Select the best method of finding an accurate solution to a system of linear equations

Flura [38]

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3 years ago

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What is the volume of this cone?

olchik [2.2K]

Answer:

The volume of the cone is approximately 453.0 cm³

Step-by-step explanation:

The volume of a cone is one third that of a cylinder with the same height and radius. That gives us 1/3 πr²h, where r is radius and h is height.

However, we are not given the height of the cone, but the side length. We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length. You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:

$a^2 = b^2 + c^2$

So we can find the height of the cone with that:

$10.8^2 = 7.4^2 + h^2\\h^2 = 10.8^2 - 7.4^2\\h^2 = 116.64 - 54.76\\h^2 = 61.88\\h = \sqrt{61.88}\\h \approx 7.9$

Now that we have the cone's height, we can solve for its volume:

$v = \frac{1}{3} \pi r^2 h\\v = \frac{1}{3} \pi \times 7.4^2 \times 7.9\\v = \frac{1}{3} \pi \times 54.76 \times 7.9\\v = \frac{1}{3} \pi \times 432.6\\v = \pi \times 144.2\\v \approx 453.0 cm^3$

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3 years ago

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