Solve for x. Simplify completely.
x^2-9=55

To solve the quadratic equation 2x^2-2x-12=0, the quadratic formula is used yielding two solutions, x = 3 and x = -2.

To find the solutions for the quadratic equation 2x^2-2x-12=0, we can use the quadratic formula. The general form of a quadratic equation is ax^2 + bx + c = 0. For the given equation, the coefficients are a = 2, b = -2, and c = -12. Applying the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a), we substitute in our coefficients to get:

x = (2 ± √((-2)^2 - 4(2)(-12))) / (2(2))

x = (2 ± √(4 + 96)) / 4

x = (2 ± √(100)) / 4

x = (2 ± 10) / 4

Thus, the two solutions for x are:

Therefore, the two solutions of the quadratic equation 2x^2-2x-12=0 are x = 3 and x = -2.

To solve the equation 2x^2 - 2x - 12 = 0, we can use the quadratic formula. The solutions are x = 3 and x = -2.

To solve the equation 2x^2 - 2x - 12 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

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

For our equation, a = 2, b = -2, and c = -12. Plugging in these values, we get:

$$x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(2)(-12)}}{2(2)}$$

Calculating the values inside the square root:

$$x = \frac{2 \pm \sqrt{4 + 96}}{4}$$

$$x = \frac{2 \pm \sqrt{100}}{4}$$

$$x = \frac{2 \pm 10}{4}$$

So the two solutions to the equation are:

$$x = \frac{2 + 10}{4}$$

$$x = \frac{12}{4}$$

$$x = 3$$

and

$$x = \frac{2 - 10}{4}$$

$$x = \frac{-8}{4}$$

$$x = -2$$

Answer:

961.6

Step-by-step explanation:

43.5694   22.07 = 961.6

Answer: B

Step-by-step explanation:

Answer:

B. {3,9,12}

Step-by-step explanation:

test approved

To solve the equation with absolute value expressions, isolate the absolute value terms and solve two separate equations. The solutions are x = -1 and x = 1.

To solve the equation 1/2 - x/3 = 5/6 with the absolute value expressions, we need to isolate the absolute value terms and solve two separate equations. First, rewrite the equation as |-x/3| = 5/6 - 1/2. Since the absolute value of a number is always positive, we can remove the absolute value symbols by considering the positive and negative cases separately.

For the positive case, we have -x/3 = 5/6 - 1/2. Simplifying, we get -x/3 = 1/3. Multiplying both sides by -3, we find x = -1. For the negative case, we have -(-x/3) = 5/6 - 1/2. Simplifying, we get x/3 = 5/6 - 1/2. Combining like terms, we have x/3 = 1/3. Multiplying both sides by 3, we find x = 1. Therefore, the solution set to the equation is {-1, 1}.

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To solve the equation 9(p-4)=-18, distribute the 9, then add 36 to both sides, and finally, divide by 9 to isolate p, resulting in p = 2.

To solve the equation 9(p-4)=-18, we need to isolate the variable p. Here's a step-by-step solution:

The solution to the equation 9(p-4)=-18 is p = 2.

The volume of the composite solid is approximately 438 mm³.

Given is a composite solid, composed of a half cylinder [cut vertically] as a roof and a rectangular prism of dimension 5 mm, 11 mm, 6 mm, as base.

We need to find the volume of the solid.

So, to find the volume of the whole solid we will just add the volume of the half cylinder and the rectangular prism.

Volume of a rectangular prism = length × width × height

Here, Length = 11 mm, Height = 6 mm and Width = 5 mm.

Volume of cylinder = π × radius² × height

Since here the cylinder is half so the volume = [π × radius² × height] ÷ 2

The diameter of the cylinder is the width of the prism, height is length of the prism,

Now, let calculate the volume,

Volume = [5 × 11 × 6] + [(3.14 × 2.5² × 11) ÷ 2]

Volume = 330 + 108

Volume = 438 mm³

Hence the volume of the composite solid is approximately 438 mm³.

Learn more about composite solid click;

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soup can is in the shape of cylinder

given, base area = 9 pi

base area = area of circle = pi * r^2 = 9 * pi

r = 3

total surface area of cylinder = 2 *pi*r(h+r)

= 2*3(10+3) pi=  78 pi

area for the label needed to wrap around the can with

no overlaps 78 pi inches^2

The question is asking to find the parametric equations of the line with the equation 2x+3y=5, which are x=t and y=(5-2t)/3 where t is a parameter.

To obtain parametric equations for the line 2x + 3y = 5, first, solve for y, yielding y = (5 - 2x)/3. Introduce a parameter, often denoted as t, representing the 'time' a point travels on the line. When x = t, substitute it into the y equation, resulting in y = (5 - 2t)/3. Hence, the parametric equations for the line are x = t and y = (5 - 2t)/3. These equations express x and y in terms of the parameter t, allowing the representation of various points on the line as t varies, providing a concise and dynamic description of the line's behavior in a parametric form.

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Answer:

0.94635 Liters in a Quart

Step-by-step explanation:

The width of a rectangle with an area of 96 square feet and a width to length ratio of 2:3 is 8 feet.

In this mathematics problem, we are given the area of a rectangle (96 square feet) and the ratio between its width and length (2:3). The equation representing the area of a rectangle is Length x Width. Given that the area of the rectangle is 96 sq ft, and the ratio of width to length is 2:3. Let's assign the width to be 2x and the length to be 3x. Then, you would multiply these two together and set it equal to the area: (2x) * (3x) = 96 square feet. Simplifying this gives 6x2 = 96. Dividing both sides by 6 gives you x2 = 16. Taking the square root of both sides gives x = 4. Therefore, the width of the rectangle, which is 2x, is 2 * 4 = 8 feet.

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Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Total number of shirts purchased for her team = 12

Number of shirts places in the first bag = 5

We need to find the number of ways a group of 5 shirts be placed in that first bag.

We will use "Combination" to find the number of different ways :

As we know the formula for Combination.

[tex]^nC_r=\frac{n!}{r!\times (n-r)!}\\\\here, n=12\\\\r=5\\\\So,\ it\ becomes,\\\\^{12}C_5=\frac{12!}{5!\times 7!}\\\\=\frac{12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2}\\\\=792[/tex]

Hence, there are 792 ways to do so.

Therefore, Option 'C' is correct.

In a right triangle, use the Pythagorean theorem and the cosine function to find the measure of angle P.

In triangle PQR, where angle Q is a right angle, we can use the Pythagorean theorem to find the measure of angle P. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, PR is the hypotenuse and PQ and QR are the other two sides.

Using the given measurements, PQ = 33.8 and PR = 57.6. To find the measure of angle P, we can use the cosine function. Cosine is the ratio of the adjacent side to the hypotenuse, so we have cos P = PQ / PR.

Plugging in the given values, we have cos P = 33.8 / 57.6. Using a calculator, we find that cos P ≈ 0.586. To find the measure of angle P, we can take the inverse cosine of this value, which is approximately 54.3 degrees.

The bird can travel approximately 5.7 miles in 2.1 hours.

To find the number of miles the bird can travel in 2.1 hours, we need to convert the speed from feet per second to miles per hour. There are 5280 feet in a mile and 3600 seconds in an hour, so the bird's speed is 4.0 * 3600 / 5280 = 2.727 miles per hour. Multiplying this speed by 2.1 hours gives us a total distance of 2.727 * 2.1 = 5.7207 miles, rounded to the nearest tenth, which is 5.7 miles. Therefore, the answer is option C) 5.7 mi.

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Answer:

answer is A bud

Step-by-step explanation:

i just took the test lol

To find the dimensions of a rectangle with a given area and perimeter, set up and solve a system of equations.

Let's assume that the length of the rectangle is x cm and the width is y cm.

Given that the area of the rectangle is 180 cm², we have the equation x*y = 180.

Also, the perimeter of the rectangle is 58 cm, which gives us the equation 2x + 2y = 58.

By solving these two equations simultaneously, we can find the dimensions of the rectangle.

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