A rectangular prism has a length of 8 feet, a width of 3 feet, and a height of 5 feet. What is the surface area of the rectangular prism?

gpe = 1/2 of the unit measures

 since 9 is a whole number the gpe would be 1/2 g

x+y=12

x-y=4

x=y-4

y-4+y=12

2y-4=12

2y=16

y=8

x=8-4=8

8+4=12

 the 2 numbers are 8 & 4

The equivalent expression to the given expression is [tex]8x^12y^3[/tex].

We have given that,

The  expression (2x^4y)^3

We have to determine the,

Which expression is equivalent to (2x^4y)^3

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

The answer is D.

2^3 is 8.

(x^4)^3 is x^12 and y^3 is simply y^3.

Put them together to get the final answer.

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Rounded to the nearest hundredth, they are:

[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]

[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]

To solve the quadratic equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex], we can use the quadratic formula:

[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]

where [tex]\(a = 2\), \(b = 5\)[/tex], and [tex]\(c = 5\)[/tex].

Substituting the values into the quadratic formula:

[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 2 \cdot 5}}}}{{2 \cdot 2}}\][/tex]

[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 40}}}}{{4}}\][/tex]

[tex]\[x = \frac{{-5 \pm \sqrt{{-15}}}}{{4}}\][/tex]

Since the discriminant [tex](\(b^2 - 4ac\))[/tex] is negative, the solutions will involve imaginary numbers.

Using the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\),[/tex] we can rewrite [tex]\(\sqrt{{-15}}\)[/tex] as [tex]\(i\sqrt{{15}}\):[/tex]

[tex]\[x = \frac{{-5 \pm i\sqrt{{15}}}}{{4}}\][/tex]

So, the solutions to the equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex] are complex numbers. Rounded to the nearest hundredth, they are:

[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]

[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]

These solutions represent the points where the graph of the quadratic equation intersects the x-axis. They lie on the complex plane.

Answer:

[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]

Step-by-step explanation:

Given: The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.

To find: The base of the given parallelogram.

Solution: It is given that The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.

Now, area of parallelogram is given as:

[tex]A=b{\times}h[/tex] where b is the base and h is the height of teh gievn parallelogram.

Substituting the given values, we have

[tex]6x^2+x+3=b{\times}3x[/tex]

⇒[tex]\frac{6x^2+x+3}{3x}=Base[/tex]

⇒[tex]\frac{6x^2}{3x}+\frac{x}{3x}+\frac{3}{3x}=Base[/tex]

⇒[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]

which is the required expression for the base of the given parallelogram.

In the given diagram, we are given two triangles, triangle ABC and triangle DEF.

And we are given a line or reflection l.

Triangle DEF is the mirror image of triangle ABC.

Therefore, all sides of the triangle ABC would be congruent to sides of triangle DEF.

AB = DF

AC = DE and

BC = EF.

We can see than BC is the smallest side of triangle ABC and EF is the smallest side of triangle DEF.

Answer:

$180,997.50.

Step-by-step explanation:

1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.

2. Select the rate-per-period column corresponding to the period interest rate.

3. Locate the value in the cell where the periods row intersects the rate-per-period column.

4. Multiply the annuity payment by the table value from step 3.

Future value = annuity payment × table value

FV = $7500.00 * 24.133 = $180,997.50

As per quadratic equation, all values of 't' for which the ball's height is 15 feet are 33.25 and (- 31.813).

"Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x)."

Given, [tex]h = 15[/tex] feet.

Therefore, the quadratic equation for [tex]h = 15[/tex] will be:

A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 feet per second.

The ball's height h (in feet) after t seconds is:

[tex]h = 7+23t-16t^{2}[/tex]

[tex]15 = 7+23t-16t^{2}[/tex]

⇒ [tex]15-7-23t+16t^{2} = 0[/tex]

⇒ [tex]16t^{2} -23t - 8 = 0[/tex]

⇒ [tex]t = [- (-23)[/tex] ± [tex]\sqrt{(23)^{2} - 4(16)(- 8)}[/tex] ]/(2 × 16)

⇒ [tex]t =[/tex] [23 ± 1041]/32

⇒ [tex]t =[/tex] [23 + 1041]/32, [23 - 1041]/32

⇒ [tex]t =[/tex] 33.25, - 31.813

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Answer:

34.77

Step-by-step explanation:

The area of a triangle with sides of length 6 cm, 4 cm, and 7 cm is approximately 11.95 cm² when calculated using Heron's formula and rounded to two decimal places.

The original question appears to be incomplete as there's no clear indication of which measure is being sought for the triangle with sides of length 6 cm, 4 cm, and 7 cm. However, if the goal is to use these sides to determine the area of a triangle, we can use Heron's formula, since the lengths given do not form a right triangle.

First, calculate the semiperimeter (s):

(s) = (a + b + c) / 2

(s) = (6 + 4 + 7) / 2

(s) = 17 / 2

(s) = 8.5 cm

Now, apply Heron's formula which is Area [tex](A) = \sqrt{[ (s)((s)-a)((s)-b)((s)-c) ][/tex]:

[tex]A = \sqrt{[8.5(8.5-6)(8.5-4)(8.5-7)]}\\A = \sqrt{[8.5(2.5)(4.5)(1.5)]}\\A = \sqrt{[8.5 \times 2.5 \times 4.5 \times 1.5]}\\A \approx 11.95 cm^2 after\ calculating\ the\ square\ root[/tex]

Thus the area of the triangle is approximately [tex]11.95 cm^2[/tex] (rounded to two decimal places). Note that the question's original instructions to round to two significant figures would result in an answer of [tex]12 cm^2[/tex].

Answer:

512/2500

Step-by-step explanation:

area = pi x r^2

615.75 = 3.14 x r^2

r^2 = 615.75/3.14 =196.0987 round to 196.1

r = sqrt(196.1) = 14.00357 round to 14

radius = 14 kilometers

Mike will use 1 1/2 pounds of pork for his meatloaf recipe, which calls for a 3 to 1 ratio of beef to pork and a total of 6 pounds of meat.

Mike's meatloaf recipe has a total of 6 pounds of meat and uses a 3 to 1 ratio of beef to pork. To find out how much pork he will use, we can express the total amount of meat as the sum of beef and pork parts.

First, we know that there are 3 + 1 = 4 parts in total because of the given ratio. Since the ratio is 3 to 1, for every 4 parts of meat, 1 part is pork. Therefore, we calculate the weight of each part by dividing the total weight by the number of parts:

6 pounds ÷ 4 parts = 1.5 pounds per part

Since one part is pork, Mike will use 1.5 pounds of pork for his meatloaf. Expressed as a mixed number, that's 1 1/2 pounds of pork in simplest terms.

Answer:

H = .2L; H = .4

Step-by-step explanation: