Simplify this problem please

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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The statement that is true for the graph of function shown below is option (B) both graphs have exactly one asymptote is the correct answer.

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).

For the given situation,

The diagram shows the graph that has 2 functions f(x) and g(x).

The function f(x) is increasing function and the function g(x) is decreasing function.

An asymptote of a curve y = f (x) that has an infinite branch is called a line such that the distance between the point (x, f (x)) lying on the curve and the line approaches zero as the point moves along the branch to infinity.

Here the two functions f(x) and g(x) approaches zero at asymptote of 1.

Hence we can conclude that the statement that is true for the graph of function shown below is option (B) both graphs have exactly one asymptote is the correct answer.

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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

12/5 = 2.4 times larger

3 x 2.4 = 7.2 inches wide

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.

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

The actual distance between the cities are 40 miles.

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

According to the question we are given that On a map, 1 inch equals 5 miles. two cities are 8 inches apart on the map.

that is, 1cm : 5 miles

Here two cities are 8 inches apart on the map.

then 8 inches equals to

5 x 8 = 40 miles.

The actual distance is 40 miles.

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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:

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.

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.

gpe = 1/2 of the unit measures

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

Answer:

H = .2L; H = .4

Step-by-step explanation:

The measure of ∠WZX is B; y, because Triangle UVW is similar to triangle ZXW.

The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

We can see that Angles UVW ad ZXW are congruent,

Then because of the vertical angle theorem; angles UWV and XWZ are congruent.

So if there are 2 angles in each triangle which are congruent to each other, then the triangle angle sum theorem state that the third angle also has to be congruent in each.

BUT congruent angles do not make the triangles congruent due to the length of the sides can change and the measures of the angles remain unchanged.

Hence, The measure of ∠WZX is B; y, because Triangle UVW is similar to triangle ZXW.

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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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