Design an equation for the volume of a box made from a cardboard sheet of length q and width p and square cutouts of side length x.

The required ratio of area of cubes is 25 : 16.

Volume of cube 1 = 125
Volume of cube 2 = 64

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Volume of cube 1 = 125
    a³ = 125
    a = 5
Volume of cube 2 = 64
       A³ = 64
        A = 4
Area of cube 1 = a² x 6
= 5² x 6
= 150
Area of cube 2 = A² x 6
= 4² x 6
= 96
Now ,
The ratio of areas of cube 1 to cube 2 = 150:96.
= 25:16

Thus, the required ratio of area of cubes is 25 : 16.  

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The term that you want is 5C2*p^2*q^3 representing 2 successes and 3 failures.  This term's value is

(5C2)(0.5^5) = 10*0.03125 = 0.3125 = P(2 successes in 5 trials) =31.3%

The division to the expression Divide 40x/ 64y by 5x/ 8y is (a) 1

From the question, we have the following parameters that can be used in our computation:

Divide 40x/ 64y by 5x/ 8y

As an expression we have

40x/ 64y ÷ 5x/ 8y

So, we have

40x/ 64y ÷ 5x/ 8y = 40x/ 64y * 8y/5x

Divide the variables

This gives

40x/ 64y ÷ 5x/ 8y = 40/64 * 8/5

Lastly, we have

40x/ 64y ÷ 5x/ 8y = 1

Hence, the solution to the expression is (a) 1

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8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.

To multiply 8 times the square root of 3 by 9 times the square root of 27, we can simplify the expression using the properties of square roots and perform the multiplication.

First, let's simplify the square roots:

Square root of 3 can be written as √3.

Square root of 27 can be written as √(9 * 3), which further simplifies to √9 * √3 = 3 * √3.

Now, we have:

8 * √3 * 9 * √27 = 8 * √3 * 9 * (3 * √3) = 8 * 9 * 3 * √3 * √3 = 216 * 3 * √3 * √3.

Since the square root of 3 multiplied by itself (√3 * √3) simplifies to 3, we have:

216 * 3 * 3 = 1944.

Therefore, 8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.

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To find the coordinates of the vertices A'B'C' of the new triangle after translation and reflection, subtract 4 from the y-coordinate of each vertex and change the sign of the y-coordinate.

To find the coordinates of the vertices A'B'C' of the new triangle, we first translate the original triangle 4 units down. This means we subtract 4 from the y-coordinate of each vertex. So, the new coordinates of A', B', and C' are: A' (1, -3), B' (2, -1), and C' (5, -4).

Next, we reflect the translated triangle across the x-axis. To do this, we change the sign of the y-coordinate of each vertex. So, the final coordinates of A'B'C' are: A' (-1, 3), B' (-2, 1), and C' (-5, 4).

To convert the exponential equation 4c = 256 into a logarithmic form, one can apply the logarithm to both sides, simplifying using the property that the logarithm of a power is the exponent times the logarithm of the base, yielding the equivalent equation c = 4.

The question requires us to convert the exponential equation 4c = 256 into a logarithmic form. To achieve this, we need to recognize that a logarithm function is the inverse of an exponential function. Therefore, applying a logarithm to both sides of the equation will allow us to solve for the variable c.

It's important to note that any logarithmic base can be used, but common practice is to use either base 10 (common logarithm) or the natural base e (natural logarithm).

Since 256 is 4 raised to the 4th power (4⁴), we can write the equation as 4c = 4⁴. By applying the logarithm, we then get the equivalent logarithmic equation log(4c) = log(4⁴).

Using the property of logarithms that states the logarithm of a number raised to an exponent will be the product of the exponent and the logarithm of the number, we can simplify this to c*log(4) = 4*log(4). Since log(4) is a common factor on both sides, dividing by log(4) gives us c = 4.

The image is the product of a transformation while a pre-image is the original image on which a transformation operation is performed.

The image is the product of a transformation or it is the figure obtained after a transforms operation is performed.

A pre-image is the original image on which a trabsosfiemarion operation is performed.

The pre-image is differentiated from the image by the labelling convention used as well as by studying the transformation performed.

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Answer:

The answer is the table B

Step-by-step explanation:

we have

[tex]f(x)=2x^{3}-26x-24[/tex]

Using a graphing tool

see the attached figure to better understand the problem

Relation of graph to the x-axis

Interval (-∞,-3) -----> below (the function is negative)

Interval (-3,-1) -----> above (the function is positive)

Interval (-1,4) -----> below (the function is negative)

Interval (4,∞) ----->above (the function is positive)

Step-by-step explanation:

Please find the attachment of graph representing the axis of symmetry.

We are asked to choose the graph from our given choices, which shows the axis of symmetry for the function:

[tex]f(x)=(x-2)^2+1[/tex]

We can see that our function represents a parabola.

Since we know that axis of symmetry is a vertical line that divides parabola into two congruent parts. The axis of symmetry intersects parabola at its vertex.

Let us find the vertex of our given parabola using formula: [tex]x=\frac{-b}{2a}[/tex], where,

a = Coefficient of [tex]x^{2}.[/tex]

b = Coefficient of x.

To apply this formula we will represent our parabola as a quadratic equation [tex](ax^2+bx+c)[/tex] as:

[tex]f(x)=x^2-4x+4+1[/tex]

[tex]f(x)=x^2-4x+5[/tex]  

Upon substituting a= 1 and b= -4 in the formula we will get,

[tex]x=\frac{-(-4)}{2*1}[/tex]

[tex]x=\frac{4}{2}[/tex]

[tex]x=2[/tex]  

Therefore, the vertical line passing through point x = 2 will be the axis of symmetry for our given function and graph B is the correct choice.

Factoring Polynomials with Four Terms, and Factoring Trinomials by Grouping can be used to rewrite square trinomials and difference of squares binomials as separate factors

Answer:

triangle given is not a right triangle

Step-by-step explanation:

Given:-

- The side lengths of a triangle are given as:

                                     24 , 32 , 42

Find:-

is it a right triangle? explain

Solution:-

- Any triangle which conforms to the pythagorean theorem can be classified as a right angle triangle.

- The Pythagorean theorem states that the square of the longest side length known as hypotenuse (H) should be equal to the sum of square of other two side lengths ( Perpendicular / opposite [ P ] and Base / Adjacent [ B] ).

- This can be mathematically expressed as:

                                     H^2 = P^2 + B^2

- From the given side lengths. The largest side length is hypotenuse H = 42. While P and B can be used interchangeably for the other two side lengths. So using the theorem we have:

                                     42^2 = 32^2 + 24^2

                                     1764 : 1024 + 576

                                    1764 ≠ 1600

- We see that the three side lengths of the triangle does not conform to theorem. So we can conclude that the triangle given is not a right triangle.

Since 1764 is not equal to 1600, the triangle is not a right triangle.

To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the sides as follows:

a = 24, b = 32, c = 42

Using the Pythagorean theorem:

c² = a² + b²

Plugging in the values:

42² = 24² + 32²

1764 = 576 + 1024

1764 = 1600