Let a and b be irrational numbers. Is (ab)^2 always rational, sometimes rational, or never rational?

Final answer:

Using the formula L = 0.8T², we find that a pendulum 30 ft long has a period of approximately 6.1 seconds, which corresponds to Option D.

Explanation:

The question is about finding the period, T, in seconds for a pendulum that is 30 ft long, using the formula L = 0.8T2. First, to solve for T given that L = 30, we rearrange the equation to T = √(L/0.8). Plugging in L = 30, we have T = √(30/0.8), which simplifies to T = √(37.5).

Calculating further, we find T ≈ 6.12 seconds. Therefore, the answer closest to the period in seconds for a pendulum that is 30 ft long is 6.1 seconds (Option D).

The width of the rectangle is 6.1 in.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.

Perimeter of the rectangle = 2(L + W) unit

WE have been given that  length of a rectangle is 3 inches less than 4 times the width.

Length = 4x-3

width = x

If the perimeter is 55 inches, then

Perimeter of the rectangle = 2(L + W) unit

55= 2(4x-3 +x)

55 = 2(5x-3)

27.5 = 5x-3

27.5+3 = 5x

30.5/5 = x

6.1=x

Thus, Width is 6.1 in

The length (4 x 6.1 -3) = 21.4

Hence,  the width of the rectangle is 6.1 in.

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These two equations do not have the same solution. x = 4 for the first equation and x = -4 for the second equation.

In the equation 5x + 10 = 30, we are adding 10 to the product of 5 and x. To find x, we can first subtract 10 from both sides of the equation to get 5x = 20. Then we divide both sides of the equation by 5 to solve for x, giving us x = 4.

5x + 10 = 30

5x = 30 - 10

5x = 20

x = 20/5 = 4

In the equation 5(x + 10) = 30, we are first adding x and 10 together, then multiplying the result by 5. To solve for x, we can start by dividing both sides of the equation by 5 to get x + 10 = 6. Then we subtract 10 from both sides to solve for x, giving us x = -4.

5(x + 10) = 30,

5x + 50 = 30

5x = 30 - 50

5x = -20

x = -20/5 = -4

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Answer:

All of the above is the answer

Step-by-step explanation:

Yes, Given relation is a function.

Here,

Points are given as,

(3, 6) (10, 13) (11, 1) (13, 6)

What is a function?

A function is defined as a relation between a set of inputs having one output each.

Now,

The given relation is a function because we don't have any repeated x values. Each input (x) leads to exactly one output (y). if we plotted all the points, then we would not be able to pass a single vertical line through more than one point. Hence, this graph complies vertical line test.

So, Given relation is a function.

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x = the age of Heather

One half of Heather's age two years from now plus one-third of her age three years ago is twenty years

(x + 2)/2 + (x - 3)/3 = 20

by solving the equation we find

x = 24 years

Answer:

Hence, the value of x is [tex]x\leq -18[/tex]

Step-by-step explanation:

Consider the provided inequity.

[tex]\frac{x}{3}\leq -6[/tex]

We need to solve the above inequity of x.

Multiply both the side by 3.

[tex]3\times\frac{x}{3}\leq 3\times -6[/tex]

[tex]x\leq -18[/tex]

Hence, the value of x is [tex]x\leq -18[/tex]

64-22 = 42

42/2 = 21

21+22 = 43

21 + 43 = 64

 the numbers are 21 & 43

The larger number is 43 and the smaller number is 21.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The numbers will be calculated as:-

Let the larger number be L and the smaller number be S.

L + S = 64

From the given data the larger number is 22 more than the smaller number

L = S + 22

Put L = S + 22 in the above equation.

S + 22 + S  = 54

2S  = 64  -22

2S = 42

S = 42 / 2 = 21

L = S +22 = 21 + 22 = 43

Therefore, the larger number is 43 and the smaller number is 21.

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Complementary angles are angles that add up to 90 degrees but may not have the same measure. A counterexample to the statement would be two angles that are complementary but not congruent.

Complementary angles are angles that add up to 90 degrees. Congruent angles are angles that have the same measure.

A counterexample is a situation where the statement is false. In this case, a counterexample would be two angles that are complementary but not congruent.

For example, let's consider a 45-degree angle and a 45-degree angle. These angles are complementary because their sum is 90 degrees. However, they are not congruent because they have different measures.

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A segment with endpoints X (6, 2) and Y (- 1, - 3) when rotated 90 degrees about the origin will result in new endpoints X' (-2, 6) and Y' (3, -1).

This problem deals with the concept of point rotation in a 2D coordinate plane around the origin. When any point (X, Y) is rotated 90 degrees counter-clockwise about the origin, the new position, let's say (X', Y'), can be calculated by using the formulas X' = -Y and Y' = X. Therefore, applying these rotations to the points X(6,2) and Y(-1,-3), we get X'(-2, 6) and Y' (3, -1). So, the endpoints X Prime and Y Prime of the rotated segment are (-2, 6) and (3, -1) respectively.

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After rotating a 90-degree rotation about the origin, the coordinates of X (6, 2) and Y (-1, -3) transform to X' (-2, 6) and Y' (3, -1) respectively.

When a point (x, y) is rotated 90º counterclockwise about the origin, it transforms to (-y, x). Let's apply this rule to the endpoints X (6, 2) and Y (-1, -3).

The coordinates of X prime would be (-2, 6) that is, (-y, x).

The coordinates of Y prime would be (3, -1) that is, (-y, x).

Thus, the transformed coordinates for X and Y would be (-2, 6) and (3, -1) respectively after a 90-degree rotation about the origin.

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As per the radius and given angle the length of the arc will be equal to 2.09 cm.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given information in the question,

Radius, r = 4 cm

Angle, θ = 30°

The formula for an arc's length is stated as:

= 2πr(θ ÷ 360)

So,

The length of arc = 2π(4)(30/360)

The length of the arc = 2.09 cm.

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Answer:

The answer is 4.5 cups of cereal and 1.5 cups of mixed nuts

Step-by-step explanation:

Let 'c' be the number of cups of cereal.

Let 'n' be the number of cups of mixed nuts.

One batch of his recipe makes 6 cups of snack mix, so equation becomes:

[tex]c+ n=6[/tex]     ..... (1)

Also given that Brad uses 3 times as much cereal as mixed nuts, so equation becomes:

[tex]c=3n[/tex]     ......(2)

Substituting (2) in (1)

[tex]3n+n=6[/tex]

=> [tex]4n=6[/tex]

=> [tex]n=1.5[/tex]

Since c = 3n, then

[tex]c=3*1.5=4.5[/tex]

So, the answer is 4.5 cups of cereal and 1.5 cups of mixed nuts.

Answer:

open circles on 1 and 2