What is the length of segment LM?

Final answer:

The square root of 100 is rational, as is the square root of 0.25.

Explanation:

The square root of 100 is a rational number. A rational number is a number that can be expressed as a quotient or fraction of two integers, where the denominator is not zero. In this case, the square root of 100 is 10, which can be written as 10/1, making it a rational number.

The square root of 0.25 is also a rational number. The square root of 0.25 is 0.5, which can be expressed as 1/2, making it a rational number.

Answer:

Step-by-step explanation:

A relation from a set X to a set Y is called a function, if each element of X is related to one and exactly one element in Y. Though many elements of X can be related to one element in Y (many to one).

{(3, 7),(3, 6),(5, 4),(4, 7)} → is not a Function (as (3, 7), (3, 6) share same x)

{(1, 5),(3, 5),(4, 6),(6, 4)} → is a Function

{(2, 3),(4, 2),(4, 6),(5, 8)} → is not a Function (as (4, 2), (4, 6) share same x)

{(0, 4),(3, 2),(4, 2),(6, 5)} → is a Function

Answer: ^^^ that person was correct

Step-by-step explanation:

Step-by-step explanation:

It is given that, the total distance an object travels varies directly with the length of time it travels.

[tex]d\propto t[/tex]

If an object travels 32 meters in 18 seconds so,

[tex]32= 18k[/tex].....(1) (k is a constant)

If distance travelled is 80 meters, then the time taken is t say.

[tex]80= kt[/tex].....(2)

On solving equation (1) and (2), we get the value of t as,

t = 45 seconds

Hence, this is the required solution.

Answer: 24 video games

Step-by-step explanation: jasmine has 1,128 bucks originally. she gets some megadeth and metallica cd's (cause if she's got taste, that's probably what she got) and that adds up to 72 bucks. now she wants to buy a whole bunch of video games, which cost 43 each (imagine she got fortnite mod's. ew) so we put that in an equation-

$1,128 - $72 = $1,056

$1,056 divided by 43 equals 24.55813953488372.

when dealing with money, you always round down, so the total number of games she bought was 24

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Answer:

a. the distance of the home from a school

Step-by-step explanation:

The distance your home is from a flood plain can potentially increase your homeowner's insurance.  If your house is close to a flood plain, your insurance will increase.

The distance your home is from a fire station or a fire hydrant either one can lower your insurance.  If your home is within so many feet of a hydrant, you get a discount on your insurance; if it is close enough to a fire station, you get a discount as well.

Since the distance a home is from a school has no bearing on the cost of repairing or replacing the home, this will not affect your homeowner's insurance.

When we rotate a figure and there is no change in the shape of the figure then it has rotational symmetry.

We know that the order of rotation for a square is 4.

Hence, we have [tex]\frac{360}{4} =90^{\circ}[/tex]

Thus, the angle of rotational symmetry of square are

[tex]90^{\circ}, 180^{\circ}, 270^{\circ}[/tex]

Hence, the minimum angle  of rotational symmetry is  [tex]90^{\circ}[/tex]

Therefore, the minimum angle of rotational symmetry for a square is 90 degrees.

The value of the positive integer is,

⇒ 11

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Here, 12 is added to the square of a positive integer, the result is 133.

Let a positive integer = x

Hence, We can formulate;

⇒ 12 + x² = 133

⇒ x² = 133 - 12

⇒ x² = 121

⇒ x = √121

⇒ x = 11

Thus, The value of the positive integer is,

⇒ 11

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T he end behavior of f(x) can be described as:

As x → -∞, f(x) → +∞

As x → +∞, f(x) → +∞

To determine the end behavior of f(x) = (x − 3)²(x + 5)(x − 2)³, we need to consider the degree and leading coefficient of the polynomial.

1. Degree of the Polynomial:

The degree is the highest sum of exponents of the variable x in any term. In this case:

(x - 3)² contributes a degree of 2 (x² term)

(x + 5) contributes a degree of 1 (x term)

(x - 2)³ contributes a degree of 3 (x³ term)

Adding these degrees, we get a total degree of 2 + 1 + 3 = 6.

2. Leading Coefficient:

The leading coefficient is the coefficient of the term with the highest degree. Since all factors have a leading coefficient of 1, the leading coefficient of the entire polynomial will also be 1 (positive).

3. End Behavior Based on Degree and Leading Coefficient:

Even Degree & Positive Leading Coefficient: When the degree is even and the leading coefficient is positive, both ends of the polynomial will approach positive infinity. In other words, as x approaches both positive and negative infinity, f(x) will also approach positive infinity.

Therefore, the end behavior of f(x) can be described as:

As x → -∞, f(x) → +∞

As x → +∞, f(x) → +∞

Complete question:

What is the end behavior of [tex]f(x) = (x - 3)^{2} (x + 5)(x - 2)^{3}[/tex]?

Answer: The simplified form of 48 over 192 is 1 over 4.

Step-by-step explanation:

Since, A fraction is in its simplest form when the numerator and denominator cannot be any smaller, while still being whole numbers.

Also, for find the simplified form of a fraction,

We divide both numerator and denominator by their H.C.F,

Here, the given fraction is,

[tex]\frac{48}{192}[/tex]

Since, 48 = 2 × 2 × 2 × 2 × 3

192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

H.C.F(48,192) =  2 × 2 × 2 × 2 × 3  = 48

[tex]\implies \frac{48/48}{192/48}=\frac{1}{4}[/tex]

Hence, The simplified form of 48/192 is 1/4.

The simplified form of 48/192 is 1/4.

First, let's find the GCD of 48 and 192.

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The factors of 192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.

The common factors are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

So, the greatest common divisor (GCD) of 48 and 192 is 48.

Now, we divide both the numerator and denominator by 48:

48/48 = 1

192/48 = 4

Therefore, the simplified form of 48/192 is 1/4.

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Answer:

The correct option is 3.

Step-by-step explanation:

Total digits 0 to 9 are

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Total number of digits is 10. It means total possible ways to select the first digit of the password is 10.

Since the reparation is allowed, therefore the possible ways to select the second and third digit of the password is 10.

Total possible ways to form a three-digit passwords is

[tex]10\times 10\times 10=1000[/tex]

Therefore the correct option is 3.

There are 1,000 possible three-digit passwords that can be formed using the digits 0 through 9 when repetition of digits is allowed, calculated as 10 possibilities for each of the three positions (10 x 10 x 10).

To determine how many possible three-digit passwords can be created using the digits 0 through 9 with repetition allowed, we consider each of the three positions in the password separately. For each position, we can use any of the 10 digits (0-9), leading to 10 possibilities for each digit.

Therefore, the total number of combinations for a three-digit password is:

By the rule of product, we multiply the possibilities for each digit:

10  imes 10  imes 10 = 1,000

Thus, there are 1,000 possible three-digit passwords when digits can be repeated.

Quadratic equations can be expressed in standard form or in vertex form.

The true statement about [tex]\mathbf{y = ax^2 + bx + c}[/tex] and [tex]\mathbf{y = a(x - h)^2 + k}[/tex] is that: the value of a remains the same

The original expression is given as:

[tex]\mathbf{y = ax^2 + bx + c}[/tex]

He wants to rewrite it as:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

Expand the above equation

[tex]\mathbf{y = a(x - h)(x - h) + k}[/tex]

Open brackets

[tex]\mathbf{y = a(x^2 - hx - hx + h^2) + k}[/tex]

[tex]\mathbf{y = a(x^2 - 2hx + h^2) + k}[/tex]

Remove bracket

[tex]\mathbf{y = ax^2 - 2ahx + ah^2 + k}[/tex]

Compare the above equation to: [tex]\mathbf{y = ax^2 + bx + c}[/tex]

[tex]\mathbf{ax^2 = ax^2}[/tex]

[tex]\mathbf{-2ahx = bx}[/tex]

[tex]\mathbf{ah^2 + k = c}[/tex]

Analyzing the above equations

[tex]\mathbf{ax^2 = ax^2}[/tex]

Divide both sides by [tex]\mathbf{x^2}[/tex]

[tex]\mathbf{a = a}[/tex]

The above equation means that, the value of a remains unchanged.

Hence, option (c) is true

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Answer:

Quadratic formula for given equation is [tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]

Step-by-step explanation:

Given Quadratic Equation is  7x² = 9 + x

We need to find correct Quadratic formula for the given quadratic equation.

If the quadratic equation is in standard for,

ax² + bx + c = 0

then quadratic formula is given by,

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

First we rewrite the quadratic equation,

7x² - x - 9 = 0

by comparing with standard form of equation we get,

a = 7  ,   b = -1  and c = -9

oNw putting these value in quadratic formula we get,

[tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]

Therefore, Quadratic formula for given equation is [tex]x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}[/tex]

It’s AB and DE so it would be b