MODELING WITH MATHEMATICS The backboard of the basketball hoop forms a right triangle with the supporting rods, as shown. Use the Pythagorean Theorem to approximate
the distance between the rods where they meet the backboard. Round your answer to the nearest hundredth

The limit of a graph can be read by a function is said to have a limit if the value of the function is less than or equal to a particular value.

Limit

One way to think about the limit of a function at a number at x = an is as the value that the function begins to take as it gets closer to that value. Approaching the location where x = a can be done from either the left or the right side.

From a limx to a f (x)

As an illustration, if f(x) is defined as the limit of x, then x is the highest value that f can take. A function is said to have a limit if the value of the function is less than or equal to a particular value. For a given function, there can be multiple limits, but only one of them can be larger than the others.

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The equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.

The equation y = 2x - 4 can be written in slope-intercept form as y = 2x + b, where b is the y-intercept. To find the slope and y-intercept of the equation, we need to solve for b.

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we can set x equal to 0 in the equation to get y = 2(0) - 4. This simplifies to y = -4, so the y-intercept is -4.

The slope is the rate at which the line rises. To find the slope, we can take the coefficient of x, which is 2. So the slope of the equation y = 2x - 4 is 2.

In summary, the slope of the equation y = 2x - 4 is 2 and the y-intercept is -4. We can write the equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.

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The roots of equation in quadratic form 3[tex]x^{2}[/tex]- 10x + 8 = 0 are: x= -2/3 , -4 .. A polynomial equation of the second degree can be used to define quadratics.

A quadratic issue in mathematics involves multiplying a variable by itself, often known as "squaring," which is a mathematical operation. This vocabulary is based on the fact that a square's area is equal to the product of its side length and itself. Quadratum, the Latin word for square, is the source of the word "quadratic."

here

= 3[tex]x^{2}[/tex] - 10x + 8 = 0

= 3[tex]x^{2}[/tex]+ 2x  - 12x + 8 = 0

=  2 ( x + 4 ) + 3x( x + 4 )

=  ( x + 4 )( 3x + 2 )

x = -4 and x = -2/3

The roots of equation in quadratic form 3[tex]x^{2}[/tex]- 10x + 8 = 0 are: x= -2/3 , -4 .

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Basic Formula: ax + by = c

where a 0 and a, b, and c are all real numbers. m ...

Form of the Slope Intercept: y = mx + b

where (x,y) is a line connecting the points y and x.

In two-point form, y y 1 = m (x x 1) y y 1 = m (x x 1)

In the case where (x1,y1) (x 1, y 1) and (x2,y2) (...

Form of Intercept:

x/ x0 x 0 and y/ y0 y 0 equal 1.

where y0 y 0 = y-in and x0 x 0 = x-intercept...

Different forms of a two-variable linear equation are possible, including standard form, intercept form, and point-slope form. For instance, the equation 2x+3y=9 may be expressed using either of the following forms: 2x+3y-9=0 (standard form), y = (-2/3)x + 3, and Form of the Intercept: y - 5/3 = -2/3(x + (-2)) (point-slope form).

Find the value of the variable that causes the equation to be true in order to solve linear equations. Utilize the inverse of the variable's multiplier and divide or multiply both sides by it. To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.

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The expression 5xyz2 3zy have 5 and -3. It is possible to compare expressions and phrases.

In the expression

5xyz² – 3zy, the terms are 5xyz² and –3zy.

Coefficient of xyz² in the term 5xyz² is 5.

coefficient of zy in the term –3zy is –3.

In the expression 1 + x + x² , the terms are 1, x and x²

Therefore,

5xyz² = 5

- 3zy = -3

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Answer:

$165

Step-by-step explanation:

5% interest rate = 1 month

10% interest rate = 2month

10% = 0.1

Take $150 times 0.1 = $15

Find the total cost by taking

$150 + $15 = $165

So, the total cost of Jill's uniform is $165

The graph of the quadratic equation which represents the parabola can be opened upward or opens downward depending upon the nature of the equation and coefficient

If the equation is in the form of [tex]y^{2} =ax+b[/tex]  where [tex]a[/tex] is called the leading coefficient

The graph of a quadratic function opens upward or downward depending on the value of the leading coefficient a if the leading coefficient is greater than zero, ([tex]a[/tex]>0)  the parabola opens upward, and if the leading coefficient is less than zero,([tex]a[/tex]<0) the parabola opens downward.

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The slope of the line that passes through (6, 1) and (10, 8) is 7 / 4.

The slope of a line is the change in dependent variable with respect to the change in the independent variable. The slope of a line is rise over run.

In other words, the slope of a line is a measure of its steepness.

Hence, let's find the slope of the line that passes through (6, 1) and (10, 8).

Therefore,

slope = Δy / Δx

slope = y₂ - y₁ / x₂ - x₁

x₁ = 6

x₂ = 10

y₁ = 1

y₂ = 8

Therefore,

slope = 8 - 1 / 10 - 6

slope = 7 / 4

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Answer: 7/4 is the slope

The correct answer c. 0.300

All the golfers have similar skill levels, which means that they are equally as likely to win the tournament.

The sum of all 10 golfers probability to win the tournament is 100/10 = 10%.

What is the probability that one of the first three golfers that registered for the tournament will win?

Each one of them has a 10% probability of winning

3*10% = 30% = 0.3

So the correct answer is:

c. 0.300

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Full Question :Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same. What is the probability that one of the first three golfers that registered for the tournament will win?

a. 0.111

b. 0.001

c. 0.300

d. 0.9

e. 0.850

Answer:

n = -56

Step-by-step explanation:

1/8n=−7

1/8 * n = −7

n * 1/8 = −7

n/8 = −7

8 * n/8 = -7 * 8 ==> multiply each side by 8 to isolate n and remove fractions

n = -56

__________________________________________________________

Hello! In this question, we are going to solve for the variable "n".

__________________________________________________________

Explanation:

In the question, we were given the equation:

[tex]\frac{1}{8} n=-7[/tex]

We will solve for the variable "n" by getting it by itself, which would then be our "n" value.

__________________________________________________________

Solve:

Let us solve for n:

[tex]\frac{1}{8} n=-7\\\\\text{To get "n" by itself, we will multiply by 8 to eliminate the fraction}\\\text{Whatever you do to the left side of the equal sign, you do to the right}\\\text{Multiply both sides by 8}\\\\8\times\frac{1}{8} n=-7\times8\\\\n=-56\\\\\text{Since "n" is now by itself, we can't simplify any further, therefore our }\\\text{ "n" value would be \boxed{-56}.}[/tex]

__________________________________________________________

Answer:

[tex]\boxed{n=-56}[/tex]

__________________________________________________________

Additional info:

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An equation is like a sentence, just using a different language. Mathematical equations are telling you to do something, giving you information on how to respond, or come up with an answer. It's up to you to learn this language. However, once you know it, you can write in this language.

A mathematical equation, also known as a statement, shows that two separate expressions are equal. The two expressions are usually connected by the "equal-to" (=) sign. You can find the expressions in a mathematical statement by looking at the left-hand side and the right-hand side of the equation, using the = sign as the point of reference.  

The most popular equations are algebraic equations or expressions, in which letters are used as variables. Variables are placeholders that can assume any value. They can also be referred to as unknowns. You must solve for the correct value of the variable to make the equation true.

Let us look at an example to understand.

4x + 2x = 12

The letter x is the variable. You must find the value of x. Finding this value will make the right-hand side of the equation equal to the left-hand side. Let's solve this together.

In this case, since both variables are the same, you can add the values on the left-hand side.

6x = 12

Now, we divide both sides by the value of '6', which will help us solve for x. Consider this to be a way to unravel the equation. Also, remember that whatever is done to one side must be done to the other.

x = 2

This is exactly how to write an algebraic expression.

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Answer:

26

Step-by-step explanation:

Answer:

there is supplementary angle

Answer:

If 10% of the school brings lunch, and it's 31 people, we know that there are a total of 310 students. 10 times 31 is 310.

To check this, 90% of 310 is 279, and 310-279=31!

Answer:

310

Step-by-step explanation:

100 / 10 = 10

31 * 10 = 310

Enter 5/100 for five hundredths to divide the numerator by the denominator using a forward slash. Make sure there is space between the whole and fraction components when using mixed numbers.

The procedure used to express repeated multiplication is known as exponentiation in mathematics. As an illustration, 10 can be expressed as "10 raised to 3," which equals [tex]10^{3}[/tex] , if it is multiplied three times.

here ,

Exponentiation: 2/5^ 2  = 4/25

Or, two fifths raised to the power of squared is equal to four twenty-fifths. The mathematical equivalent of multiplying a number by itself a certain number of times is what is known as the number's exponential value.

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Answer:

How To Find if Triangles are Congruent 1 SSS (side, side, side) 2 SAS (side, angle, side) 3 ASA (angle, side, angle) 4 AAS (angle, angle, side) 5 HL (hypotenuse, leg)

hope this helps

mark me brainliest

Step-by-step explanation:

The simplification of the given expression is found as 2.

The stated expression is-

= (5⁻² x 10⁻⁴) / (2⁻⁵ x 5⁻⁶)

Taking the reciprocal of the numbers.

= (2⁵ x 5⁶) / (5² x 10⁴)

Cancel the common power

= (2⁵ x 5⁴) / ( (2x5)⁴)

Expanding the power

= (2⁵ x 5⁴) / ( 2⁴ x 5⁴)

Again cancel the common power.

= 2

Thus, the simplification of the given expression is found as 2.

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The correct question is-

What is the value of (5⁻² x 10⁻⁴) / (2⁻⁵ x 5⁻⁶)?

Answer:

Step-by-step explanation:

x^2 = 225

x = √15

Answer:

5x and 3x are like term

Step-by-step explanation:

as per the question 5x plus 9 is equal to 3x The common is X that means 5x and 3x as 5 plus 3 is nine

In this function, we use Java's HashMap to locate duplicate elements in an array. The input array's items are kept as keys and their occurrences as values in a hash map. Any key that has a value greater than one (>1) is considered to be a duplicate element.

In Java, you may discover duplicates in an array using a variety of ways. This article will teach you how to use Java's Brute Force method, Sorting method, HashSet, HashMap, and Java 8 Streams to locate duplicate elements in an array. Let's examine each one in turn.

Private static void new HashMap(); HashMapInteger, Integer> map = new

HashMap; findDuplicatesUsingHashMap(int[] inputArray);

for (int element: inputArray)

if (map.get(element) == null) map.put(element, 1);

else map.put(element, map.get(element)+1);

Set> Set entry "Integer, Integer" map entrySet =. entrySet();

for (EntryInteger, Integer> entry: entrySet)

if(entry.getValue() > 1)

System.out.println("Duplicate Element: "+entry.getKey()+" - found "+entry.getValue()+" times.");

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By using the concept of algebraic expression, it can be calculated that-

Expression equivalent to 18x + 6y - 3 is 3(6x + 2y - 1)

What is algebraic expression?

An algebraic expression is an expression that consists of numbers, variables, and operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to represent relationships between numbers, or to represent solutions to equations. These expressions are often used in mathematics, engineering, and computer programming. Algebraic expressions can also be used to create equations or to solve problems. Algebraic expressions can be written in both standard form and expanded form, and can be evaluated to find values for the variables.

The given expression is 18x + 6y - 3

Now,

18x + 6y - 3

3(6x + 2y - 1)

Expression equivalent to 18x + 6y - 3 is 3(6x + 2y - 1)

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The interest on Ethan's CD account will be $700 * 1.8% = 12.6$ dollars after one year. Since the CD earns 1.8% interest each year, the interest will be the same amount each year, so the total interest on the CD after 6 years will be $12.6 * 6 = 75.6$ dollars. This means that the CD will be worth $700 + 75.6 = $775.6$ after 6 years.

a) A procedure for identifying outliers is identifying if there are values that are more than 1.5 IQR from the quartiles. Thus, the value of 810 is an outlier in the given distribution.

b) As the distribution contains a high outlier, it means that the distribution is right skewed.

The first quartile of a data-set is the element that represents the 25th percentile of the distribution.

For a distribution of 34 students, the first half of the distribution has 16 values, hence the first quartile is the mean of the 8th and 9th values.

From the stemplot, these values are 170 and 180, hence:

Q1 = (170 + 180)/2 = 175.

The third quartile is the 75th percentile of the distribution, hence it is the mean of the 8th and 9th values of the second half of the distribution.

From the stemplot, these values are 39 and 41, hence:

Q3 = (390 + 410)/2 = 400.

The IQR is the difference between the quartiles, hence:

IQR = Q3 - Q1 = 400 - 175 = 225.

Values that are more than 1.5 IQR from the quartiles are considered outliers, hence the bounds are given as follows:

Hence the value of 810 is a high outlier. This high outlier will influence the mean, making it higher than the median, and thus the distribution is right skewed.

The stemplot is given by the image shown at the end of the answer.

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The probability P(A and B) has a value of 0.08

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

These mean that

P(A) = 0.2

P(B) = 0.4

From the question, we have

The events are independent events

The probability A and B is calculated as

P(A and B) = P(A) * P(B)

Substitute the known values in the above equation, so, we have the following representation

P(A and B) = 0.2 * 0.4

Evaluate

P(A and B) = 0.08

Hence, value is 0.08

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The quotient is 2x2+5x2+2.

The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, both the constant term (the term without a variable) and the leading coefficient (the coefficient of the highest power) must be divisible by the fraction's denominator.

Since we have already provided it

[tex]\frac{(6x^2+15x^3+10x^2+10x+4)}{(3x^2+2)}[/tex]

We will now factor the numerator to determine the quotient:

Use the theorem that says [tex]a_0=4[/tex] and [tex]a_n=6[/tex].

[tex]a_0[/tex] divisions are 1, 2, and 4.

[tex]a_n[/tex] is divided into 1, 2, 3, and 6.

Check the following logical figures as a result: ±[tex]\frac{1,2,4}{1,2,3,6}[/tex]

[tex]-\frac{2}{1}[/tex] is a root of the expression, so factor out [tex]x+2[/tex]

[tex]=(x+2)\frac{6x^4+15x^3+10x^2+10x+4}{x+2}[/tex]

[tex]= \frac{6x^4+15x^3+10x^2+10x+4}{x+2} \\=6x^3+3x^2+4x+2[/tex]

We'll factor it in once more now:

[tex]=(6x^3+3x^2)+(4x+2)\\=2(2x+1)+3x^2(2x+1)\\=(2x+1)(3x^2+2)[/tex]

Finally, we have our factored form:

[tex]= (x+2)(2x+1)(3x^2+2)\\=\frac{(x+2)(2x+1)(3x^2+2)}{3x^2+2} \\=(x+2)(2x+1)\\=2x^2+5x+2[/tex]

The complete question is:-

What is the quotient: (6x4 + 15x3 + 10x2 + 10x + 4) ÷ (3x2 + 2)?

a. 2x2 – 5x + 2

b. 2x2 + 5x – 2

c. 2x2 + 5x + 2

d. 2x2 – 5x – 2

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Discontinuous classes can be made continuous by using interpolation, which expression values between known points. For example, a discontinuous class of heights can be made continuous by using interpolation to estimate heights between known points.

Discontinuous classes can be made continuous by using interpolation. Interpolation is a mathematical process that estimates values between known points. This can be done in a variety of ways, such as linear interpolation which estimates values using the slope between two known points, or polynomial interpolation which uses a polynomial equation to estimate the values between known points. For example, if you have a discontinuous class of heights, you can use interpolation to estimate values between the known heights. This would result in a continuous class of heights, which may be more useful than the discontinuous class. Interpolation can also be used to estimate other types of values, such as temperature, pressure, or any other type of value that can be represented on a continuous scale.

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The set of vectors spanning the null space of A is {(0,0,z)}.

A set of vectors spanning the null space of a matrix A is a set of vectors that, when multiplied by the matrix A, result in the zero vector. In other words, these vectors are in the null space of A because they are mapped to the zero vector under the transformation represented by A.

To find a set of vectors spanning the null space of matrix A, you can use the following steps:

To find a set of vectors spanning the null space of the matrix A= 1 1 2 -1 2 3 6 -2 -2 1 2 2 0 -2 -4 0:

Write the matrix A in row-reduced echelon form:

1 1 2 | -1

0 0 0 | 0

0 0 0 | 0

The pivot columns are the first and second columns, which contain the leading 1's.

Assign variables x and y to the pivot rows:

1 1 2 | -1

0 0 0 | 0 x

0 0 0 | 0 y

Set the variables corresponding to all other rows in the pivot columns equal to 0:

1 1 2 | -1

0 0 0 | 0 0

0 0 0 | 0 0

Set the variables corresponding to the rows in the non-pivot column equal to a free variable z:

1 1 2 | -1

0 0 0 | 0 0 z

0 0 0 | 0 0 z

The set of vectors spanning the null space of A is {(0,0,z)}.

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The top three factors that contribute leading to my success are

There are several factors that I believe are important to a successful venture, business or individual. But in my opinion my main factors are:

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The volume of a cube is 15.625 cubic cm.

What is the volume of a cube?

A cube is a three-dimensional shape having 6 square faces, all the faces are of equal length, breadth, and height.

The volume of the cube is given by side * side * side.

The volume of a cube is given by:

V = a³,

where a is the side length of the cube.

Each side of a cube is 2.5 cm long.

Then, the volume of the cube will be:-

V = (2.5)³,

=  15.625

Hence, the volume of a cube is 15.625 cubic cm.

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