Simplify:
[tex]\frac{a^3-2a^2-15a}{a^3+a^2-30a}[/tex]

The solution of the quadratic equation k² - 4k + 1 = 5 will be 2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

k² - 4k + 1 = 5

Simplify the equation, then we have

k² - 4k + 1 = 5

k² - 4k - 4 = 0

Factorize the equation, then we have

k² - 4k - 4 = 0

k² - 2k - 2k - 4 = 0

k(k - 2) - 2(k - 2) = 0

(k - 2)(k - 2) = 0

k = 2, 2

The solution of the quadratic equation k² - 4k + 1 = 5 will be 2.

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The correct equation is given as,k² - 4k + 1 = 5

An acute triangle is a triangle with all three angles less than 90 degrees.

An example of an acute triangle is a triangle with angles measuring 30 degrees, 55 degrees, and 95 degrees. Using the Law of Cosines, we can calculate the side lengths of this triangle. The side opposite the 30 degree angle is 4.8, the side opposite the 55 degree angle is 5.2, and the side opposite the 95 degree angle is 8. The Law of Cosines states that the following equation must be true: a2 = b2 + c2 - 2bc Cos A. In this case, a2 = 82, b2 = 52, and c2 = 42. We can then solve for the sides of the triangle by plugging in the values for a2, b2, and c2 into the equation. The result is that the side lengths of this triangle are 4.8, 5.2, and 8.

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In general, a larger sample size is more likely to represent the population than a smaller sample size. This is because a larger sample size increases the chances that the sample will be representative of the population.

When the sample size is that larger, there is a lower chance of getting a skewed or biased sample. A larger sample size also tends to have less variability in the sample statistics, making it more likely to provide accurate estimates of population parameters.

However, it is important to note that increasing the sample size does not guarantee that the sample is representative of the population. The sampling method used, and the way the sample is selected, can also have an impact on the representativeness of the sample.

Hence, surveying 100 students is more likely to represent the population than surveying a smaller sample size like 10 students, but it does not guarantee a perfect representation of the population.

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From the linear function, at 50 degrees, the seller will sell 58 hot dogs, at 114 degrees, she will sell 35 hot dogs and from the line of best fit she will sell 3 hot dogs at every 10 degrees rise in temperature

When plotted, a linear function is a sort of mathematical function that visually displays a straight line. A formula of the form y = mx + c, where m is the line's slope and c is its y-intercept, is used to describe it.

The linear function given is;

y = (3/10)x + 8

Where;

a) At 50 degrees, the number of hot dogs

Substituting the values into linear function;

y = 3/10(50) + 8

y = 150 / 3 + 8

y = 50 + 8

y = 58

The seller will sell 58 hot dogs at 50 degree

b) The temperature at which they will sell 35 hot dogs is;

y = (3/10)x + 8

35 = 3/10(x) + 8

35 * 10 = 3x + 8

350 = 3x + 8

3x = 350 - 8

3x = 342

x = 342 / 3

x = 114

The temperature at which they'll sell 35  hot dogs is 114 degrees

c) Based on the line of best-fit, for every 10 degree rise in temperature, she will sell 3 hot dogs.

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Dilation rules refer to the mathematical rules and formulas used to calculate the image of a point, shape, or figure after it has undergone a dilation transformation.

Here are some of the most common dilation rules:

It's important to note that, the rules mentioned above are general rules of dilation and they might vary depending on the specific dilation transformation.

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Answer:

Step-by-step explanation:

To write 45.52 as a fraction you have to write 45.52 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

45.52 = 45.52/1 = 455.2/10 = 4552/100

And finally we have:

45.52 as a fraction equals 4552/100

The length of each piece of fabric is, 3/4 yards.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

There are 3 pieces of fabric.

And, The total length of the pieces of fabric is 2 1/4 yards.

Here,  Each piece of fabric is the same length.

Hence, The length of each piece of fabric is,

⇒ 2 1/4 ÷ 3

⇒ 9/4 × 1/3

⇒ 3/4 yards

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The equation in slope-intercept form is y = (-2/5)x - 9/2.

Slope-intercept form is an equation of a line that is written in the form of y=mx+b, where m is the slope of the line and b is the y-intercept. The slope-intercept form makes it easy to identify the slope and y-intercept of a line from an equation.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Therefore, for a line with a slope of −2/5 that passes through the point (15, −9/2), we can solve for b using the point-slope formula.
Point-slope formula:  y - y1 = m(x - x1)
Plugging in the given information, we get:
-9/2 - (-9/2) = (-2/5) (15 - 15)
Solving this equation yields b = -9/2.
Therefore, The equation in slope-intercept form is y = (-2/5)x - 9/2.

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Answer:  2.78 Yards, 8.33 ft,

Step-by-step explanation:

Answer:

100 in. = 100 inches, 8 feet 4 inches, or 2.77777777778 yards.

Step-by-step explanation:

When the slope is given as 2, the result of the slope intercept form is y = 2x + c where m stands for the slope and c for the y-intercept .

The intersection point is the location on the y-axis where the slope of the line crosses. where the y-axis crosses that point on a line or curve. By using y = mx+c as the equation for the straight line, where m stands for the slope and c for the y-intercept, this is proven. The slope (m) and y-intercept (b) of the line are denoted in the intercept form of the equation. For equations of the intercept form (y=mx+b), the slope and y-intercept, respectively, are m and b. Furthermore, some equations may be rewritten to appear as slope intercepts. For instance, the slope and y-intercept change to 1 and 0 respectively when y=x is represented as y=1x+0.

given

slope ( m ) = 2

= y = 2x + c

When the slope is given as 2, the result of the slope intercept form is y = 2x + c.

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The statement '15 more than the sum of 5 and a number' is equivalent to the mathematical expression (5+n)+15.

Therefore the answer is (5+n)+15.

The statement "15 more than the sum of 5 and a number" is asking for an expression that represents the value that is 15 greater than the result of adding 5 and a number together. The mathematical way to express this is:

15 + (5 + n)

Where n is the number that we are adding to 5.

15 is being added to the sum of 5 and n. The parentheses around the 5 and n indicate that those two values are being added together before the 15 is added to them.

In other forms of representation

15+(5-n) or (5+n)+15 or (5-n) +15 or 15+5n does not convey the meaning you want it to convey as these forms does not represent "15 more than the sum of 5 and a number"

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The average retail price of Raymond's vehicle is $24,400.

What is Average Retail Price?

Average price is a measure of a range of prices. It is calculated by taking the sum of the values and dividing it by the number of prices being examined. The average price reduces the range into a single value, which can then be compared to any other point to determine if the value is higher or lower than what would be expected.

average retail value = $17,600

All the additions to the average retail value are;

$1,700 for 4-wheel drive

$475 for an entertainment system

$800 for a special trim package

$225 for power locks

$125 for a sliding rear window

$325 for a towing package

$250 for power windows

$3,125 for a diesel engine

$450 for less than expected mileage

Deductions

$675 for having a manual transmission

Average retail price = Average retail value + additions - deductions

Average retail price = $17,600 + ($1,700+$475+$800+$225+$125+$325+$250+$3,125+$450) - $675

Average retail price = $17,600 + $7,475 - $675

Average retail price = $24,400

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The four types of bar graphs as follows:

Vertical Bar Graph.

Horizontal Bar Graph.

Grouped Bar Graph.

Stacked Bar Graph.

Rectangular bars are used in the particular type of data visualisation known as a bar graph, with the length of each bar matching to the value it represents. With the aid of rectangular bars that display the data's measure, the provided data is shown vertically in a graph or chart in a vertical bar graph. These graphs are referred to as horizontal bar graphs when the offered data is shown horizontally using rectangular bars that display the data's measure. These graphs are referred to as horizontal bar graphs when the offered data is shown horizontally using rectangular bars that display the data's measure.

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Answer:

2^2 would be 4

Step-by-step explanation:

According to the Common Segments Theorem, if a segment is merged with two congruent segments, the subsequent segments will also be congruent

a piece removed from a geometric form by one or more points, lines, or planes. Examples include the region of a circle enclosed by its chord and arc, or the portion of a sphere enclosed by two parallel planes. Segment is a service that makes it easier to acquire and use data from users of your digital domains because it is a customer data platform (CDP) (websites, apps, etc). Your first-party customer data may be gathered, transformed, sent, and archived using Segment. between two points on a line or curve; a segment. a segment of a solid figure or plane that is removed by an intersecting line.

given

According to the Common Segments Theorem, if a segment is merged with two congruent segments, the subsequent segments will also be congruent.

The overlapping segments that result are congruent if two collinear segments that are next to a common segment are also congruent. Intermingling Angle Theorem.

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On solving the provided question, we can say that the - by solving algebraic equation x= 0 and y= 4.

A mathematical statement in which two expressions are rendered equal to one another is known as an algebraic equation. A variable, coefficients, and constants make up an algebraic equation in most cases. Check out algebraic expressions as well. Equations, or the equal sign, simply indicate equality. With mathematics, and algebraic expression is one that is constructed using variables, constant algebraic numbers, and algebraic operations. An algebraic expression is, for instance, 3x2 2xy + c.

y+ (2/3)x = 4

12—3y

3y +6x 12

2x+3y=12

by subtracting2frorn1.

4x=o

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When we decrease the exponent of 10 by 1, the number becomes one-tenth of the previous number.

For the fixed base(10), if the exponent decrease by 1, the number will becomes one-tenth of the previous number.

The Power Rule for Exponents is (a^m)^n = a^m*n. To increase a number with an exponent to a power, we need to multiply the exponent times the power. Negative Exponent Rule is x^-n = 1/x^n. We need to invert the base to change a negative exponent into a positive.

Exponents are used to represent repeated multiplication of a number by itself. For example, 7 * 7 * 7 can be showed as 73. Here, the exponent is 3 that stands for the number of times the number 7 is multiplied. The base here is 7 that is the actual number which is getting multiplied. So, initially exponents or powers shows the number of times a number can be multiplied. If the power is 2, it means the base number is multiplied two times with itself.

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The polynomial function in given graph for g(x) is

g(x)= -x^2.

What are polynomial functions?

Polynomial is made up of two words, poly and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms"

Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants. for e.g.

f(x) = 3x^2 - 5.

Types of Polynomial Function:

Constant Polynomial Function -  A constant polynomial function is a function whose value does not change. It remains the same and also it does not include any variables.

Zero Polynomial Function - Polynomial functions with a degree of 0 are known as zero Polynomial functions.

Linear Polynomial Function - Polynomial functions with a degree of 1 are known as Linear Polynomial functions.

Quadratic Polynomial Function - Polynomial functions with a degree of 2 are known as Quadratic Polynomial functions.

Cubic Polynomial Function - Polynomial functions with a degree of 3 are known as Cubic Polynomial functions.

Quartic Polynomial Function - Polynomial functions with a degree of 4 are known as Quartic Polynomial functions.

Now,

In given graph, We fill find g(x) by putting value of x and seeing the corresponding result of y.

As for    x      y is

            1       -1

             2      -4

            3       -9

            -1       -1

            -2      -4

Therefore, from given values we can conclude that polynomial function for g(x)= -x^2.

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The range of possible values of the third side of the triangle is 3 < x < 25. That is, the possible whole number values are 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24.

From the given information, we are to determine all possible values for the length x of the third side of the given triangle

From the given information,

One of the sides of the triangle is 11 centimeters in length

and

The length of the other side is 14 centimeters

From one of the properties of a triangle,

The third of a triangle is greater than the positive difference of the other two sides and the third side is lesser than the sum of the other two sides.

if the third side of the triangle is x

Then,

x < 14 + 11

x < 25

and

x > 14 - 11

x > 3

Thus,

x > 3 and x < 25

3 < x and x < 25

3 < x < 25

Thus, the range of possible values is 3 < x < 25.

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Each member would receive 0.8 pizza.we divided the number of pizzas (400) by the number of members (5) to get 8.

1. Divide the number of pizzas (4) by the number of members (5): 4 ÷ 5 = 0.8

2. Each member would receive 0.8 pizza.

Each member would receive 8 pizza.

1. Multiply the number of pizzas (4) by the number of members (100): 4 x 100 = 400

2. Divide the number of pizzas (400) by the number of members (5): 400 ÷ 5 = 8

3. Each member would receive 8 pizza.

If The Robotic team ordered 4 pizza and only 100 members showed up, each member would receive 8 pizza if the pizzas are shared equally. To calculate this, we first multiplied the number of pizzas (4) by the number of members (100) to get 400. Then, we divided the number of pizzas (400) by the number of members (5) to get 8. Therefore, each member would receive 8 pizza.

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The equation of the line that is parallel to 3y - x = - 12 and passes through (18, 2) will be 3y - x + 12 = 0.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation is given below.

3y - x = - 12

The equation of the line that is parallel to the given line is given as,

3y - x + d = 0

The equation that passes through (18, 2) will be given as,

3(2) - 18 + d = 0

6 - 18 + d = 0

d = 18 - 6

d = 12

Then the equation of the parallel line will be 3y - x + 12 = 0.

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Answer:

Step-by-step explanation:

no way to answer

The expression which can be rewritten as (x+7)(x - 1) as required in the task content is; Choice C; (x+3)²-16.

It follows from the task content that the expression which can be rewritten as ( x + 7 ) ( x - 1 ) be determined.

By polynomial expansion, the expression (x+7)(x - 1) can be written as;

x² + 7x - x - 7

= x² + 6x - 7.

By observation, it follows that the expression which seems to have a degree of 2 is; (x + 3)² - 16.

On this note, by checking; we have;

x² + 6x + 9 - 16

= x² + 6x - 7

Ultimately, the expression which could be rewritten as (x+7)(x - 1) and is to be identified is; Choice C; (x + 3)² - 16.

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The average rate of change of the given function is 20.

It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.

The average rate of change of a function f(x) over the interval [a,b] is given by the formula:

(f(b) - f(a)) / (b - a)

So, for the function f(x) = x² + 2 as x changes from 5 to 15, we can plug in the values to find the average rate of change:

(f(15) - f(5)) / (15 - 5) = (15² + 2 - 5² - 2) / (15 - 5) = (225 - 25) / 10 = 200 / 10 = 20

So the average rate of change of the function is 20.

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Answer:

y = 43, x = 23

Step-by-step explanation:

[tex]180 - 63 = 3y - 12\\117 = 3y - 12\\129 = 3y\\y = 43[/tex]

Supplementary angles add up to 180 and alternative angles (Z-pattern) are the same

[tex]180 - 63 = 5x + 2\\117 = 5x + 2\\115 = 5x\\x = 23[/tex]

The expression that shows time, t, it will now take Rashid to make the trip relative to the speed, v with which he slows down is t = (240 - (v/120) * 240) / (120 - v)

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

The relation between time, t, and the speed at which Rashid slows down, v, is given by the formula:

t = (240 - (v/120) * 240) / (120 - v)

t = time

v= speed.

This formula can be derived by using the distance formula (distance = speed x time) and the fact that the distance traveled is constant (240 km).

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