the 1-mile race is equal to how many feet?

The horizontal distance covered by the ball is 119.5 ft.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the height of a kicked ball can be modeled by the quadratic function h = - 0 .01x² + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet.

The horizontal distance covered by the ball will be calculated as,

h = - 0 .01x² + 1.18x + 2

Equate h to zero and solve for the distance x,

- 0.01x² + 1.18x + 2 = 0

Use the quadratic formula,

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

[tex]x = \dfrac{-1.18\om\sqrt{(1.18^2)-(4\times(-0.01)\times2}}{2\times-0.01}[/tex]

[tex]x=\dfrac{-1.18\pm\sqrt{1.4+0.08}}{-0.02}[/tex]

x = ( -1.18 - 1.21 ) / 0.02

x = 119.5 ft

The horizontal distance will be 119.5 ft.

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By using the given table we can find the two solutions of the equation:

f(x) = g(x)

are:

x = 1

x = 0.

Here we have a table for the functions f(x) and g(x), and we want to solve the equation:

f(x) = g(x)

So we just need to find a value of x, such that both functions have the same output.

To check that, just look at the table and find a row (horizontal line) where the values of f(x) and g(x) are the same ones.

If you look when x = 0, we have:

f(x) = 1

g(x) = 1

So x = 0 is a solution.

And for the next row, when x = 1.

f(x) = 0.25

g(x) = 0.25

So x = 1 is also a solution.

These are the two solutions to the given equation.

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In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

y = 10x, we can say that the algebraic equation represents "the value of y is twice the value of x.

Also, for the equation y = x + 10, we can say "the value of y is two more than the value of x.

Hence, In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.

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The point of intersection of a triangle's angle bisectors is known as the incentre.

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Answer:

no real solutions

Step-by-step explanation:

the easiest method would be to graph the equation and see how many intersection points with the x-axis there are; that represents the  number of solutions

when we graph the equation we first want to add 3 to each side of the equation to get the following:

y = 2x²-8x+11

what we see is that the parabola does not intersect the x-axis at all; therefore, there are no 'real' roots or solutions

Answer:

Step-by-step explanation:

x =(4-√24)/4=1-1/2√ 6 = -0.225.

The best method to apply in solving the given equation x² = 9 is the factorization method.

Factorisation is defined as the breaking or deterioration of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.

In x² = 9, we need to remove the power of 2 in order to separate just x.

This implies finding the square root √x² which is equal to x.

However, there are 2 possible answers to any square root, a positive or a negative answer.

x = √9

x = ± 3

0r we can solve this equation by the splitting method.

Rearrange the equation

x² = 9

(x - 3)(x + 3) = 0

On solving, we get

x = +3 and x = -3

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Answer:

A = 154 cm² , C = 44 cm

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

given r = 7 , then

A = [tex]\frac{22}{7}[/tex] × 7²

  = [tex]\frac{22}{7}[/tex] × 49

  = 22 × 7

  = 154 cm²

the circumference (C) of a circle is calculated as

C = 2πr

  = 2 × [tex]\frac{22}{7}[/tex] × 7

  = 2 × 22

  = 44 cm

The most common way to convert a base-2 number to base-3 number is to convert a base-2 number to decimal or base-10 number first then convert base-10 number to base-3 number. You actually can directly convert it to base-3 number, but it is more complicated to do.

There is two ways to convert base-2 number to decimal or base-10 number, using positional notation methods and doubling methods. Positional notation methods are done as follow:

       1     -   0  -   1   -  1   -  0   -   1

       2⁵       2⁴    2³    2²    2¹      2⁰

After we get base 10, then convert base-10 number to base-3 number like this:

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8.6 cm2 is the area of a triangle with a base of 4.8 cm and a height of 3.6 cm.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices.

According to our question-

Base: 4.8 cm.

Size = 3.6 cm

Area of triangle = base/height/half

= 1/2×4.8×3.6 cm^2

=8.6 cm^2.

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If the parent graph is made steeper or less steep (y = ½ x), the transformation is called a dilation.

And if the parent graph is changed so that it falls to the right instead of rising to the right (y = -x), the transformation is called a reflection.

If x is replaced by x/A in a formula and A>1, then the effect on the graph is to expand it by a factor of A in the x-direction (away from the y-axis). If A is between 0 and 1 then the effect on the graph is to contract by a factor of 1/A (towards the y-axis). We use the word "dilate'' to mean expand or contract.

f y is replaced by y/B in a formula and B>0, then the effect on the graph is to dilate it by a factor of B in the vertical direction. As before, this is an expansion or contraction depending on whether B is larger or smaller than one. Note that if we have a function y=f(x), replacing y by y/B is equivalent to multiplying the function on the right by B: y=Bf(x). The effect on the graph is to expand the picture away from the x-axis by a factor of B if B>1, to contract it toward the x-axis by a factor of 1/B if 0<B<1, and to dilate by |B| and then flip about the x-axis if B is negative.

When dilating a line, check if the center is on the line.  If the center lines on the line, the line remains the same.

The line whose equation is y = x + 3 is dilated by a scale factor of 2  centered at the origin. Write the equation of the line after the dilation.

M= 1 , b =3

0=0 +3

0 ≠ 3

center not on line

(0 ,3)→(0 ,6)        d2   y intercept

(1 ,4)→(2 ,8)        d2   y intercept

y = mx + b

y =x +6

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The Additive Inverse of 924 is -924

⇒ The number that, when added to 924, will result in a sum of zero is the additive inverse of 924. The formula to solve the issue where x is the additive inverse of 924 is as follows:

924 + x = 0

⇒ When we solve the preceding equation for x, we obtain x = -924. As a result, the answer to the question "What is the additive inverse of 924?" is -924.

∴Therefore Additive Inverse of 924 = -924

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The value of x in the line is 0.5 units and the value of y is 1.7 units.

The length of the lines are indicated on the diagram. The line below is bisected into two equal halves.

Therefore, let's find the value of x in the line segments.

5x + 8 = 21x

5x - 21x = -8

-16x = -8

divide both sides of the equation by -16

x = -8 / -16

x = 1 / 2

Therefore, let's find the value of y in the line segments.

20y - 2 = 17y + 3

20y - 17y = 3 + 2

3y = 5

divide both sides of the equation by 3

y = 5 / 3

y = 5 / 3 = 1.66666666667 = 1.7

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We can see here that in order to restore stuff, here are some steps to take:

Restoration is the process of returning an object or structure to its original condition or a close approximation of it. This can include cleaning, repairing, and/or preserving items such as furniture, antiques, artwork, historic buildings, and more.

The goal of restoration is to preserve the integrity of the item and maintain its historical or sentimental value. This process can include various techniques such as carpentry, metalworking, painting, and conservation.

To still restore a stuff,

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A multiple of 10 cannot be equals to a prime number. Multiple of 10 is always equals to a composite number.

As given in the question,

Multiple of a given number 10 are equals to :

10 , 20 , 30, 40, 50, ........, so on.

Prime number are those numbers which have only two factors one and the number itself.

Number 10 itself is not a prime number.

Factors of 10 are equals to :

1, 2, 5, 10

More than two factors.

All the Multiples of 10 cannot be a prime number as they have more than two factors.

Multiple of 10 represents the composite number.

Therefore, multiple of 10 cannot be equals to a prime number they are composite number.

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To write a function from a table of values, you can use the data in the table to determine the pattern or relationship between the input (x) and output (y) values. Once you have identified this pattern or relationship, you can use mathematical notation to express it as a function in the form of y = f(x).

For example, if you have a table of values that shows a linear relationship between x and y, you can use the slope-intercept form of a linear equation (y = mx + b) to write the function. You can use the values in the table to find the slope (m) and the y-intercept (b) and then plug them into the equation to get the function.

You may also use the interpolation method to estimate a function from a table of values with a non-linear relation.

It's helpful to plot the data points on a graph to help identify the pattern or relationship, and to check that the function you've written correctly represents the data in the table.

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Complete question is: How do you write a function from a table of values?

The two Ordered pairs given as (1,2) and (2 ,1) are not equal because the position of the elements in both the ordered pairs are not equal .

What are Ordered Pairs ?

The Pair of elements can be called as Ordered Pair if the pair of elements are written in specific order .

Two Ordered Pairs [tex](a_{1} ,b_{1} )[/tex] and [tex](a_{2} ,b_{2} )[/tex] are considered as equal if and only if the elements ; [tex]a_{1} =b_{1}[/tex] and [tex]a_{2} =b_{2}[/tex] .

The Ordered Pairs are given as : (1,2) and (2 ,1) ,

On comparing the elements of both the ordered pairs ,

we get that , [tex]1\neq 2[/tex] and [tex]2\neq 1[/tex] ,

Therefore , the ordered pairs (1,2) and (2 ,1) cannot be considered as equal ordered pairs .

The given question is incomplete , the complete question is

Are (1,2) and (2 ,1) equal Ordered Pairs ?

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Answer: For the first 30 hours, Andrew will earn 4 (30) = $120. For each additional hour beyond 30 that Andrew works, he will earn 5 (h - 30). Therefore, the function that gives Andrew's total wages when he works more than 30 hours is

Step-by-step explanation: For the first 30 hours, Andrew will earn 4(30) = $120.  For each additional hour beyond 30 that Andrew works, he will earn 5(h - 30).  Therefore, the function that gives Andrew's total wages when he works more than 30 hours is:

w = 120 + 5(h - 30).

So, if he works 35 hours, he will earn:

120 + 5(35 - 30) = 120 + 5(5) = 120 + 25 = $145.

If he works 42 hours, he will earn:

120 + 5(42 - 30) = 120 + 5(12) = 120 + 60 = $180.

I hope this helps!

To calculate the percent change in David's water intake from Tuesday to Wednesday, we can use the following formula:

percent change = (new value - old value) / old value * 100

In this case, the old value is the number of cups of water David drank on Tuesday (16 cups) and the new value is the number of cups of water he drank on Wednesday (12 cups).

Plugging these values into the formula:

percent change = (12 - 16) / 16 * 100 = -25%

So David's water intake decreased by 25% from Tuesday to Wednesday.



_______________


The original amount in the problem is the amount of water David drank on Tuesday, which is 16 cups.

It was given in the problem as the base value to calculate the percent change in David's water intake from Tuesday to Wednesday.
_____________
The change in David's water intake in this problem is the difference between the amount of water he drank on Tuesday and the amount of water he drank on Wednesday.

On Tuesday, he drank 16 cups of water, and on Wednesday, he drank 12 cups of water.

So the change in David's water intake is:

16 cups - 12 cups = 4 cups

David drank 4 cups less water on Wednesday than on Tuesday.

Step-by-step explanation:

The original amount is 16 cups.

The new amount is 12 cups.

The amount of change is the difference of the two:

Percent change is the change from the original amount:

This is a drop or decrease in percent.

Answer:

solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1

Step-by-step explanation:

To solve these simultaneous equations, we need to find the values of x and y that satisfy both equations.

Given:

y = x

y = x² - 6

We can substitute the first equation into the second:

x = x² - 6

we can subtract x from both sides to get:

0 = x² - 7x + 6

Then we can factor it:

(x-6)(x-1) = 0

Therefore x = 6 or x = 1

So the solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1

There are two solutions, (6,6) and (1,1)

When writing a piecewise function from a graph, the domain of each rule is determined by the x-values of the graph.

A piecewise function is a function that is defined by different rules for different ranges of the input (x-values). Each rule corresponds to a different interval of the domain.

To determine the domain of each rule when writing a piecewise function from a graph, you can use the following steps:

Identify the intervals of the x-axis where the graph changes behavior.

Write the domain of the function for each interval.

Write the rule for each interval of the domain.

For example, if a graph has a behavior change at x = 1, x = 3, and x = 5, then the domain of the function can be written as:

f(x) = {

y1, x < 1

y2, 1 ≤ x < 3

y3, 3 ≤ x < 5

y4, x ≥ 5

}

The domain for each rule is the interval of x-values between the changes in behavior. In this example, the first rule applies to x values less than 1, the second rule applies to x values between 1 and 3, the third rule applies to x values between 3 and 5, and the fourth rule applies to x values greater than or equal to 5.

Here, note that when writing a piecewise function, it is important to make sure that there are no gaps or overlaps in the domain of the function and that the x-values where the graph changes behavior are included in the domain of at least one of the rules.

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Answer:

The Mode Is:

7 and 4

Step-by-step explanation:

Both 7 and 4 shows up 3 times

Answer: 7 and 4

Step-by-step explanation: Mode is most reapeated

Using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.

In mathematics, a quantity or ratio known as A% stands for a percentage of 100.

There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.

To represent percentages, the symbol "%" is typically written after the number.

So, we know that:

The bond is $350.

The return is 125% when Greg turns 30.

Then, the amount after she turns 30 will be as follows:

350/100 * 125

437.5

Bonds value: 437.5 + 350 = $787.5

Therefore, using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.

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The required 15th term will be 19 given rules for a sequence.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The term-to-term rule for the sequence is to subtract 3 each time. If the 13th term is 25, we can use this rule to determine the 15th term.

We know that the 13th term is 25 and the rule is to subtract 3 each time, so:

13th term: 25

14th term: 25 - 3 = 22

15th term: 22 - 3 = 19

Therefore, the 15th term will be 19.

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The points that the cooking group leader did label are (0,15) and (30,0). Thus, the correct answer is C.

As your first step, find the function that best represents x and y:

Hence, the function is:

The group leader labeled (0,15) on the y-axis, which means that when the number of small jars is 0, the group can use 15 large jars. This means that 15 large jars can hold 240 oz of spaghetti sauce, which is true since:

The group leader also labeled (30,0) on the x-axis, which means that when the number of large jars is 0, the group can use 30 small jars. This means that 30 small jars can hold 240 oz of spaghetti sauce, which is true since:

The function that represents this line is 8x + 16y = 240, where x is the number of small jars and y is the number of large jars. The line passes through (0,15) and (30,0) as the two intercepts.

This question should be written as:

A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts. Which points did the group leader label?

The correct answer is C.

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The triangle with sides 25cm, 5cm and 24cm is not a right triangle.

Now, According to the question:

Let us assume that :

ABC is a right triangle,

A = 25cm

B = 5 cm

C = 24 cm

We have to find if the given sides of a triangle form a right triangle.

By using Pythagoras theorem for a right triangle,

[tex]A^2 = B^2+C^2[/tex]

[tex](25)^2 = (5)^2 + (24)^2[/tex]

LHS:[tex](5)^2 + (24)^2[/tex]

= 25 + 576

= 601

RHS:[tex](25)^2[/tex]

= 625

LHS ≠ RHS

Since, the Pythagorean theorem does not apply, the given sides do not form a right triangle.

Therefore, the triangle with sides 25cm, 5cm and 24cm is not a right triangle.

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Answer: B (-9, -3, 0, 5, 7)

Step-by-step explanation:

Answer:

d) b+b+3c and 2b+3c

Step-by-step explanation:

b+b=2b

2b+3c=2b+3c

Sometimes we are given exponential equations with different bases on the terms. In order to solve exponential functions with different bases we must know logarithms and how to use them with exponentiation. We can access variables within an exponent in exponential equations with different bases by using logarithms and the power rule of logarithms to get rid of the base and have just the exponent.

Exponential equation is an equation whose power or base number (base) and power contains a variable.

An example of an exponential equation:

32^x-3 = 81^x+5   →   the exponential equation with the power contains the variable x

(2x - 5)^x = (2x - 5)^3x-4  →  the exponential equation with bases and powers contains the variable x

So, in the exponential equation, it can only be the exponent that contains the variable or it can also be the base and the exponent that contain the variable. This variable is denoted by a letter, it can be from a to z. But, in general, the variable symbol that is often used in questions is the letter x.

The solution to the exponential equation is the set of all x values that satisfy the exponential equation, or we can also call it a set of solutions. So, how to solve the exponential equation varies depending on the form of the equation. The two examples of equations above are two of several forms of existing exponential equations. This means that there are still other forms of exponential equations and each equation has its own way of solving it

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The likelihood that all three marbles selected will be red is 0.0588 to the nearest 1000th.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

Total number of marbles=7+6+5

=18

the probability, to the nearest 1000th, that all three marbles drawn will be red,

=(7/18)*(7/18)*(7/18)

=0.0588

The probability, to the nearest 1000th, that all three marbles drawn will be red is 0.0588.

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