how do i find the surface area and volume of this shape?

The nature of the roots for the equation ax² + bx + c is

α + β = -b/a and αβ = c/a

where α and β are the two roots of the equation.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A quadratic equation ax² + bx + c.

Now,

There will be two roots of the equation α and β,

Now,

The nature of the roots are

α + β  = -b/a

αβ = c/a

Thus,

The roots are α and β and α + β = -b/a and αβ = c/a.

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The nature of roots of quadratic depends on its discriminant, formula is D=√(b²-4ac).

It is the value of the unknown variable for which the quadratic equation holds true. Its nature can be real, imaginary, rational, irrational, equal and unequal as well that depends on the value of the discriminant.

For equation ax²+ bx + c =0 , expression b²- 4ac is called discriminant  and denoted by D.

Given equation is ,  ax²+ bx + c =0

then, according to quadratic formula for the roots of quadratic equation

x = {-b±√(b²-4ac)}/4ac

Let us take a real number

k > 0

√k can be defined and is a positive quantity  but √-k can not be defined.

The quantity which is under square root in the expression for roots is

b²-4ac, which is called discriminant of the quadratic equation. It is represented by D.

If D>0 and is perfect square then the equation will have two real, rational and distinct roots.

If D>0 and is not a perfect square then the equation will have two real, irrational and distinct roots.

If D=0 the equation will have two real and equal roots.

If D<0, the equation will have no real roots.

Hence, nature of roots formula for quadratic equation depends on the value of √b²-4ac.

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78 ft is the total length of the 3 cables.

Given data :

[tex]24^{2}[/tex]+[tex]10^{2}[/tex] =  [tex]d^{2}[/tex]

576  +100 = [tex]d^{2}[/tex]

676 = [tex]d^{2}[/tex]

d = 26

d = 26 is the length of the cable.

3 x 26 = 78 ft is the total length of the 3 cables.

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There is about a 7.3% probability that it will take Zach 555 or more throws to score his first ringer.

To solve this problem, we can use a geometric distribution, which models the number of trials it takes to get a success in a series of independent Bernoulli trials (trials with two outcomes: success or failure) with a fixed probability of success.

In this case, the probability of success is 40% (the probability of scoring a ringer), and the probability of failure is 60% (the probability of not scoring a ringer). We can use the formula for the probability mass function of a geometric distribution to calculate the probability that it takes Zach 555 or more throws to score his first ringer:

P(X ≥ 555) = 1 - P(X < 555)

= 1 - (P(X = 1) + P(X = 2) + ... + P(X = 554))

= 1 - (0.4 + (0.4 * 0.6) + (0.4 * 0.6^2) + ... + (0.4 * 0.6^554))

To calculate this probability, we can use a computer to sum up the series, or we can use a calculator with a geometric distribution function. Using a calculator, we get P(X ≥ 555) ≈ 0.073, or about 7.3%.

This means that there is about a 7.3% probability that it will take Zach 555 or more throws to score his first ringer.

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In this case, the probability of success is 40% (the probability of scoring a ringer), and the probability of failure is 60% (the probability of not scoring a ringer). We can use the formula for the probability mass function of a geometric distribution to calculate the probability that it takes Zach 555 or more throws to score his first ringer:

P(X ≥ 555) = 1 - P(X < 555)

= 1 - (P(X = 1) + P(X = 2) + ... + P(X = 554))

= 1 - (0.4 + (0.4 * 0.6) + (0.4 * 0.6^2) + ... + (0.4 * 0.6^554))

To calculate this probability, we can use a computer to sum up the series, or we can use a calculator with a geometric distribution function. Using a calculator, we get P(X ≥ 555) ≈ 0.073, or about 7.3%.

Answer: you should expect 218,750 tons of pollutants from City B.

Step-by-step explanation:

When two variables vary "directly", it means that they fit into the equation y=mx, where y varies directly with x, with the multiplier m to be determined by the information you are given.

For this problem, P (pollutants) varies directly with N (people) so the equation is P=mN for their relation.

You are given that City A has P = 260,000 tons of pollutants and N = 416,000 people. Plug these into the equation above (P=mN) and you get 260,000=(m)(416,000). If we divide each side by 416,000, you get that m=0.625. So now you have the multiplier for your equation: P=(0.625)N.

Use the complete equation now to find out how many P (pollutants) City B will produce.

P=(0.625)N

P=(0.625)(350,000)      [[350,000 was the given "N" or amount of people in City B]]

P=218,750 tons of pollutants

Answer:

look this up next time..with this said, obtuse

Step-by-step explanation:

If Francisco wins 650.16 per month, he will earn a total of 7,801.92 per annum. Note that this is a multiplication exercise.

It is to be noted that Multiplication is a mathematical operation that involves multiplying two or more numbers together. It is often represented using the symbol "x" or "*".

Since there are 12 months in a year,  and Francisco earns 650.16 per annum,

Hence,

12 x 650.16 = 7,801.92

Thus, it is correct to state that where Francisco gets 650.16 per month, by the year's end, he will have earned a total of 7,801.92.

Note that Per Year and Per Annum are synonyms and can be used interchangeably.

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Answer:

1/15

step by step

divide both numerator and denominator by 2

2÷2=1

30÷2=15

Answer: $9.45

Step-by-step explanation:

The first cup is $3.95

2 refills are $1.50 times 2 = $3

A bagel is $3

3.95+3+3 - 0.50 = $ 9.45

Answer:

$9.45

Step-by-step explanation:

add 3.95, 1.50, 1.50, and 3.00, then subtract the $.50 and you get 9.45

the graphing system of linear inequalities of two variables are bounded by solid line or dashed line.

The linear inequalities of two variables are the mathematical expressions denoted by greater than > or less than< or combination of ≤ or ≥ between two algebraic terms.

the way we solve linear inequalities are same as the way in how we solve linear equation. The graph of linear inequalities of two variables are bounded by solid line or dashed line depending on the unequal sign presented.

hence, there is a difference between the graph of linear equation and linear inequalities.

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The required total number of Lucy's coins,when we have 15% of quarter coins are 80.

percentage, a general worth demonstrating 100th pieces of any amount. One percent (represented 1%) is a hundredth part; in this way, 100% addresses the total and 200 percent determines two times the given amount. rate.

Quarters coins = 12

Let x be total number of coins Lucy has,then

15% of x = 12

15x/100 = 12

x = 1200/15

x = 80 coins

Thus, there are 80 coins in total.

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The point on the ellipse that is farthest from the origin will be the point that is closest to one of the foci.

To find the points on the ellipse that are nearest to and farthest from the origin, we need to consider the equation of the paraboloid and the equation of the ellipse.

The equation of a paraboloid is given by:

[tex]z = ax^2 + by^2 + c[/tex]

where a, b, and c are constants.

The equation of an ellipse is given by:

[tex](\frac{x}{a})^2 + (\frac{y}{b})^2 = 1[/tex]

where a and b are the semi-major and semi-minor axes of the ellipse, respectively.

If the plane intersects the paraboloid in an ellipse, then the equations of the paraboloid and the ellipse must be equal at the points of intersection. Therefore, we can set the equation of the paraboloid equal to the equation of the ellipse and solve for the x and y values.

[tex]z = ax^2 + by^2 + c[/tex]

[tex](\frac{x}{a})^2 + (\frac{y}{b})^2 = 1[/tex]

Substituting the equation of the paraboloid into the equation of the ellipse, we get:

[tex](\frac{x}{a})^2 + (\frac{y}{b})^2+c = 1[/tex]

We can then solve this equation for the values of x and y that correspond to the points on the ellipse that are nearest to and farthest from the origin.

The point farthest away from the origin occurs at the point on the ellipse that is farthest from the center, which is called the "foci" of the ellipse. The distance from the center of the ellipse to the foci is called the "eccentricity" of the ellipse. The eccentricity is denoted by the letter "e" and is calculated using the following formula:

[tex]e = \frac{\sqrt{(a^2 - b^2)}}{a}[/tex]

where a and b are the semi-major and semi-minor axes of the ellipse, respectively.

Therefore, to find the point on the ellipse that is farthest from the origin, we need to calculate the eccentricity of the ellipse and then use this value to determine the location of the foci. The point on the ellipse that is farthest from the origin will be the point that is closest to one of the foci.

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The domain and the range of this function shown in the graph include the following;

In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: Each interval on this graph represent 1 unit and the less than or equal to (≤) would be used because the dotted point is shaded (closed).

By critically observing the graph shown above, we can reasonably and logically deduce the following:

Domain = -5 ≤ x < 1 or [-5, 1].

Range = -4 ≤ y < 7 or [-4, 7].

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Answer:

Step-by-step explanation:

You want to know the pay for a paper route and dog walking if 2 days' paper route pay and 3 days' dog walking pay will total half of $110, while dog walking pays $5 less than the paper route.

Let p represent the pay for a day's pay for the paper route. Then (p-5) is the day's pay for dog walking. The total pay is ...

  2p +3(p -5) = 110/2

Simplifying the equation, we have ...

  5p -15 = 55

  p -3 = 11 . . . . . . . . divide by 5

  p = 14 . . . . . . . . add 3

  p -5 = 14 -5 = 9 . . . . . pay for dog walking

The paper route and dog walking pay 14 and 9 dollars per day, respectively.

__

Additional comment

We could write two equations, and solve by substitution. We would get the same single equation by doing that. In this solution method, it works well to let the variable represent the largest contributor (highest pay).

We could also solve the two equations by any of several other methods. The attached graph shows the solution by graphing.

The assumed mean method is used to determine the mean or arithmetic mean of grouped data. If there is a large amount of data available, this method is suggested over calculating the mean directly.

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

           A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                   Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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Taking the function given in the question [tex]f(x) = \frac{10}{x^{2} +1}[/tex] , there are no vertical asymptotes since there no any real values for x , which makes the function undefined.

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.

To calculate the vetical asymptotes of a function simply equate the denominator of the equation to zero , which when solved gives the values of x at which the function is undefined. Thus the obtained values of x are the vertical asymptotes to the given function.

In the given function f(x), let's equate the denominator to zero to find the vertical asymptotes,

[tex]x^{2} +1 =0[/tex]

Solving the above equation, we get

x = [tex]\sqrt{-1}[/tex]

which is imaginary, hence there is no vertical asymptote for the given function.

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Using the SAS(Side-Angle-Side) Theorem, ASA(Angle-Side-Angle) Theorem, SSS(Side-Side-Side) Theorem and AA(Angle-Angle) Theorem we can easily prove that two triangles are similar.

When the sides and angles of two triangles match, the triangles are said to be congruent. When the angles of two triangles match, the triangles are said to be similar. Thus, two triangles can be superimposed side to side and angle to angle.

Hence, when the sides and angles of two triangles match that triangle is congruent and When the angles of two triangles match that triangle is similar.

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The product is 225.

Augmentation is an activity that addresses the fundamental thought of rehashed expansion of a similar number. The numbers that are multiplied are referred to as the factors, and the result that is produced when two or more numbers are multiplied together is referred to as the product of those numbers. Repeated addition of the same number can be made easier by using multiplication.

Given 15 x 15

the product can be done in many ways,

like add 15times 15 we get the answer,

or 15 is written as 10 + 5

so (10 + 5) x 15

10 x 15 + 5 x 15

150 + 75 = 225

Therefore, 15 x 15 is  225

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The sailboat and the medical aid should meet at the points

(0, 7) and (5, 12).

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

The intersection point between the two graphs y = - x² + 6x + 7 and y = x + 7 is the point where they meet each other.

Now, For the equation y = - x² + 6x + 7,

When x = 0, y = 7 ⇒ (0, 7).

when x = 1, y = 12 ⇒ (1, 12).

Now for y = x + 7,

when x = 1, y = 8 ⇒ (1, 8).

when x = 2, y =9 ⇒ (2, 9).

Now by taking the graph paper with each box of 1 square unit will plot these points and we obtain that at (0, 7) and (5, 12) these graphs intersect each other.

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S angle is equal to 118°,Professor Delta was shooting hoops in the gym.

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Using the vertical line test, there are only two graphs that represent functions (graph function): graph, 1 and graph 6.

A graph function is a graph that represents a function on a coordinate plane, which means that every point on the graph fulfills the function equation. In a graph function, an x corresponds to only one y.

If we want to know whether a graph represents a function or not, we can perform a vertical line test. In this test, we can drag a vertical line from left to right on the graph. If the vertical line intersects with the graph at one point at a time, then it's a function.

Otherwise, if the vertical line intersects with the graph at two or more points at a time, then it's not a function. It could happen when an x value gives two or more y values (1 input results in multiple outputs), which means the graph is not a function.

Now we take a look at the given picture.

Graph 1: when we drag a vertical line from left to right on the graph, it intersects with the graph at one point at a time. So yes, the graph represents a function.

Graph 2: when we drag a vertical line from left to right on the graph, it intersects with the graph at two points. So no, the graph doesn't represent a function.

Graph 3: when we drag a vertical line from left to right on the graph, it intersects with the graph at one point at first. But later on, it crosses two points in the graph. So no, the graph doesn't represent a function.

Graph 4: when we drag a vertical line from left to right on the graph, it intersects with the graph at two points. So no, the graph doesn't represent a function.

Graph 5: when we drag a vertical line from left to right on the graph, it also intersects with the graph at two points. So no, the graph doesn't represent a function.

Graph 6: when we drag a vertical line from left to right on the graph, it intersects with the graph at one point at a time. So yes, the graph represents a function.

So there are only two graphs that represent functions: graph, 1 and graph 6 since the other graphs fail the vertical line test.

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The required lengths of side of triangle are 15 in, 16 in and 17 in.

Given :

The sum of the angles of a triangle is always 180°

Given that :

Sides of a triangle are consecutive integers.

Also given that,

Perimeter of triangle is 48.

Let the sides of triangle are x, x + 1 and x + 2.

x + x + 1 + x + 2 = 48

3x = 48 - 3

3x = 45

divide by 3 on both sides

x = 15

The length of the triangles  

x + 1 = 15 + 1 = 16

x + 2 = 15 + 4 = 17

The side lengths of the triangle are 15, 16 and 17.

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Answer:

YZ = 20 cm

Step-by-step explanation:

Δ XYZ and Δ CBA are similar ( AA postulate )

The corresponding sides are then in proportion , that is

[tex]\frac{YZ}{BA}[/tex] = [tex]\frac{XY}{CB}[/tex] ( substitute values )

[tex]\frac{YZ}{8}[/tex] = [tex]\frac{25}{10}[/tex] = 2.5 ( multiply both sides by 8 )

YZ = 8 × 2.5 = 20 cm

Answer:

4700 workers

Step-by-step explanation:

We know that 60% of the worker are men

1880 people work for the company who aren't men

100% - 60% = 40%

40% of workers =  1880

40% = 0.4

If 0.4 = 1880

100% of the workers x

100% = 1

We have equations

0.4 = 1880

1 = x

Cross multiply

0.4x = 1880

Divided both sides by 0.4

x = 4700 workers total

To find the number of men workers, we take

4700 - 1880 = 2820 men workers

So, there are a total of 4700 workers!

1880 women workers & 2820 men workers!

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Answer:

60% are men. 40% women

x - amount of men, 1 880 amount of women

60:x = 40:1 880

40x = 60(1 880)

40x = 112 800

x = 2 820

Percentage = Rate / Base

= 1 880 / (1 - 0.60)    (1-0.60 to find out the percent of not men)

= 1 880 / 0.40

= 4 700

Women: 4 700 * 0.4 = 1 880    (this statement is true)

Men: 4 700 * 0.6 = 2 820       (therefore, it is too)

Step-by-step explanation:

The number of terms in the expression 5xy² 3xyz is 1.

Various parts of an algebraic expression , which are separated by + or – are called terms of the algebraic expression.

Calculation:

The given expression 5xy²3xyz.

Step 1: Write down the given expression    

          The given expression is 5xy²3xyz.

Step 2: Find number of terms in the expression

We know that Various parts of an algebric expression , which are separated by + or – are called terms of the algebric expression.

In the expressions the term is 5xy²3xyz.

Hence number of terms in the expression 5xy²3xyz is 1.

The number of terms in the expression 5xy² 3xyz is 1.

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No, the range and the domain are very different concepts because the domain is just a collection of natural numbers, whereas the output values are referred to as the range.

A function's authorized range of values is known as its domain. The x values in a function like f make up this set (x). A function's range is the collection of values that it can take as input. When we enter an x value, the function outputs this set of values.

here

The set of all feasible function inputs is known as a function's domain. The function f(x) = 2x can be represented by this box.

The domain is the set of all natural numbers when x = 11, 12, 13, 14, etc.,  the values that are returned are referred to as the range.

No, the range and the domain are very different concepts .

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The mean for the discrete probability distribution is 3.73

Generally, To calculate the mean of a discrete probability distribution, you can use the formula:

Mean = ∑x * P(x)

Using this formula, the mean of the given distribution is:

Mean = (2 * 0.2) + (6 * 0.3) + (10 * 0.3) + (14 * 0.2) = 4

To calculate the standard deviation of a discrete probability distribution, you can use the formula:

Standard Deviation = √∑(x - mean)^2 * P(x)

Using this formula and the mean that we calculated above, the standard deviation of the given distribution is:

Standard Deviation = √( (2 - 4)^2 * 0.2 + (6 - 4)^2 * 0.3 + (10 - 4)^2 * 0.3 + (14 - 4)^2 * 0.2 )

= √( (-2)^2 * 0.2 + (2)^2 * 0.3 + (6)^2 * 0.3 + (10)^2 * 0.2 )

= √( 4 * 0.2 + 4 * 0.3 + 36 * 0.3 + 100 * 0.2 )

= √( 0.8 + 1.2 + 10.8 + 20 ) = √( 13.8 )

= approximately 3.73

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Theorems apply for equilateral triangles are theorem 1 and 2, In theorem 1 each angle of an equilateral triangle is the same and measures 60 degrees each while in theorem 2 a triangle is said to be equilateral if and only if it is equiangular.

Theorem can be defined as  a statement which has been proved true by a special kind of logical argument called a rigorous proof.

There are different types of theorem such as:

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Answer:6

Step-by-step explanation: 2 1/4 is a mixed fraction and needs to be changed into an improper fraction:

The whole number 2 is multiplied by the denominator 4 which gives 8 and we add 1 from the numerator this gives 9 and we put this over the denominator 9/4

9/4÷3/8=

The first fraction stays the same and we flip over the second fraction and use the multiplication sign in between

9/4 x 8/3=72/12=6

The tops of the fractions are multiplied together to give 72

The bottoms of the fractions are multiplied together to give 12

Answer:

If you are refering to the 4th in a sequence being 3/5 the first.

3/5, 6/10, 12/20, 24/40

24/40 would be your answer.

If you are looking for 3/5 in 4ths

2.4/4

The 3 ways to prove similarity are Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).

The three theorems are as follows :

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