write the equation in standard form for the circle with center (5,0) passing through (5, 9/2)

Answer:

Y=x^2+7x-3

complete the square to re-write the quadratic function in vertex form.

pls help

Step-by-step explanation:

To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.

y = x^2 + 7x - 3

y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)

y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)

y = (x + 7/2)^2 - 49/4 - 3

y = (x + 7/2)^2 - 61/4

So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

We have,

To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.

First, let's calculate the weight of the water in the pool.

The weight of an object is given by the formula:

Weight = mass x gravitational acceleration

Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.

The volume of the pool is given by the formula:

Volume = length x width x depth

Volume = 50 ft x 30 ft x 6 ft = 9000 ft³

Now, let's calculate the weight of the water:

Weight = density x volume x gravitational acceleration

Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb

To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.

The work required to pump the water out is given by the formula:

Work = weight x height

Work = 290,400 lb x 8 ft = 2,323,200 ft-lb

Therefore,

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

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Ryan makes a profit of £240.  the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

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Answer:

112°

Step-by-step explanation:

Finding the unknown angle in a quadrilateral:

        Sum of all angles of a quadrilateral = 360

                                      a + 49 + 72 + 127 = 360

                                                     a + 248  = 360

                                                                a = 360 - 248

                                                                a = 112°

The slope between the points (-3, 0) and (0, -1) is -1/3.

The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.

Let us consider the first two points (-3, 0) and (0, -1).

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

Substituting the values we have:

m = (-1 - 0) / (0 - (-3)) = -1/3

Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.

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Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation:

Answer:

10 sides

Step-by-step explanation:

We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:

S = (n - 2) x 180 degrees

If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:

1440 = (n - 2) x 180

Dividing both sides by 180, we get:

8 = n - 2

Adding 2 to both sides, we get:

n = 10

Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.

The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.

The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.

z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.

z = {x-μ}/{σ}  = {-20-0}/{8}  = −2.5

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.

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The zeroes of the function are -12 and 5.

Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.

According to the question:

To find the zeros of the function

f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.

So we start with the equation:

x² + 7x - 60 = 0

Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:

x² + 7x - 60 = (x + 12)(x - 5) = 0

Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:

x + 12 = 0 or x - 5 = 0

Solving for x, we get:

x = -12 or x = 5

The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.

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Jen has 54 pages left to read to meet her assignment requirement.

The inequality that represents this situation is p ≥ 85 - 31

To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.

The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:

p = 85 - 31

p = 54

Therefore, Jen has 54 pages left to read.

To represent this situation with an inequality, we can use:

p ≥ 85 - 31

This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).

Solving for p:

p ≥ 85 - 31

p ≥ 54

This means that Jen must read at least 54 more pages to meet her assignment requirement.

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Option (A) x+1 is a positive odd integer.

Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.

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Answer:

circumference=50.24

Step-by-step explanation:

c=2x3.14xr

c=2x3.14x(8)

c=50.24

the answer to the problem that you need to is 1024

The given numbers are in decimal and binary system and the final result of the given operation is [tex](4675.31)_{10}[/tex].

A binary integer (base-2) is converted to an equivalent decimal number using the binary to decimal conversion formula. (base-10). In mathematics, integers are expressed using a number system. It is a method to display numerical data. The four various numeral systems are as follows:

System of Binary Numbers (Base-2)
system of octal numbers (Base-8)
System of Decimal Numbers (Base-10)
System of Hexadecimal Numbers (Base-16).
We are the two numbers:-

[tex](4623.56)_{10} , (110011.11)_{2}[/tex]

these are in decimal and binary system respectively.

now, we will express them in same system ( here we choose decimal system).

[tex](110011.11)_{2} = (2^{5} + 2^{4} + 0 + 0 + 2^{1} + 2^{0} + 2^{-1} + 2^{-2} )_{10} \\= (2^{5}+2^{4}+0*2^{4}+0*2^{3}+2^{1}+2^{0}+2^{-1}+2^{-2})_{10} \\= (32+16+2+1+0.5+0.25)_{10} \\= (51.75)_{10}[/tex]

Now, addition is done below:-

4623.56+51.75= 4675.31.

hence, the final result of the given operation= [tex](4675.31)_{10}[/tex]

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The upper bound of a + b can be found by adding the upper bounds of a and b.

For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.

For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.

So the upper bound of a + b is:

5.5 + 3.5 = 9

Therefore, the upper bound of a + b is 9cm.

Probability of D2 being sunny = 0.78.

On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.

Therefore, we need to find the chances that D2 is sunny.

There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.

Now, Let us find the probability of D2 being sunny.

We have the following possible cases for D2.

D1 = Sunny; D2 = Sunny

D1 = Sunny; D2 = Rainy

D1 = Rainy; D2 = Sunny

D1 = Rainy; D2 = Rainy

The probability of D1 being sunny is 0.9.

When a sunny day follows a sunny day, the probability is 0.8.

When a sunny day follows a rainy day, the probability is 0.6.

Therefore, the probability of D2 being sunny is given by the formula:

Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.

Therefore, the probability that D2 is sunny are 0.78 or 78%.

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Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Step-by-step explanation:

Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.

In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.

The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:

[tex]nCk = n! / (k! *(n-k)!)[/tex]

where n! denotes the factorial of n, i.e., the product of all positive integers up to n.

by the question.

Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:

[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]

Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]

Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).

Since a_i >= 4 for i=1, we have:

[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]

Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:

[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]

This gives us:

[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]

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The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.

Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

Give a short note on Median?

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

The smallest number in the data set that is not an outlier: 15

The median of the first half of the data set: 17

The median of the entire data set: 20.5

The median of the second half of the data set: 22

The largest number in the data set that is not an outlier: 35

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

The parabolic trajectory of the falling prey can be described by the equation y = 228 – x2/57, where y is the height above the ground and x is the horizontal distance traveled in meters. In this case, the prey was dropped at a height of 228 m and flying at 19 m/s. To calculate the total distance traveled by the prey, we can use the equation for the parabola to solve for x.

We can rearrange the equation y = 228 – x2/57 to solve for x, which gives us[tex]x = √(57*(228 – y))[/tex]. When the prey hits the ground, the height (y) is 0. Plugging this into the equation for x, we can calculate that the total distance traveled by the prey is[tex]x = √(57*(228 - 0)) = √(57*228) = 84.9 m.\\[/tex] Expressing this answer to the nearest tenth of a meter gives us the final answer of 84.9 m.

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Answer:

3x, 4x | 5, 3

Step-by-step explanation:

The value of the unknown lengths in these similar triangles is FH is 6.67 units and EG is 27 units.

A triangle is a polygon with three sides and three angles. It is a two-dimensional shape that is commonly studied in mathematics, geometry, and other fields. The sum of the angles in a triangle is always 180 degrees, and the lengths of the sides can vary. Triangles can be classified based on the lengths of their sides and the measures of their angles. Common types of triangles include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many important properties and are used in various applications, including construction, engineering, and physics.

Here,

1. Let x be the length of FH. We have:

AB/EF = BD/FH

12/8 = 10/x

Cross-multiplying, we get:

12x = 80

x = 80/12

x ≈ 6.67

Therefore, FH ≈ 6.67.

2. Let y be the length of EG. We have:

AC/BD = FH/EG

15/9 = 5/y

Cross-multiplying, we get:

5y = 135

y = 135/5

y ≈ 27

Therefore, EG ≈ 27.

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Answer:

x = 4

Step-by-step explanation:

Alternative interior angles means these angles are equal in magnitude and sign

[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]

In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.

According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.

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In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.

The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.

Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.

Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.

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Answer:

If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:

4 tires * 160,000 km = 640,000 km

If Mavis drives 25,000 km in a year, she will need to replace her tires after:

640,000 km ÷ 25,000 km/year = 25.6 years

Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:

$140.00/tire * 4 tires = $560.00

So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.

Step-by-step explanation:

source: trust me bro

The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.

The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.

The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.

A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.

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