Write a quadratic function in standard form to represent the data in the table.
X=2,4,6,8,10
Y=3,1,3,9,18

Answer:

A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)

Step-by-step explanation:

You would take three fourths of each coordinate to get the x and y values.

Answer:

A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)

Step-by-step explanation:

You would take three fourths of each coordinate to get the x and y values.

Answer:

Step-by-step explanation:

Answer: The first box in the model is 60. The box above it is 300. The box above 20 is 70. The answer is 74.

Step-by-step explanation: Self-explanatory.

The dilated polygon and polygon are created. And the scale factor of the polygon STUVWXYZ to JKLMNOPQ will be 9.

Dilation is the methodology of expanding the dimensions of an object without impacting its appearance.

The coordinate of the polygon ABCDEFGH is given as,

(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)

a) If the scale factor is 3, then the coordinate of the polygon JKLMNOPQ is given as,

⇒ 3 [(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)]

⇒ (9, -9), (12, -12), (15, -9), (24, -18), (30, -12), (27, -9), (24, -12), (15, -3)

b) If the scale factor is 1/3, then the coordinate of the polygon STUVWXYZ is given as,

⇒ 1/3 x [(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)]

⇒ (1, -1), (4/3, -4/3), (5/3, -1), (8/3, -2), (10/3, -4/3), (3, -1), (8/3, -4/3), (5/3, -1/3)

c) The polygon JKLMNOPQ and STUVWXYZ are similar. Then the scale factor is given as,

Scale factor = 9/1

Scale factor = 9

The diagram is given below.

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Answer:

x = 5 + [tex]\sqrt{7}[/tex]

x = 5 - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

The given quadratic equation is:

x^2 - 10x + 18 = 0

We can solve this equation using the quadratic formula, which states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -10, and c = 18. Substituting these values into the quadratic formula, we get:

x = (-(-10) ± sqrt((-10)^2 - 4(1)(18))) / 2(1)

Simplifying the expression inside the square root, we get:

x = (10 ± sqrt(100 - 72)) / 2

x = (10 ± sqrt(28)) / 2

x = (10 ± 2sqrt(7)) / 2

Simplifying further, we get:

x = 5 ± [tex]\sqrt{7}[/tex]

[tex]9x^2-6x+1=2 \iff (3x)^2-2(3x)+1=2\\[/tex]

[tex](3x - 1)^2 = 2[/tex]

[tex]3x-1=-\sqrt{2} \iff 3x = 1 - \sqrt{2} \implies x_{1} = \dfrac{1-\sqrt{2} }{3}\\[/tex]

[tex]3x-1=\sqrt{2} \iff 3x = 1 + \sqrt{2} \implies x_{2} = \dfrac{1+\sqrt{2} }{3}\\[/tex]

[tex](-0.14, \ 0.8)[/tex]

There is a 2.28% chance that more than 250 books were borrowed in a week.

Probability can also be calculated using other methods, such as counting techniques and probability distributions. Probability distributions provide a way to model the behavior of random events and describe the likelihood of different outcomes occurring.

Probability has many applications in fields such as statistics, finance, engineering, and science. It is used to make predictions, analyze data, and make decisions based on uncertain information. Understanding probability is an important skill for many professions, as it allows individuals to make informed decisions and assess risk.

To solve this problem, we need to use the standard normal distribution and calculate the z-score.

First, we find the z-score:

z = (x - μ) / σ

z = (250 - 190) / 30

z = 2

We can then use a standard normal distribution table or calculator to find the probability of getting a z-score of 2 or higher.

Using a standard normal distribution table, we find that the probability of getting a z-score of 2 or higher is approximately 0.0228.

To convert this to a percentage, we multiply by 100:

0.0228 x 100 = 2.28%

Therefore, there is a 2.28% chance that more than 250 books were borrowed in a week.

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The complete question is:

The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a % chance that more than 250 books were borrowed in a week.

A linear equation in the form p = mn + b that gives the price they can charge for n shirts is p = -0.003x + 22.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (1000, 19), a linear function in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 19 = (16 - 19)/(2000 - 1000)(x - 1,000)

y - 19 = -0.003(x - 1,000)

y = -0.003x + 3 + 19

p = y = -0.003x + 22

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Measure of angle B is 40 degree

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.

From the figure,

As △ABC is inscribed in the circle, the points  A , B and C   lie on the circumference of the circle .

As  O  is the center of the circle.

Given , angle (BAC) is 50 degree

We know, a triangle drawn from two ends of a diameter of a circle makes an angle of 90° at the circumference.

so, angle (ACB) is 90 degree

Now, in triangle ABC

[tex]\angle ABC +\angle BCA +\angle BAC =180^0\\[/tex]

[tex]\angle B + 90^0 +50^0 = 180^0\\[/tex]

[tex]\angle B =40^0[/tex]

Hence, [tex]\angle B = 40^0[/tex]

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The function that is non-linear is function D.

A function is linear if its graph is represented by a straight line, and that line is usually written as:

ax + by = c

Where x is the horizontal variable and y the vertical variable.

For example, here we can see that A, B, and C are represented by straight lines, thus, these are linear functions.

But if you look at graph D, you can see that it is not linear, it's shape is like an "M", so that is the non-linear function.

The correct option is D.

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Answer:

Have a good day and time and I6ykjjuu7ttggfszd to the 5tjyyv

By answering the above question, we may infer that Hence, the probability likelihood is 0.2752. (rounded to four decimal places).

Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.

We may utilize the complement of the CDF to respond to this query.

For x 0, the complement of the CDF is defined as 1 - F(x) = e(-x).

Thus, the likelihood that an old ICU patient will be there for more than five days is as follows:

[tex]1 - F(5) = e^(-0.3030 * 5) = 0.2052[/tex]

Hence, the likelihood is 0.2052. (rounded to four decimal places).

We may utilize the difference between the CDF at two distinct values to get an answer to this query.

The likelihood that an old ICU patient will be there for two to four days is as follows:

[tex]F(4) - F(2) = (1 - e^(-0.3030 * 4)) - (1 - e^(-0.3030 * 2)) = e^(-0.3030 * 2) - e^(-0.3030 * 4) = 0.2752[/tex]

Hence, the likelihood is 0.2752. (rounded to four decimal places).

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For function f(x)= -4x²-4x-1,   f(x+h)= -4x² - 8xh - 4h² - 4x - 4h - 1, (f(x+h) - f(x))/h= -8x - 4h - 4

The input values of a function are called the domain, and the output values are called the range. The domain can be any set of values, but each input value must have a unique corresponding output value. If there are multiple input values that produce the same output value, the function is not considered to be well-defined. Functions are used to model a wide range of phenomena in many different fields, including science, engineering, and economics. They are also used in calculus to study rates of change and slopes of curves.

To find f(x+h), we need to replace x with (x+h) in the given function:

f(x+h) = -4(x+h)² - 4(x+h) - 1

= -4(x² + 2xh + h²) - 4x - 4h - 1

= -4x² - 8xh - 4h² - 4x - 4h - 1

To find (f(x+h) - f(x))/h, we first need to find f(x):

f(x) = -4x² - 4x - 1

Then we can substitute f(x+h) and f(x) in the formula:

(f(x+h) - f(x))/h = (-4x² - 8xh - 4h² - 4x - 4h - 1 - (-4x² - 4x - 1))/h

= (-4x² - 8xh - 4h² - 4x - 4h - 1 + 4x^2 + 4x + 1)/h

= (-8xh - 4h² - 4h)/h

= -8x - 4h - 4

So, f(x+h) = -4x² - 8xh - 4h² - 4x - 4h - 1, and (f(x+h) - f(x))/h = -8x - 4h - 4.

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The distance between the media center and the office is 4 times 100, or 400 feet.

Distance Formula. ⇒ [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] Using this formula in the equation, we get

Using the distance formula, we can find the distance between the media center and the office:

[tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]

where (x1, y1) are the coordinates of the media center (-20, 22) and (x2, y2) are the coordinates of the office (-20, 18).

[tex]d = \sqrt{((-20 - (-20))^2 + (18 - 22)^2)}\\= \sqrt{(0 + (-4)^2)}\\= \sqrt{(16)}\\= 4[/tex]

Since one unit on the coordinate plane represents 100 feet.

Hence, the distance between the media center and the office is 4 times 100, or 400 feet.

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Answer:

b

Step-by-step explanation:

3 + 3 = 6 lol

6 how many apples

The multiple of the unit fraction 3/8​ is 15/40.

What is fraction ?

A fraction is a number that represents a part of a whole. It is a way of representing a quantity that is not a whole number. Fractions are written with two numbers, one above the other and separated by a horizontal line. The number above the line is called the numerator, and the number below the line is called the denominator.

To find the multiple of a fraction, you simply multiply the numerator and the denominator by the same number. For example, to find the multiple of 3/8, you can multiply both the numerator and the denominator by 2:

3/8 * 2/2 = 6/16

So the multiple of 3/8 by 2 is 6/16.

Similarly, you can find the multiple of 3/8 by any other number by multiplying both the numerator and denominator by that number. For instance, if you want to find the multiple of 3/8 by 5, you can multiply both the numerator and the denominator by 5:

3/8 * 5/5 = 15/40

Therefore, the multiple of the unit fraction 3/8​ is 15/40.

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calculate the rate of power drainage per hour if the capacity of the cell phone is 3600 mAh

Therefore, the area of triangle XYZ is (1/2)bh = (1/2)(15)(15√3) = 225√3. Therefore, the area of triangle XYZ is 225√3.

Triangle is a three-sided polygon that has three angles and three sides. It is one of the basic shapes in geometry and is a very important concept in mathematics. It is also used in various fields, such as physics and engineering. Triangles can be classified into different types, such as right triangles, isosceles triangles, acute triangles, obtuse triangles, and equilateral triangles. Triangles are also used to form polygons, such as quadrilaterals, pentagons, and hexagons.

To find the area of triangle XYZ, we must first calculate the length of each side of triangle XYZ. The length of each side can be determined by multiplying the length of each side of triangle ABC by five.

Since all three sides of triangle ABC are equal in length, then each side of triangle XYZ will be 5 times the length of triangle ABC. Therefore, the length of each side of triangle XYZ is 5 times the side length of triangle ABC, or 15.

The area of the triangle can be calculated using the Triangle Area formula, A = (1/2)bh, where b is the base of the triangle and h is the height of the triangle. Since we know the length of each side of triangle XYZ, we can use these values to calculate the base and height of the triangle. The base of the triangle is 15, and the height of the triangle is 15√3.

Therefore, the area of triangle XYZ is (1/2)bh = (1/2)(15)(15√3) = 225√3. Therefore, the area of triangle XYZ is 225√3.

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The formula for the volume of a cone is:

V = (1/3)πr^2h

Solving for r:

V = (1/3)πr^2h

3V = πr^2h

r^2 = (3V)/(πh)

r = sqrt[(3V)/(πh)]

Given that V = 660cm^3, h = 14cm and π = 22/7:

r = sqrt[(3 × 660)/(22/7 × 14)] ≈ 7 cm

So the radius is approximately 7 cm.

To find the value of h:

V = (1/3)πr^2h

660 = (1/3)(22/7)(7^2)h

660 = (22/3)(49/7)h

660 = (22/3)(7)h

h = 660 / [(22/3)(7)]

h = 9.45 cm (rounded to two decimal places)

Therefore, the value of h when the volume of the cone is 660 cm^3 is approximately 9.45 cm.

The compound figure has a 41 square metre surface area.

The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.

The compound figure's area can be calculated by breaking it up into smaller shapes and adding the areas of each one.

Then, divide the figure into two rectangles:

The first rectangle is 2 m by 9 m in size and has a surface area of 18 m².

The surface area of the second rectangle, which is 3 m by 7 m in size, is 21 m².

Next, we may determine the areas of the two triangles:

Due to its 2 m base and 2 m height, the first triangle has an area of 1/2 x 2 m x 2 m, = 2 m².

The second triangle has a base of 3 m and a height of 2 m, and its area is 1/2 x 3 m x 2 m = 3 m².

The two rectangles' overlap can then be subtracted:

The overlap is a rectangle that is 2 m by 3 m in size, or 6 m2, and measures 2 m by 3 m.

The total area of the compound figure is calculated by adding the areas of the two rectangles, the two triangles, and then deducting the overlap between the rectangles.

Total area is (18 m² + 21 m²) + (2 m² + 3 m²) - 6 m².

Total area: 41 m².

Hence, the compound has a 41 square metre size.

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21 is  the value of f(g(2)) in functions.

What is a function, exactly?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). Mathematics is rife with functions , and the sciences depend on them for constructing physical relationships.

f(x) = 2x² + x - 13

g(x) = x - 6

the value of f(g(2))

   g(2) = 2 - 6

          = -4

   f(g(2)) =  2x² + x - 13

               = 2(-4)² + 2 - 13

              = 32 - 11

               = 21

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The number of messages are: Martina sent 21 messages, Ryan sent 14 messages, and Keith sent 42 messages.

We may build equations that link unknown values in a problem and describe those numbers using variables. We may modify these equations algebraically to get solutions for the unknowable numbers by employing variables. As a result, issue solving is more effective and we can come up with generic answers that may be used in a variety of situations. Moreover, employing variables enables us to see patterns and trends as well as better grasp the connections between various amounts in a situation.

Given that,

Ryan sent 7 fewer messages than Martina.

R = M - 7

Keith sent 2 times as many messages as Martina.

K = 2M

Martina, Ryan, and Keith sent a total of 77 text messages.

M + R + K = 77

Substitute the value of equation 1 and 2 in equation 3:

M + (M - 7) + 2M = 77

4M - 7 = 77

4M = 84

M = 21

Substitute the value of M in equation 1 and equation2:

R = M - 7 = 21 - 7 = 14

K = 2M = 2(21) = 42

Hence, the number of messages are: Martina sent 21 messages, Ryan sent 14 messages, and Keith sent 42 messages.

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1. Patrick makes more per hour by $6.

2. Betthany makes more per hour by $5.25

3. Tommy makes more per hour by $ 1.25.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

The rate of Change of Critters and Co

Slope= Rise/ Run

        = 15/2

        = 7.5

So, the equation is y = 7.5x

and, rate of Change of Little Paws

= (52.50-35) / (6-4)

= 17.5 / 2

= 8.75

So, the equation is y = 8.5x + 5

and, rate of Change of The Waging Tail

= 8.25

1. Patrick makes more per hour by $6.

2. Betthany makes more per hour by $5.25

3. Tommy makes more per hour by $ 1.25.

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Therefore, when w = 1/2, the expression w + 1/2w + 2 evaluates to 17/4.

You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. Variable x in the preceding example is equivalent to 6, as 6 + 6 = 12. We can substitute our variables with their values before evaluating the expression if we are aware of their values.

To evaluate the expression for w = 1/2, we substitute w = 1/2 into the expression:

w + 1/2w + 2

= 1/2 + 1/2(1/2) + 2 (substitute w = 1/2)

= 1/2 + 1/4 + 2 (simplify multiplication)

= 9/4 + 2 (convert 1/2 to 2/4 and add fractions)

= 17/4 (add fractions)

Therefore, when w = 1/2, the expression w + 1/2w + 2 evaluates to 17/4.

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The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as,

H² = P² + B²

The height of Triangle ΔABC is given as,

17² = h² + 15²

289 = h² + 225

h² = 289 - 225

h² = 64

h = 8 units

The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.

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answer is 14.

4-(2*-5)

4-(-10)

=4+10

=14.

Answer:

Step-by-step explanation:

[tex]\tt 4-2(-5)[/tex]

Follow the PEMDAS order of operations:-

P: Parentheses

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

1) Multiply and/ or divide:-

[tex]\tt 4 -\left(-10\right)[/tex]

2) Addition/Subtraction:-

_____________________

Hope this helps! :)

We can rewrite the sum of logarithms as:

log(8) + log(3) =  log(24)

Remember that if we have two logarithms of the same base, then we can write:

log(a) + log(b) = log(a*b)

Here the base of the logarithms is the same, then we can use that rule, we can rewrite the given sum as:

log(8) + log(3) = log(8*3) = log(24)

That is the expression rewritten as a single logarithm.

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Answer: The equation of a circle with center (a,b) and radius r is given by:

(x - a)^2 + (y - b)^2 = r^2

In this case, the center is (9,10) and the point on the circle is (7,4). To find the radius, we can use the distance formula between the center and the point on the circle:

r = sqrt((7 - 9)^2 + (4 - 10)^2) = sqrt((-2)^2 + (-6)^2) = sqrt(40)

So, the equation of the circle is:

(x - 9)^2 + (y - 10)^2 = 40

Alternatively, we can also expand the equation to get:

x^2 - 18x + 81 + y^2 - 20y + 100 = 40

Simplifying and rearranging, we get:

x^2 + y^2 - 18x - 20y + 41 = 0

Therefore, the equation of the circle is either (x - 9)^2 + (y - 10)^2 = 40 or x^2 + y^2 - 18x - 20y + 41 = 0.

Step-by-step explanation:

Answer:

4 jumps in 24 minutes

Step-by-step explanation:

Rate: 1 jump every 6 minutes

24/6 = 4