what is the vertex of the graph of the function f(x)=2(x-2)SQUARE ROOT 2+3

The distance from the midpoint of AB to the midpoint of AC is equal to: D. √37.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

For line segment AB, we have:

Midpoint of AB = [(-6 - 8)/2, (6 - 2)/2]

Midpoint of AB = [-14/2, 4/2]

Midpoint of AB = [-7, 2].

For line segment AC, we have:

Midpoint of AC = [(-6 + 4)/2, (-4 + 6)/2]

Midpoint of AC = [-2/2, 2/2]

Midpoint of AC = [-1, 1].

In Mathematics and Geometry, the distance between two (2) endpoints that are on a coordinate plane can be calculated by using the following mathematical equation (formula):

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(-1 + 7)² + (1 - 2)²]

Distance = √[6² + 1²]

Distance = √[36 + 1]

Distance = √37 units.

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Answer:

Step-by-step explanation:

x+y=15

2x+3y=34

The answer of the given question based on the equation problem is , one coin is worth 5 points and one gem is worth 11 points.

An equation is the  mathematical statement that shows  equality between the two expressions. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The LHS and RHS may contain one or more variables, constants, mathematical operations, and functions.

Let's denote the value of one coin by x and the value of one gem by y. We can set up two equations based on the given information:

3x + 5y = 70 (equation 1)

6x + 2y = 52 (equation 2)

We can use these equations to solve for x and y. One way to do this is to multiply equation 2 by 5 and subtract it from equation 1 multiplied by 2:

6x + 10y = 140 (equation 1 multiplied by 2)

-30x - 10y = -260 (equation 2 multiplied by 5, with signs flipped)

-24x = -120

x = 5

Now that we know that one coin is worth 5 points, we can substitute this value into either of the original equations to solve for y. Let's use equation 1:

3(5) + 5y = 70

15 + 5y = 70

5y = 55

y = 11

Therefore, one gem is worth 11 points.

In summary, one coin is worth 5 points and one gem is worth 11 points.

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Answer:

Step-by-step explanation:

a. To write the product a.sin(3x)cos(2x) as a sum, we can use the identity:

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

Using this identity, we can write:

a.sin(3x)cos(2x) = a.sin(3x)cos(x + x)

= a[sin(3x)cos(x) + cos(3x)sin(x)]

= a[sin(x)cos(3x) + sin(3x)cos(x)]

= a.sin(x)(cos(3x) + sin(3x))

Therefore, the product a.sin(3x)cos(2x) can be written as the sum a.sin(x)(cos(3x) + sin(3x)).

b. To write the product cos(7x)cos(2x) as a sum, we can use the identity:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Using this identity, we can write:

cos(7x)cos(2x) = cos(7x)cos(-x - (-x + 2x))

= cos(7x)cos(-x)cos(-(-x+2x)) - sin(7x)sin(-x)cos(-(-x+2x))

= cos(7x)cos(x)cos(x) + sin(7x)sin(x)sin(x)

= cos(7x)cos^2(x) + sin(7x)sin^2(x)

Therefore, the product cos(7x)cos(2x) can be written as the sum cos(7x)cos^2(x) + sin(7x)sin^2(x).

An equation which represents this graph include the following: D. y = 2x/3 + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 - 0)/(0 + 3)

Slope (m) = 2/3

At data point (0, 2) and a slope of 2/3, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 2/3(x - 0)

y - 2 = 2x/3

y = 2x/3 + 2

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

You have to try to eliminate all the other variables and isolate 'x':

Z=(x+h)k

Subtract 'h' from both sides:

Z-h=x(k)

Divide 'k' from both sides:

[tex]\frac{Z}{k} -h[/tex]

So, [tex]x=\frac{Z}{k}-h[/tex].

The area of the triangle JTR is 1/2x² + 7/2x + 5 square units

From the question, we have the following parameters that can be used in our computation:

Base = x + 5

Height = x + 2

The area of the triangle is calculated as

Area = 1/2 * Base * Height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * (x + 5) * (x + 2)

So, we have

Area = 1/2 * (x² + 7x + 10)

This gives

Area = 1/2x² + 7/2x + 5

Hence, the area is 1/2x² + 7/2x + 5

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Answer:

Step-by-step explanation:

Given a right triangle with an acute angle marked θ next to a side marked 7 and opposite a side marked 8, you want the primary trig function values for angle θ.

The hypotenuse of the triangle can be found using the Pythagorean theorem:

  c² = a² +b²

  c² = 7² +8² = 113

  c = √113 . . . . length of the hypotenuse

You are reminded of the side length ratios for the different trig functions by the mnemonic SOH CAH TOA.

  Sin = Opposite/Hypotenuse

  sin(θ) = 8/√113

  Cos = Adjacent/Hypotenuse

  cos(θ) = 7/√113

  Tan = Opposite/Adjacent

  tan(θ) = 8/7

__

Additional comment

If you are required to "rationalize the denominator", then you need to replace 1/√113 with (√113)/113.

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The amount of time it would take to inflate the balloon to two-thirds of its maximum volume is 16 minutes.

In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):

Volume of a sphere = 4/3 × πr³

Where:

r represents the radius.

Note: Radius = diameter/2 = 55/2 = 27.5 feet.

For maximum volume, we have the following:

V ∝ R³

2/3V = v

2/3R³ = r³

r = 27.5 × ∛(2/3)

Radius, r = 24

Since the radius of this spherical hot-air balloon increases at a rate of 1.5 feet per minute, time to reach a radius of 24 feet can be calculated as follows;

Time = 24/1.5

Time = 16 minutes

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Complete Question:

A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to Two-thirds of its maximum volume? Use π = 3.14 and V = four-thirds pi r cubed.

Answer :

Step-by-step explanation:

According to the question It's given that :

Two cones of the same height, the first has a radius of 8 inches and the second has a radius of 12 inches with a height of 9 inches.

Here,

Since, Both the cones are of the same height.

Formula of volume of cone = 1/3 πr²h

where,

For first cone,

[tex] \implies [/tex] Volume = 1/3 × 3.14 × (8)² × 9

[tex] \implies [/tex] 1/3 × 3.14 × 64 × 9

[tex] \implies [/tex] 1/3 × 3.14 × 576

[tex] \implies [/tex] 1/3 × 1808.64

[tex] \implies [/tex] 602.88 in³

For second cone,

[tex] \implies [/tex] Volume = 1/3 × 3.14 × (12)² × 9

[tex] \implies [/tex] 1/3 × 3.14 × 144 × 9

[tex] \implies [/tex] 1/3 × 3.14 × 1296

[tex] \implies [/tex] 1/3 × 4069.44

[tex] \implies [/tex] 1356.48 in³

Now, How much more water can the second cone hold than the first cone?

Volume of 2nd cone - Volume of 1st cone

[tex] \implies [/tex] 1356.48 - 602.88

[tex] \implies [/tex] 753 (approximately)

Therefore, 753.98 in³ is the answer .

The given expression is needed to be written in the the form a^n.

The required expression is a ^ -5/4

We have,

The given expression is

1/ a^5/4

We know,

the identity that a negative exponent means the reciprocal.

1/ a^b = a^-b

So, the given expression is

1/ a^5/4

=a ^-5/4

The required expression is a ^-5/4

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Step-by-step explanation:

I think u have to find the degrees of x

The value of x in the figure is,

⇒ x = 65 degree

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, We can formulate;

The value of third angle in first triangle is,

180 - (50 + 62)

180 - 112

68 degree

And, The value of third angle in second triangle is,

180 - (53 + 80)

180 - 133

47 degree

Thus, The value of third angle in mid triangle is,

180 - (47 + 68)

180 - 115

65 degree

So, By definition of vertically opposite angle is,

⇒ x = 65 degree

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The dot plot that would be a representative sample of the population is the third dot plot (option c).

A sample is a fraction of the population being studied; due to this, samples are expected to be representative, which means they should reflect the general trends or behaviors in the population. Due to this, it is expected a representative dot plot shows the most common number of books are 4 and 7 and there are no students who read 9 books per month.

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A graph of the function represented by [tex]y=\sqrt[3]{x-2}[/tex] for the domain -6 ≤ x ≤ 10 is shown in the image attached below.

In Mathematics, a cubic function is sometimes referred to as a cubic polynomial and it can be defined as a type of polynomial in which the degree of the highest term (coefficient or exponent) is equal to three (3).

In this context, we can reasonably infer and logically deduce that a graph that represents the parent cubic function was shifted by 2 units to the right in order to create or produce the transformed cubic function [tex]y=\sqrt[3]{x-2}[/tex].

In conclusion, we would use an online graphing calculator to plot the graph of the given cubic function [tex]y=\sqrt[3]{x-2}[/tex] over the interval -6 ≤ x ≤ 10 as shown below.

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The formulas for the area and perimeter of the given shape are:

A = 1/2 x b x h + 1/2 x πr²

P = b + h + 1/2r

We

To find the area and perimeter of the given shape, we need to break it down into its constituent parts:

The right-angled triangle and the two-quarter circles.

Let's label the sides of the right-angled triangle as follows:

The side adjacent to the right angle (the base) has length b.

The side opposite the right angle (the height) has length h.

Now, let's find the area of the triangle.

The formula for the area of a triangle is:

A = 1/2 x base x height

So, in this case, we have:

A (triangle) = 1/2 x b x h

Next, let's find the perimeter of the shape.

The perimeter is the total length of the boundary of the shape.

To find the perimeter, we need to add up the lengths of all the sides of the triangle and the two-quarter circles.

The base and height of the triangle are already labeled as b and h, respectively.

The two-quarter circles each have a radius of r.

The formula for the circumference of a circle is:

C = 2πr

But since we only have quarter circles, we need to divide the circumference by 4:

C (quarter circle) = 1/4 x 2πr = 1/2πr

Therefore, the length of each quarter circle is:

L (quarter circle) = 1/2πr x π/2 = 1/4r

So the total perimeter of the shape is:

P = b + h + 2 L (quarter circle) = b + h + 1/2r

Now, to find the area of the entire shape, we need to add the area of the triangle and the two-quarter circles.

The area of each quarter circle is:

A (quarter circle) = 1/4 x πr²

So the total area of the two-quarter circles is:

A (circles) = 2 A (quarter circle) = 1/2 x πr²

Therefore, the total area of the shape is:

A = A(triangle) + A(circles) = 1/2 x b x h + 1/2 x πr²

Thus,

The formulas for the area and perimeter of the given shape are:

A = 1/2 x b x h + 1/2 x πr²

P = b + h + 1/2r

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Given that x = 7.7 m and = 25° the value of  AB is given as 3.254

We have the following data to work with

x = 7.7 m and = 25°,

then we have sin 25 = ∅ = 25 degrees

sin 25 = ab / 7.7

cross multiply from here

AB = sin25 x 7.7

= 0.4226 x 7.7

= 3.254

Hence we would say that in the triangle if x = 7.7 m and = 25°, the value of AB would be solved to be 3.254

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The solution or roots of this quadratic function are x = -7 and x = -5.

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factorization method as follows;

x² + 12x + 35 = 0

x² + 7x + 5x + 35 = 0

x(x + 7) + 5(x + 7) = 0

(x + 7)(x + 5) = 0

x = -7 or x = -5.

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[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=384 \end{cases}\implies 384=\cfrac{4\pi r^3}{3}\implies 384(3)=4\pi r^3 \\\\\\ \cfrac{384(3)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{384(3)}{4\pi }}=r\implies 4.5\approx r[/tex]

Answer:

[tex] \frac{4}{3} \pi {r}^{3} = 384[/tex]

[tex]r = 4.5 [/tex]

So the radius of this sphere is approximately 4.5 feet.

AH is the diagonal of the cube through the interior.

Option A is the correct answer.

We have,

A diagonal through the interior of a cube refers to a straight line that passes through the interior of the cube and connects two opposite corners of the cube.

It does not lie on any of the faces of the cube but passes through the center of the cube.

From the cube,

The diagonal through the interior of the cube is:

AH, CF, BG, and DE.

Thus,

AH is the diagonal of the cube through the interior.

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Answer:

C: It would be double the original volume.

Step-by-step explanation:

The volume of a rectangular prism is given by the formula:

Volume = length × width × height

If the height of the rectangular prism is doubled, then the new volume would be:

New volume = length × width × (2 × height)

= 2 × (length × width × height)

= 2 × (original volume)

Therefore, if the height of the entrance hall is doubled, the new volume would be double the original volume.

So the answer is option C: It would be double the original volume.

Answer:

y = 7x + 32

Step-by-step explanation:

The general equation of the slope-intercept form is

Given two points which line on the same line, we can find the slope, m, using the slope formula, which is

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex],

If we allow (-4, 4) to be our x1 and x2 point and (-5, -3) to be our y1 and y2 point, we can find the slope by plugging the points into the slope formula:

[tex]m=\frac{-3-4}{-5-(-4)}\\ \\m=\frac{-7}{-5+4}\\ \\m=\frac{-7}{-1}\\ \\m=7[/tex]

Since we now know the slope, we can b, the y-intercept by plugging in any of the two points for x and y and the slope (7) and solving for b:

Let's try the first point (-4, 4):

4 = 7(-4) + b

4 = -28 + b

32 = b

Thus, the equation of the line passing through the points (-4, 4) and (-5, -3) in slope-intercept form is y = 7x + 32

a) Independent

b) Dependent

c) No

(a) The events are independent because the grade each person earns does not affect the other person's grade.
(b) The events are dependent because the grades of you and your study partner are likely to be influenced by each other's study habits and collaboration.
(c) Not necessarily. Two events can occur at the same time and still be independent, such as flipping two coins at the same time. However, if the occurrence of one event affects the probability of the other event happening, then they are dependent.
(a) You and a randomly selected student from your class both earn A's in this course.

Answer: Independent

Explanation: The events are independent because your performance in the course does not affect the performance of the randomly selected student, and vice versa. They are not disjoint, as both events can occur at the same time.

(b) You and your class study partner both earn A's in this course.

Answer: Dependent

Explanation: In this case, the events are dependent because your performance and your study partner's performance could be related (e.g., by studying together, you both improve your chances of earning an A). They are not disjoint, as both events can occur at the same time.

(c) If two events can occur at the same time, must they be dependent?

Answer: No

Explanation: Two events can occur at the same time without being dependent. For example, independent events can both occur at the same time, but their occurrence is not influenced by each other. Only when the occurrence of one event affects the probability of the other event occurring are they considered dependent.

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The probability of drawing a white ball is 0.4, then drawing a red ball probability is 0.3, and drawing a yellow ball or a red ball probability is 0.6.

Given data:

Number of  red balls = 6

Number of yellow balls = 6

Number of white balls = 8

Number of balls  in a jar = n = 6 + 8 +6 = 20 balls

Where assume that:

R =  event where you draw a red ball.

W =event where you draw a white ball.

Y = event where you draw a yellow ball.

P(R) = 6/20 = 3/10 = 0.3

P(W) = 8/20 = 2/5 = 0.4

P(R) or P(Y) = P(Y) + P(R) - P(Y or R)

= 6/20 + 6/20 - 0

= 12/20

= 3/5 = 0.6

Therefore, The probability of drawing a red ball is 0.3, a white ball is 0.4, and a yellow ball or a red ball is 0.6.

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Answer:

Approximately 5.988 inches

Step-by-Step Explanation:

The formula for the volume of a cone is:

V = (1/3)πr^2h

where V is the volume, r is the radius of the base, h is the height, and π is the mathematical constant pi.

We are given that the volume of the cone is 37.7 cubic inches, and the height is 4 inches. We can plug these values into the formula and solve for the radius:

37.7 = (1/3)πr^2(4)

37.7 = (4/3)πr^2

r^2 = (37.7 x 3) / (4 x π)

r^2 = 8.9717

r ≈ 2.994 inches

Now that we know the radius of the base, we can find the diameter by doubling the radius:

d = 2r ≈ 5.988 inches

Therefore, the diameter of the base of the cone is approximately 5.988 inches.

Answer:

  746.0 feet

Step-by-step explanation:

You want to know the horizontal distance to a lighthouse if the angle of elevation to the 145-ft high beacon is 11°.

The tangent ratio is useful for solving this problem. It tells you ...

  Tan = Opposite/Adjacent

  tan(11°) = (145 ft)/(distance)

Solving for distance, we get ...

  distance = (145 ft)/tan(11°) ≈ 746.0 ft

The ship's horizontal distance from the lighthouse is 746.0 feet.

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Answer:

Step-by-step explanation:

use integration

Answer:

36 cm²

Step-by-step explanation:

Area of a triangle = 1/2bh = 1/2(9)(8) = 36

Answer:

z = -675

Step-by-step explanation:

z : 15 = -45

For that, we can change it into

z/15 = -45

z = -45*15

z = -675

A skewed distribution is neither symmetrical nor normal as the data values trail off more sharply on one side than on the other. It occurs due to the lower or upper bounds on data. In symmetric distribution left and right sides mirror each other.

a. The given data distribution is skewed as the data is not even on either side.

b. The median is defined as the middle value of a data set. Here 20 is the median as it is the mid point.

c. The average of the given numbers is known as mean and it is obtained by dividing sum of numbers divided by total numbers.

Mean = 207 / 11 = 18.81

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The distance between the two kites is approximately 145.8 feet.

The Law of Cosines is a trigonometric formula that relates the sides and angles of a triangle. Specifically, it relates the length of one side of a triangle to the other two sides and the angle between them

We can use the Law of Cosines to solve for the distance between the two kites. Let's call the distance between the kites "d".

From the problem statement, we have two sides of the triangle formed by the two strings (97 feet and 115 feet) and the included angle (28 degrees). We can use the Law of Cosines to solve for the third side

d^2 = 97^2 + 115^2 - 2(97)(115)cos(28)

Using a calculator, we get

d² ≈ 21251.4

Taking the square root of both sides, we get

d ≈ 145.8 feet

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