Write a flow proof.
Given: ∠A and ∠C are right angles.
∠A B E ≅ ∠C B D, AE ≅ CD

Prove: BE ≅ BD

Step-by-step explanation:

16. [tex]PQ = \frac{IK}{2} ⟹ \frac{24}{2} [/tex]

[tex]PQ = 12[/tex]

I can't really solve no. 17

The fourth, fifth, sixth, and seventh term of the sequence an = n+1/ n+2 are 5/6, 6/7, 7/8, and 8/9.

According to the given question.

We have a rule for finding the terms of a sequence i.e.

an = n+1/ n+2.

Therefore,

The fourth term of the sequence is given by

[tex]a_{4}[/tex] = 4 + 1/ 4 + 2 =  5/6

The fifth term of the sequence is given by

[tex]a_{5}[/tex]  = 5 + 1/5 + 2  = 6/7

The sixth term of the sequence is given by

[tex]a_{6}[/tex] = 6 + 1/(6 + 2) = 7/8

And, the seventh term of the sequence is given by

[tex]x_{7}[/tex] = 7 + 1/( 7 + 2) = 8/9

Hence, the fourth, fifth, sixth, and seventh term of the sequence an = n+1/ n+2 are 5/6, 6/7, 7/8, and 8/9.

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Answer:

D.

[tex]x > - 3[/tex]

Step-by-step explanation:

[tex] - 2x - 7 > 5x + 14 \\ - 2x - 5x < 14 + 7 \\ - 7x < 21 \\ x < \frac{21}{ - 7} \\ x > - 3[/tex]

Answer: 100 is four times as large as 25.

Step-by-step explanation:

[tex]100 \div25=4[/tex]

Hence, 100 is four times as large as 25.

Answer:

The answer is 100 is four times as large as 25

Step-by-step explanation:

Division compares numbers by telling you how many times larger the first number is then the second number. In this problem, 100/25=4.

Put another way, 25 x 4 = 100. Therefore,100 is four times as large as 25

Answer:

$0.05

Step-by-step explanation:

First, find the total amount of crackers and the total cost.

Crackers: 6*18=108 crackers

$5.40/108=0.05

$0.05

Answer:

A. F/5 = 4

Step-by-step explanation:

F is the total of fish so F is divided by the total of dolphins, which is 5

so F/5 = 4

Answer:

F/5=4

Step-by-step explanation:

F is the total amount of fish. Since there are 5 dolphins to feed, you should divide F by 5.

The volume of the globe is (c) 5575.3 cubic inches.

It is given in the question that the diameter of the globe is 22 inches.

We have to find the volume of the globe.

We know that a globe is spherical in shape and the volume of a sphere is given by:-

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

Where, r is the radius of the sphere

We know that,

Diameter/2 = Radius

Hence, we can write

22/2 = radius

Radius of the globe = 11 inches

Hence, volume of the globe is given by :-

(4/3) * (22/7) *11*11*11 = (88/21) *1331 = 5575.3 cubic inches.

The answer is (c)

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The speed written in standard form is 0.000008056  miles per second.

Here we know that the average speed of a garden snail is:

8.056 x 10⁻⁶ miles per second.

Notice that it is written in scientific notation and we want to write this in standard form, so we just need to expand the product.

Notice that the exponent is -6, this means that we need to "move" the decimal point 6 times to the left, so we will get:

S = 8.056 x 10⁻⁶ miles per second.

S = 0.000008056  miles per second.

That is the speed written in standard form.

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The formula for calculating the Hight of the cone as follows h = 3(V/(πr²))

Thus, the volume of a cone is one-third that of a cylinder with the same base radius and height.

Cone and cylinder volumes are related in exactly the same manner as pyramid and prism volumes are related. If the heights of a cone and then a cylinder are the same, the volume of the cylinder equals three times that of the cone.

The volume, V, formula of a cone with radius, r, and height, h.

The volume of the cone  using the formula:

V = 1/2πr²h

h = 3(V/(πr²))

The formula for calculating the Hight of the cone as follows h = 3(V/(πr²)).

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Answer:

(-5, 4)

(-4, 5)

(-2, 5)

(-10, 4)

Step-by-step explanation:

Given points:

To translate a point 3 units down, subtract 3 from its y-coordinate.

To reflect a point across the x-axis, the y-coordinate becomes its additive inverse.

Therefore, the mapping rule is:

[tex](x,y) \rightarrow (x, -(y-3))[/tex]

Translated points:

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Answer:

Step-by-step explanation:

Point slope form y-y₁ = m(x-x₁)

-2 - (-2) = m(3 - 13)

0 = m(-10)

m/slope = 0

The 5th term of the given geometric sequence is 768.

A geometric sequence is a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.

a(n) = a(n-1) . r

Where:

a(n) = nth term

r = ratio

The given geometric sequence is:

   3,12,48,192, . . .

Find the ratio

r = a(n)/a(n-1)

  = a(2)/a(1) = 12/3 = 4

Use the formula for the nth term.

a(n) = a(1) . r^(n-1)

In the given sequence a(1) = 3.

Substitute a(1) = 3, r = 4, and n = 5:

a(5) = 3 . 4⁵⁻¹

      = 3 . 4⁴ = 768

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The position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.

The position is the object can depend on where you are, and the description might also change if it is based on where other objects are.

The velocity is the time rate of change of position of a body in a specified direction. the rate of speed with which something happens.

Acceleration is the act or process of moving faster or happening more quickly: the act or process of accelerating rapid acceleration is the acceleration of economic growth.

a(t) = 3t

d^2/dx^2=(3t)

x(t) = [tex]\int\limits {3t} \, dt[/tex]

    = 3 *t^2 / 2

Hence the position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.

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Step-by-step explanation:

u simply add 307 and 206 to 2,040 giving u 2553

The linear function is:

f(x) = $10*x

Where the domain is:  [10, 25]

And the range is: [$100, $250]

Here we know that x represents the number of hours that he works per week, and we also know that he wins $10 per hour, then if he works x hours, the amount that he wins is x times $10, so the equation is just:

f(x) = $10*x

Now we also want to get the domain and range for this function. We know that he needs to work at least 10 hours and at maximum of 25 hours, so we have the restrictions:

10 ≤ x ≤25

So the domain is D: [10, 25]

To find the range we evaluate in the values of the domain, the minimum of the range is f(10) = $10*10 = $100

The maximum of the range is f(25) = $10*25 = $250

Then the range is R: [$100, $250]

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Answer:

1.2

Step-by-step explanation:

Answer:[tex]2/3+5/9= \frac{2x3}{3x3} + 5/9 =6/9 +5/9+\frac{6+5}{9} = 11/9[/tex]

Step-by-step explanation: answer : 11/9

Hope this helps u ; )

According to the question, the given simplification based inequality equation can be solved by substituting the values to the standard equation.

Given expression = [tex]-5q-\frac{7}{4} +8q < \frac{5}{8}[/tex]

Substituting the value of the variable 'q' as (5/6) and solving the left hand side expression:

Therefore, the expression can be re-written as:

Required expression = [tex]-5(\frac{5}{6} )-\frac{7}{4} +8(\frac{5}{6} )=\frac{15}{6}-\frac{7}{4} =\frac{3}{4}[/tex]

The calculated left hand side value is (3/4) which is greater than the right hand side value as (5/8).

[tex]\frac{3}{4} > \neq \frac{5}{8}[/tex]

Hence, the given inequality fraction expression is greater than the given value.

What is an inequality equation?

Inequality equation are those expression which some variables which are least in nature. They can be solved with the help of algebraic expressions using addition, subtraction, multiplication and division.

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There are 91% of players weighing less than or equal to 246 pounds that the players' weights are given in the box plot.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that the box plot

Here, the total number of players = 40

And the minimum weight of players  = 152 pounds

Third quartile (Q₃) = 246

In the box plot, approximately 10 of the 11 coverage intervals occur between 152 and 254.

So the approximate percentage of students that weigh 246 kg or less would be

⇒ (10 / 11)×100

⇒ 90.90

Therefore,  there are 91% of players weigh less than or equal to 246 pounds.

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The total number of fiction books are 2385.

What is constant of proportionality?

The constant of proportionality is the ratio of two proportional values at a constant value is known as the constant of proportionality. When either their ratio or product results in a constant, two variables' values are said to be proportionally related. The ratio between the two stated quantities determines the value of the proportionality constant.

Given that,

Let the total number of fiction books be f and nonfiction books be n.

The constant of proportionality between the number of fiction book(f) and the number of non-fiction books(n) in a library is 15/22 .

f/n= 15/22

Also, the total number of nonfiction books is 3498.

Therefore,

f/3498 = 15/22,

f= 15/22 x 3498,

f= 15 x 159,

f= 2385.

Hence, the total number of fiction books in the library are 2385.

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The variable expression for the word phrase, "the product of a number z and 7", is C. 7z.

A variable expression is defined as a mathematical phrase that contains variables and numbers combined together with any mathematical operations. The most common variable used to denote something is the variable x.

Given the word phrase "the product of a number z and 7"

let z be the variable denoted for a number

and a product of a number z and 7 can be written as:

7z

Therefore, the variable expression for the word phrase "the product of a number z and 7" is 7z.

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According to the question, ABCD is a rectangle with different coordinate values and they are as follows: A(-2,7); B(4,4); C(2,0); D(-4,3), The perimeter will be 14cm.

Using the standard definition of the perimeter that is perimeter is the sum of all the sides.

Therefore,

Perimeter = Sum of all the sides

Perimeter = -2+7+4+4+2+0-4+3 = 14 cm

And using the standard formula of the area that is the multiplication of length and width.

Now,

Area = (4)(4) = 16 cm

Hence, the calculated area = 16 cm^2 and calculated perimeter = 14 cm.

What is the area and perimeter of a rectangle?

The perimeter of a rectangle can be calculated by adding all the four lengths from all the sides. Similarly, to know the area of the rectangle by multiplying length and width.

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The value of x using the given equation is -5.

Define the solution of an equation.

A solution of an equation is defined as the set of all possible values of unknown variables that will make the equality hold.

Solving for the value of x

Given the equation, 4(x - 5) + x = 8x - 10 - x

4x - 20 + x = 8x - 10 - x

5x - 20 = 7x - 10

Rearranging the equation, we get,

7x - 10 - 5x + 20 = 0

2x + 10 = 0

x = -10 / 2

x = -5

Hence, the value of x on solving given equation is -5.

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Circle J has a radius of 10 units and BC = 5.4 units then the measure of AB is 14.6 units.

A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both rays and spoke of a chariot wheel.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.

Since AC is the diameter of circle J and the radius is 10,  AC = 2(10) or 20 units.

AB + BC = AC

Where the value of BC = 5.4, we get

substitute the value of BC in the above equation, then we get

AB + 5.4 = 20

subtract 5.4 from both sides

AB + 5.4 - 5.4 = 20 - 5.4

simplifying the above equation,

AB = 14.6

Therefore, the measure of AB is 14.6 units.

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The given infinite geometric series 2/3+4/9+8/27+ ...... is convergent and the sum is 2

The given geometric series is:

  2/3 + 4/9 + 8/27 + ......

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 2/3

a(2) = 4/9

a(3) = 8/27

Hence, the common ratio is

   r = a(2) / a(1) = (4/9) / (2/3) = 2/3

An infinite geometric series is convergent if 0 < | r | < 1.

Since r = 2/3, then the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 2/3  and r = 2/3 into the formula:

S = (2/3) / (1 - 2/3)

   = (2/3) / (1/3)

   =  2

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Probability of spinner pointer not landing on green is equal to 2/3 if the spinner lands on a line it is spun again.

As given in the question,

Total colors in the spinner is equal to 6

Each color is 2 times

Total number of colored region =6

Number of green region = 2

Probability of pointer landing on green color  P(G)= 2 /6

Probability of pointer not landing on green P(G') = 1- P(G)

                                                                            = 1- (2/6)

                                                                             = 2/3

Therefore, probability of spinner pointer not landing on green is equal to 2/3, if the spinner lands on a line it is spun again.

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2. For the given cylinders, we have that:

A. The volume is of 72π cm³ and the curved surface area is of 48π cm².

B. The volume is of 112π cm³ and the curved surface area is of 56π cm².

5. There are 330 liters of water in the container.

The volume of a cylinder of radius r and height h is given as follows:

V = πr²h.

The curved surface area of a cylinder of radius r and height h is given as follows:

S = 2πrh.

For problem 2 item a, we have that the parameters are given as follows:

r = 3, h = 8.

Hence:

The volume is of 72π cm³ and the curved surface area is of 48π cm².

For problem 2 item b, we have that the parameters are given as follows:

r = 8/2 = 4, h = 7.

Hence:

The volume is of 112π cm³ and the curved surface area is of 56π cm².

For item 5, the parameters are given as follows:

r = 0.65/2 = 0.325m, h = 1m.

Hence the volume is:

V = πr²h = π(0.325)² = 0.33 m³.

Each m³ has 1000 liters, hence:

0.33 x 1000 = 330 liters.

There are 330 liters of water in the container.

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The statement that the orthocenter of a right triangle is located at the vertex of the right angle is always true.

The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.

You can see in the image, there is a right-angled triangle ABC right angled at B. When we draw perpendiculars from each of  vertices of the triangle, they intersect at the vertex of the right angle. Hence, we can say that the orthocenter of a triangle is always located at the vertex of the right angle.

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1) The line of symmetry is; Vertical Line x = 0

2) The line of symmetry is; Vertical line x = 4 and horizontal line y = -4

3) The line of symmetry is; Vertical Line x = 3

1) A line of symmetry is a line that divides a figure into two parts such that each part is the mirror image of the other.

From the given image, we can see that the line of symmetry here is a vertical line at x = 0. This is because that is the half way point of the object such that when mirrored, it produces the exact same image.

2) The line of symmetry here for the given object is;

x = 4 and y = -4

3) The line of symmetry here for the given parabola curve is;

x = 3

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