One of the legs of a right triangle measures 2 cm and the other leg measures 7 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

The correct answer is option c. There are no real-valued functions that have a domain of all real numbers and a range of all integers.

A function maps an input (or domain) to a unique output (or range). In order for a function to have a domain of all real numbers, it must take any real number as an input and provide a unique output. However, for a function to have a range of all integers, it must be the case that every output is an integer.

Since the real numbers are not countable and the integers are countable, there can be no function that maps every real number to a unique integer. In other words, there is no one-to-one correspondence between the real numbers and the integers, which means that it is not possible to find a function that maps every real number to an integer.

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Complete Question:

which function(s) has the following properties? there may be more than one answer, so select all that apply.

Answer:

4 x 10^5

Step-by-step explanation:

To divide (4.8x10^3) by (1.2x10^-2), we need to divide 4.8 by 1.2, and then multiply the result by 10^3 / 10^-2.

4.8 divided by 1.2 is 4.

10^3 / 10^-2 can be simplified as 10^3 * 10^2 = 10^(3+2) = 10^5.

So, the expression can be written as:

(4.8x10^3) / (1.2x10^-2) = (4 / 1.2) x 10^5

= 4 x 10^5

The standard form of this expression is 4 x 10^5.

Figure ABCD has vertices A(-3, 2), B(2, 2), C(2, -4), and D(-3, -2) then the area of Figure ABCD be 25 square units.

A vertex in geometry is a location where two or more curves, lines, or edges come together. The intersection of two lines to form an angle, as well as the corners of polygons and polyhedra, are vertices according to this definition.

A polygon's vertex is a location where the sides or edges of the item or two rays or line segments meet. Vertex is a noun, whereas vertices is the plural. Vertices are the points at which the edges of the three-dimensional shape converge. Edges are the lines that separate two faces, while faces are flat surfaces.

The area of the trapezoid exists equal to

A = 1/2 (AD + BC) AB

To estimate the distance between the points in the graph we have

AD = 4 units, BC = 6 units and AB = 5 units

substitute the values in the above equation, we get

A = 1/2 (4 + 6)5 = 25 square units

Therefore, the correct answer is option c) 25 square units.

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The correct explanation is Chen read for less time as compared to Sierra, as 420 minutes is less than 220 minutes.

Time is an important aspect of reading as it determines how much one can read in a certain period.

In this case, we have two individuals, Sierra and Chen, who read for different times in a week. To determine which one read more time, we need to convert the units of time into minutes, the same unit of measurement.

D. Chen read for less time because an hour a day for 7 days is equal to 210 minutes.

This explanation is correct as 1 hour a day for 7 days is equal to 420 minutes, not 210 minutes.

Therefore, the correct explanation is option (D).

Complete Question:

Sierra read for 220 minutes in 1week. Chen read for an hour a day for 7 days. Which explanation is correct?

A. Sierra read for more time because 220 is greater than

B. Sierra read for less time because minutes are less than hours.

C. They read for the same amount of time because 1 week is equal to 7 days.

D. Chen read for less time because an hour a day for 7 days is equal to 210 minutes.

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An expression  x² - 8x + 5 in the form  (x - a)² - b is:  (x - 4)² - 11

Consider a quadratic expression x² - 8x + 5

To convert this expression into the form (x - a)² - b we us completing the square method.

We know that for a quadratic equation ax² + bx + c = 0, steps of completing the equare method:

1) Write the equation ax² + bx + c = 0 such that c is on the right side.

2) If a ≠ 1, divide the complete equation ax² + bx + c = 0 by 'a' so that the coefficient of x² will be 1.

3) Add the (b/2a)², on both sides.

Comparing expression  x² - 8x + 5 with ax² + bx + c we get,

a = 1, b = -8 and c = 5

the value of the expression (b/2a)² is:

(b/2a)²

= [-8/(2 × 1)]²

= (-8/2)²

= (-4)²

= 16

We add and subtract the value of the expression  (b/2a)² in expression  x² - 8x + 5

So the expression would be,

x² - 8x + 5 + 16 - 16

= x² - 8x  + 16 + 5 - 16       ......(commutative property of addition)

= (x - 4)² - 11

The required expression is:  (x - 4)² - 11

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You could fit up to 64 5ft round tables in the Franklin Room, with a maximum amount of 512 chairs. The tables would be spaced out between two aisles in the room.

The Franklin Room is 49 ft by 49 ft, meaning it has an area of 2,401 ft2. Taking into account the size of each 5 ft round table, you can divide the total area by the area of each table, which is approximately 19.625 ft2. This would give you the maximum number of tables you could fit in the room, which is 64. Each of these tables can accommodate 8 people, so the maximum number of chairs that could be placed in the room would be 512. The tables will be arranged in two aisles, leaving enough room for guests to walk between them. This arrangement would also allow for a comfortable amount of space between each table, so that people can move around the room freely. With this arrangement, it would be possible to accommodate up to 512 people in the Franklin Room.

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Answer:

Jamie has $12.50 of her allowance left if the books cost $2.50 each.

Step-by-step explanation:

To calculate this, first calculate the total cost of the books:

5 books x $2.50/book = $12.50.

Then subtract the cost of the books from the amount Jamie has saved:

$38 - $12.50 = $25.50.

Finally, subtract the cost of the books from the amount Jamie has saved to get the amount she has left:

$25.50 - $12.50 = $12.50.

Answer:

$25.50

Step-by-step explanation:

We know Jamie bought 5 books, each worth $2.50, d. We need to know the cost of all five, so we’ll go ahead and multiply 5 times $2.50 to get $12.50.

Since we know how much the books cost, all we have to do now is subtract the amount she spent from her allowance. $38.00 - $12.50 is 25.50, the amount of money Jamie has left.

Applying the secant-secant theorem, the value of x is: 12.

The secant-secant theorem states that if you draw two lines from a point outside a circle that intersect the circle at two different points, then the product of the length of one line segment and the length of the portion of the line outside the circle is equal to the product of the length of the other line segment and the length of its portion outside the circle.

Based on the secant-secant theorem, we have:

EF * ES = ED * EC

Substitute the values:

8(8 + 10) = 9(2x - 17 + 9)

Solve for x:

144 = 18x - 72

144 + 72 = 18x

216 = 18x

216/18 = x

x = 12

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Note that where in a Rhombus ACDB, m∠CDB = 60 degrees and BC = 10. The diagonals cross at point M. The length of the side of ACDB is 10.

A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term equilateral quadrilateral refers to the fact that all of its sides are the same length.

Note that the above-described Rhombus is described accordingly. Since the diagonals are perpendicular to each other and bisect one another each at an inner angle that is 90° each, then we can say that;

∠MDC = 30°
MC = 1/2BC

= 1/2 * 10
= 5

Thus,

DC = MC/Sin30°
= 5/1/2
= 5 * 2
= 10

Thus, the measure of a side of a Rhombus - ACDB is 10.

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Answer:

both Ella and Ethan jogged 1/6 of the way home.

Step-by-step explanation:

To solve the problem, we need to find the fraction of the distance that each twin jogged.

Let's start with Ella. If she ran 1/3 of the way, walked 1/6 of the way, and jogged the rest of the way, then the fraction of the way she jogged is:

1 - 1/3 - 1/6 = 2/6 - 1/6 - 1/6 = 1/6

So Ella jogged 1/6 of the way home.

Now let's look at Ethan. If he ran 1/2 of the way, walked 1/3 of the way, and jogged the rest of the way, then the fraction of the way he jogged is:

1 - 1/2 - 1/3 = 6/6 - 3/6 - 2/6 = 1/6

So Ethan jogged 1/6 of the way home, which is the same as Ella.

Therefore, both Ella and Ethan jogged 1/6 of the way home.

Yes, you can relate a given quantity to the indicated amount using more than one symbol.

In mathematics, symbols are used to represent mathematical objects and operations, making it easier to understand and communicate mathematical ideas.

Each symbol has a specific meaning and can be used in different ways to represent the same quantity.

For example, the number 7 can be represented by the numeral 7, the Roman numeral VII, or even the symbol 7 in scientific notation. All of these symbols represent the same quantity, but they each have a different context and use.

The numeral 7 is commonly used in everyday life, the Roman numeral VII is used in ancient times and in some specific contexts, and the scientific notation 7 x 10⁰ is used in scientific and mathematical calculations.

Similarly, in algebra, a variable such as x can represent a quantity and can be used in different ways to represent the same value.

For example, the equation x + 3 = 6 can be solved for x to find that x = 3. This same value can also be represented by the expression 3x, which shows that x is equal to 3.

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The ordered pairs that are solutions to y + 2 = -3(x - 4) include :

To find the ordered pairs, insert the x value in an ordered pair, into the equation. If the y value that you are given is the same as the one in the ordered pair, then the ordered pair is a solution to the equation.

Ordered pair ( 5, - 5 ) :

y + 2 = - 3 ( 5 - 4 )

y + 2 = - 3

y = - 3 - 2

y = - 5

Ordered Pair ( 2, 4 )

y + 2 = - 3 ( 2 - 4 )

y + 2 = 6

y = 6 - 2

y = 4

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Options for this question are:

The weight of the fourth sack if the average weight of the sacks is given as 6.5 kilograms is 8.5 kilograms

Total weight of 3 sacks = 17.5 kilograms

Weight of the fourth sack= x

Average weight of 4 sacks = 6.5 kilograms

Average weight= Total weight of 4 sacks / number of sacks

6.5 = (17.5 + x) / 4

cross product

6.5 × 4 = 17.5 + x

26 = 17.5 + x

subtract 17.5 from both sides

26 - 17.5 = x

x = 8.5 kilograms

Hence, the fourth sack weighs 8.5 kilograms

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The slopes of the lines are 4/13, 18/7 and -4/7

Line 1

The points on this line are

(x, y) = (-4.5, -3) and (2, -1)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

Slope = (-1 + 3)/(2 + 4.5)

Slope = (2)/(6.5)

Rewrite as

Slope = 4/13

Line 2

Here, we have

(x, y) = (-4.5, -4) and (-1, 5)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

Slope = (5 + 4)/(-1 + 4.5)

Slope = (9)/(3.5)

Rewrite as

Slope = 18/7

Line 3

Here, we have

(x, y) = (2, 0) and (-3.5, 2)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

Slope = (2 - 0)/(-3.5 - 0)

Rewrite as

Slope = -4/7

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A limit describes a function's value as it gets closer to a certain value as its inputs increase. All calculus is based on the concept of a limit.

There are one-sided limits (left- and right-hand limits), infinite limits, and limitations at infinity in addition to regular, two-sided limits.

Let's look at an example to better grasp what limits are. Beginning with the function f (x) = x + 2 f(x) = x + 2 f(x) = x + 2f, left parenthesis, x, right parenthesis, equals, x, plus, 2. The value f approaches as we move closer and closer to x = 3 x=3 x=3, which is the limit of f at x = 3 x=3 x=3.

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The values of the two limits are lim x->33- g(x) = -15 and lim x->33+ g(x) = -6.

Option (B) is correct.

What is a limit in calculus?

The limits in mathematics describe the behavior of a function as the input approaches a certain value. The symbols for limits are "lim" followed by the variable and the value that the variable is approaching, with an arrow indicating the direction of the approach.

For the given function g(x), we have the following limits:

lim x->33- g(x) = -15.1

This means that as x approaches 33 from below, the value of g(x) approaches -15.1. We can see this from the values in the table, as x gets closer to 33 from below, g(x) gets closer to -15.1.

lim x->33+ g(x) = -6.1

This means that as x approaches 33 from above, the value of g(x) approaches -6.1. We can see this from the values in the table, as x gets closer to 33 from above, g(x) gets closer to -6.1.

So, the values of the two limits are lim x->33- g(x) = -15.1 and lim x->33+ g(x) = -6.1.

Hence, The values of the two limits are lim x->33- g(x) = -15 and lim x->33+ g(x) = -6.

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To find the arc length, we use the formula L = rθ, where r is the radius of the circle, θ is the central angle of the arc in radians, and L is the arc length.

Arc length refers to the distance covered along the curved portion of a circle or any other curved shape. It is an important concept in geometry and trigonometry and is used to measure the size of circular arcs, the size of angles, and in many other mathematical applications.

To find the arc length, we need to use the formula for the circumference of a circle and the central angle of the arc.

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle.

The central angle of the arc is given in radians and is defined as the angle between two radii that meet at the endpoints of the arc.

To find the arc length, we use the formula

=> L = rθ,

where L is the arc length, r is the radius of the circle, and θ is the central angle of the arc in radians.

To convert the central angle from degrees to radians, we use the formula θ = (π/180) x degrees, where degrees are the central angle in degrees.

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The solution to the given inequality  4(2x + 5) ≥ 4, are - 3, - 5, and - 10.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is - 4(2x + 5) ≥ 4.

- 8x - 20 ≥ 4.

- 8x ≥ 24.

8x ≤ - 24.

x ≤ - 3.

The solutions are, - 3, - 5, and - 10.

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Following Answers are:

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To calculate the 10% down payment required by the bank, you can use the following formula:

Down payment = 2700 x 10%

                          = $270

To calculate the loan amount, you can subtract the down payment from the total cost of the moped:

Loan amount = 2700 - 270

                      = $2430

To calculate the monthly loan payment, you need to know the interest rate, the loan amount, and the number of months in the loan term. You can use the following formula to calculate the monthly payment:

Monthly payment = (Loan amount x Interest rate) / (1 - (1 + Interest rate)^(-Number of months in loan term))

In this case:

Monthly payment = ($2430 x 8%) / (1 - (1 + 8%)⁻⁶)

Monthly payment = $44.38

The breakdown of each of the 6 payments would be $44.38 per month.

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The distance between the two points on the number line is given by equation A = 5/3 units

Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )

The distance from A to B is the same as the distance from B to A

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

This formula is used to find the distance between any two points on a coordinate plane or x-y plane

Given data ,

Let the distance between the points on the line be A

Now , the equation will be

Let the first point be P ( -4/3 , 0 )

Let the second point be Q ( 1/3 , 0 )

Now , distance between the two points is usually given by

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

Substituting the values in the equation , we get

D = √ [ ( 1/3 - ( -4/3 ) ] ²

On simplifying the equation , we get

D = √ ( 5/3 )²

D = 5/3 units

Hence , the distance is 5/3 units

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Answer:

24 bog ole hotdogs

Step-by-step explanation:

Answer:

12 hot dogs in 30 minutes

Step-by-step explanation:

1. Write it as a fraction

      1. 2/5

2. Write what we know of the answer as a fraction

     1. ?/30

3. For the denominator to get to 30, we must multiply 5 by 6. However, we also have to multiply the numerator by 6.

        1. 2*6=12.

4. Therefore, the answer is 12/30, or he will eat 12 hot dogs in half an hour.

Answer:

You can think of a sequence as a function with sequential natural numbers as the domain and the terms of the sequence as the range. Values in the domain are called term numbers and are represented by n. Instead of function notation, such as a(n), sequence values are written by using subscripts.

If Pete sells 50 pizzas, he will make a profit of $75. The equation can be used to determine the profit is y = 5.50x - 200.

Pete's Pizzas charges $5.50 per pizza and has spent $200 in supplies to start his business.

We can use the following equation to determine the total profit he will make after he sells x amount of pizzas:

y = 5.50x - 200

where y is the total profit, 5.50 is the revenue per pizza, x is the number of pizzas sold, and -200 is the fixed cost for the supplies.

For example, if Pete sells 50 pizzas, we can plug in the values into the equation:

y = 5.50 * 50 - 200

y = 275 - 200

y = 75

So, if Pete sells 50 pizzas, he will make a profit of $75. The equation can be used to determine the profit for any number of pizzas sold by simply changing the value of x.

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Answer:

2 - √5 is an irrational number

Step-by-step explanation:

The sum or difference between a rational number and an irrational number is always irrational.

Here 2 is a rational number and √5 is an irrational number. Hence 2 - √5 is an irrational number.

Answer:

Step-by-step explanation:

When a die is rolled twice in succession and the face values of the two rolls are added together, there are all 36 ways.

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

Event A: It is observed that there are 10 cases where the sum is greater than 8.

The cases are, (3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6).

Thus, the probability for event A is 10/36 = 5/18.

Event B: It is observed that half of the cases are where the sum is an even number.

The probability for event B is 1/2

Answer:

the probability for event A is 10/36 = 5/18. The probability for event B is 1/2

Step-by-step explanation: I copied it from 2800818 (the one with a Pokémon picture) All credit goes to him/her

The steps to solve the equations are his below.

Here are the steps to solve a system of two linear equations:

Write the equations in slope-intercept form (y = mx + b) or standard form (ax + by = c).

Identify the coefficients and the constant terms of each equation.

Choose one equation and solve for one variable (e.g. x or y).

Substitute the value of the variable found in step 3 into the other equation.

Solve for the other variable by rearranging the equation obtained in step 4.

Substitute the values of both variables back into either equation to check the solution.

Graph the two equations on the same set of axes to visually check if the solution is correct.

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The All are equivalent expression except 2/4 - 1/2 given in the question.

A mathematical expression known as an algebraic expression is one that includes variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division. Generally speaking, two of something are regarded as being equivalent. Similar to this, equivalent mathematical expressions are those that are true even when they appear to be different. When the values are put into the formula, however, both expressions yield the same result.

Expression Equivalent

X - 2/4 Equivalent to 1/2 X - 1

2/4 - X Equivalent to X - 1/2

2/4 - 1/2 Not Equivalent to 1/2 X - 1 or X - 1/2

X + 1/2 Equivalent to X - 1/2

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Answer:

D

Step-by-step explanation:

15+3x=15

15-15+3x=15-15

3x=0

3x/3=0/3

x=0

Answer:

Nick can bake 16 cupcakes at most

Step-by-step explanation:

If you divide 200 by 16, you get 16.667. Because .667 is not a full cupcake, you cannot round up to get 17 cupcakes.

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