a body of mass 10.5 kg fell to the ground . calculate the weight of the body.​

The Least number of baseball cards Isabella could have is 49

To solve the problem, the multiples of seven will be necessary to ascertain the one that will:

multiples of 7: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63....

14 is short of 1 when divided by 5 but it is divisible by 2 without remainder

49 is the least number that fall short of 1 card to make it a multiple of 5 and have a remainder one when divided by 2

Hence the answer is 49

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Answer:

Gerald received the higher rate of increase

Step-by-step explanation:

The measure of the line AC is 15√3/2

The measure of the line BC is 15/2

Triangle ABC is the display style for a triangle with vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces.

One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs, Right triangles follow the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs of a right triangle (a2 + b2 = c2). Special right triangles have extra characteristics that simplify computations involving them. The 3-4-5 right triangle is one of the two most well-known.

Sin 60⁰=x/15

√3/2=x/15

x=15√3/2

The measure of the line AC is 15√3/2

Cos 60⁰= y/15

1/2=y/15

y=15/2

The measure of the line BC is 15/2

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Margin did the successful candidate win is 5375 - 4300 = 1075.

Given:

In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled.

116 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had.

Number of valid votes = 9791 - 116 = 9675.

Let the number of votes of successful candidate = 5x

Let the number of votes of opponent = 4x

5x + 4x = 9675

9x = 9675

divide by 9 on both sides

x = 9675/9

x = 1075

Hence the votes for successful candidate = 5*1075 = 5375.

votes for opponent = 4*1075 = 4300.

Margin by which the successful candidate wins = 5375 - 4300 = 1075.

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Answer: 19.2, 1.7, 15.93, 0.0512

Step-by-step explanation:

We can multiply these straight across but the trick with decimals is that your answer needs to have the same decimal place distance as what you are multiplying. In the first question, we go one decimal place. In the second, we go two decimal places. In the fourth, we go four decimal places.

Answer:

see explanation

Step-by-step explanation:

(a)

perimeter (P) is calculated as

P = 2(l + b) ← l is the length and b the breadth

given l = x and P = 20 , then

2(x + b) = 20 ( divide both sides by 2 )

x + b = 10 ( subtract x from both sides )

b = 10 - x

Using Pythagoras' identity in the right triangle

x² + (10 - x)² = 8²

x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )

2x² - 20x + 36 = 0 ( divide through by 2 )

x² - 10x + 18 = 0 ← as required

(b)

solve using the method of completing the square

x² - 10x + 18 = 0 ( subtract 18 from both sides )

x² - 10x = - 18

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 5)x + 25 = - 18 + 25

(x - 5)² = 7 ( take square root of both sides )

x - 5 = ± [tex]\sqrt{7}[/tex] ( add 5 to both sides )

x = 5 ± [tex]\sqrt{7}[/tex]

Then

x = 5 - [tex]\sqrt{7}[/tex] ≈ 2.35 ( to 3 significant figures )

x = 5 + [tex]\sqrt{7}[/tex] ≈ 7.65 ( to 3 significant figures )

Answer: 5n - 4

Step-by-step explanation:    

n is the number, 5 times the number is 5n.  4 less means subtract 4.  So the correct expression is 5n - 4

Answer:

  6922 TV sets

Step-by-step explanation:

You want the production in the 15th year if production in the first year is 1000 and it increases yearly by a constant amount. The total production in the first 10 years is 29035.

An arithmetic series is one that has a constant difference from one term to the next. If a1 is the first term of the series, and d is the common difference between terms, the n-th term is ...

  an = a1 +d(n -1)

And the sum of n terms is ...

  Sn = (2a1 +d(n-1))(n/2)

To find the 15th term, we can make use of the given values to find the common difference, then use the formula for the n-th term.

  S10 = (2(1000) +d(10 -1))(10/2) . . . . . sum formula with a1=1000

  29035 = 10000 +45d . . . . . . . . . . . simplified

  d = (29035 -10000)/45 = 423 . . . . the increase in production each year

Production in the 15th year is ...

  a15 = 1000 +423(15 -1) = 1000 + 5922 = 6922

The output in the 15th year was 6922 TV sets.

Graph for the modulus function is as follows.

What is modulus function?

A modulus function is a function that determines a number or variable's absolute value.

Main body:

Given that,

Which graph represents the function f(x) = 4⌈x⌉?

Now,

to represent the graph of Y =  IxI-4 .

So,

Taking x = 0, we get

Y =  IxI -4

Y =  I0I -4

Y = -4

Taking x = 1, we get

Y =  IxI - 4

Y =  I1I -4

Y = -3

Taking x = 2, we get

Y =  IxI - 4

Y =  I2I - 4

Y = -2.

Taking x = -1, we get

Y =  IxI - 4

Y =  I-1I - 4

Y = 1 -4

Y = -3

Taking x = -2, we get

Y =  IxI - 4

Y =  I-2I - 4

Y = -2

Hence the graph for the function is as follows.

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Answer:

n=90/80

Step-by-step explanation:

you make n the subject of the formular

As a percentage, a card at random 5, 6, 7, 8 9, 7.5, 6.42, 5.62. Per cent is derived from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century.

Therefore,

45/5 = 9

45/6 = 7.5

45/7 = 6.42

45/8 = 5.62

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An equation that can be used to find the amount of time Hiroshi spends on his math homework would be 1/4(30 + 60 + x) = x

In this question, Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework.

So,  his total homework time would be,

(30 + 60 + x)minutes

Also, we have been given One fourth of his total homework time is spent on math.

We need to find an equation that can be used to find the amount of time Hiroshi spends on his math homework.

So, we get an equation,

1/4(30 + 60 + x) = x

Therefore, an equation that can be used to find the amount of time Hiroshi spends on his math homework would be 1/4(30 + 60 + x) = x

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Answer:

c

Step-by-step explanation:

Answer:

y = 2x + 2

Step-by-step explanation:

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

(y-6)/(-6-6)= (x-2)/(-4-2)

(y-6)/-12 = (x-2)/-6

y-6 = 2x-4

y = 2x -4 + 6

y = 2x + 2

Answer:

The last number is 4

Step-by-step explanation:

Yes, the graph goes through those two points.

What is Graph?

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Explanation for the answer:

The equation can be graphed by plotting the two given points and drawing a line through them. Such a graph is shown in the attachment.

You can graph a line for any linear equation from any two points that fit the equation. So you can use the points (0, -75) and (15, 0) to graph the line representing the situation.

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Answer:

2:52

Step-by-step explanation:

Multiply by 2

Answer:

80

Step-by-step explanation:

the mean of a data set is calculated as

mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{88+72+68+78+94}{5}[/tex] = [tex]\frac{400}{5}[/tex] = 80

The length of triangle AB is 22.5.

Triangle A = 7.5

Triangle B = 15

Whole = 22.5

As per the given question

Figure is made of 2 triangles.

Triangle A

Triangle B

9

7

As it is 2 triangles so

So A = 7.5

      B = 15

The whole is = 15 + 7.5

                             =22.5

Each part is 7.5 and 15 respectively and whole is 22.5 per square unit.

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By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.

In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.

Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.

For this exercise, the elements of the given data set would be listed in ascending order as follows:

Set = {-4, -3, -3, -1, 0, 1, 2, 2}

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If price p(x) =26(4)^{-x/5}, the revenue when 15 units are sold is equal to $6.09.

From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (expression):

R(x) = x × P(x)

Where:

Since the revenue function, we would simply substitute the value of the unit price and evaluate as follows:

Revenue, R(x) = x × 26(4)^{-x/5}

Substituting the given parameters into the formula, we have;

Revenue, R(x) = 15 × 26(4)^{-15/5}

Revenue, R(x) = 15 × 26(4)^{-3} or (15 × 26)/4³

Revenue, R(x) = 15 × 26(0.015625) or 390/64

Revenue, R(x) = 6.09375 ≈ $6.09.

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Complete Question:

The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)^{-x/5}, find the revenue if 15 units are sold. Round to two decimal places.

Solution to the fraction  (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9) = -38

Fractions are expressed in mathematics as a number value that defines a part of a whole or group of objects

To simplify the fraction into a simple form the following steps are followed;

Evaluate (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)

(-7 + 3) x 9 + ⅖ x (-1.1 - 3.9)

Add the numbers

(-4) x 9 + ⅖ x (-1.1 - 3.9)

Evaluate the exponent

(-4) x 9 + ⅖ x (-5)

Multiply the number

-36 + ⅖ x (-5)

-36 -10/5

Subtract the number from each other

-36 -10/5

=-36-2

Answer = -38

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Answer: 81.25

Step-by-step explanation:

Answer:

Armando lost 65 coins each level.

Step-by-step explanation:

Given information,

→ Armando lost 975 coins playing his favorite video game.

→ He lost the same number of coins in each of the 15 levels he played.

Forming the equation,

→ 15x = 975

Now required value of x will be,

→ 15x = 975

→ x = 975/15

→ [ x = 65 ]

Hence, he lost 65 coins each level.

Answer:48

Step-by-step explanation:12x4=48

The triangle proof that shows that angle Q and angle S are congruent to each other is explained below.

The side-angle-side congruence theorem (SAS) states that if the two sides and an included angle in one triangle is congruent to two corresponding sides and an included angle in the other triangle, then both triangles are congruent to each other.

If two triangles are congruent to each other, the CPCTC theorem states that all their corresponding parts are also equal or congruent to each other.

The triangle proof is given as:

Statements                                     Reasons                                                      

1. PR bisects ∠PQS                        1. Given

2. ∠1 ≅ ∠2                                      2. Definition of bisection

3. PQ ≅ PS                                     3. Given

4. RP ≅ PR                                     4. Reflexive property

5. ΔQPR ≅ ΔSPR                           5. SAS theorem

6. ∠Q ≅ ∠S                                    6. CPCTC

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Answer:

3(3+4) IS NOT EQUAL TO 3^3

Step-by-step explanation:

3(3+4)

Expand brackets to get 21 (3x3 = 9, 3x4 = 12, 9 + 12 = 21)

3^3 = 3 x 3 x 3

3x3 = 9

9 x 3 = 27

21 < 27

A set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers.

What are Real numbers?

The set of real numbers is represented by the letter R.

Every number (except complex numbers) is contained in the set of real numbers. For example: 2, -8, 33/5, -1/5, 0, etc.

What are Integers?

The set of integers is represented by the letter Z.

An integer is any number in the infinite set, Z = (..., -3, -2, -1, 0, 1, 2, 3, ...}

Integers can further be divided into

What are Natural numbers?

The set of natural numbers is represented by the letter N.

A natural number is a positive integer.

N = { 1, 2, 3, 4, ... }

According to the given question:-

Set of real numbers comprises of Rational numbers, irrational numbers, integers, whole numbers, etc.

Hence a set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers i.e.

N = { 1, 2, 3, 4, ... }

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Answer: y=-2x-5

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