Solve the equation for the specified variable.

M = F/a

a=

Answer:

y = 5x

Step-by-step explanation:

It can be observed that as ‘x’ increases, ‘y’ also increases.

It can also be observed that

[tex]\frac{y}{x}[/tex] = the same constant for all four sets of values

k =[tex]\frac{10}{2} = \frac{20}{4} = \frac{30}{6} =\frac{40}{8}[/tex]=5

It can concluded that y is directly proportional to x:

y = kx                      Where k = constant of proportionality

For these four sets of values:

y = 5x

The required expression is n/6 +3

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: The statement " 3 added to the quotient of a number divided by 6

Let the number be n

Dividing the number by 6 we get the quotient as n/6

Again adding 3 to the quotient we get

3+n/6

Hence, The required expression is n/6 + 3

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Answer: The constants in the expression are -3 and 2.

In the expression:

2 y

x−3+²7 - 12/2

X-3+

The term -3 is a constant and does not change its value regardless of the values of any variables. The term 2/2 can also be simplified to 1, which is another constant. Hence, the constants in the expression are -3 and 2.

Step-by-step explanation:

Answer:

1.  sin∠EDA is equal to sin∠EBC

2.  sin∠CEB is not equal to sin∠EBC

3.  cos∠BEC is equal to sin∠EBC

4.  cos∠ADE is not equal to sin∠EBC

5.  sin(90 - m∠EBC) is not equal to sin∠EBC

6.  cos(90 - m∠EDA) is equal to sin∠EBC

Step-by-step explanation:

From inspection of the given diagram, ∠EAD = ∠ECB = 90°.

According to the vertical angles theorem, ∠BEC = ∠DEA.

According to AA similarity theorem, ΔADE ~ ΔCBE

Therefore, ∠EDA = ∠EBC.

This means that:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Since  cos∠BEC = CE/BE  and  sin∠EBC = CE/BE  then:

As  ∠BEC ≠ ∠ADE  then:

As  sin(90° - x) = cos(x)  then  sin(90 - m∠EBC) = cos∠EBC.

As  cos∠EBC ≠ sin∠EBC  then:

As  cos(90° - x) = sin(x)  then  cos(90 - m∠EDA) = sin∠EDA.

As  sin∠EDA = sin∠EBC  then  cos(90 - m∠EDA) = sin∠EBC.

Hence:

The solution is, each tour guide have an equal number of 8 students.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

there are 12 students in each class.

Four classes are on a field trip.

There are 6 tour guides.

total students = 12*4

                       = 48

so, each guide have = 48/6

                                  = 8

Hence, The solution is, each tour guide have an equal number of 8 students.

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The quotient of 2 3/4 divided by 4 1/2 is approximately 0.622222222.

The outcome of dividing two numbers is referred to mathematically as the quotient. It is the amount produced when a numerator is divided by a denominator.

For example, consider the expression "10 ÷ 2". 10 is the numerator, and 2 is the denominator. The quotient of this expression is 5. This has the following notation in mathematics:

10 ÷ 2 = 5

The quotient can also be a fraction, in which case it represents a ratio of two numbers. For instance, the fraction representation of the equation "5 2" is as follows:

5 ÷ 2 = 5/2

In this case, the quotient represents the ratio of 5 to 2.

The quotient is an important concept in mathematics, as it is used in many areas, including arithmetic, algebra, and calculus. It is used to solve problems involving division and ratios, and it is a basic building block for more advanced mathematical concepts.

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Olivia could have used a translation and a rotation to move ABCDE onto A'B'C'DE".

Distance in numerical measurement of how far apart to 16 places in point are in space age is often measured in unit like came miles with as for free system also can be conceptualized in the term of time as Indian distance between two points in the time.

A translation would involve shifting the figure ABCDE along some axis by a certain distance, while a rotation would involve rotating the figure ABCDE around a fixed point. By combining the two transformations, Olivia could move ABCDE onto A'B'C'DE".

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The conversion factor of litre to quarts is 1 litre = 1.057 quarts and its meaning is discussed below.

What is a conversion factor?

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor to convert minutes to hours is 60 minutes = 1 hour.

The metric unit of a volume known as the litre is mostly used to measure liquids.

An English measurement of volume equal to the one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system.

The standard value of converting liquid to quarts is 1 litre = 1.057 quarts.

This means that volume of 1 litre of a substance is equivalent to the volume of 1.057 quarts of the same substance.

Therefore the conversion factor of litre to quarts is 1 litre = 1.057 quarts.

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The synthetic division process involves dividing the polynomial by a linear factor in a compact manner. In this case, we are dividing the polynomial 4x^4 - 9x^3 + 14x^2 - 12x - 1 by x - 1.

To perform synthetic division, we first write the coefficients of the polynomial in a row and add a zero at the end. Then, we divide the first coefficient (4) by the leading coefficient of the divisor (x - 1), and write the result (4) above the next coefficient (-9). Next, we multiply the divisor (x - 1) by the first quotient (4) and subtract the result from the row. The new row of coefficients is the result of this subtraction. Repeat this process until all coefficients have been processed or a remainder is left.

Here is the process:

4 -9  14 -12 -1 | 0

+------------------

-4  4  14 -12 -1

-4  4  14 -12 -1

-4 -4  10  12  1

So the result of the division is 4x³ + 10x² + 12x + 1, with a remainder of -4.

Thus, the final answer is 4x³ + 10x² + 12x + 1 + (-4) = 4x³ + 10x² + 12x - 3.

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Answer: To calculate the simple interest, you can use the formula:

I = Prt

where I is the interest, P is the principal (the amount borrowed), r is the interest rate as a decimal, and t is the time in years.

In this case, P = $4,200, r = 0.03, and t = 6/12 = 0.5 (since the interest is paid over 6 months, which is half of a year). Plugging these values into the formula, we get:

I = Prt = 4,200 * 0.03 * 0.5 = $63

So, Jimena will pay the store $63 in simple interest.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

7, 11, 15, 19, 23

Step-by-step explanation:

Since the common difference is 4 each successive term is 4 more than the previous term

If we let aₙ be the nth term,

a₁ = 7

a₂ = 7 + 4 = 11

a₃ = 11 + 4 = 15

a₄ = 15 + 4 = 19

a₅ = 19 + 4 =23

The first five terms are: 7, 11, 15, 19, 23

We can also use the generalized formula for the nth term:

aₙ = a₁ + d(n - 1)

where a₁ = first term

d = common difference

Plugging in the known values we get
aₙ = 7 + 4(n- 1)

aₙ = 7 + 4n - 4

aₙ = 3 + 4n

Substituting n = 1, 2, 3, 4, 5 into the above equation will yield the same values

Maybe your teacher prefers one of the above approach.

Answer:

17%

Step-by-step explanation:

area represents the populations

United States has a radius of 4.2 cm and

India has a radius of 8.7 cm.

If 4% of the world's population is in United States,

what percentage of the world's population is in India

US π r² = π*4.2²

India π r² = π*8.7²

so india/US = 4.29

so india = 4.29 *4% = 17%

The number of different ways that the letters of "recommend" can be arranged is 90720.

What is arrangement?

Generally speaking, an arrangement of objects is just a collection of them. A combination (order is ignored) or permutation is used to determine the number of "arrangements" of the components (order is significant). An arrangement is a group of hyperplanes that divides a space into cells.

If there are n different objects in the system then the number of different ways of arrangement of n objects is n!

If the repetition of the objects are allowed in the system the number of different ways of arrangement is -

n! / (no. of repetition of object 1)! .... (no. of repetition of object r)!

Total number of letters in the word "recommend is 9.

The number of different ways of arangement of the 9 letters is 91

The repetition of letter "e" is 2 and repetition of letter "m" is 2.

The number of different ways that the letters of "recommend" can be arranged is -

9! / 2! × 2!

(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1) × (2 × 1)

(9 × 8 × 7 × 6 × 5 × 3 × 2 × 1)

90720

Therefore, the number of different ways is 90720.

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The domain of the linear function shown in the graph is given as follows:

{x | 2 ≤ x ≤ 9}.

The domain of a function is composed by the set containing all the possible input values for the function, hence it is composed by all the values of x assumed by the function.

The bounds of the domain in this problem are given as follows:

Hence the correct option regarding the domain of the function is given by the second option.

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Answer: Sure! To simplify the expression -3y + 4 - 2 + 6y, we'll follow these steps:

Start by combining like terms:

-3y + 6y = 3y

Next, add the constant terms:

3y + 4 - 2 = 3y + 2

Finally, simplify the expression by substituting the values:

3y + 2 = 3y + 2

So the simplified expression is 3y + 2.

Step-by-step explanation:

Answer: Let's call the increase from 15 to 20 as "z".

So, 20 is (z / 15) * 100% greater than 15, or x = (z / 15) * 100.

And, 15 is (z / 20) * 100% less than 20, or y = (z / 20) * 100.

Since z is the same in both equations, we can set the two equations equal to each other:

x = (z / 15) * 100

y = (z / 20) * 100

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

An isosceles triangle has two sides of equal length.

All interior angles in an isosceles acute triangle are less than 90°.

Therefore, it is not possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100° as two sides are not of equal length and 100° > 90°.

If we are to write the following polynomial in descending powers of the variable and with no missing powers 3x^3 -70, it would be 3x^3 - 70 + 0x^2 + 0x + 0

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Hence, it can be seen that descending order is basically when the power of a term decreases for each succeeding term. For example, x3 + x2 + x or 2 x4 + 3 x2 + 7 x are arranged in descending order. Descending order is more commonly used.

The polynomial in descending powers of the variable with no missing powers is:

3x^3 - 70 = 3x^3 - 70 + 0x^2 + 0x^1 + 0x^0

= 3x^3 - 70 + 0x^2 + 0x + 0

Note: The polynomial can also be written as 3x^3 - 70x^0.

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The equation of the line that is perpendicular to 5x-8y=-6 and passes through (4,-4) is y = (-8/5)x + 16/5.

Parallel lines are two or more lines in a coordinate plane that are equidistant from each other at all coordinates.

The given line can be rewritten in slope-intercept form as y=(5/8)x+(3/4), where the slope is 5/8. So, any parallel line will also have a slope of 5/8.

Using the point-slope form of a line, we can write the equation of the line as:

y - (-4) = (5/8)(x - 4)

Simplifying, we get:

y = (5/8)x - 23/8

Therefore, the equation of the line that is parallel to 5x-8y=-6 and passes through (4,-4) is y = (5/8)x - 23/8.

The slope of the given line is 5/8, so the slope of any line perpendicular to it will be -8/5.

y - (-4) = (-8/5)(x - 4)

Simplifying, we get:

y = (-8/5)x + 16/5

Therefore, the equation of the line that is perpendicular to 5x-8y=-6 and passes through (4,-4) is y = (-8/5)x + 16/5.

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Answer:

Part A: 23

Part B: n < 77

Step-by-step explanation:

All possible values of r for which this infinite geometric series is defined is the interval (-1,1).

The infinite geometric series is given by:

[tex]\[2 6r 18r^2 54r^3 \dotsb\][/tex]

This is a geometric series, so it is defined when the absolute value of the common ratio (r) is less than 1. The common ratio of this series is r, so the series converges when |r| < 1. Mathematically, this can be expressed as follows:

|r| < 1

-1 < r < 1

Therefore, all possible values of r for which this infinite geometric series is defined is the interval (-1,1).

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The velocity of the particle v as a function of time t is given by v(t) = 36 - 0.10 * t^2 cm/s and the position x as a function of time t is given by x(t) = 36 * t - 0.05 * t^3 cm.

The problem states that at time t = 0, the particle has an initial velocity of v = 36 cm/s and is located at x = 0 cm. The particle is accelerating with a=-0.10 V v. This means that the velocity of the particle is changing by -0.10 V v each second. This can be expressed in terms of the time t as v(t) = 36 - 0.10 * t^2 cm/s. The position of the particle at any time t can be expressed as x(t) = x0 + v0 * t + 1/2 * a * t^2, where x0 is the initial position and v0 is the initial velocity. In this case, x0 = 0 and v0 = 36, so the position of the particle at any time t can be expressed as x(t) = 36 * t - 0.05 * t^3 cm. This means that the particle will move away from the origin (x=0) and its velocity will decrease each second.

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Answer:

Step-by-step explanation:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Triangles PQR and ZQX are similar!

Square side => a

XZ / (PQ - PZ) = PR / PQ

a / (12 - a) = 8 / 12

a = 4.8

The side length of the square PZXY is sqrt(2).

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side².

We have,

Since triangle PQR is a right triangle, we can use the Pythagorean theorem to find the length of QR:

QR² = PQ² + PR²

QR² = 1² + 1²

QR² = 2

QR = √2

Since PZXY is a square, its sides are equal in length.

Let's denote the length of one side of the square as s.

Then, we can write:

PR = PX + RX

1 = s + QY

Since QY = PZ = s and PX = QX = QR - QY = sqrt(2) - s,

we can substitute these values into the equation for PR to get:

1 = s + (√2 - s)

1 = √2

Therefore,

The side length of the square PZXY is √2.

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Approximately 99.7% of the vehicles travel between 53 miles per hour and 77 miles per hour.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The mean and the standard deviation for this problem are given as follows:

Hence:

Meaning that the approximate percentage is of 99.7%.

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Answer:

frequency

Step-by-step explanation:

Hopefully you pass but without seeing the boxes i cant see! but the answer should be D or E

This formula divides the number of cars in Cell C92 by the average number of people in Cell B92, and calculates the cars per person on day one.

This formula divides the number of cars in Cell C92 by the number of people in Cell B92, and calculates the cars per person on day one. By typing =C92/B92, you can easily calculate the number of cars per person in a single cell. This formula can be used for any data set, and will always give an accurate result. It is an effective way to compare the ratio of cars to people in a given situation, and to compare the results to other data sets. The formula is also simple to use and understand, which makes it a powerful tool for quickly analyzing data. It is a useful tool for making decisions, as it allows you to assess the ratio of cars to people quickly and accurately.

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Therefore , the solution of the given problem of expression comes out to be 10⁸ One hundred million.

In arithmetic, addition, algebra, and division are necessary. They result in the following when combined: An equation, some statistics, and a mathematical function Values, parameters, and arithmetic processes like additions, subtractions, matrix multiplication, and divisions can all be found in a declaration of fact. Different phrases and terms can be compared and evaluated.

Here,

Given :

Expression : 100000000

To convert into short expression

So,

=> 10⁸

Thus ,One hundred million.

Therefore , the solution of the given problem of expression comes out to be 10⁸ One hundred million.

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