An arithmetic sequence begins with 56, 59, 62, 65, 68, ...
Which option below represents the formula for the sequence?
O f(n) = 56 + 3(n − 1)
-
Of(n) = 53+ 3(n-1)
O f(n) = 56 + 3(n)
Of(n) = 53 + 3(n + 1)

No, I'm not agree with Noah. Because the equation 1. 20(d+5)=42 is a mathematical equation and can be false depending on the value of the variable d.

The equation 1. 20(d+5)=42 is a mathematical equation that contains a variable d. The equation states that when you multiply 20 with (d+5) the result should be 42.

The equation is true if there is a value of d that makes the equation true. For example, if d=1, then 20(1+5)=20(6)=120 which is not equal to 42, so this value of d does not make the equation true.

On the other hand, if d=-7, then 20(-7+5)=20(-2)= -40 which is equal to 42, so this value of d makes the equation true.

Therefore, the equation can be true or false depending on the value of the variable d. In general, without knowing the specific context or situation in which the equation is being used, it is impossible to determine if the equation accurately represents a situation or not.

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Answer:

64 sequences of 4 fish are possible.

Answer:

Step-by-step explanation:

9 - 3 = 6

6/10 = 3/5

Answer:

6/10 and/or 3/5(this is the answer simplified

Step-by-step explanation:

Subtract: 9/10 - 3/10

= 9 - 3/10

= 6/10

= 2 · 3/ 2 · 5

= 3/5

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 3/5. In other words - nine tenths minus three tenths is three fifths.

In an amphitheater, seat are arranged in 50 semi-circular row-facing a dome Tate. The first row contain 23 seat, and each row contain 4 more eat than the previous row. Therefore, there are 6050 seat are in the amphitheater.

Given that:

There are total 50 semi circular row.

In the first row there are 23 seats.

The given problem is AP series:

Arithmetic Series:

An arithmetic sequence is defined as an algebraic sequence in which each successive term has an equal difference. It is obtained by adding a constant to any preceding term. For the first term 'a' and the tolerance 'd' of the AP, here is a list of commonly used arithmetic progressions to solve various AP related problems:

where l is the last term in the arithmetic progression.

Now,

Sum of n terms  = n/2 [ 2a + (n-1)d]

                          = 50/2 [ 2× 23 + (50 -1)4]

                          = 25 [46 + 49×4]

                          = 25 × 242

                          = 6050

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The table that is a justification for the given solution to the system of equations is table 1

The two linear equations are

y=4x-9 and

y=2x-5

We that the following points for x : -1, 0, 1, 2, 3

When we substitute the values in the two equations we will have

x           y₁              y₂

-1         -13             -9

0           -9             -5

1             -5            -3

2            -1              - 1

3            3                1

Conclusively the values of y₁, and y₂ are shown in the table above

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The projected Population in 2020 is given by 4146.

Compounding is the method through which interest is added to both the principle balance already in place and the interest that has previously been paid. Thus, compounding may be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has previously accrued over the course of prior periods are used to compute compound interest.

Number of years to compound is 10 years from 2010 to 2020.

The population deplition is 0.6 % = next year population is 99.4% of present.

So population after 10 years = 4403 * [tex].994\x^{10}[/tex] = 4145.84 =4146

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Perfect squares NEVER be irrational numbers.

Repeating decimals will ALWAYS be rational numbers.

Irrational numbers will NEVER be able to be written as fractions.

A square number, also known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number since it equals 3² and is represented by the symbols 3 × 3.

A number whose decimal representation eventually becomes periodic is known as a repeating decimal, also known as a recurring decimal.

All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to express an irrational number as the ratio of two integers.

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Complete question

Fill in the following statements with either "sometimes ", "always ", or "never " in order to make it a true statement.

Perfect squares _______be irrational numbers

Repeating decimals will_____be rational numbers

Irrational numbers will____ be able to be written as fractions

Since the square root of a negative number does not exist in the real numbers, there are no real solutions for x. Therefore, the system of equations has no solutions.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.

To solve this system of equations algebraically, we can substitute y = x-3 into the first equation

y = x² - 15x + 60

x-3 = x² - 15x + 60

x² - 16x + 63 = 0

We know that this quadratic equation has no real solutions because its discriminant (b^2 - 4ac) is negative, so the system of equations has no real solutions.

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Answer:

Step-by-step explanation:

122121

The equation of the line found is:

y = 3x + 1.

Since the rate of change is always the same, that is, when x changes by 1, y always changed by the same value, this is a linear equation.

Linear equation:

A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant. The standard form of linear equations in two variables is of the form Ax + By = C. where x and y are variables, A and B are coefficients, and C is a constant.

The equation of a line is given by:

y = mx + b

In which:

m is the slope, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

From the table, when x =0 and y =1 , thus b = 1.

When x = and y = 1 . When x =1 and y = 4 , when x = 2 and y =7  , and so on. That is, when x changes by 1, y changes by 3, and the slope is m = 3.

The equation of the line is:

    y = 3x + 1.

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The length of the ramp is 161.62 inches when the barrel turns 47 times in being rolled up the ramp.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

The circumference of the circular base of the barrel is given by the formula C = πd, where C is the circumference and d is the diameter of the base.

In this case, d = 1.1 inches, so C = π1.1 inches = 3.46 inches.

Since the barrel turns 47 times, the distance it travels is 47 times the circumference of the base,

47 × 3.46 inches = 161.62 inches

Therefore, the length of the ramp is 161.62 inches.

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Answer: The input values for this function are the number of hours traveled, represented by the variable h. Therefore, appropriate input values for this function would be any positive number representing a number of hours traveled.

For example, some appropriate input values could be:

h = 1: This represents 1 hour of travel, or a total distance of 140 miles.

h = 2: This represents 2 hours of travel, or a total distance of 280 miles.

h = 3.5: This represents 3.5 hours of travel, or a total distance of 490 miles.

Note that the input values do not have to be whole numbers, they can be any positive number representing a number of hours traveled.

Step-by-step explanation:

A reflex angle is an angle which measures more than 180 degrees and less than 360 degrees.

There are different types of angles in geometry, such as obtuse, acute and right angles, which all are under 180 degrees.

Assume, z is an acute or obtuse angle, and r is the reflex angle, then:

z + r = 360

r = 360 - z

Therefore, we can find the related reflex angle(r), if we know the value of the acute or obtuse angle(z).

A reflex angle equals the summation of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,

Reflex angle = 180° + Acute angle

Reflex angle = 180° + Right angle

Reflex angle = 180° + Obtuse angle

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The probability that the sum of the 2 dice rolls will not be greater than 8 are 8 : 13.

When the probability of an event occurring is know, it is easy to calculate the probability that the event does not occur. Hence, If P(A) is the probability of event A, then 1 - P(A) is the probability that the event does not occur.

the probability that the sum of the 2 dice rolls being greater than 8 are expressed in the ratio 5:13 and expressed in fraction as 5/13

then;

probability that the sum of the 2 dice rolls will not be greater than 8 = 1 - 5/13

probability that the sum of the 2 dice rolls will not be greater than 8 = (13 - 5)/13

probability that the sum of the 2 dice rolls will not be greater than 8 = 8/13

Therefore probability that the sum of the 2 dice rolls will not be greater than 8 can be expression as the ratio 8 : 13

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Answer:

36

Step-by-step explanation:

let the number be 10x+y

x - y = 3 (eq 1)

given: y = 2x (eq 2)

putting 2 in 1

x - 2x = 3

-x = 3 (we can ignore the negative sign for now because we only need to find the absolute value)

y = 6

number is 36

Answer:

scale factor = 3

Step-by-step explanation:

since the origin is the centre of dilatation then the scale factor is the ratio of corresponding coordinates, image to original.

given D (12, - 4 ) and D' (36, - 12 ) , then

scale factor = [tex]\frac{36}{12}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3

Recently, the Town of Aberdeen announced they were going to acquire a large parcel of land for a new park initiative.

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The four ways are 1) Factoring 2) Completing the Square 3) Quadratic Formula  and 4) Graphing

1. Factoring: Factoring is the process of breaking down an expression into its simplest components. To solve a quadratic equation using factoring, you must start by writing the equation in standard form (ax² + bx + c = 0). Then, you must factor the equation into two binomials (x + a)(x + b) = 0. Once this is done, you can solve for x by setting each factor equal to zero and solving for x.

2. Completing the Square: Completing the square is another method of solving a quadratic equation by rewriting it in the form of (x + a)² = b. To do this, you first start by writing the equation in standard form (ax² + bx + c = 0). Then, you must rearrange it so that all the terms are on one side of the equation and the constant is on the other side. Next, divide the coefficient of x² by two and then square this number. Finally, add this number to both sides of the equation, which will then allow you to solve for x.

3. Quadratic Formula: The quadratic formula is a useful tool for solving quadratic equations.

4. Graphing : is another method useful for solving quadratic equation.

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Answer:

  25%

Step-by-step explanation:

Of the 12 girls and 16 boys in Mr. Johnson's class, 3 girls and 4 boys wear glasses. You want to know the percentage of students in the class who wear glasses.

The percentage is the fraction multiplied by 100%. The fraction is the ratio of glasses-wearers to total students.

  percentage = (girls w/ glasses + boys w/ glasses)/(girls + boys)×100%

  percentage = (3 +4)/(12+16) × 100% = 7/28 × 100% = 25%

25% of the students in Mr. Johnson's class wear glasses.

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The equivalent expression of 5[tex]x^{3/2}[/tex] is  5√(x³). The correct option is last one.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

5[tex]x^{3/2}[/tex]

To find the equivalent expression:

We have to simplify the expression,

5[tex]x^{3.1/2}[/tex]

= 5(x³)[tex]){1/2}[/tex]

= 5√(x³)

The above expression is an equivalent expression.

Therefore, 5√(x³) is an equivalent expression.

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Answer: 7

Step-by-step explanation:

1. You need to know that the input value means the x-value, which means x = 3.

2. Input 3 in the function

3. Solve 3+4

4. 3+4 = 7

Answer:

put y=4 then four comes with- and 4-3=2

40% of Damien’s marbles are 6/5 or 1.2.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Damien has three marbles.

40% of Damien’s marbles are blue.

That means,

40% of 3 blue marbles.

So, using the percentage formula,

40% of 3,

= 40 x 3/100

= 120/100

= 12/10

= 6/5

= 1.2

Therefore, 1.2 marbles are blue.

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The required true statements for the given lines are 1 and 4.

An element or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.

Statement A: E and C are co-linear.

It is true, E and C are lie in same line

statement 2: Lines I and m intersect at point D.

It is false, I and m intersect at point E.

statement 3: AE and DC are line segments on line I

It is false,because AE and DC are line segments placed in different line.

statement 4: EA and EC are rays on the line m.​

It is true, as EA and EC are in same line m.

Thus, required true statements are 1 and 4.

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Answer:

1 and 4

Step-by-step explanation:

The slope of the line through (-9,6) and (-6,-9) is -5

Now, According to the question:

Let's know:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The formula for the slope of a line when two points (coordinate pairs)

[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are given is :

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] ,  where m denotes the slope of the line.

Applying this formula, we get:

[tex]m = \frac{-9-6}{-6-(-9)}[/tex]

[tex]m = \frac{-15}{-6+9}[/tex]

m = [tex]\frac{-15}{3}[/tex]

m = -5

Hence, The slope of the line through (-9,6) and (-6,-9) is -5.

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The complete question is this:

What is the slope of the line through (-9,6) and (-6,-9) ?

[tex] \longmapsto \: 2(2x - 1 + x + 9) = 103 \\ \\ \longmapsto \: 2(3x + 8) = 106 \\ \\ \longmapsto \: 6x +16 = 106 \\ \\ \longmapsto \: x = \frac{90}{6} \\ \\ \longmapsto \: x = 15 [/tex]

So,

[tex]l = 2 \times 15 - 1 = 29 \\ \\ b = 2 + 15 = 17[/tex]

The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the breadth (or width) of the rectangle.

In this case, we know that the perimeter is 106 cm, so we can set up the equation:

106 = 2(l + (X + 9))

106 = 2l + 2X + 18

We also know that the length of the rectangle is 2X - 1, so we can set this equal to l:

2X - 1 = l

Now we have a system of two equations with two unknowns (l and X). We can substitute the value of l from the second equation into the first equation and solve for X:

106 = 2(2X - 1 + (X + 9))

106 = 2(3X + 8)

106 = 6X + 16

90 = 6X

X = 15

Now that we know the value of X, we can substitute it back into the equation for the length of the rectangle to find the length:

l = 2X - 1 = 2(15) - 1 = 29 cm

And then we can use the value of X again to find the breadth:

w = X + 9 = 15 + 9 = 24 cm

So the length of the rectangle is 29 cm and the breadth is 24 cm.

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Therefore , the solution of the given problem of percentage comes out to be  athletes who took move  285 to finish the race is 64%.

A percentage is what is used to describe a fraction of a whole when it is stated as a number range between 0 and 100. 100% of something, 50% of something, and 0% of something are all equal. After dividing the portion of the whole by the entire, multiply the result by 100 to arrive at a percentage.

Here,

For the table to get the total frequency is:

=> 3+6+9+7

=>9+9+7

=>25

The frequency greater than 285 is

9+7 = 16

So,

the percentage of the athletes who took move  285 to finish the race is:

=> 16/25 * 100

=> 0.64 * 100

=> 64%

Therefore , the solution of the given problem of percentage comes out to be  athletes who took move  285 to finish the race is 64%.

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The exponential function that models the population of bluefin tuna after x years is given as follows:

y = 1550(0.96)^x.

The parameters of the exponential function are given as follows:

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

When he first started monitoring the population, there were about 1,550 bluefin tuna in the bay, meaning that the parameter a is given as follows:

a = 1550.

One year later, he estimated that the population of bluefin tuna had decreased to about 1,488, hence the parameter b is obtained as follows:

b = 1488/1550 = 0.96.

Hence the function is defined as follows:

y = 1550(0.96)^x.

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To fill one urn with one white ball and the second urn with the remaining nine white and ten black balls.

Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. A coin flip is the most basic illustration. There are only two outcomes that can occur when you flip a coin: either heads or tails.

The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or P(A) = f/N

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Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.

Age of Myrka = 3x + Age of Geoff

3x + 3 = 48

3x = 48 - 3

3x = 45 x = 15

Geoff is therefore 15 years old.

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