Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his investment after x years: f(x)

A variable-containing expression that divides by a variable, contains fractional or negative exponents, or is enclosed in a radical is not a polynomial.

As long as the polynomial is specified over the real numbers, it is possible for it to have negative coefficients, fractional coefficients, or even radical coefficients.

There cannot be a negative exponent in a polynomial. The exponent of a variable in any term of a polynomial must, by definition, be a nonnegative integer, such as 0, 1, 2, 3, 4, etc. The exponents of variables do not contain fractions, decimals, or negative numbers. There cannot be a variable with a fractional exponent in a polynomial.

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In 2x^3, 3 is the greatest degree of the exponent. 2x^3 is a cubic polynomial as a result.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An example of a polynomial of a single indeterminate x is x² − 4x + 7.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.

For instance, the polynomial 3x+2x-5.

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

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At 2 miles, both the bus and the taxi will cost $6.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given that the fare on bus is $3 per mile.

The taxi fare of taxi is $4. 00 plus $1. 00 per mile.

Assume that at x miles both fare will be the same.

The fare for x miles in bus is $3x.

The fare for x miles in taxi is $4 + $x

Equate to the fares:

3x = 4 + x

Subtract x from both sides:

3x - x = 4

2x = 4

Divide both sides by 2:

x = 4/2

x = 2.

The fare for 2 miles in bus is $3×2 = $6.

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The range of the function y = √(x +5)  is y ≥ 0

The domain of a function is the set of all possible values of x

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

we have

y = √(x +5)

Remember that the radicand of the function must be greater than or equal to zero

so (x +5) ≥ 0

solve for x

x ≥ -5

The domain is the interval ----> [-5,∞)

For x= -5

y = √(-5 +5) = 0

so

The range is the interval ----> [0,∞)

y ≥ 0

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To find the y-coordinate of the solution, we can substitute in this value for y and round it to the nearest tenth: y = -2.2

system of coordinates, Arrangement of reference lines or curves for locating points in space The Cartesian (named for René Descartes) system is the most popular one in two dimensions.

To solve for y in the equation 5x + 2y = 21, we can start by isolating y on one side of the equation. To do this, we can subtract 5x from both sides of the equation:

5x + 2y = 21

5x - 5x + 2y = 21 - 5x

2y = 21 - 5x

To solve for y, we can then divide both sides of the equation by 2:

2y = 21 - 5x

y = (21 - 5x) / 2

To solve for y in the equation -21 + 6y = -34, we can start by isolating y on one side of the equation. To do this, we can add 21 to both sides of the equation:

-21 + 6y = -34

-21 + 21 + 6y = -34 + 21

6y = -13

To solve for y, we can then divide both sides of the equation by 6:

6y = -13

y = -13/6

y = -2.1666666666666665

To find the y-coordinate of the solution, we can substitute in this value for y and round it to the nearest tenth:

y = -2.2

So, the y-coordinate of the solution is -2.2.

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Answer:

Find the value of xx in the equation below.

11=

11=

\,\,x -6

x−6

Step-by-step explanation:

Answer: 8 feet

Step-by-step explanation:

you take 33-25 to get the sum of 8. so the squid is 8 feet longer than the shark.

On solving the provided question, we can say that by the help of unitary method total 28 + 40 = $ 68

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

One package of chicken costs  = $7

steaks cost  = $4 per pound.

cost of 4 chicken = 4 * 7 = $28

cost of 10 steaks = 4*10 = $40

total 28 + 40 = $ 68

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The value of each trigonometric ratio is given by :

sin A = 5/13 , cos A = 12/13, tan A = 5 / 12

cosec A = 13 /5 , sec A = 13/12 , cot A = 12 /5.

As given in the question,

Let us consider a triangle be ABC,

Figure is attached.

Side length is given by:

AC = 39

AB = 36

BC = 15

AC represents the longest side

( 36 )² + (15)² = (39)²

⇒AB² + BC² = AC²

By Pythagorean triplets ABC is right angled triangle.

All trigonometric ratio with respect to angle A is given by :

sin A = BC / AC

        = 15/39

        = 5/13

cos A = AB / AC

         = 36 /39

         = 12 /13

tan A = BC / AB

         = 5 /12

cosec A = 1/ sin A

              = 13 /5

sec A = 1/ cos A

         = 13 /12

cot A = 1 / tan A

         = 12 /5

Therefore , the value of all six trigonometric ratio is equal to

sin A = 5/13 , cos A = 12/13, tan A = 5 / 12

cosec A = 13 /5 , sec A = 13/12 , cot A = 12 /5.

The above question is incomplete , the complete question is :

Find the value of each trigonometric ratio tan A

Figure is attached.

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In parallelogram, x=7 and AC = 44 units are the values of x and AC .

What do math parallelograms mean?

A unique kind of quadrilateral known as a parallelogram is defined by having both pairs of its opposite sides parallel and equal.

                       A parallelogram ABCD with the coordinates AB II CD and AD II BC can be seen in the provided illustration. Moreover, AB = CD and AD = BC. Non-Example: A parallelogram is not represented by a trapezium.

Here in parallelogram ABCD , AC and Bd are diagonals intersecting at E.

BE = 2x + 2, BD = 5x – 3, and AE = 4x – 6

Using (i)

   BE  = BD/2

 2x + 2 = (5x- 3)/2

2(2x + 2) = 5x - 3

  4x + 4 = 5x - 3

   x = 7

Now , AE = 4(7)-6 = 28-6 = 22

AC =2 AE = 2 (22) =44 units.

Hence, x=7 and AC = 44 units.

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Answer:

x = 90

Step-by-step explanation:

The diagram shows that angles 1 and 4 correspond with each other. Given that the two lines should be parallel, corresponding angles have the same answer. When corresponding angles cross at the same relative location (known as the junction), they will have the same angle measure.

So, set the 1st and 4th angles equal to each other.

3x-160 = x+20

2x = 180

x=90

Answer:x=90

Step-by-step explanation:Angles 1 and 4 must be equal to each other, as they are corresponding angles, so you set 3x-160 equal to x+20 and after solving, you get x is equal to 90.

Answer:468

Step-by-step explanation:cause of the max mark is 650 /100=6.5 (1%)

then 6.5*72=468

Answer:

To find out how many cups a single jug of water fills, you can divide the total number of cups filled by the number of jugs:

184 cups / 23 jugs = <<184/23=8>>8 cups/jug

This means that one jug of water fills 8 cups.

Step-by-step explanation:

Given line in point-slope form:

Point-slope form is:

We know that to graph a line it is enough two have two points.

One of the points is (x₁, y₁) = (1, - 3).

Find one more point, when x = 3:

The point is (3, 1).

Plot and connect these two points to get the line.

A recursive formula for the sequence is:  f(n+1) = f(n)-99.4, n ≥ 1

Consider the given sequence.

99.4, 0, -99.4, -198.8, . . .

We can observe that each next term of the sequence is decreased by -99.4

i.e., f(0) = 99.4

f(1) = f(0) - 99.4

f(1) = 99.4 - 99.4

f(1) = 0

f(2) = f(1) - 99.4

f(2) = 0 - 99.4

f(2) = -99.4

From these calculations we can say that the n-th term would be,

f(n) = f(n - 1) - 99.4

Therefore, recursive formula:  f(n+1) = f(n) - 99.4

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The null hypothesis exists that the standard deviation σ exists equivalent to 0.62. The alternative hypothesis exists that it does not equivalent 0.62.

Statistical hypothesis testing employs null and alternate hypotheses. While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no association between variables.

A proposed claim or defense in the hypothesis test is referred to as an alternative hypothesis in statistics. In most cases, it supports the research premise and shows that there is a statistical relationship between the variables. It is one of the two statements in statistical hypothesis testing that are mutually exclusive.

H₀: σ = 0.62

H₁: σ ≠ 0.62

The null hypothesis exists that the standard deviation σ exists equivalent to 0.62.

The alternative hypothesis exists that it does not equivalent 0.62.

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The value of the equation A = 14 ± 9 μg/g and the term ±9 represents the margin of error

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 14 ± 9 μg/g   be equation (1)

Now , the value of A can have two values p and q

where , the value of p = 14 + 9 μg/g

p = 23 μg/g

And , the value of q = 14 - 9 μg/g

q = 5 μg/g

On simplifying the equation , we get

It means the margin of error which is no sampling method can guarantee that the sample matches the exact population

]Hence , the researchers are confident that the true average concentration for all the males with epilepsy in the study is between 5 μg/g and 23 μg/g

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There are 100 pennies in 1 dollar, so Priya collected 2400/2.5=<<2400/2.5=960>>960 pennies.

This means Priya raised 960/100=$<<960/100=9.60>>9.60. Answer: \boxed{9.60}

The prime factor trees for 24 and 84 are attached in the image below. The Lowest Common Multiple of 24 and 84 is 168.

A natural number other than 1 whose only factors are 1 and itself is said to be a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). A prime factor is a natural integer, other than 1, whose sole factors are itself and 1. Actually, 2, 3, 5, 7, 11, and so forth are the first few prime numbers. The term "Lowest Common Multiple" refers to the common multiple of two or more natural integers that is the lowest (LCM).

The prime factors of 24 are: 2,2,2 and 3.

The prime factors of 84 are: 2,2,3 and 7.

Now, The Lowest Common Multiple (LCM) of 24 and 84 is calculated using the prime factors of both the numbers.

LCM= 2*2*2*3*7= 168

Hence, The Lowest Common Multiple of 24 and 84 is 168.

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The sine of an acute angle in a right triangle is the ratio of the angle of the triangle to the opposite side of the hypotenuse.

Trigonometric ratios:

Trigonometric ratios are the ratios of the lengths of the sides of a triangle. These ratios in trigonometry relate the aspect ratio of a right triangle to each angle. A basic trigonometric ratio is the ratio of sin, cos, and tan, or the ratio of sin, cos, and tangent. Other important trigonometric ratios cosec, sec, and cot can be derived from sin, cos, and tan, respectively.

Acute Sine Ratio:

The tangent function examines the ratio of his two legs of a right triangle. You can also use the ratio of leg length divided by hypotenuse length.

In a right triangle, each angle has an opposite side and an adjacent side. And there is always a hypotenuse. On the opposite side and the hypotenuse we are dealing with the sine ratio. The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse. In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

Let's examine some properties of the sine ratio using the Pythagorean theorem. For a right triangle, let the lengths of the triangle be a, b, and c. where a is the length of the other side of A and b is the length of the other side of B.

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The correct option is (d).

The function that could be used to model the current population is P(t) = 1,260(1.02)

This function models the growth of the population over time, t. The base population is 1,260 and the growth factor is 1.02, which represents a 2% increase. The function multiplies the base population by the growth factor to find the new population after one year.

The other options are not correct because:

P(t) = 1,260(1.2) is incorrect because the growth factor is incorrect, it's 1.2 which represents a 20% increase, which is too much compared to the 2% increase mentioned in the problem statement.

p(t) = 1,260(1.002) is incorrect because the growth factor is incorrect, it's 1.002 which represents a 0.2% increase, which is too small compared to the 2% increase mentioned in the problem statement.

P(t) = 1,260(0.02) is incorrect because the growth factor is incorrect, it's 0.02 which represents a 2% increase, but it is not raised to the power of t.

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The work would be finished 3 times faster if they had been doing the work at the same time. The correct option is B.

Assumption;

Provided each one of the workers works for an hour which is equivalent to the time it takes to finish the hole.

In essence, the total time required to finish the ditch by 2 workers is; 2 hours.

Hence, for 3 workers working simultaneously, the time required is

1hour  = 60 minutes

However, since they took 1 hour turns on the job, it follows that; The total time used is;

Total time = 3 × 1hr = 3 hours = 180 hours

Hence they could have finished the work in;

R = 180/60 times faster =3 times faster.

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The correct answer is that we cannot conclude that being able to read is beneficial for them as there can be various cause and effect relation.

A research is conducted to collect information about a specific topic for the purpose of study. A group of population is asked to fill a survey form or answer questions based on the research topic.

This data is collected and analyzed to get the required result.

Here, in this question kindergarten students are the population from whom data is collected . Here, the conclusion is that having the ability to read and write from before only doesn't means they will have academic intelligence later.

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The sum of length of the parallel sides of a trapezium exists 300 cm.

A trapezoid, which is often referred to as a trapezium, is a flat, closed object with four straight sides and one set of parallel sides. A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. Also possible are parallel legs on a trapezium.

Four sides, four corners/vertices, and four angles make up a trapezium, which is a closed shape or polygon. A trapezium has parallel sides on each of its opposing angles.

One set of the sides of a trapezium is parallel only. Since no trapezium is a rectangle, they are not all the same.

Area of trapezium = (a + b)/2 × h

where h is the perpendicular height, and a and b are parallel sides.

So, (a + b) exists sum of length of bases of a trapezium.

Let the equation be

Area of trapezium = (a + b)/2 × h

substitute the values in the above equation, we get

⇒  4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}

simplifying the equation, we get

⇒ (84/280) × 10000 = a + b

⇒ a + b = 300 cm

Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.

The complete question is:

Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.

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The sum of length of the parallel sides of a trapezium exists 300 cm.

A trapezoid, also known as a trapezium, is a closed, flat object with one pair of parallel sides and four straight sides. The parallel bases and the non-parallel legs of a trapezium are called the bases and the legs, respectively. A trapezium with parallel legs is another option.

A trapezium is a closed shape or polygon with four sides, four corners, and four angles. Each of the opposing sides of a trapezium has parallel sides.

A trapezium has only one set of parallel sides. They are not all the same since no trapezium is a rectangle.

Area of trapezium = (a + b)/2 × h

where h is the perpendicular height, and a and b are parallel sides.

So, (a + b) exists sum of length of bases of a trapezium.

Let the equation be

Area of trapezium = (a + b)/2 × h

substitute the values in the above equation, we get

⇒  4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}

simplifying the equation, we get

⇒ (84/280) × 10000 = a + b

⇒ a + b = 300 cm

Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.

The complete question is:

Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.

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Answer:12+2y

Step-by-step explanation:Multiple the -2 by each value inside of the parenthesis, -2 * -6 = 12, -2 * -y = 2y, then add these together to get 12+2y.

To prove the inverse :

You assemble the functions (that is, insert x into one function, plug that function into the suggested inverse function, then simplify) and check that you end up with simply "x" to establish (or refute) that two functions are the inverses of one another. The functions are inverses if you get x; otherwise, they are not.

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The general solution is [tex]$$y=c_3 e^x+c_4 e^{-x}+\frac{1}{2} x \sinh x \text {. }$$[/tex]

Consider the following differential equation: y'' − y = cosh x

The given differential equation in the operator form will be: (D^2-1)y=coshx

The auxiliary equation of the corresponding homogeneous equation will be:

m^2-1 = 0

=>m^2=1

=>m=+1,-1

So, the complementary function will be [tex]y_c=c_1 e^x+c_2 e^{-x}.\alpha[/tex]

Now, let [tex]y_1=e^x, y_2=e^{-x}.[/tex]

Compute the Wronskian determinant:

[tex]$$\begin{aligned}W\left(y_1, y_2\right) & =\left|\begin{array}{ll}y_1 & y_2 \\y_1^{\prime} & y_2^{\prime}\end{array}\right| \\& =\left|\begin{array}{ll}e^x & e^{-x} \\e^x & -e^{-x}\end{array}\right| \\& =-e^x e^{-x}-e^x e^{-x} \\& =-2\end{aligned}$$[/tex]

Since the given differential equation is already in the form [tex]$y^{\prime \prime}+P(x) y^{\prime}+Q(x) y=f(x)$[/tex] (that is, the coefficient of y'' is 1 ),

So identify:

f(x)=cosh x

Then, calculate the values of u_1' and u_2', using formulas as follows:

[tex]$$\begin{aligned}u_1^{\prime} & =-\frac{y_2 f(x)}{W} & u_2^{\prime} & =\frac{y_1 f(x)}{W} \\& =-\frac{e^{-x} \cdot \cosh x}{-2} & & =\frac{e^x \cdot \cosh x}{-2} \\& =\frac{e^{-x} \cdot\left(\frac{e^x+e^{-x}}{2}\right)}{2} & \text { and } & =-\frac{e^x \cdot\left(\frac{e^x+e^{-x}}{2}\right)}{2} \\& =\frac{1}{4}\left(1+e^{-2 x}\right) & & =-\frac{1}{4}\left(e^{2 x}+1\right)\end{aligned}$$[/tex]

Integrate on both sides of u_1' and u_2' with respect to ' x', to get:

[tex]$$u_1=\frac{x}{4}-\frac{e^{-2 x}}{8} \text { and } u_2=-\frac{x}{4}-\frac{e^{2 x}}{8} .$$[/tex]

So, the particular solution is,

[tex]$$\begin{aligned}y_p & =u_1 y_1+u_2 y_2 \\& =\left(\frac{x}{4}-\frac{e^{-2 x}}{8}\right) e^x+\left(-\frac{x}{4}-\frac{e^{2 x}}{8}\right) e^{-x} \\& =\frac{1}{4} x\left(e^x-e^{-x}\right)-\frac{1}{8}\left(e^{-x}+e^x\right) \\& =\frac{1}{2} x \sinh x-\frac{1}{8}\left(e^{-x}+e^x\right)\end{aligned}$$[/tex]

Thus, the general solution of the given differential equation is,

[tex]$$\begin{aligned}y & =y_c+y_p \\& =c_1 e^x+c_2 e^{-x}+\frac{1}{2} x \sinh x-\frac{1}{8} e^{-x}-\frac{1}{8} e^x \\& =\left(c_1-\frac{1}{8}\right) e^x+\left(c_2-\frac{1}{8}\right) e^{-x}+\frac{1}{2} x \sinh x \\& =c_3 e^x+c_4 e^{-x}+\frac{1}{2} x \sinh x\end{aligned}$$[/tex]

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Answer:

A fraction is a mathematical expression that represents the division of two numbers, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the number of parts in the whole. A fraction with a numerator of 6 and a denominator of negative 8 can be simplified to -3/4. To find an equivalent fraction, we can multiply or divide both the numerator and denominator by the same number without changing the value of the fraction. In this case, the fraction with a numerator of negative 8 and a denominator of 6 is equivalent to -4/3.

Step-by-step explanation:

The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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