You put $ 1500 into an account that pays 7% annual interest compounded continuously. How long will it be before you have $2000 in your account?

Answer:

(x-1)(x+1+3)=(x-1)(x+4)

All the expressions have a value of 3 except the expression 6 - 5.3.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

The math operation can be addition, subtraction, multiplication, or division.

We have,

-3( 4 - 5 )

= -3 x -1

[minus x minus = positive]

= 3

|-2| + 1 ( 3 - 2)

The absolute value is always positive.

= 2 + 1 x 1

= 2 + 1

= 3

-8 ÷ -4 + 1

Minus gets canceled.

= -8/-4 + 1

= 2 + 1

= 3

6 - 5. 3

= 6 - 15

= -9

Thus all the expressions have a value of 3 except the expression

6 - 5.3.

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Solution :

Properties of Functions:

Definition of a Function: A function is a rule or formula that associates each element in the set X (an input) to exactly one and only one element in the set Y (the output). Different elements in X can have the same output, and not every element in Y has to be an output.

Definition of the Domain of a Function: The set of all possible inputs of a function is defined as the domain. The domain of a real-valued function defined by a formula for y in terms of x will be the set of all x input-values that result in a real y output-value unless the domain of the function is further restricted.

Definition of the Range of a Function: The set of all possible outputs of a function is defined as the range. The range of a real-valued function defined by a formula for y in terms of x will be the set of all y output-values that result from the x input-values in the domain.

Function Notation: Given that f(x) is given by some formula containing x, f(B) will be the same formula with each x replaced by B.

Linear Function Definition: If a function may be written in the form f(x) = mx + b where x is the independent variables and m and b are constants, then f(x) represents a linear function. The variable m is defined as the slope and the point (0, b) represents the y-intercept. An equation in this form is known to be in Slope-Intercept Form.

Linear Function Slope Definition: Given that f(x) = mx + b, then m is defined as the slope where:

for any two points (x1, y1) and (x2, y2) on the line.  Graphically, the slope represents the change in y with respect to x on the graph of the line.

Linear Functions of Parallel Lines If two linear functions are given by f(x) = m1x + b and g(x) = m2x + b, and m1 = m2, then the graphs of f(x) and g(x) will consist of two lines that are parallel to each other.

Linear Functions of Perpendicular Lines If two linear functions are given by f(x) = m1x + b and g(x) = m2x + b, and m1 = -1/m2, then the graphs of f(x) and g(x) will consist of two lines that are parallel to each other.

Graphs of Even Functions Given a function f(x), if f(c) = f(-c) for all c in the domain, then f(x) is an even function and its graph will have symmetry with respect to the y-axis.

Graphs of Odd Functions Given a function f(x), if f(c) = -f(-c) for all c in the domain, then f(x) is called an odd function and its graph will have symmetry with respect to the origin.  Symmetry with respect to the origin implies that a 180-degree rotation of the graph about (0,0) results in an identical graph.

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After the inverse variation y = -28 when x = 2.

So,

To convert to an equation, multiply by k, the variation constant.

To find k, apply the given condition.

x = 8 when y = -7:

So, the equation is: y = -56/x

Therefore, y = -28 when x = 2.

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For the relations in this problem, we have that:

1.

2.

3.

A relation represents a function if each value of the input is mapped to only one value of the output.

For a point in the format (x,y), we have that:

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.

In a graph, the domain and the range are found as follows:

For the first relation, we have that input 10 is mapped to outputs 20 and 50, hence:

For the second relation, we have a graph with no vertically aligned points, hence:

For the third relation, we have a graph with vertically aligned points, hence:

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The total amount of that Harry will need for the project is nineteen and one third feet and Hence the option B is correct.

Addition of Fraction

Wood 1:

Length of each = 2 3/4 feet

Number of pieces = 4

Total = Length of each × Number of pieces

= 2 3/4 × 4

= 11/4 × 4

= 11 meters

Wood 2:

Length of each = 1 2/3 feet

Number of pieces = 5

Total = Length of each × Number of pieces

= 5/3 ×5

= 25/3 meters

Total amount of wood needed for the project = 11meters + 25/3 meters

= 11 +25/3

= (33+25)/3

= 58/3

=19 1/3 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and one third feet

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Answer:

x = 11

Step-by-step explanation:

3x = 2 + 31​

To find the value of x, combine like terms

3x= 33

Divide each side by 3

3x/3 = 33/3

x = 11

Find the value of x.

3x = 2 + 31

x = 11

=> 3x = 2 + 31

First, add the like terms.

=> 3x = 33

Transfer 3 to RHS

=> x = 33/3

Divide 33 by 3

=> x = 11

Answer:

9.53 x 10^5

Step-by-step explanation:

a x 10b

a = 9.53

b = 5

Answer:

9.53

Step-by-step explanation:

math math math math math math

Answer:

1.  y-intercept = 5

2.  x-intercept = -2.5

3.  slope = 2

4.  y = 2x + 5

Step-by-step explanation:

Part 1

The y-intercept is the point at which the line crosses the y-axis, so when x=0.  From inspection of the given graph, the y-intercept is 5.

Part 2

The x-intercept is the point at which the line crosses the x-axis, so when y=0.  From inspection of the given graph, the x-intercept is -2.5.

Part 3

The slope of the line is the measure of its steepness.  To find the slope of a line, substitute two points on the line into the slope formula.

Two points on the line are the y-intercept and the x-intercept:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-5}{-2.5-0}=\dfrac{-5}{-2.5}=2[/tex]

Therefore, the slope of the line is 2.

Part 4

Slope-intercept form of a linear equation:

[tex]\boxed{y=mx+b}[/tex]

Where:

Substitute the found slope and y-intercept from Part 3 and Part 1 into the formula to create an equation for the line:

[tex]y=2x+5[/tex]

The probability of taking out a pencil from the bag having 9 pens, 7 pencils and 6 crayons is 0.32.

We are given that:

We have-

Number of pens = 9

Number of pencils = 7

Number of crayons = 6

Now, the total number of objects in the bag = 9 + 7 + 6

Now, the total number of objects in the bag = 22

We have to find the probability of taking out a pencil from the bag.

P ( taking out a pencil from the bag ) = 7 / 22

P ( taking out a pencil from the bag ) = 0.32

Therefore, we get that, the probability of taking out a pencil from the bag having 9 pens, 7 pencils and 6 crayons is 0.32.

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The solution is 9.

To find the solution, firstly rewriting the given equation -

√(5x+4) - √x = 4

Now, shifting √x from Left Hand Side to Right Hand side of the equation. Rewriting the equation -

√(5x+4) = √(x) + 4

Taking square of complete equation

(√(5x+4))² = (√(x) + 4)²

Solving the square of equation

5x + 4 = x + 16 + 8√x

Simplifying the equation

5x - x - 8√x = 16 - 4

4x - 8√x = 12

Rewriting the equation

4x - 12 = 8√x

Again taking square on both sides

(4x - 12)² = (8√x)²

16x² + 144 - 2×4x×12 = 64x

16x² + 144 - 96x = 64x

16x² + 144 - 96x - 64x = 0

16x² + 144 - 160x = 0

Dividing the equation by 16

x² + 9 - 10x = 0

x² - 10x + 9 = 0

x² - 1x -9x + 9 = 0

x(x - 1) -9(x - 1) = 0

(x - 1) (x - 9) = 0

x = 1, 9

Keep the value of x in equation to find the solution

x = 1

√(5×1 + 4) - √1 = 4

√(5 + 4) - 1 = 4

√9 - 1 = 4

3 -1 = 4

2 ≠ 4

x = 9

√(5×9 + 4) - √9 = 4

√(45 + 4) - 3 = 4

√49 - 3 = 4

7 - 3 = 4

4 = 4

Hence, the solution is 9.

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The temperature when the plane reaches an altitude of 8,000 feet is 50.7°.

From the information, there is a 1.1 degree drop in temperature for every thousand feet that an airplane climbs into the sky and the temperature on the ground is 59.5 degree

Therefore, the temperature when the plane reaches an altitude of 8,000 feet will be:.

= 59.5 - 1.1(8000/1000)

= 59.5 - 1.1(8)

= 59.5 - 8.8

= 50.7

Therefore, the temperature when the plane reaches an altitude of 8,000 feet is 50.7°.

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To find the difference of two expressions, we can write them in a subtraction sentence:

[tex](5x-4) -( 2x+4)[/tex]

Solve:

[tex]= 5x-4 -2x-4\\= 3x-4 -4\\= 3x-8[/tex]

3x-8

Answer:

d=1, 1+12=13 Variable can be a number or any number .

The least common denominator is (x+5)(x-8).

identify the denominator of  [tex]\frac{8}{x^2 -3x -40}[/tex]  , [tex]\frac{-2}{x^2 -8x}[/tex]

::[tex]x^2 -3x -40[/tex] , [tex]x^2-8x[/tex]

Find the least common multiple of :[tex]x^2 -3x -40[/tex] , [tex]x^2-8x[/tex]

x(x+5)(x-8)

In arithmetic and number theory,  the smallest amount  common multiple, lowest  integer , or smallest  integer  of two integers a and b, usually denoted by least common multiple(a, b),  is that the  smallest positive integer that is divisible by both a and b.Since division of integers by zero is undefined, this definition has meaning  as long as  a and b are both different from zero. However, some authors define least common multiple(a,0) as 0 for all a, since 0  is that the  only common multiple of a and 0.

The least common multiple  is that the  "least common Denominator" (lcd) that can be used before fractions can be added, subtracted or compared.

The least common multiple of more than two integers a, b, c, . . . , usually denoted by least common multiple(a, b, c, . . .),  is additionally  well defined: It is the smallest positive integer that is divisible by each of a, b, c, . . .

A multiple of  variety  is the product of that number and an integer.  for instance , 10  may be a  multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5  and a couple of . Because 10  is that the  smallest positive integer that is divisible by both 5 and 2,  it's  the least common multipleof 5 and 2.

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Answer:

[tex] \frac{3}{5} [/tex]

Step-by-step explanation:

[tex] -\frac{ 9}{10 } \times - \frac{2}{3} [/tex]

you're going to cancel the 9 using the three then, cancel the 10 using the 2 then you'll have

[tex] - \frac{3}{5} \times - \frac{1}{1} [/tex]

then you will get your answer after finding the product and remember a negative multiplied by a negative is a positive , therefore we. have a positive answer

Using proportions, some equivalent measurements are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for unit conversion problems, as unit conversion involve rates between the variables.

Each meter has 100 centimeters, hence:

1 centimeter - 0.01 meters.

Each hour has 60 minutes, hence:

Each feet has 12 inches, hence:

3 and 1/3 feet - 40 inches.

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-7² = -49

Given options are as follows -

a. (-6)^2

b. (1/3)^2

c. 0.5^2

d. -7^2

by solving 1 option we get

(-6)×(-6)

= 36

we get a positive value

because we know that (-)×(-) = +

so this option is not less than zero

again by solving 2 option we get

1/3^2

1/3× 1/3

= 1/9

it is also a positive value

because we know that (+)×(+) = +

so this option is not less than zero

Further by solving 3 option we get

(0.5)²

(0.5)×(0.5)

= 0.25

again it is also a positive value

so this option is not less than zero

but for the option 4

-(7)²

= -49

which is a negative value .

A negative number is any number that is less than zero

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Answer:

Step-by-step explanation:

A=(3,-6) B=(1,2) C=(7,-1)

The inverse for the function f (x) = 2 / 3 x - 3 will be f ⁻¹ (x) = 3 / 2 x + 9 / 2.

We are given the function:

f (x) = 2 / 3 x - 3

we need to find the inverse of the function.

First we will write the function in the form of x.

y = 2 / 3 x - 3

y + 3 = 2 / 3 x

2 x = 3 y + 9

x = 3 / 2 y + 9 / 2

So, the inverse function will be:

f ⁻¹ (x) = 3 / 2 x + 9 / 2.

Therefore, the inverse for the function f (x) = 2 / 3 x - 3 will be f ⁻¹ (x) = 3 / 2 x + 9 / 2.

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Answer:

1884 metres per second

31.4meters x 60 seconds = 1,884 speed

---------

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The total cost of the book including the sales tax is $10.85.

For the given question;

The original price of the book is $9.95.

The sales tax rate is 9%.

Then, 9% of 9.95 is;

= (9×9.95)/100

= 0.8955

The total cost will become;

Selling cost = original cost + sales cost

Selling cost = 9.95 + 0.8955

Selling cost = 10.84555

or rounding off.

Selling cost = $10.85.

The mistake done by the student is, he multiplied the original cost 9.95 by 1.9 which is incorrect.

Thus, the cost of the book is estimated as $10.85.

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Answer:

41

Step-by-step explanation:

how all work! 1) Find two consecutive odd integers with a sum of 80. Let x= first consecutive integer 39. Let x+2= second. 41. 2x=78 x+x+2= 80. 2x+2=80.

X= 39 & 41

The equivalent equation for the given equation is 5n+10d=365. Therefore, option A is the correct answer.

The given equation is 0.05n + 0.1d = 3.65.

Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.

Now, multiply by 100 on both sides of the given equation.

That is, 100(0.05n + 0.1d) = 3.65×100

⇒ 0.05n×100+0.1d×100=365

⇒5n+10d=365

The equivalent equation for the given equation is 5n+10d=365. Therefore, option A is the correct answer.

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Answer:

274.89

Step-by-step explanation:

Answer: 274.89

Step-by-step explanation: You look at the nearest hundredth and which is 2 numbers right of the decimal and see if the number in the hundredths place is higher or lower than 5 if it is 5 or above you round up if not you round down.

Answer:

88.9294

Step-by-step explanation:

So for this problem we need to convert the top 2% into a z-score, which can be done using a calculator. You also first have to convert top 2% into 98% percentile. In doing so you'll approximately get: [tex]z\approx2.054[/tex]

This z-score just represents how many standard deviations away this is from the mean.

So this means that the minimum score would be represented as: [tex]76.4 + 2.054(6.1)\\88.9294[/tex]

This can be rounded as needed, but this would approximately be the minimum score to be in the top 2%

It should be noted that the product of ✓b × ✓b = b.

From the information, it should be noted that we want to find the product of ✓b × ✓b.

In this case, it's important to multiply the roots

Therefore, ✓b × ✓b = ✓b²

Then, we will rewrite the expression. In this case, it should be noted that the square root will cancel the square.

Therefore, the product of ✓b × ✓b = b.

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Answer:

Step-by-step explanation:

b

The solving of equation 3²x=4 in both the given cases gives the answer x = 0.631.

So,

(1) Common logarithm:

(2) Logarithm with base 3:

Therefore, the solving of equation 3²x=4 in both the given cases gives the answer x = 0.631.

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A magnitude 1.0 star is about 2.5 times brighter than a magnitude 2.0.

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x = expression or equation

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

We use the given formula:

[tex]m_2 - m_1 = -2.5 log \frac{b_2}{b_1}[/tex]

now m2 = 2.0 and m1 = 1.0

Hence,

[tex]m_2 - m_1 = -2.5 log \frac{b_2}{b_1}\\\\= > 2.0 - 1.0 = -2.5 log \frac{b_2}{b_1}\\\\= > -1.0 = -2.5 log \frac{b_2}{b_1}\\\\= > log \frac{b_2}{b_1} = 0.4\\\\= > \frac{b_2}{b_1} = 10^{0.4} = 2.5 approx.[/tex]

Thus,  magnitude 1.0 star is about 2.5 times brighter than the magnitude 2.0 star.

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