In right triangle ABC, altitude CD with length h is drawn to its
We also know AD=2 and DB=8. What is the length of
hypotenuse.
AC?

Answer:

Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40

Marie is $10 000 richer

Step-by-step explanation:

Albert

(a) $1000 at 1.2 % compounded monthly

A = P (1 + r/n )^nt

A = 1000(1 + 0.001)¹²⁰ = $1127.43

(b) $500 losing 2%

0.98 × 500 = $490

(c) $500 compounded continuously at 0.8%

A = Pe^rt

  = 500e^0.008 * 10

 =  $541.64

(d) Balance

Total = 1127.43 + 490.00+ 541.64 = $2159.07

Marie

(a) 1500 at 1.4 % compounded quarterly

A = 1500(1 + 0.0035)⁴⁰ = $1724.99

(b) $500 gaining 4 %

1.04 × 500 = $520.00

(c) Balance

Total = 1724.99 + 520.00 = $2244.99

Hans

$2000 compounded continuously at 0.9 %

A = 2000e^0.009 * 10

  = $ 2188.35

Max

(a) $1000 decreasing exponentially at 0.5 % annually

A = 1000(1 - 0.005)¹⁰= $951.11

(b) $1000 at 1.8 % compounded biannually

A = 1000(1 + 0.009)²⁰ = $1196.29

(c) Balance

Total = 951.11 + 1196.29 = $2147.40

Marie is $10,000 richer at the end of the competition.

Hope this helps!!! :)

Step-by-step explanation:

8x³ + 216

(2 * 2 * 2 * x * x * x) + (2 * 3 * 2 * 3 * 2 * 3)

Answer:

97.5/100

Step-by-step explanation:

To write 97.5% as a fraction in simplest form, we first convert the percentage to a decimal by dividing it by 100: 97.5% / 100 = 0.975. We can then express this decimal as a fraction by using the fact that any number can be represented as a fraction with the number as the numerator and a power of 10 as the denominator: 0.975 = 0.975/1. Finally, we simplify the fraction by dividing the numerator and denominator by the greatest common factor, which in this case is 1: 0.975/1 = 97.5/100. Therefore, 97.5% can be written as the fraction 97.5/100 in simplest form.

Answer:

39/40

Step-by-step explanation:

97.5/100

   Step 1: Write down the percent divided by 100;

   Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 until you get an integer at the numerator.

   Step 3: Simplify (or reduce) the fraction if it is not in the simplest form.

The value of x for the triangle is equal to 17.32.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Calculate the perpendicular side for both triangles by using the Pythagorean theorem.

H² = P² + B²

Here, H is the hypotenuse, P is perpendicular and B is the base.

For the first triangle, the perpendicular is calculated as,

P² = x² - 10²......................................................1

For the second triangle, the perpendicular will be,

P² = ( 30² - x² ) - 20²  .......................................2

Equate the equation 1 and 2 and solve,

x² - 10² = ( 30² - x² ) - 20²

x² - 100 = 900 - x² - 400

2x² = 900 - 400 + 100

2x² = 600

x√ = 300

x =√300

x = 17.32

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Answer: There is no y-intercept on this equations

Step-by-step explanation:

so yes you were wrong

Answer:

a. [tex]1 * 10^{-10}[/tex]

Explanation:

A converted to standard notation is the same number.

The value of P({2}) for the given Finite set is found as P({2}) = 1/6.

For the stated question;

P({2}) will contain only element with is not present in set P({1}) counting from P({1, 2}).

Thus,

P({2}) = P({1, 2}) - P({1})

P({2}) = 2/3 - 1/2

P({2}) = 1/6

Thus, the value of P({2}) for the given Finite set is found as P({2}) = 1/6.

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Answer:

2.51 x 10^5

Step-by-step explanation:

Scientific notation gives you a number between 1 and 10 multiplied by a power of ten. In this case, you'll want to use the significant digits, 251, and divide or multiply by a power of ten to get a number between 1 and 10.

251,000 can become 2.51 (which is between 1 and 10) multiplied by 10 to a certain exponent. All you need to do is calculate the exponent.

2.51 x 10^(?) = 251,000

For each power of 10, the decimal moves a space. Since you want the decimal to move 5 spaces, you'll want to multiply 2.51 by 10^5.

2.51 x 10 = 25.1

2.51 x 10^2 = 251

2.51 x 10^3 = 2510

2.51 x 10^4 = 25,100

2.51 x 10^5 = 251,000

Answer:

Step-by-step explanation:

Let x be the number.

The square of the number is x2

Increased by twice the number means add 2x.

So your equation is :

X2 +2x = 48.

Can you take it from here?

The asked number is 12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, When the square of a certain number is added to the number, the result is the same as when 48 is added to three times the number.

Let the number be x,

x²+x = 48X3 + x

x² = 144

x = 12

Hence, The asked number is 12.

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The appropriate estimate for the diameter of the speck of dust is 2 × 10⁻⁵ inches. So the answer is option A, 2 × 10⁻⁵ in.

In scientific notation, numbers are written with the base 10 much like in decimal notation. Scientific notation is the term used when a number is expressed as the product of two numbers.

Where the first number is more than or equal to one but less than ten and the second number is the power of ten expressed in exponential form.

Step - 1 Move the decimal point up to the first number that is equal to 1 but less than 10.

Step - 2 Count the number of places that the point moved.

Step - 3 Now Write the resultant number as a product with a power of 10.            

Here we have

Diameter of a speck of duct = 0.00002 inches

Convert the given decimal into a scientific notation

As we learn above

Move the decimal point up to a whole number toward the right

=> 0.00002 = 2. = 2

Count the number of zeros or places moved

=> n = 5

Now write the number as a power of 10, Now write the above whole number part as the product of 10

=> 2 × 10⁻⁵     [ ∵ The power is moved right we need to use negative ]    

Therefore,

The appropriate estimate for the diameter of the speck of dust is 2 × 10⁻⁵ inches. So the answer is option A, 2 × 10⁻⁵ in.

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Answer:

203 dollars

Step-by-step explanation:

100 percent = 145

10 percent = 14.5

30 percent = 43.5

43.5 + 14.5 + 145 = 203

The value of f(5) When a polynomial f(x) is divided by x -5 is 4

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

If f(x) has a remainder of 4 when divided by x - 5

Then it means that if f(x -5) = f(0)

x -5 = 0

x = 5

so if you substitute 5 into f(x) which is f(5) it will give 4

so therefore f(5) = 4

In conclusion f(5) is same as 4

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The complete sentence will be;

⇒ x² + x + 1/4 = ( x + 1/2)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x² + x + __ = (_____)²

Now,

Since, The expression is,

⇒ x² + x + __ = (_____)²

Hence, We can add the number to form the complete square as;

⇒ x² + x + 1/4 = x² + x + (1/2)²

                     = ( x + 1/2)²

Thus, The complete sentence will be;

⇒ x² + x + 1/4 = ( x + 1/2)²

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Answer:

Length of each side of regular hexagon = 19 inches

Step-by-step explanation:

When the length of all sides is equal and measure of all angles is equal . it is known as Regular hexagon. In a regular hexagon, each inside angle is 120 degrees.

Perimeter of Regular hexagon = 6a

where a is each side of regular hexagon

According to the given information

Perimeter of regular hexagon = [tex]\frac{342}{3}[/tex]

                                                  = 114 inches

Perimeter of regular hexagon = 6a

                                          114   = 6a

                                           19   =  a

Length of each side of regular hexagon = 19 inches

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In 2000, the population of the state was 23.1 million, After 13 years , the population of the state reach 28.3 million.

What is population?

The term "population" refers to all citizens who are present in a nation or who are temporarily absent from it, as well as all aliens who have made a nation their permanent home. The number of residents in a given area is depicted by this indicator. The annual changes in population brought on by births, deaths, and net migration are measured as growth rates.

Given:

[tex]A = 23.1e^0^.^0^1^5^2^t[/tex] models the population of US

where A is in million

t is years after 2000.

(a) We have to find the population in 2000.

In 2000, t = 0

Plug t = 0 in the above equation

[tex]A(0) = 23.1e^0^.^0^1^5^2^(^0^)\\A = 23.1[/tex]

Hence, in 2000 the population is 23.1 million.

(b) To find when the population of the state reach 28.3 million.

Plug A = 28.3 in above equation and solve for t.

[tex]28.3 = 23.1e^0^.^0^1^5^2^t\\e^0.0152t = \frac{28.3}{23.1} \\t*ln(0.0152) = ln( \frac{28.3}{23.1})\\t = 13.35718\\t = 13[/tex]

Hence, after 13 years the population of the state reach 28.3 million.

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Answer:

<-4,4>

Step-by-step explanation:

-4 * <1,-1> = <-4 * 1, -4 * -1> = <-4, 4>

Answer:

a)  A' = (2, 4)

b)  A'' = (1, -2)

Step-by-step explanation:

When reflecting a shape in a vertical line, each vertex of the shape will be the same distance from the vertical line but in the opposite direction.  

Therefore, the x-values change but the y-values remain the same.

To reflect point A in x = -1, determine the number of horizontal units the point is from x = -1.  Count the same number of units on the other side of the vertical line (remembering that the y-value remains unchanged).

The x-value of point A is x = -4.  This is 3 units to the left of x = -1.

Therefore, the x-value of point A' is 3 units to the right of x = -1.

The y-value of point A is y = 4, so the y-value of point A' is also y = 4.

Therefore, the coordinates of the point A' are:

To translate point A' by the given vector, translate the point:

Therefore, the coordinates of the point A'' are:

Answer:

-5

-9+5

Step-by-step explanation:

The equation, which represents the given condition x >= 6.2.

What is the inequality equation?

Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤, or ≥.

We have,

Six more than 5 times a number x is greater than or equal to 6.

So,

5x  >= 31

5x >= 31/5

x >= 6.2

Hence, the equation, which represents the given condition x >= 6.2.

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Complete equation:

Six more than 5 times a number x is greater than or equal to 6.

Answer:

x> -10

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

A. is the answer

Step-by-step explanation:

A. Since there is one value of  y  for every value of  x

B. is not a function x  =  − 4  produces  y  =  4  and  y  =  3

C. is not a function x  =  6  produces  y  =  6  and  y  =  3

D. is not a function   x  =  6  produces  y  =  3  and  y  =  5

The value of x when both the function give the same value is 10

Solution:

Given f(x) = 0.2x , g(x) = 0.5(x-6)

let x = 0 , f(x) = 0 , g(x) = -3

let  x = 1 , f(x) = 0.2 , g(x) = -2.5

let  x = 2 , f(x) = 0.4 , g(x) = -2

let  x = 3 , f(x) = 0.6 , g(x) = -2.5

let  x = 4 , f(x) = 0.8 , g(x) = -2 and so on till x=10

let x=10, f(x) = 2, g(x) = 2

∴ The value of x when both the values of the function are same is x = 10

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The value of x when both the function give the same value is 10

What are functions?

Function, in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Given f(x) = 0.2x , g(x) = 0.5(x-6)

let x = 0 , f(x) = 0 , g(x) = -3

let  x = 1 , f(x) = 0.2 , g(x) = -2.5

let  x = 2 , f(x) = 0.4 , g(x) = -2

let  x = 3 , f(x) = 0.6 , g(x) = -2.5

let  x = 4 , f(x) = 0.8 , g(x) = -2 and so on till x=10

let x=10, f(x) = 2, g(x) = 2

∴ The value of x when both the values of the function are same is x = 10

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Answer:

f(x) = (x+2)(x+4)

Step-by-step explanation:

4 + 2 = 6

4 * 2 = 8

f(x) = (x+2)(x+4)

Answer:

ANS:- 15.9

Step-by-step explanation:

5814/365 = 15.9

The total distance ran during these days, written as a mixed number, is (38 + 3/4)mi

We know that the student ran a distance of (3 + 1/2) miles each day for 5 days, so the amount that the student ran in these 5 days is given by the product:

5*(3 + 1/2) mi = (15 + 5/2) mi

Now, on the next 5 days, the student ran a distance of (4 + 1/4) miles, so the total distance that the student ran in these days is:

5*(4 + 1/4) mi = (20 + 5/4)mi

Now to get the total distance that the student ran on the 10 days we need to add the two distances above, we will get:

(15 + 5/2) mi +  (20 + 5/4)mi

So we have a sum of mixed numbers, we can rewrite this as:

(15 + 5/2) mi +  (20 + 5/4)mi = (15 + 20)mi + (5/2 + 5/4)mi

(15 + 20)mi + (5/2 + 5/4)mi = 35mi + (10/4 + 5/4) mi

35mi + (10/4 + 5/4) mi = 35mi + 15/4mi

35mi + 15/4mi = 35mi + 12/4 mi + 3/4 mi

35mi + 12/4 mi + 3/4 mi  = (38 + 3/4)mi

That is the total distance that the student ran on the 10 days.

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Answer: x=±2/3

Step-by-step explanation:

The first thing we want to do is isolate the variable, x² in this case.

We can divide both sides by 9 which yields the equation x²=[tex]\frac{4}{9}[/tex].

Then we can take the square root of both sides, x=2/3.

Note: When the exponent is an even number both positive and negative x values will yield the same positive answer, so x=±2/3

(a) The depreciation for the first year is $99,732.40.  (b) If the Machine was sold at the end of the fifth year, the gain or loss is $498,662

We know that in accounting, depreciation is the loss on a fixed asset over the accounting period that benefited from it.

Using straight line method of depreciation,

Depreciation = [tex]\frac{Cost os asset-Residual value}{Estimated number of years}[/tex]

Applying the figures we have

Depreciation = [tex]\frac{637362-138700}{5}[/tex]

Depreciation= [tex]\frac{498662}{5}[/tex]

Depreciation= $99,732.40

(b) If the machine is sold at the end of the fith year, the loss is accumulated depreciation for 5 years

Loss= $(99,372.4*9) = $498,662

(c)    The journal appears as follows

                                           Journal

                                            $                                                        $

Coat of machine           637,362.00     Depreciation             498,662

                                                               Balance                     138,700

Totals                             637,362.00                                        637,362.

In conclusion, the depreciation for the first year and loss after the fifth year are $99,732 and $498,662 respectively.

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The inverse of y is [tex]\sqrt{4-x} ,-\sqrt{4-x}[/tex].

What is the inverse of a function?

A function whose inverse returns the initial value for the specified output is called an inverse function of the function. The inverse function of y, or[tex]f^{-1}[/tex] (y), will return the value x if f (x) produces an output of y.

Given equation is [tex]y=-x^{2} +4[/tex]

We find the inverse function f(x) by substituting x and y.

We compute the resulting equation for x. We change the variable to:

[tex]x=4-y^{2}[/tex]

Now, solve the equation [tex]x=4-y^{2}[/tex] for y

We get, y = [tex]\sqrt{4-x} ,-\sqrt{4-x}[/tex]

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Answer:I hope this helpful mark me brainlist if correct then no if wrong

Step-by-step explanation:

P times 3 =-0.0027

Use the commutative property to reorder the terms

3p=-0.0027

Divide both sides of the equation by 3

p=-0.009 or p=-9/1000

The distance for Tucker to walk is 1 mile, only then both the donors would have the same amount. This was found using linear equations.

What are linear equations?

A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.

Since it's given that Tucker's mother will give flat $5. So let that be the RHS of the equation. Now his grandmother will give him $5 for every mile he walks.

Let that be 5x.

Now the equation would be: 5x=5

Which results in x=1.

Therefore at 1 mile, both of the donors' amounts would be the same.

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