find the distance of line ab if a (3,5) and b (-3,-3)

Answer:

a)56,152.5

b)40.2%

c)10.87%

Step-by-step explanation:

a) $63,000-$6,847.5=$56,152.5

b) marginal tax rate of a $63,000 income is 40.2%

c) 6,847.5 is 10.869047619% of 63,000 but it has to be to nearest hundreth so it is 10.87% because the thousandths place is a 9 so you round up to 10.87%.

The commutative property for addition just means the sum is the same no matter what order you add the terms. This property is also true for multiplication of real numbers.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations depend on it as a fundamental property, and numerous mathematical arguments.

A commutative property in mathematics states that if integer positions are switched around or combined while performing addition or multiplication operations, the result will remain the same.

According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. For addition and multiplication, the property is true, but not for division or subtraction.

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Answer:

9:30 p.m.

Step-by-step explanation:

Starting at noon (12:00 p.m.) the temperature is 5 degrees Celsius and drops 2 degrees every hour. In the attached image I have drawn it out to better see it.

Starting at noon and subtracting 2 every hour gives us…
12:00=5

1:00 = 3
2:00 = 1

3:00 = -1

(And so on until we get)

9:00= -13 degrees

So how do we get to 14 if it is dropping 2 degrees an hour? Simple! How much does it drop every half hour? 1 degrees! So for ever 30 minutes the temperature drops 1 degrees.

This means that at 9:30 the temperature will be -14 degrees Celsius.

The length of the shorter piece is 33 inches.

132 inches of the board is cut into 2 pieces. The board is divided into 2 parts.

One piece is three times the length of the other.

let ,one piece = x

The other piece = 3x

The length(x) of the shorter part  can be found below

x + 3x = 132

4x = 132

divide both sides by 4

x = 132 / 4

x = 33

Therefore the length of the shorter piece is 33 inches.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares.

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The domain is (-2, -4] and the range is (3 , -5) .

The domain of a function is the set of values that we are allowed to plug into our function.

As, the graph stretches from -2 to -4.

and, it is also defined at (-2)

So, the domain is (-2, -4]

Range is height of the graph.

The smallest value is -3 and highest value is 5.

So, the range is (3 , -5)

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12 yards

Step-by-step explanation:

18 ÷ 6=3

3 × 3=12

12 yards lost after 18 minutes

The length l of the hypotenuse as function of x is l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} }+x^{2} }[/tex]

Given,

A right triangle is formed in the first quadrant by x and y axes and a line through the point (3, 2).

The length of sides of triangle are y and x.

By Pythagoras theorem, the length of the hypotenuse is:

l = [tex]\sqrt{y^{2}+x^{2} }[/tex]

Now, we can choose two points to get the value of slope (x₁, y₁) = (3, 2) and (x₂, y₂) = (x, 0)

By using the formula, we get the slope:

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{0-2}{x-3}[/tex] = [tex]-\frac{2}{x-3}[/tex]

The slope is same when passing through (x, 0) and (0, y) because its in the same line.

m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] = [tex]\frac{y-0}{0-x}[/tex] = [tex]\frac{y}{-x}[/tex]

That is, m = [tex]-\frac{y}{x}[/tex]

These slopes are equal. So, we can equate them,

[tex]-\frac{2}{x-3}[/tex] = [tex]-\frac{y}{x}[/tex]

[tex]-\frac{2(-x)}{x-3}[/tex] = y

y = [tex]\frac{2x}{x-3}[/tex]

Substitute this to the equation,

l = [tex]\sqrt{y^{2} +x^{2} }[/tex]

l = [tex]\sqrt{(\frac{2x}{x-3})^{2} +x^{2} }[/tex]

l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} } +x^{2} }[/tex]

That is, the hypotenuse has a length of

l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} } +x^{2} }[/tex]

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El primer socio adquirió un terreno de 324 000 metros cuadrados, el segundo socio un terreno de 180 000 metros cuadrados y el tercer socio un terreno de 36 000 metros cuadrados. Al tercer socio le corresponde la fracción de 1 / 15 de todo el terreno.

Tenemos que el precio es directamente proprocional a la extensión del terreno, de modo que cada socio tiene una participación en el terreno. a) Entonces la participación de cada persona es la siguiente:

Primer socio

x = (3 / 5) · (540 000)

x = 324 000

Segundo socio

x = (1 / 3) · (540 000)

x = 180 000

Tercer socio

x = (1 - 3 / 5 - 1 / 3) · (540 000)

x = 36 000

b) Y la fracción del total correspondiente al tercer socio es:

x = 1 - 3 / 5 - 1 / 3

x = 1 / 15

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Answer:

-1,093

Step-by-step explanation:

-10,844 + 9751 = -1,093

Answer:

Step-by-step explanation:

a) You can calculate by multiplying the decimal numbers-

  4.3 x 6 = -25.8

-25.8 = The sum of the rational numbers

b) You multiply -4.5 by 5 to get the sum of the first 5 numbers-

 -4.5 x 5 = -22.5a

Then you subtract -22.5 from -25.8

 -25.8 - (-22.5) = -3.3 --------------- -25.8 + 22.5 = -3.3

So, the sixth number is -3.3

According to the question, the given rational expression can be simplified and as shown below:

Rational expression = [tex]\frac{-5x^{3} y}{15xy^{3} }[/tex]

To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.

Rational expression = [tex]\frac{-x^{2} }{3y^{2} }[/tex]

The final expression of the given equation is [tex]\frac{-x^{2} }{3y^{2} }[/tex] .

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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Answer:

a^3-64b^3

Step-by-step explanation:

(a-4b)(a^2+4ab+16b^2)

Multiply.

(a-4b)(a^2+4ab+16b^2)=

=a^3 + 4a^2b+16ab^2-4a^2b-16ab^2-64b^3

Combine like terms.

a^3 + 4a^2b+16ab^2-4a^2b-16ab^2-64b^3=

=a^3-64b^3

Hope this helps!

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If the expression is log₅ 25/x. then the expansion of this looks like

(log 25-log x)/ log 5.

Given that the expression is log₅ 25/x.

We are told to find the expanded value of the expression.

The change of base formula is used in writing a logarithm operation as a fraction of logarithms with a new base.

The expression is log₅ 25/x.

log₅ 25/x=log (25/x)/log 5

(We know that [tex]log_{a} b[/tex]=log b/ log a)

=(log 25-log x)/ log 5         (We know that log (u/v)=log u-log v)

Hence if the expression is log₅ 25/x. then the expansion of this looks like (log 25-log x)/ log 5.

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1) The graph that best models the situation is; Graph A

2)  The expression that describes the end behaviors of the function modeled by the graph is; As x increases without bound, f(x) approaches the line y = 0

We are told that Hugh wants to start a workout program. Sinmce he starts with running three times a week, we can liken this to the y-intercept. Thus; y-intercept = 3

Now, we are told that he increases the running per week by 17%. This means that the slope of the graph will be 17% or 0.17.

Looking at the given graphs, only graphs A and B have their y-intercepts at y = 3.

Now, looking at both graphs, the one with slope closest to 17% will be graph A.

2) The expressions describe the end behaviors of the function modeled by the graph is; D: As x increases without bound, f(x) approaches the line y = 0

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Answer:

95

Step-by-step explanation:

Given that,

→ (4 + 8²) + (10 - 7)³

Simplifying the problem,

→ (4 + 8²) + (10 - 7)³

→ (4 + 64) + (3)³

→ 68 + 27 = 95

Thus, the answer is 95.

Answer:

95

Step-by-step explanation:

Given that,

→ (4 + 8²) + (10 - 7)³

Simplifying the problem,

→ (4 + 8²) + (10 - 7)³

→ (4 + 64) + (3)³

→ 68 + 27 = 95

Thus, the answer is 95.

Step-by-step explanation:

The inverse for the function f (x) = 1 / 5 x³ will be f ⁻¹ (x) = ∛ (5 x).

We are given the function:

f (x) = 1 / 5 x³

we need to find the inverse of the function.

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

y = 1 / 5 x³

5 y =  x³

x³ = 5 y

x = ∛ (5 y)

So, the inverse function will be:

f ⁻¹ (x) = ∛ (5 x)

Therefore, the inverse for the function f (x) = 1 / 5 x³ will be f ⁻¹ (x) = ∛ (5 x).

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Answer: 69

Step-by-step explanation:
34
+
35
=
69

Answer:

69

Step-by-step explanation:

30 + 30 = 60

4 + 5 = 9

60+9= 69

Basic addition, also can be solved with a calculator

Hope this helped :)

Answer:

1

Step-by-step explanation:

[tex]\mathrm{a^0=1~if~a \neq 0}[/tex] (Assuming a doesn't equal 0)

[tex]= 1[/tex]

The probability that a camper entering the Luray Caverns has Canadian license plates is 0.3214.

A = a vehicle entering the Luray caverns has Canadian license plates

B = it is a camper

P(A) = 0.12

P(B) = 0.28

P(A∩B) = 0.09

P(A|B) = P(A∩B) / P(B)

P(A|B) = 0.09 / 0.28

P(A|B) = 0.3214

Hence,  the probability that a camper entering the Luray Caverns has Canadian license plates is 0.3214

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Answer:

x = -7 and x = 4

Step-by-step explanation:

Note, I am taking the polynomial equation as
[tex]x^2 - 28 = -3x[/tex]

Otherwise it does not become a polynomial of one variable and cannot be solved

Zeros of a polynomial are the values of x where the polynomial value itself is 0

Standard equation for a polynomial of degree 2 is ax² + bx + c = 0 where a, b and c are constants

Degree is the highest exponent. Here the highest exponent is 2 so the polynomial has degree 2. Such a polynomial is called a quadratic polynomial

So we first have to convert
x² - 28 = - 3x into  this form ax² + bx + c

1. Add 3x to both sides
x² - 28 + 3x = -3x + 3x =0

==> x² + 3x - 28  = 0
With a = 1, b = 3 and c = -28

2. Factor x² + 3x - 28  = 0

Here a = 1, b = 3 and c = -28

Factoring means find two expressions x+a and x +b such that (x + a) (x + b) = x² + 3x - 28  = 0

Then we can state that
x + a = 0           ==> x = -a as one solution
x + b = 0           ==> x = -b as the other solution

To factor, find two numbers m and n(could be negative) such that mn = c and m + n = b

28 has factors 7 and 4 so that is a good start

-28 = -7 x 4 or could also be 7 x -4

How do we choose?
Add both and see what gives you +3

-7 +  4 = -3  Nope
7 + -4 = 7-4 = 3 YES

So the factors are 7 and -4

(x + m) = (x + 7)
(x + n)  = (x -4)

So the original quadratic polynomial becomes

(x + 7)(x -4) =

This means

x + 7 = 0 ==> x = -7

x -  4 = 0 ==> x = 4

So the solutions(also called roots) of x² + 3x - 28  = 0 are:

x = -7 and x = 4

Both the above values satisfy the quadratic equation

Answer:

ABC corresponds to DEF

BCA corresponds to EFD

CAB corresponds to FDE

Step-by-step explanation:

The questions is asking you to find where the point on the small triangle are on the larger triangle, so if it said something like B corresponds to __, your answer would be E. This one just ask for three in a row, so do the points in order. That is all you have to do!

Answer: ABC correspond to DEF.    BCA coressponds to EFD.  CAB corresponds to FED

Step-by-step explanation:

Its telling you what letters coordinate with what letters for example ; FDE corresponds to CAB  

Answer:

-7 < -4

Step-by-step explanation: