Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total $1215 x $445
was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?

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:

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

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:

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!

Please mark as brainliest if correct!

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:

1

Step-by-step explanation:

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

[tex]= 1[/tex]

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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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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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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12 yards

Step-by-step explanation:

18 ÷ 6=3

3 × 3=12

12 yards lost after 18 minutes

Answer:

-1,093

Step-by-step explanation:

-10,844 + 9751 = -1,093

Answer:

-7 < -4

Step-by-step explanation:

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.

If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.

Probability is that branch of mathematics that deals with the numerical description of the possibility of an event to occur. The probability of any event is a number between 0 and 1 where 0 represents the impossibility of the event to occur while 1 represents certainty of that event to occur.

As the probability of the job a and job b are independent of each other, the probability that both jobs will be offered can be determined by using the formula;

P(A∩B) = P(A) × P(B)

Here, P(A∩B) represents the probability of both the events happening together

As P(A) = 0.25

P(B) = 0.20

P(A∩B) = 0.25 × 0.20

P(A∩B) = 0.05

Hence, the probability that both jobs will be offered is calculated to be 0.05.

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Answer:

Step-by-step explanation:

Expand using which formula? If it is using Sum/Difference Formulas, the expanded solution would be:

Solution:

[tex]z^3-17z^2+78z-54[/tex]

Hope this helps!

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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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: 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 :)

It will take the painter more than 40 hours to paint all 20 rooms in stately wayne manor .

Time taken for the first 3 rooms =9hrs

Learning curve rate = 85%

Time taken for the next 20 rooms =?

Time taken for 1 room = 9hrs / 3 rooms = 3 hrs

If it takes 3 hrs to paint 1 room

Therefore, it will take x hrs to paint 20 rooms would take;

Hence, 20 rooms multiplied 3 hrs = 60 hours

It may take 60 hours to complete painting the 20 rooms.

At a learning curve rate of 85%, 15% will be the progress rate

Therefore, it will take additional 15% of 60 hours to paint the 20 room.

60+9(15% of 60) =69 hours

The painter would take more than 40 hours to paint the 20 rooms given his efficiency and learning curve rate.  The answer is derived by relating the data provided in the question to the desired answer.

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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 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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