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Gnesinka [82]
2 years ago
8

Simplify the function f (x) = one-half (27) Superscript StartFraction 2x Over 3 EndFraction. Then determine the key aspects of t

he function.

Mathematics
2 answers:
AleksandrR [38]2 years ago
6 0

Answer:

(See explanation)

Step-by-step explanation:

The function is:

f(x) = \frac{1}{2}\cdot 27 \cdot \frac{2\cdot x}{3}

Its simplified form is presented hereafter:

f(x) = 9\cdot x

The resultant expression is a linear function, first-order polynomial, whose domain and range are the set of the real numbers.

Alex2 years ago
6 0

Answer: on edge its: 1/3, 27, all real numbers, y>0

Step-by-step explanation:

You might be interested in
A basketball has a diameter of 9.5
zubka84 [21]

Answer:

C. \dfrac{4}{3}\pi\cdot(4.75)^3\ cm^3

Step-by-step explanation:

The volume of the ball with radius R can be calculated using formula

V=\dfrac{4}{3}\pi R^3

A basketball has a diameter of 9.5 cm, so its radius is

R=\dfrac{D}{2}=\dfrac{9.5}{2}=4.75\ cm

Hence, the volume of air the basketball can hold is

V=\dfrac{4}{3}\pi\cdot(4.75)^3\ cm^3

4 0
2 years ago
A square pyramid has sides of 8 m. Each face is an equilateral triangle. What is the lateral area of the pyramid?
tia_tia [17]

Answer:

The lateral area is equal to

LA=64\sqrt{3}\ m^{2}

Step-by-step explanation:

In this problem the lateral area is equal to the area of one equilateral triangle multiplied by 4

To find the area of one equilateral triangle calculate the height

The area of the triangle is equal to

A=\frac{1}{2}bh

we have

b=8\ m

Applying the Pythagoras theorem

h^{2}=8^{2} -4^{2} \\h^{2}=64-16\\ h=\sqrt{48} \\ h=4\sqrt{3}\ m

The area of one triangle is equal to

A=\frac{1}{2}(8)(4\sqrt{3})\ m^{2}

so

The lateral area is equal to

LA=4\frac{1}{2}(8)(4\sqrt{3})=64\sqrt{3}\ m^{2}

3 0
1 year ago
The plot shown below describes the relationship between the average income in a city and the average rent for a 111-bedroom apar
Nikitich [7]

Answer:

The average change in rent can be determined by substituting the value of <em>X</em> as 5000 in the regression equation.

Step-by-step explanation:

A simple linear regression line is used to predict the value of the dependent variable from the independent variable.

The general form is:

Y=\alpha +\beta X

Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variables in the model are changed.

The dependent variables are also known as response variables.

In this case the dependent variable is the average  change in rent for a 1-bedroom apartment.

Independent variables are the variables that are being altered to see a proportionate change in the dependent variable. In a regression model there can be one or more than one independent variables.

The independent variables are also known as the predictor variables.

In this case the independent variable is the average income in a city.

So, for an increase of $5,000 in incomes the average change in rent can be determined by substituting the value of <em>X</em> as 5000 in the regression equation.

6 0
2 years ago
Please help me on this question
Serggg [28]
    -4 = 8m + 18n
-18n = 8m + 4
 /-18    /-18  /-18
     n = 8m/-18 + 4/-18
     
I'm not sure so yeah
7 0
2 years ago
Read 2 more answers
12. A cyclist travels 40 km at a speed of x km/h. Find the time
GREYUIT [131]

Answer:

Step-by-step explanation:

distance = rate times time, so

           

           distance

time = --------------

               rate

Here the distance is 40 km and the rate is x.  Then

              40 km

time = --------------  =  (40/x) hr

             x km/hr

If the speed is reduced by 2 km/hr, we get:

              40 km                                            40 km                  40

time = -------------------------------  or time = ----------------------- = --------- hr

             (x km/hr - 2 km/hr)                      (x - 2) (km/hr)       x - 2

The difference between the times is:

 40          40

-------- - --------- = 1 hr          Solve this for the original speed, x

x - 2         x

40x - 40x + 80                                80

-----------------------  =  1 hr     or     ------------ = 1     or 80 = x^2 - 2x

     x(x - 2)                                     x(x - 2)

Rewriting this in standard quadratic form:  x^2 - 2x - 80 = 0

Here a = 1, b = -2 and c = -80, and so the discriminant b^2 - 4ac is:

(-2)^2 - 4(1)(-80) = 324

The solutions are:

   

      -(-2) ± √324       2 ± 18

x = -------------------- = ------------ = 1 ± 9, or 10 (discard the other root)

              2                      2

The original speed was 10 km/hr

7 0
2 years ago
Read 2 more answers
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