Suppose that the functions g and h are defined for all real numbers x as follows. gx = x − 3x
hx = 5x + 2
Write the expressions for (g - h)(x) and (g * h)(x) and evaluate (g + h)(−2).


Answer 1


Step-by-step explanation:

Given the functions g(x) = x − 3x  and h(x) = 5x + 2, we are to calculatae for the expression;

a) (g - h)(x)  an (g * h)(x)

(g - h)(x)  = g(x) - h(x)

(g - h)(x)  = x − 3x -(5x+2)

(g-h)(x) = x-3x-5x-2

(g-h)(x) =-7x-2

b)  (g * h)(x) =  g(x) * h(x)

 (g * h)(x)  = (x − 3x)(5x+2)

(g * h)(x) = 5x²+2x-15x²-6x

(g * h)(x) = 5x²-15x²+2x-6x

(g * h)(x) = -10x²-4x

c) To get (g + h)(−2), we need to first calculate (g + h)(x) as shown;

 (g + h)(x)  an (g * h)(x)

(g + h)(x)  = g(x) +h(x)

(g + h)(x)  = x − 3x + (5x+2)

(g+h)(x) = x-3x+5x+2

(g+h)(x) =3x+2

Substituting x = -2 into the resulting function;

(g+h)(-2) = 3(-2)+2

(g+h)(-2) = -6+2

(g+h)(-2) = -4

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Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What is the length and width?



Area of rectangle = 196\,m^2

Length of rectangle = 14 m

Width of rectangle = 14 m

Step-by-step explanation:


Perimeter of rectangle is 56 m

To find: the maximized area of a rectangle and the length and width


A function y=f(x) has a point of maxima at x=x_0 if f''(x_0)<0

Let x, y denotes length and width of the rectangle.

Perimeter of rectangle = 2( length + width )


Also, perimeter of rectangle is equal to 56 m.



Let A denotes area of rectangle.

A = length × width


Differentiate with respect to x


Put (dA)/(dx)=0




At x = 14, (d^2A)/(dx^2)=-2<0

So, x = 14 is a point of maxima



Area of rectangle:


Length of rectangle = 14 m

Width of rectangle = 14 m

Drag the tiles to the correct boxes to complete the pairs. Match the percent error with its scenario.10%


The percent error matching with its scenario :

1) 15%




Here, from the given information we get:

the percent error are:

Leo = (11.5-10)/10 = 0.15

Candice = (13.2-12)/ 12 =0.1

Josie = (24-20)/20 = 0.2

Lenny = (18-16)/16 = 0.125

Now, we have,

For percentage, multiply each number by 100;

Leo = 15%

Candice = 10%

Josie = 20%

Lenny = 12.5%

To learn more on percentage click:



1) 15%




The sum of two numbers is -14, if one number is subtracted from the other, their difference is 2, find the numbers.



-10 and -12

Step-by-step explanation:

Suppose a regional computer center wants to evaluate the performance of its memory system. One measure of performance is the average time between failures of its disk drive. To estimate the value, the center recorded the time between failures for a random sample of 45 drive failures. The sample mean has been computed to be 1,762 hours and the sample standard deviation is 215. Estimate the true mean time between failures with a 90% confidence interval? Interpret the confidence interval.



The 90% confidence interval is (1408.325 hours, 2115.675 hours).

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = (1-0.9)/(2) = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645

Now, find M as such

M = z*s

In which s is the standard deviation of the sample. So

M = 1.645*215 = 353.675

The lower end of the interval is the mean subtracted by M. So it is 1762 - 353.675 = 1408.325 hours.

The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 2115.675 hours.

The 90% confidence interval is (1408.325 hours, 2115.675 hours).

The parallelogram shown below has an area of 15 units^2Find the missing height.



I do believe the answer is 5: 15/3=5 and the height should be equal to the side of the parallelogram

Step-by-step explanation:

Which is true about the solution to the system of inequalities shown


pls provide the problem


look below for question

Step-by-step explanation:

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3  

Only values that satisfy y > 3x + 1 are solutions.

Only values that satisfy y < 3x – 3 are solutions.

Values that satisfy either y > 3x + 1 or y < 3x – 3  are solutions.

There are no solutions.