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1 year ago

The profit from a business is

Mathematics

1 answer:

GuDViN [60]1 year ago

3 0

First of all we will understand the question!!

The question is saying that you are given a function and you have to find the value of x which will give the maximum profit... Lets solve it by finding the extrema using the vertex

 $\rm \: p(x) = - 5 {x}^{2} + 30x + 8$ 

Identify the coefficients a and b of the quadratic function

 $\rm \: p(x) = { - 5x}^{2} + 30x + 8 \\ \rm \: a = - 5 \: and \: b \: = 30$ 

Since a<0, the function has the maximum value at x, calculated by substituting a and b into x=-b/2a

$\rm \: x = \frac{30}{ 2 \times (- 5)}$

Solve the equation for x

$\rm \: x = 3$

The maximum of the quadratic function is at x=3

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3p+2≥−10 Solve the inequality. Graph the solution.

Alisiya [41]

Answer:
p is greater or equal to 4.

Why?
Subtract 2 on both sides
Then divide 3 on both sides
You’ll get the answer above

5 0

3 years ago

Read 2 more answers

What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79

Julli [10]

Answer:

Tn = Tn-1 + 2(n-1) + 5

Kindly note that Tn-1 means T subscript n-1

Step-by-step explanation:

Here, we want an expression for the nth term.

First term is 7

Then first common difference is 7

second common difference is 7 + 2

Third common difference is 9 + 2

So within the common differences, the nth term is 7 + (n-1) 2

Now, the nth term of the series would be;

Tn = Tn-1 + 7 + 2(n-1)

Tn = Tn-1 + 7 + 2n -2

Tn = Tn-1 + 2n + 5

Now there is a fix to this,

n for the term is not the same n for the common difference.

the 7th term works with the 6th common. difference, while the 8th term work for the 7th common difference.

So we might need to rewrite the final expression as follows;

Tn = Tn-1 + 2(n-1) + 5

6 0

3 years ago

Which of the following graphs shows the solutions to the equations

Over [174]

X - 1 < = 6
x < = 6 + 1
x < = 7.....2nd number line is correct

3 0

3 years ago

Peter has changed his diet to eat healthier. 2/3 of his meals are gluten free and of those gluten free meals 1/2 are vegan. How

vfiekz [6]

1 1/2 of his total diet in gluten free and vegan

4 0

2 years ago

Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 -

rosijanka [135]

Answer:

Step-by-step explanation:

Our equations are

$y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\$

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by D and its formula is

$D=b^2-4ac\\$

Where

a= the coefficient of the $x^{2}$

b= the coefficient of $x$

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant and evaluate our answer accordingly .

Let us start with

$y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\$

Hence we have two real roots for this equation.

$y = 2x^2 - 6x + 5\\$

$y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D$

Hence we do not have any real root for this quadratic

$y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\$

Hence D>0 and thus we have two real roots for this equation.

$y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\$

Hence we have one real root to this quadratic equation.

7 0

2 years ago