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3 years ago

Solve 9x2 + 12x + 4 = 0. By using the quadratic formula

2 answers:

5 0

$Discriminant= b^{2}-4.a.c \\ \\ We\:need\:to:-b+ \sqrt{discriminant} /2a \\ \\ 9x^{2} +12x+4=0 \\ => 12^{2} -4.9.4 \\ 144-144=0 \\ \sqrt{0} =0 \\ \\ -12+ 0/18= \frac{-12}{18} = \frac{-2}{3} \\ \\ That`s\: enough=>x= \frac{-2}{3} \\ \\ \framebox[1.1\width]{Good Luck!} \par$

disa [49]3 years ago

4 0

So 9x^2+12x+4=0

so the quadratic formulat is (-b+/-(squrt(b^2-4ac)))/(2a)=x
subsitute
ax^2+bx+c=

9=a
12=b
4=c

(-12+/-(squrt(12^2-4(9)(4))))/(2(9))=x
(-12+/-(squrt(144^2-144)))/18)=x

(-12+/-0)/18)=x
-12/18=x
-2/3=x

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A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

7 0

3 years ago

Betty had 1 1/4 hours to finish a test. She was nervous and it took her 1/2 an hour to calm down. How much time did she have lef

Airida [17]

Answer:

Betty had 45 minutes to take her test in mixed number form it is

Step-by-step explanation:

1 hour

1/4 an hour = 15 minutes

1/2 an hour is 30 minutes

1 hr 15- 30= 45

45= 3/4 of and hour remaining to test

5 0

2 years ago

The quotient of 9 and a number less 4

valina [46]

Answer:

ead the excerpt from "The Most Dangerous Game,” by Richard Connell.

His foot touched the protruding bough that was the trigger. Even as he touched it, the general sensed his danger and leaped back with the agility of an ape. But he was not quite quick enough; the dead tree, delicately adjusted to rest on the cut living one, crashed down and struck the general a glancing blow on the shoulder as it fell; but for his alertness, he must have been smashed beneath it. He staggered, but he did not fall; nor did he drop his revolver. He stood there, rubbing his injured shoulder, and Rainsford, with fear again gripping his heart, heard the general's mocking laugh ring through the jungle.

Which analysis best explains the effect of adding the female character

Step-by-step explanation:

7 0

3 years ago

The outside temperature can be estimated based on how fast crickets chirp. At 104 chirps per minute, the temperature is 63 degre

Rasek [7]

Answer:

For 124 chirps per minute the temperature is 68 ºF.

For 68 chirps per minute the temperature is 54 ºF.

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form

$f(x)=b+mx$

b is the constant term or the y intercept. It is the value of the dependent variable when x = 0.

m is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.

We know that

At 104 chirps per minute, the temperature is 63 ºF.

At 176 chirps per minute, the temperature is 81 ºF.

This information can be converted to Cartesian coordinates (x, y). Where x = the number of chirps per minute and y = the temperature in ºF.

To find a linear function that let us find the outside temperature from how fast crickets chirp we must:

Find the slope:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{81-63}{176-104}=\frac{1}{4}$

Find the equation:

$81=\frac{1}{4}\cdot 104+b$

Solving for b

$b=81-\frac{1}{4} (176)=37$

Therefore, the linear function is

$y=\frac{1}{4} \cdot x+37$

Now, using this linear function we can know the temperature when we know the chirps per minute:

For 124 chirps per minute the temperature is:

$y=\frac{1}{4} \cdot (124)+37=68$

For 68 chirps per minute the temperature is:

$y=\frac{1}{4} \cdot (68)+37=54$

6 0

3 years ago

Hannah Ortega is considering expanding her business. She plans to hire a salesperson to cover trade shows. Because of compensati

mariarad [96]

Answer:

a) Total Cost for EzRecords = $13000

Cost per unit of EzRecords = $162.50

Total Cost for ProOffice = $10000

cost per unit of ProOffice = $200.00

b) Total Cost for EzRecords = $25000

Cost per unit of EzRecords = $125.00

Total Cost for ProOffice = $17500

cost per unit of ProOffice = $175.00

Step-by-step explanation:

a) Total Cost = Fixed Cost + Variable Cost

Fixed Cost = $7500

Variable Cost = cost of making a unit of output × number of units produced.

Variable Cost of EzRecords products = $100 × 80 = $8000

Variable Cost of proOffice products = $150 × 50 = $7500

Fixed Cost for EzRecords = (20/30) × 7500 = $5000

Fixed Cost for ProOffice = (10/30) × 7500 = $2500

Variable cost for EzRecords = $8000

Variable cost for ProOffice = $7500

Total cost for EzRecords = Fixed Cost + Variable Cost = $5000 + $8000 = $13000

Total Cost for ProOffice = $2500 + $7500 = $10000

Cost per unit for EzRecords = (total cost of production)/(total units produced) = 13000/(80) = $162.50

Cost per unit of ProOffice = 10000/50 = $200.00

b) Total Cost = Fixed Cost + Variable Cost

Fixed Cost = $7500

Variable Cost = cost of making a unit of output × number of units produced.

Variable Cost of EzRecords products = $100 × 200 = $20000

Variable Cost of proOffice products = $150 × 100 = $15000

Fixed Cost for EzRecords = (20/30) × 7500 = $5000

Fixed Cost for ProOffice = (10/30) × 7500 = $2500

Variable cost for EzRecords = $20000

Variable cost for ProOffice = $15000

Total cost for EzRecords = Fixed Cost + Variable Cost = $5000 + $20000 = $25000

Total Cost for ProOffice = $2500 + $15000 = $17500

Cost per unit for EzRecords = (total cost of production)/(total units produced) = 25000/(200) = $125.00

Cost per unit of ProOffice = 17500/100 = $175.00

8 0

3 years ago