factor x(20-x)=96 its for solving quadratics

Answer:

a. The length of the box = (40 - 2·x) cm

The height of the box = x cm

The width of the box = (25 - 2·x) cm

b. The formula for the volume of the box as a function of x is 4·x³ - 130·x² + 1000·x

c. The value of x that would maximize the volume of the box is x = 5 cm

d. The largest volume of the box is 2250 cm³

Step-by-step explanation:

a. The given parameters are;

The length of the cardboard = 40 cm

The width of the cardboard = 25 cm

The length of the box = (40 - 2·x) cm

The height of the box = x cm

The width of the box = (25 - 2·x) cm

b. The formula for the volume of the box = The area of the base of the box × Height of the box

The area of the base of the box =  (40 - 2·x) × (25 - 2·x) = 1000 - 80·x - 50·x + 4·x²

∴ The area of the base of the box = 4·x² - 130·x + 1000

The height of the box = x

The volume of the box = (4·x² - 130·x + 1000) × x = 4·x³ - 130·x² + 1000·x

The volume of the box in terms of x, V = 4·x³ - 130·x² + 1000·x

c. At the extremum point, dV/dx = 12·x² - 260·x + 1000 = 0

x = (260 ± √((-260)² - 4 × 12 × 1000))/(2 × 12)

x = (260 ± 140)/(24)

x = 5 or x = 16.[tex]\bar 6[/tex]

At x = 5, the volume of the box is V = 4×5³ - 130×5² + 1000×5 = 2250

The volume of the box is V = 2250 cm³

At x = 16.67, the volume is 4×16.67³ - 130×16.67² + 1000×16.67 = -925.[tex]\overline {925}[/tex]cm³

Therefore, the value of x that would maximize the volume of the box is x = 5 cm

d. The largest volume of the box is 4×(5 cm)³ - 130×(5 cm)² + 1000×(5 cm) = 2250 cm³.

Answer:

A

Step-by-step explanation:

I am a little confused with the "all trees $42" answer but if that means she could buy that size for $42 then I believe that is the answer that should be chosen because for question B, 6 per ft. would likely be 48 because 6x8 = 48, and I don't believe half ft would be $3. As for C, 22 plus 24 is 46. (24 would = $6 x 4 additional ft)

Answer:

3/k = 4/5

k = 3 divided by 4/5

k = 3.75

Step-by-step explanation:

Answer:

x=-9

Step-by-step explanation:

-7x=63

x = 63 ÷ -7 = -9

Answer:

4x3=3x4

Step-by-step explanation:

Answer:

£198

Step-by-step explanation:

Divide 1584 by 8 because each ticket costs £8 to get £198

Answer:

The second equation does not have the same solution, or -15 = -10 + z

Step-by-step explanation:

Every other equation is = to -2, while the one shown above is -5.

Answer:

t = 33 seconds

It is the amount of time when the temperature of the body will rise from 100 to fatal 104 in the absence of sweat.

Step-by-step explanation:

weight of the farmer = 176 lb

Sweating = 1 litre per hour

60% of above sweating is evaporated by the latent heat from farmers body.

Temperature outside = 104

Temperature of the Farmer = 100

Time to rise the temperature 4 degrees = ?

We need to use the specific heat formula to calculate the time to rise the temperature of the body of farmer.

Before, that let's convert weight of the farmer in Kg

W = 176 lb

1 lb = 0.453592 kg

176 lb = 79.8 kg

w = mg

g = 10

mass = m = 79.8/10

mass = 7.98 kg

Q = mc∆T

c = specific heat of water =  4,186

∆T  = Temperature Change = 104-100

∆T  = 4

Q = 7.98 x 4186 x 4

Q = 133617

t = Q/P

Power of Sun's Heat = 3.846×1026

t = 33 seconds

It is the amount of time when the temperature of the body will rise from 100 to fatal 104 in the absence of sweat.

Answer:

y² + 10y + 6x + 58 = 0

Step-by-step explanation:

Focus of the parabola has been given as (-7, -5) and directrix as x = -4

Let a point on the parabola is (x, y).

By the definition of a parabola, "distance of a point on parabola is equidistant from focus and directrix".

Distance from focus of the given point = [tex]\sqrt{(x+7)^2+(y+5)^2}[/tex]

Distance of the point from directrix = [tex]\sqrt{(x+4)^2}[/tex]

Therefore, equation of the parabola will be,

[tex]\sqrt{(x+7)^2+(y+5)^2}=\sqrt{(x+4)^2}[/tex]

[tex](x+7)^2+(y+5)^2=(x+4)^2[/tex]

x² + 14x + 49 + y² + 10y + 25 = x² + 8x + 16

y² + 14x + 10y + 74 = 8x + 16

y² + 10y + 6x + 58 = 0

Answer:

(y+5)^2/6 - 11/2

Step-by-step explanation:

Answer:

=10

Step-by-step explanation:

5x-4x². (x=2)

5(2)-4(2)²

=10-0

=10

Answer:

Step-by-step explanation:

-4.32193257293

Answer:

slope=1/2

y-intercept=2

slope-intercept form: y=1/2x+2

Step-by-step explanation:

Answer:

let the email be written by him.

Answer:

-3/4

Step-by-step explanation:

Answer:

x= -3/4

Step by Step explanation:

Step 1: Simplify both sides of the equation.

−8(4x+6)=−24

(−8)(4x)+(−8)(6)=−24     (Distribute)

−32x+−48=−24

−32x−48=−24

Step 2: Add 48 to both sides.

−32x−48+48=−24+48

−32x=24

Step 3: Divide both sides by -32.

-32x/-32 =24/-32

Answer:

x= -3/4

Answer:

2.2 gigabytes

Step-by-step explanation:

Let us represent

x = the number of gigabytes of data Samuel can use while staying within his budget

Therefore, our equation is:

$41.50 + $5 × x = $52.50

41.50 + 5x = 52.50

Subtract 41.50 from both sides

41.50 - 41.50 + 5x = 52.50 - 41.50

5x = 11

x = 11/5

x = 2.2 gigabytes.

The number of gigabytes of data he need to keep his monthly cost at $52.50 is 2.2 gigabytes

Answer:

The percentage change = 6.05%

Step-by-step explanation:

New value = £209.99

Old value = £198

Percentage change = [New Value - Old Value] / [Old Value] × 100

                                 = [209.99 - 198] / [198] × 100

                                 = [11.99] / [ 198] × 100

                                 = 0.06 × 100

                                 = 6.05%

Therefore, the percentage change = 6.05%

Answer:

acc = force /mass

30/40 = 0.75 m/s2

Answer:

12 cm

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the altitude )

Here A = 84 and b = 14 , then

[tex]\frac{1}{2}[/tex] × 14 × h = 84

7h = 84 ( divide both sides by 7 )

h = 12

The altitude is 12 cm

Answer:

m= 2/8

equation= y=1/2x+2

Step-by-step explanation:

give brainliest pls pls pls

Answer:

m=1/4

y=1/4x+2

Step-by-step explanation:

slope is rise over run.  it rises 1 and runs 4

the equation for a liner function is y=mx+b.  Since 1/4 is the slope, replace m with 1/4.  b is the y intercept, and from the graph, you know the y intercept is 2.

Step-by-step explanation:

450450450=100%

? =110%

110×450450450/100

495495495 mins=2nd month

add

495495495+450450450=

945945945 minutes

There are 945 minutes will he read in all during the two months.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Oliver read for 450 minutes this month.

And, His goal is to read for 10% more minutes next month.

Now,

Since, His goal is to read for 10% more minutes next month.

Hence, The extra minutes for next month = 10% of 450 minutes

                                                                 = 10/100 × 450

                                                                 = 45 minutes

Thus, The total minutes to read in all during the two months is,

⇒ 450 + (450 + 45) minutes

⇒ 450 + 495 minutes

⇒ 945 minutes

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Answer:

Number of elves= 80 elves

Step-by-step explanation:

If 9 elves can pack 27 toys per hour. This means that each elf packs 3 toys per hour:

Toys per elf= 27/9 = 3

Now, we need to determine the number fo elves needed to pack 240 toys per hour:

Number of elves= number of toys/toys per elf

Number of elves= 240/3

Number of elves= 80 elves

Answer:

The taxi ride was 14 miles long.

Step-by-step explanation:

So we know that he payed 29 $. Out of this 29$ 1$ was the pick up fee. So we know that 28$ were spend on distance that the taxi had to ride. We also know that Wyatt has to pay 2$ for each mile so in order to get the total number of miles the car drove we will have to divide the amount of money that was paid for the actually distance traveled by two. And so we get that our answer is........

28$ / 2$ = 14

Given:

The series is

[tex]2x+2x^2+2x^3+...+2x^n[/tex]

To find:

Whether the given series is arithmetic, geometric, both, or neither.

Solution:

We have,

[tex]2x+2x^2+2x^3+...+2x^n[/tex]

Difference between consecutive terms are:

[tex]d_1=a_2-a_1[/tex]

[tex]d_1=2x^2-2x[/tex]

[tex]d_1=2x(x-1)[/tex]

And,

[tex]d_2=a_3-a_2[/tex]

[tex]d_2=2x^3-2x^2[/tex]

[tex]d_2=2x^2(x-1)[/tex]

Here, [tex]d_1\neq d_2[/tex].

So, the given series is not an arithmetic series.

Ratio between consecutive terms are:

[tex]r_1=\dfrac{a_2}{a_1}[/tex]

[tex]r_1=\dfrac{2x^2}{2x}[/tex]

[tex]r_1=x[/tex]

And,

[tex]r_2=\dfrac{a_3}{a_2}[/tex]

[tex]r_2=\dfrac{2x^3}{2x^2}[/tex]

[tex]r_2=x[/tex]

Similarly upto last pair of consecutive terms.

[tex]r_{n-1}=\dfrac{a_n}{a_{n-1}}[/tex]

[tex]r_{n-1}=\dfrac{2x^n}{2x^{n-1}}[/tex]

[tex]r_{n-1}=x[/tex]

Since, [tex]r_1=r_2=...=r_{n-1}[/tex], so the given series have a common ratio.

Therefore, it is a geometric series.

Answer:dasfsafasfadfadfadasdas

Step-by-step explanation:

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Answer:

3.75, or [tex]\frac{15}{4}[/tex] inches of rain during the 15 days of April.

Step-by-step explanation:

All you have to do is add [tex]\frac{1}{4}[/tex] 15 times to get that number.

[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}[/tex] = 3.75

You can also do 15 times [tex]\frac{1}{4}[/tex], which will result in the same thing.

#teamtrees #WAP (Water And Plant)

Answer: y = 40 - 3x

Step-by-step explanation:

x = # of days

y= number of hours remaining

40 minus 3 times the number of days Wally volunteers would be the formula to find the number of hours he has remaining after a certain number, x, days.

Answer:

Option.B

There is a negative correlation in the data set

The correlation shown in the data is negative correlation.

Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.

Positive correlation is defined as the relationship where the value of y increases with the increase in the value of x.

Negative correlation is defined as the relationship where the value of y decreases with the decrease in the value of x.

Here the points are in such a way that the value of y decreases with increase in x.

So it is negative correlation.

Hence the correct answer is negative correlation.

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