x^2-4x+3=0 complete the square

Answer:

a. A = 50x - x² b. length = 25 inches and width = 25 inches and the maximum area is 625 in²

Step-by-step explanation:

a. The perimeter of a rectangle P = 2(L + W) where L = length and W = width. Now, given that P = 100 inches and W = x, substituting these into the equation, we have

P = 2(L + W)

100 = 2(L + x)

dividing both sides by 2, we have

100/2 = L + x

50 = L + x

making L subject of the formula, we have

L = 50 - x

Now, the are of a rectangle A = LW. Substituting the values of L and W, we have

A = LW

A = (50 - x)x

A = 50x - x²

b. To find the largest possible area of rectangle with perimeter 100 inches, we differentiate A and equate it to zero to find the value of x that maximizes A.

So, dA/dx = d(50x - x²)/dx

dA/dx = d50x/dx - dx²/dx

dA/dx = 50 - 2x

dA/dx = 0 ⇒ 50 - 2x = 0

50 = 2x

dividing both sides by 2, we have

x = 50/2

x = 25

To find it this gives maximum value for A, we differentiate A twice.

d²A/dx² = d(50 - 2x)/dx

d²A/dx² = d50/dx - d2x/dx

d²A/dx² = -2

Since d²A/dx² = -2 < 0, so x = 25 gives maximum value for the area, A.

Since W = x = 25 in and L = 50 - x. So, L = 50 - 25 = 25 in

So, the maximum area A = LW = Lx = 25 in × 25 in = 625 in²

The dimension with perimeter 100 inches that give maximum area are length = 25 inches and width = 25 inches and the maximum area is 625 in²

Answer:

1. 24%

2. 30%

3. 30%

Step-by-step explanation:

1. 100%/25= 4%   4%*6=24%

2. 100%/50= 2% 2%*15=30%

3.  100%/40=2.5% 2.5%*12= 30%

Answer:

117 i think

Step-by-step explanation:

because you need to find the distance from a to b which is 13 units

then you need to find the distance from b to c which is 9 units

and then 9 x 13 is 117

Answer:

m                        

Step-by-step explanation:

                                              m

Answer:

There were 140 robberies in Springfield in 2012.

Step-by-step explanation:

Let's marked (named) robberies in 2012 with x, which is worth 100%

196 robberies in 2013 worth 100% + 40% = 140%

Now we will make proportion

x : 196 = 100 : 140

When we multiply external and internal members we get

140 x = 196 · 100 => 140 x = 19600 => x = 19600/140 = 140

x = 140 robberies in 2012

Answer:

Area of triangle = 1/2*b*h

[tex]\frac{1}{2} * 2.8* 7.8\\\frac{1}{2} * 21.84\\\frac{21.84}{2}\\= 10.92[/tex]

Answer:

10.92 cm²

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 perpendicular height )

Here b= 2.8 and h = 7.8 , then

A = [tex]\frac{1}{2}[/tex] × 2.8 × 7.8 = 1.4 × 7.8 = 10.92 cm²

Answer:

[tex]2x^5+3x^2+3[/tex] is a trinomial having with:

Step-by-step explanation:

Considering the trinomial

[tex]2x^5+3x^2+3[/tex]

It is clear that '5' is the highest power of the 'x' variable. so, the polynomial has a degree of 5.

'3' is the constant term. The reason is that any term with no variable is called a 'constant' term. So, '3' is the constant term.

Therefore, [tex]2x^5+3x^2+3[/tex] is a trinomial having with:

Answer:

6.25 colonies of bacteria per +pH change from 7 to 9

Step-by-step explanation:

It seems to go from 57.5 to 70 or maybe 57 or 58

Either way I will go with my guess of 57.5

Rate of Change= (70-57.5)/(9-7)=(12.5)/(2)=6.25 rate of change for colonies of bacteria per positive pH change from 7 to 9

Answer:

Step-by-step explanation:

-2

Apply this particular rule of logs:

log a - log b = log a/b

Therefore, log2 (3) - log2 (12) = log2 (3/12) = log2 (1/4)

This last result simplifies to  log2 1 - log2 4 = 0 - 2 = -2

Answer:

-2

Step-by-step explanation:

[tex]log_2(3)-log_2(12)[/tex]

~Simplify using log properties

[tex]log_2(\frac{3}{12})[/tex]

[tex]log_2(\frac{1}{4})[/tex]

~Apply log rules

[tex]-log_2(4)[/tex]

~Rewrite

[tex]-log_2(2^2)[/tex]

~Apply log rules

[tex]-2log_2(2)[/tex]

~Apply log rules

-2 * 1

~Simplify

-2

Best of Luck!

Answer:

4.) 5.3333333....

Step-by-step explanation:

Rational numbers are either repeating decimals:

[tex]\frac{1}{3}= 0.333333333....[/tex]

Include terminating decimals:

[tex]\frac{1}{8}= 0.125[/tex]

Are all numbers that can be written as a quotient of integers:

[tex]\frac{a}{b},b\neq 0[/tex]

Options (1), (2), and (3) are neither repeating, terminating, and can't be written as a quotient of integers.

Option (4) has repeating decimals, so this is rational.

:Done

Answer:

1.75=5n or 5n=1.75

Step-by-step explanation:

There are 5 n's on the bottoms so you are doing 5 times n (5n) and then 1.75 is on the top so the equation has to equal 1.75

Answer:

5n=1.75

Step-by-step explanation:

the image, the area of the tape diagram indicating 1.75 is equal to the sum of the areas of all five parts in the diagram such that each part indicates n.

here, we have assumed that  1.75 represents an area of the first rectangle , and n represents the area of each of the small rectangle

Answer:

Where is it?

Step-by-step explanation:

Answer:

an = 7 + 5n

Step-by-step explanation:

First we know that for each number of days rented the cost increase by 5 so we get an - (?) + 5n.

We also know the first number is 12 for 1 day, so for 0 days, or the starter cost, is 7. We get this by subtracting 5 from 12.

Hence the answer an = 7 + 5n

Answer:

Step-by-step explanation:

These are complementary angles because from what this shows, they add up to 90 degrees. BTW Plz give brainliest, I need 5 to get to the next level.

Answer:

x=5 I think

Step-by-step explanation:

just search it up online

9514 1404 393

Answer:

  -1

Step-by-step explanation:

Solving the given equation for y, we have ...

  x -y = 18

  y = x - 18 . . . . . add y-18

The coefficient of x is 1. That is the slope of the given line. The desired perpendicular line will have a slope that is the negative reciprocal of this:

  m = -1/1 = -1

The slope of the perpendicular line is -1.

__

The graph shows you that a line with slope -1 is perpendicular to the given line.

Answer:

-20

Step-by-step explanation:

y = -3x+1

if the input is 7, it means x=7 so substitute in the equation

y= -3*7+1 = -21+1= -20 which is the output

More information is needed to properly answer the question!

Step-by-step explanation:

(x+12)+(6x-4)+(3x+2)=180

10x+10=180

10x=170

x=17

m<W =17+12

=29

Answer:

x = 60°

Step-by-step explanation:

Two parallel lines will have the same angle if another line intersects them. That means 2x+15° = 135°.

2x = 120°

x = 60°

Answer:

opposite number of -18

Answer: 63%

Step-by-step explanation:

First find the rate of loss that would cause the average rate of loss over the 10-year period equal to 38.0%.

Assume that rate is x.

38 = (36.2 + 29.0 + 46.2 + 37.5 + 40.9 + 40.0 + 32.6 + 40.5 + 40.1 + x) / 10

38 = (343 + x ) / 10

380 = 343 + x

x = 380 - 343

x = 37%

The survival rate is the opposite of the rate of loss which means that the survival rate is;

= 1 - rate of loss

= 1 - 37%

= 63%

Answer:

x = 6, y =3

Step-by-step explanation:

4x-7y=3

x-7y=-15

Multiply the first equation by -1

-4x+7y=-3

Then add this to the second equation to eliminate y

-4x+7y=-3

x-7y=-15

------------------

-3x +0y = -18

-3x = -18

Divide by -3

-3x/-3 = -18/-3

x = 6

Now find y

x -7y = -15

6 -7y = -15

Subtract 6 from each side

6-7y-6 = -15-6

-7y = -21

Divide by -7

-7y/-7 = -21/-7

y =3

Here's your answer..........

Answer:

Step-by-step explanation:

Step one:

given data

expected amount =$200

cash already at hand=$80

savings per week=$40

let the number of weeks be x

Step two:

the linear function for the situation is the same as the equation of a straight line

y=mx+c------1

200=4x+80

solve for x

200-80=40x

120=40x

divide both sides  by 4

x=120/40

x= 3 weeks

Chandler will save for 3 weeks

Answer:

9 gallons

Step-by-step explanation:

2/46 = 0.04347826086 gallon per mile

0.04347826086 x 207 miles =

9 gallons

Answer:

i would go with option 2, just depending on how many pounds u get for $6.58 though.

Answer:

41g

Step-by-step explanation:

65.6/8= 8.2g per cake

8.2*5 cakes= 41g

Answer:

Step-by-step explanation:

65.6g = 8 cakes

We need to find the sugar for 1 cake:

65.6 ÷ 8= 8.2 (gram for 1 cake)

The sugar for 5 cakes:

8.2 × 5= 41 (gram for 5 cakes)

Answer:

80

Step-by-step explanation:

180-60=120

120-40=80