X² – 4x – 12=0
solve by completing the square

Started with 54 cookies, considering fractions, removals, and distributions, ending with 15 cookies.

let's break it down:

1. **Initial Batch**: They started with an unknown number of cookies, denoted as  [tex]\( x \).[/tex]

2. **Cookies for Teachers**: They took [tex]\( \frac{1}{4} \) of the cookies for their teachers, leaving \( \frac{3}{4}x \)[/tex]  cookies.

3. **Burnt Cookie**: They discarded one burnt cookie, resulting in [tex]\( \frac{3}{4}x - 1 \) cookies.[/tex]

4. **Cookies for Nursing Home**: They gave  [tex]\( \frac{2}{3} \) of the remaining cookies to the nursing home, keeping \( \frac{1}{3} \) of \( \frac{3}{4}x - 1 \) cookies.[/tex]

5. **Cookies for Neighborhood Kids**: They gave 3 cookies to the neighborhood kids, resulting in  [tex]\( \frac{1}{3}x - 3 \) cookies.[/tex]

6. **Cookies for Friends**: They wrapped up [tex]\( \frac{2}{3} \) of the remaining cookies for their friends, keeping \( \frac{1}{3} \) of \( \frac{1}{3}x - 3 \) cookies.[/tex]

7. **Final Count**: They were left with 15 cookies, so [tex]\( \frac{1}{3}x - 3 = 15 \).[/tex]

[tex]\[ \frac{1}{3}x - 3 = 15 \]\[ \frac{1}{3}x = 15 + 3 \]\[ \frac{1}{3}x = 18 \]\[ x = 18 \times 3 \]\[ x = 54 \][/tex]

So, they initially had 54 cookies.

Answer:

x= −6−2y

Step-by-step explanation:

Subtract 2y from both sides of the equation x= −6−2y

Answer:-6-2y

Step-by-step explanation:

X+2y=-6

subtract 2y from both sides

X+2y-2y=-6-2y

X=-6-2y

Answer:

The diameter of the smaller can is ≅ 9.14 cm

Correct statement and question:

Two cylindrical cans are mathematically similar.

The larger can has a capacity of 1 liter and a diameter of 12 cm and the smaller can has a capacity of 440 ml.

Calculate the diameter, d, of the 440 ml can.

Source:

Previous question that can be found at brainly

Step-by-step explanation:

Let's recall that:

A. The formula of the volume of a cylinder is π*r²*h, where:

r is the radius of the cylinder (half of the length of the diameter) and h, represents the height of the cylinder.

B. 1 liter = 1,000 milliliters = 1,000 cubic centimeters

Therefore, we can find the height of the larger can, this way:

V = π*r²*h

Replacing with the value we know:

d = 12 ⇒ r = 6

1,000 = 3.1416 * 6² * h

1,000 = 113.0976h

h = 1,000/113.0976

h = 8.84 cm (rounding to the next hundredth)

Now we can find the ratio of the radius to the height of the larger can to find the measures of the smaller can, this way because the cylinders are mathematically similar:

Ratio = Radius/Height

Ratio = 6/8.84

Ratio = 0.6787

It means the radius of the smaller can is 0.6787 multiplied by the value of the height of the smaller can. Let x represent the height h of the smaller can, we can write this equation to solve for x:

V = π*r²*h

Replacing with the values we know:

height = x

radius = 0.6787x

440 = π * (0.6787x)² * x

440 = 3.1416 * 0.4606x² * x

440 = 1.4471x³

x³ = 440/1.4471

x³ = 304.06

∛x = ∛304.06

x = 6.73 ⇒ height of the smaller can = 6.73 cm and radius of the smaller can = 6.73 * 0.6787 = 4.57

If radius = 4.57 cm ⇒ diameter = 2 * 4.57 = 9.14 cm

The diameter of the smaller can is ≅ 9.14 cm

The diameter of the 440 ml can is approximately 9.12 cm.

To determine the diameter of the smaller can, we use the fact that the two cans are mathematically similar. This means that their dimensions have a constant ratio, known as the scale factor.

The capacity of the larger can is 1 liter (1000 ml), and the capacity of the smaller can is 440 ml.

The scale factor for volumes is given by:

Scale Factor (Volume) = (Volume of smaller can) / (Volume of larger can) = 440 ml / 1000 ml = 0.44

Since the cans are similar, the scale factor for the linear dimensions (such as diameter) is the cube root of the volume scale factor:

Scale Factor (Diameter) = ∛(Scale Factor (Volume)) = ∛(0.44)

Using a calculator, we find:

∛(0.44) ≈ 0.76

Now, we multiply the diameter of the larger can by this scale factor to find the diameter of the smaller can:

Diameter of the smaller can = Diameter of the larger can × Scale Factor (Diameter) = 12 cm × 0.76 ≈ 9.12 cm

Therefore, the diameter of the 440 ml can is approximately 9.12 cm.

Complete question:

Two cylindrical cans are mathematically similar.

The larger can have a capacity of 1 liter and the smaller can have a capacity of 440 ml.

Calculate the diameter, d, of the 440 ml can if the diameter of the larger can is 12 cm.

Answer:

I = 130

Step-by-step explanation:

The sum of all four angles in a four-sided closed shape will ALWAYS be equivalent to 360 degrees. Also, the opposite angles of a parallelogram will ALWAYS be equivalent. This means F = H.

To begin, the measure of F, y + 7, and the measure of H, 3y - 79, are equal. This equation looks like: y + 7 = 3y - 79

Now subtract y from both sides: 7 = 2y - 79

Add 79 to both sides: 86 = 2y

And divide both sides by 2: 43 = y

Now that you have the value of y, plug 43 into y and solve for both equations:

43 + 7 = 3(43) - 79

50 = 129 - 79

50 = 50

So now we know that  the measure of angles F and H are 50. 50 + 50 is 100.

Since we know that the sum of all four sides must be equivalent to 360. subtract 100 from 360 to get the sum of the measures of angles I and G:

360 - 100 = 260

So now 260 must equal I + G. Since I and G must be equivalent, just divide 260 by 2 and you have your answer: 260/2 = 130

Answer:

p = - 3

Step-by-step explanation:

Given

x² - 6x = 12

To obtain the required form use the method of completing the square

add ( half the coefficient of the x- term )² to both sides, thus

x² + 2(- 3)x + 9 = 12 + 9

(x - 3)² = 21

Thus p = - 3

Given the quadratic functions expressed as;

x² - 6x = 12

The value of p given the quadratic expression is -3

Complete the square at the left hand side of the equation.

Add the square of the half of coefficient of x to both sides.

coefficient of x = -6

Half of coefficient of x = -6/2 = -3

Square of the result = (-3)² = 9

Add 9 to both sides of the equation

x² - 6x + 9 = 12 + 9

Factoring the left hand side

(x-3)² = 21

Comparing the result with (x+p)² = q

The value of p wil be -3

Learn more here: brainly.com/question/13981588

Answer: I believe that the answer is either C or A

Step-by-step explanation:

Typically, 7% of babies born in the River Creek hospital have birth defects, which means 93% of babies do not. In a group of 500 babies, about 35 are expected to have birth defects.

A. The typical percentage of babies having birth defects is 7%, because 7 out of every 100 is the equivalent of 7% when expressed as a percentage.

B. To find the percentage of babies that do not have birth defects is therefore 100%-7% = 93%, because the percentage of babies that have defects and those that do not should add up to 100%.

C. If you were to expect about 7% of babies to have a birth defect in a group of 500 babies, you would calculate it as: 500 x 0.07 = 35 babies. So, you would typically expect to find about 35 babies with birth defects in a group of 500 babies.

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The equation of the line perpendicular to y = -2x + 8 is y = 1/2x + 8.

A line is perpendicular to another line if their slopes are negative reciprocals of each other. The slope of the line y = -2x + 8 is -2, so the slope of a line perpendicular to it would be 1/2.

Of the above choices, only line (C) has a slope of 1/2. Therefore, the equation of the line perpendicular to y = -2x + 8 is y = 1/2x + b, where b is the y-intercept.

To find the value of b, we can substitute a point on the line y = -2x + 8 into the equation y = 1/2x + b. For example, the point (0, 8) lies on the line y = -2x + 8. Substituting this point into the equation y = 1/2x + b, we get:

8 = 1/2 * 0 + b

b = 8

Therefore, the equation of the line perpendicular to y = -2x + 8 is y = 1/2x + 8.

for such more question on perpendicular

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Answer:

Therefore,

[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]

Step-by-step explanation:

Given:

Spherical Shape Ball

[tex]Radius =15\ inches[/tex]

pi = 3.14

To Find:

Volume of Ball= ?

Solution:

Formula for Volume of Sphere is given by

[tex]\textrm{Volume of Sphere}=\dfrac{4}{3}\pi (Radius)^{3}[/tex]

Substituting the given values we get

[tex]\textrm{Volume of Ball}=\dfrac{4}{3}\times 3.14\times 15^{3}=14130\ inches^{3}[/tex]

Therefore,

[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]

Answer:

Step-by-step explanation:

bruh

Answer:

I need more information

Answer:

3.5 alligators

Step-by-step explanation:

i did khan academy

Answer:

3.5

Step-by-step explanation:

I just answered it :) it was correct btw

Answer:

[tex]486\ in^2[/tex]

Step-by-step explanation:

we know that

The surface area of the cube is equal to the area of its six square faces

so

[tex]SA=6b^2[/tex]

where

b is the length side of the cube

we have

[tex]b=9\ in[/tex]

substitute

[tex]SA=6(9)^2=486\ in^2[/tex]

Answer:

486

Step-by-step explanation:

Answer:

144 pounds

Step-by-step explanation:

Weight of object Earth: Weight of Object Planet B

100:3 = 4800:b

100/3=4800/b

100b=14400

b=144

Therefore, 144 pounds

The weight of an elephant on planet B can be calculated using the weight ratio of 100 (on Earth) to 3 (on planet B). By setting up a proportion and solving for the unknown weight, we find that the elephant weighs 144 pounds on planet B.

Since the ratio is 100 to 3, we can set up a proportion to find the elephant's weight on planet B.

First, represent the known weight ratio between Earth and planet B: 100 (earth weight) to 3 (planet B weight).

Then, set up the proportion using the weight of the elephant on Earth (4,800 pounds) and let x represent the unknown weight on planet B:

100/3 = 4800/x

To solve for x, cross-multiply and divide:

100x = 4800 * 3

Finally, divide both sides by 100 to find x:

x = (4800 * 3) / 100

x = 144 pounds

Therefore, the elephant would weigh 144 pounds on planet B.

Answer:

54π in³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V= πr²h ( r is the radius and h the height )

Here r = 3 and h = 6, thus

V = π × 3² × 6 = π × 9 × 6 = 54π in³

To find the percentage of the shaded area inside the square, we need to determine the area of the shaded region and calculate the percentage relative to the total area of the square. Without more information or measurements, we can't determine the exact size of the shaded area or the percentage.

To find the percentage of the area inside the square that is shaded, we need to determine the area of the shaded region and then calculate the percentage. Given the perimeter of the square is 40cm, we can find the length of each side by dividing the perimeter by 4, which gives us 10cm. The area of the square is found by squaring the length of one side, so the area is 10cm x 10cm = 100cm². To find the shaded area, we need to subtract the area of the square from the total area. Assuming the shaded region is a smaller square with side length x, the area of the shaded region is x². So the shaded area is 100cm² - x².

To calculate the percentage, we divide the shaded area by the total area of the square and multiply by 100. So the percentage of the area inside the square that is shaded is (100cm² - x²) / 100cm² * 100.

It's important to note that we don't have enough information to determine the exact size of the shaded area or calculate the percentage without more details or measurements of the shaded region.

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Answer:

n = 3

Step-by-step explanation:

Equation:  17.1 = 5.7 * n

Divide both sides by 5.7 to get n by itself.

Step 1:  Divide both sides by 5.7

17.1 = 5.7 * n

17.1 / 5.7 = 5.7 * n / 5.7

    divide            divide

3 = n

Answer:  n = 3

We are given the following equation and want to solve for the unknown variable, n:

[tex]17.1=5.7 \times n[/tex]

To solve for an unknown variable, we want to isolate the variable by doing operations to both sides of the equation:

For this equation, we'll divide both sides by 5.7 to isolate the unknown variable n

[tex]17.1 \boxed{\div 5.7} = 5.7 \times n \boxed{\div 5.7}[/tex]

After dividing both sides by 5.7 and simplifying, we get:

[tex]3=n[/tex]

The next step is a bit tedious, but in math, you usually want to have the variable on the LEFT side of the equation after isolation.

After reversing the equation accordingly, we have:

[tex]\boxed{n=3}[/tex]

We have a value for n, which is 3.

Let me know if you need any clarifications, thanks!

~ Padoru

Answer:

i think ainsley completed 45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Answer:



Step-by-step explanation:

A=[tex]\pi r^{2}[/tex]

A=3.14*26*26

A=2122.64

A=2122.6[tex]m^{2}[/tex]

The calculated area is 530.66 [tex]m^2[/tex], which rounds to 530.7 [tex]m^2[/tex].

To find the area of a circle with a given diameter, you first need to find the radius, which is half of the diameter. Since the diameter provided in the question is 26 meters, the radius would be 13 meters. The formula to calculate the area (A) is A = π[tex]r^2[/tex], where (pi) is approximately 3.14 and r is the radius of the circle.

Using the aforementioned radius of 13 meters, the area can be calculated as follows:

A = 3.14 x [tex](13 m)^2[/tex]= 3.14 x 169 = 530.66 [tex]m^2[/tex]

When rounded to the nearest tenth, the area of the circle is 530.7 [tex]m^2[/tex].

Answer:

3600

Step-by-step explanation:

960*3=2880

To find how many per hour: 960/24= 40

40*18=720

720+2880=3600

Answer:

3600 watts

Step-by-step explanation:

960 multiplied by 3 , then divide 18 by 24. Multiply 0.75 by 960, and then add 2880 and 720.

Answer: Area is 168ft^2

Step-by-step explanation:

Answer:

4 and -3

Step-by-step explanation:

4-3=1

4(-3)=-12

The two numbers that have a sum of 1 and a product of -12 is -4 & 3

From the question, we are determine the two unknown numbers by solving the quadratic equation

The given quadratic equation is

n² + n -12 = 0

The quadratic equation can be solved as follows

n² + n -12 = 0

By factorizing

n² +4n -3n -12 = 0

n(n+4) -3(n+4) = 0  

(n+4)(n-3) = 0

Then,

n+4 = 0 OR n -3 = 0

∴ n = -4 OR n = 3

Hence, the two numbers that have a sum of 1 and a product of -12 are -4 & 3

Learn more on Solving quadratic equations here: https://brainly.com/question/2320567

Good morning

Answer:

Step-by-step explanation:

56 increased by 25% = 56+25%

                                    = 56 + 56×(25÷100)

                                    =70

________________________________

:)

Answer: 11 more cups of flour is needed.

Step-by-step explanation: 234 - 223 = 11

We find that the cook needs 11 more cups of flour to meet the recipe's requirement of 234 cups, as they only have 223 cups.

To determine whether the cook has enough flour to follow a recipe requiring 234 cups, a simple subtraction operation is performed. The cook starts with 223 cups of flour. The amount needed subtracts the amount available: 234 cups (needed) - 223 cups (available) = 11 cups. So, the cook requires 11 more cups of flour to have enough for the recipe.

Answer:

D) 50ft

Step-by-step explanation:

(18×x) + (32×18) + [(48-18-18)×(32-11)]

= 1728

18x + 576 + (12×21) = 1728

18x = 1728 - 828

18x = 900

x = 50

Answer:

I think it's B.

Step-by-step explanation:

Answer:

I believe that the answer is A but it could be B

Answer:

The scale factor of the dilation is 3

Step-by-step explanation:

we know that

A dilation is a non rigid transformation that produce similar figures

so

Rectangle ABCD and rectangle A'B'C'D' are similar

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

[tex]z=\frac{D'C'}{DC}[/tex]

we have

[tex]D'C'=12-3=9\ units[/tex] ----> difference of x-coordinates

[tex]DC=4-1=3\ units[/tex]  ---> difference of x-coordinates

substitute

[tex]z=\frac{9}{3}=3[/tex]

The scale factor is greater than 1

so

The dilation is a enlargement

Answer:

60

Step-by-step explanation:

Step 1:  Solve for x

x + 3x + 2x = 180

6x / 6 = 180 / 6

x = 30

Step 2:  Find the measure of angle C

Angle C = 2x

Angle C = 2(30)

Angle C = 60 degrees

Answer:  60