a circle has a diameter of 14 cm. find its circumference. use 3.14 for pi

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

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Answer:

1)  Slope = -11,  y-intercept = 6

2)  Slope = 3/2,  y-intercept = -4/3

3)  Slope = 2/3,  y-intercept = -5/6

4)  Slope = -5,  y-intercept = 13

5)  Slope = 5/2,  y-intercept = -8

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

To find the slope and y-intercept of each equation, rearrange each equation so that it is in slope-intercept form.

\(\begin{aligned}&\textsf{Given equation}: & 11x + y & = 6\\&\textsf{Subtract $11x$ from both sides}: \quad & 11x + y-11x & = 6-11x\\&\textsf{Simplify}: & y & = 6-11x\\&\textsf{Slope-intercept form}: & y&=-11x+6\end{aligned}\)

Therefore:

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

\(\begin{aligned}&\textsf{Given equation}: & 9x-6y&=8\\&\textsf{Add $6y$ to both sides}: \quad & 9x-6y+6y&=8+6y\\&\textsf{Simplify}: & 9x&=8+6y\\&\textsf{Subtract $8$ from both sides}: & 9x-8&=8+6y-8\\&\textsf{Simplify}: & 9x-8&=6y\\&\textsf{Divide both sides by $6$}: & \dfrac{9x-8}{6}&=\dfrac{6y}{6}\\&\textsf{Simplify}: & \dfrac{3}{2}x-\dfrac{4}{3}&=y\\&\textsf{Slope-intercept form}: & y&=\dfrac{3}{2}x-\dfrac{4}{3}\end{aligned}\)

Therefore:

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

\(\begin{aligned}&\textsf{Given equation}: & 12x - 18y &= 15\\&\textsf{Add $18y$ to both sides}: \quad & 12x - 18y +18y&= 15+18y\\&\textsf{Simplify}: & 12x&=15+18y\\&\textsf{Subtract $15$ from both sides}: & 12x-15&=15+18y-15\\&\textsf{Simplify}: & 12x-15&=18y\\&\textsf{Divide both sides by $18$}: & \dfrac{12x-15}{18}&=\dfrac{18y}{18}\\&\textsf{Simplify}: & \dfrac{2}{3}x-\dfrac{5}{6}&=y\\&\textsf{Slope-intercept form}: & y &= \dfrac{2}{3}x-\dfrac{5}{6}\end{aligned}\)

Therefore:

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

\(\begin{aligned}&\textsf{Given equation}: & 5x + y &= 13\\&\textsf{Subtract $5x$ from both sides}: \quad & 5x + y-5x &= 13-5x\\&\textsf{Simplify}: & y&=13-5x\\&\textsf{Slope-intercept form}: & y&=-5x+13\end{aligned}\)

Therefore:

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

\(\begin{aligned}&\textsf{Given equation}: & y+3&=\dfrac{5}{2}x-5\\&\textsf{Subtract $3$ from both sides}: & y+3-3&=\dfrac{5}{2}x-5-3\\&\textsf{Simplify}: & y&=\dfrac{5}{2}x-8\\&\textsf{Slope-intercept form}: & y&=\dfrac{5}{2}x-8\end{aligned}\)

Therefore:

The percentage of shaded grid is 45% and the number of squares is 5.

a. Percentage of shaded grid

The total number of shaded and unshaded grid is 20 while the total number of shaded area is 9 now let find the percentage of the shaded grid.

Percentage of shaded grid = Shaded grid /Total grid

Percentage of shaded grid = 9/20 × 100

Percentage of shaded grid = 45%

b. Number of squares to be shaded

Number of squares = 20 grid × (70% - 45%)

Number of squares = 20 grid × 25%

Number of squares =  5 squares

Therefore the percentage is 45% .

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Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

Answer:

i think the answer is B

Step-by-step explanation:i looked at them and they seem to be related

Answer:

b. weight of a ball

Step-by-step explanation:

The weight of any thing is continuous

I hope this help you

Answer: This is a college question?

Step-by-step explanation:

Mary picked 24 apples and Betty picked 40

Answer:

24 and 40

Step-by-step explanation:

there 16 apart from each other and simplyfy it you get a ratio of 3:5

Answer:

The area is changing at the point of  \(\mathbf{61200 m^2/year}\)

Step-by-step explanation:

From the given information:

Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w

where;

L = length and w = width of the rectangle

Suppose the Length L is twice the width w

Then L = 2w --- (1)

From The area of a rectangle

A = L  × w

A = 2w  × w

A = 2w²

Taking the above differentiating with respect to time

\(\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)\)

At the time t

\(\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m\)

Replacing the values back into equation 2, we get:

\(\dfrac{dA}{dt }= 4 \times 450 \times 34\)

\(\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}\)

For one to isolate the variable by using equation rules. Inverse inequality sign if multiplying/dividing by negative. Steps to isolate variable in inequality: Simplify, move constants with inverse operations. Divide coefficient to isolate variable. Reverse direction if using negative number.

Inequalities require you to apply the same principles as those used in equations when isolating a variable. For example, if there is an inequality 3x - 5 < 7. one can isolate the variable, by first:

Add 5 to both sides to be: 3x < 12.

Then divide both sides by 3: x < 4.

So, the variable x is one that is isolated, and the solution to the inequality is one where x < 4.

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Answer:

The first one

Step-by-step explanation: the ABC triangle has a 25-degree angle and a 90-degree angle as you can see by the marks. The first triangle has a 25-degree angle and a 90-degree angle as you can see by the marks. The second one does have a 90-degree angle but it's a different shape and has no 25-degree angle. The third one has both angles 25 and 90 but if you look close it's a different shape. The last one does not have a 90-degree angle but it does have a 25-degree angle and it's a different shape.

So it would be the first option.

Answer: 25% of 200 = 50

Step-by-step explanation

Answer:

25%of 200 is 50

Step-by-step explanation:

use a calculator

Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)

We can also complete the square (which is faster):

\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)

Step-by-step explanation:

b because you have to multiply

Answer:

B

Step-by-step explanation:

Answer: It's A 7.1

ON THE EDGE 2121!

PRICES COUNTS COSTS

8 e 8e

10 420-e-t 10(420-e-t)

12 t 12t

420 3920

system%28e%2B420-e-t=5t%2C8e%2B10%28420-e-t%29%2B12t=3920%29

First equation gives highlight%28t=70%29.

Second equation simplifies to e-t=140.

Substitution gives highlight%28e=210%29.

Quantity of $10 tickets by difference, highlight%28140%29

Answer:

9/10 of a gallon

Step-by-step explanation:

Well if we look at it we first have 4/10 of gallon poured. After a bit we will have that same 4/10 of a gallon so if we add in 5/10 of a gallon to the already had 4/10 of a gallon then the bucket should be 9/10 of a gallon in that bucket.

Answer:

the first car has 25 gallons of gases while the second car has 35 gallons of gases

Answer: (0, 3)

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Answer:

0.016

Step-by-step explanation:

Remember that "of" means to multiply and percent (%) means out of 100. So we would multiply 3.2 by 0.5 and get 1.6 then you move the decimal 2 times to the right and get 0.016. Have a Great Day! ;)

Answer:

x=57

Step-by-step explanation:

To solve this problem we need to make an equation to use to solve x.

The sum of 88 and x will equal 145 so the equation will look like this, 88 + x = 145.

Whatever x is, it has to add with 88 to make 145 so we have to use reverse operations.

The opposite of addition is subtraction so we subtract 88 from 145 like so. 145 - 88 = 57, which means x = 57.

If you need me to explain further don’t hesitate to ask me and I hope I helped! :)

Inverse relationships between operations are used to solve two-step inequalities because they allow us to isolate the variable on one side of the inequality.

A two-step inequality involves two operations that need to be undone in reverse order to solve for the variable. Inverse relationships between operations are used to "undo" these operations, leading to an isolated variable.

For example, consider the inequality 2x + 5 > 11. The first operation being performed on x is multiplication by 2, and the second operation is adding 5. To solve for x, we need to undo these operations in reverse order.

The inverse relationship of multiplication by 2 is division by 2, and the inverse relationship of adding 5 is subtracting 5. Therefore, we can solve the inequality as follows:

2x + 5 > 11

2x > 6 (subtract 5 from both sides)

x > 3 (divide both sides by 2)

Here, we first subtracted 5 from both sides to undo the addition of 5, and then divided both sides by 2 to undo the multiplication by 2.

Inverse relationships between operations are used in two-step inequalities because they help to simplify the equation by undoing the operations one by one, leading to an isolated variable.

By using inverse relationships between operations, we can efficiently and systematically solve two-step inequalities and isolate the variable to find the solution set.

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Answer:

y = -4

Step-by-step explanation:

given x = -1

6x - 7y = 22

6(-1) -7y = 22

-6 - 7y = 22

-7y = 22 + 6

-7y = 28

y = -4

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Answer:

8k at 3%

17k at 9%

Step-by-step explanation:

I use my calculations.

Given matrices are from here

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=====================================================

Problem 3

a)

B - C = DNE

We cannot subtract matrices of different sizes. Matrix B is 2x2 while C is 3x2. Both matrices must have the same number of rows, and they must also have the same number of columns. The matrices don't have to be square.

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

b)

\(A+B = \begin{bmatrix}-5 & 6\\7 & 4\end{bmatrix}\)

You add the corresponding elements. For instance, in the top left corner we have -1+(-4) = -5. The other entries are treated in a similar manner.

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

c)

\(-2E = \begin{bmatrix}6 & -4 & 8\\-12 & 14 & -16\\-10 & -18 & 20\end{bmatrix}\)

You get this from multiplying each entry in matrix E by -2. Eg: top left corner has -2*(-3) = 6

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

d)

\(CD = \begin{bmatrix}4 & 7 & 8\\ 1 & 3 & 4\\14 & 17 & 16\end{bmatrix}\)

Matrix C has 3 rows and D has 3 columns. The final answer will be size 3x3

To generate each value in the answer matrix, you'll highlight rows of C to pair with columns of D. Then you'll multiply out the corresponding values, after which you add those products. This is done for every entry in the answer shown above.

For example, the first row of C is highlighted and the second column of D is highlighted. Those values pair up and multiply getting -1*(-1) + 2*3 = 1+6 = 7, which goes in the first row and second column of the answer matrix. The other entries are handled in a similar fashion.

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

e)

\(\det(B) = -46\)

The 2x2 matrix determinant formula is \(\begin{vmatrix}a & b\\c & d\end{vmatrix} = a*d - b*c\)

In this case, a = -4, b = 6, c = 5, d = 4.

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

f)

\(B^{-1} = \begin{bmatrix}-2/23 & 3/23\\ 5/46 & 2/23\end{bmatrix}\)

Swap the top left and bottom right corners of matrix B. Change the sign of the other two corner values. Then multiply each entry by 1/d where d is the determinant found back in part (e) above. Be sure to reduce any fraction as much as possible.

=====================================================

Problem 4

Answers: x = 2  and y = -10

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

Work Shown:

\(\begin{bmatrix}2x & 4\\-5 & -2\end{bmatrix}+\begin{bmatrix}3 & -7\\11 & y-1\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\\begin{bmatrix}2x+3 & 4+(-7)\\-5+11 & -2+(y-1)\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\\begin{bmatrix}2x+3 & -3\\6 & y-3\end{bmatrix} = \begin{bmatrix}7 & -3\\6 & -13\end{bmatrix}\\\\\\\)

In the top left corners of each matrix, in line 3, we have 2x+3 = 7 which solves to...

2x+3 = 7

2x = 7-3

2x = 4

x = 4/2

x = 2

In the bottom right corners, we have y-3 = -13 which solves to....

y-3 = -13

y = -13+3

y = -10

Answer:

The surface area of the cylinder is \(\mathbf{70\pi\;\textbf{cm}^2}\)

Step-by-step explanation:

The surface area of a cylinder is express

  \(S=2\pi rh\)

where \(r\) is the radius of the cylinder and \(h\) its height

Therefore, if the radius of the cylinder is

  \(r=5\;\text{cm}\)

and its height

  \(h=7\;\text{cm}\)

the surface area should be

  \(S=2\pi r h\\S=2\pi (5\;\text{cm})(7\;\text{cm}) \;\;\;\;\;\Rightarrow\;\;\;\;\; \mathbf{S=70\pi\;\textbf{cm}^2}\)

Answer:

Below.

Step-by-step explanation:

3x=400

x=400/3 or 133.33

2x= 266.66

Therefore, the tanks must have sizes, 133.33 and 266.66 gallons!

The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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