Pls help me in this khan academy exercise

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

\(n = 12\)

Step-by-step explanation:

Given

\((p^{20})(p^{-4})^2 = p^n\)

Required

What is n?

\((p^{20})(p^{-4})^2 = p^n\)

Apply law of indices

\((p^{20})(p^{-4 * 2}) = p^n\)

Express -4 * 2 as -8

\((p^{20})(p^{-8}) = p^n\)

Apply law of indices

\(p^{20 - 8} = p^n\)

\(p^{12} = p^n\)

Cancel p on both sides

\(12 = n\)

\(n = 12\)

Answer:

16

Step-by-step explanation:

plug in the numeric values.

-6 + 22

16

Answer:

{x,y}={14,8}

Step-by-step explanation:

Answer:

-17 + 12x + 2x

Step-by-step explanation:

\( - 7 - y + 2x + 13y - 10\)

\( - 7 - 10 = - (7 + 10) = - 17\)

\( - 17 - y + 2x + 13y\)

\( - y + 13y = - 1y + 13y = ( - 1 + 13)y = 12y\)

\(\boxed{\green{= - 17 + 12y + 2x}}\)

The domain and range of the function are {-4, -2, 0, 4} and {-3, -1, 0, 1} respectively.

The domain of the function is defined as the value of the independent function for which the function exist.

The range of the function is defined as the value of the dependent function for which the function exist.

From the given table, the domain are the values in the x-column which the range in the y-column are the values in the y-axis.

From the table, the domain are D = {-4, -2, 0, 4} while the range is R = {-3, -1, 0, 1}.

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Resposta:49

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Answer:

56π units²

Step-by-step explanation:

area of entire circle = πr² = π8² = 64π

360° - 45° = 315°

(315/360)(64π) = 56π units²

Answer:56 square Units

Step-by-step explanation:

The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

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The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.

Cd(CH₂CICO₂)₂ contains:

1 cadmium (Cd) atom

2 carbon (C) atoms

6 hydrogen (H) atoms

4 oxygen (O) atoms

2 chlorine (Cl) atoms

Adding these up, we get:

1 + 2 + 6 + 4 + 2 = 15

Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

The answer is (D) 15.

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Answer:

There were 6 guides on Sunday.

Step-by-step explanation:

Same ratio

On Saturday, 120 tourists and 18 guides.

On Sunday, 40 tourists and x guides.

Due to the same ratio:

\(\frac{120}{40} = \frac{18}{x}\)

\(3 = \frac{18}{x}\)

\(3x = 18\)

\(x = \frac{18}{3}\)

\(x = 6\)

There were 6 guides on Sunday.

Answer:

2x squared - 5

= 2(x)^2 - 5

= 2(4)^2 - 5

= 2(16) - 5

= 32 - 5

= 27

Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

On solving the provided question, we can say that -  95 confidence interval Z alpha 2 = 1.96, CI = (4.1 , 53.9)

The z critical value is 1.96 for a test with a 95% confidence level (e.g. = 0.05). The z critical value is 5.576 for a test with a 99% confidence level (for instance, with = 0.01).

The two red tails represent the alpha level split by two. Finding the z-score for an alpha level for a two-tailed test is what is meant when a question asks you to determine z alpha/2. The confidence interval may be subtracted from 100% to calculate alpha, which is connected to confidence levels.

for 95% confidence,

\(Z_{\frac{\alpha }{2} }\) = 1.96

CI = (5279 - 5250) ± 1.96\(\sqrt{\frac{140^2}{395} + \frac{210^2}{395} } \\\)

CI = (4.1 , 53.9)

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The amount of pizza that they eat altogether will be 7/6 pizza out of 2 pizzas.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas. This approach is used to answer the problem correctly and completely.

Jada and Han request two indistinguishable pizzas. Jada ate 1/2 of hers and Han ate 2/3 of his.

The amount of pizza that they eat altogether will be given as,

⇒ 2/3 + 1/2

Add the fraction, then we have

⇒ 2/3 + 1/2

⇒ (4 + 3) / 6

⇒ 7 / 6

The amount of pizza that they eat by and large will be 7/6 pizza out of 2 pizzas.

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Answer:

x = 64

Step-by-step explanation:

2/x = 1/32

cross multiply

2 × 32 = x × 1

64 = 1x

64 = x

The fraction that bears the same ratio to 1/27 as 3/7 does to 5/9 is 27/35.

To find the fraction that bears the same ratio to 1/27 as 3/7 does to 5/9, we can set up a proportion.

Let's represent the unknown fraction as x. The ratio can be configured as follows:

x / (1/27) = (3/7) / (5/9)

To solve this proportion, we can cross-multiply:

(x * 5/9) = (3/7) * (1/27)

Simplifying the right side:

(x * 5/9) = 3/189

To eliminate the fraction on the left side, we can multiply both sides by the reciprocal of 5/9, which is 9/5:

(x * 5/9) * (9/5) = (3/189) * (9/5)

Simplifying further:

x = 27/35

Therefore, the fraction that bears the same ratio to 1/27 as 3/7 does to 5/9 is 27/35.

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Answer:

-2 <× <35

i hop i helped you sold the question

Answer:

y=2x-7

Step-by-step explanation:

y=mx+b

Since the lines are parallels, that means that their slopes are the same, so you can use the slope which is 2.

Then you can substitute the points in to find the b.

1=2(4)+b

1=8+b

-7=b

You can substitute this into the equation and get, y=2x-7.

Please correct me if I am wrong. I hope you understand!

If Luis bought a lot tires for 24,000 pesos, sold 1/3 of the tires at 200 each, ¼ in 300, 1/6 in 400 and ¼ in 500 pesos each and earned a profit of 8,000 pesos in the end, then Luis had bought a lot of 96 tires.

As per the question statement, Luis bought a lot of tires for 24,000 pesos, and sold 1/3 of the tires at 200 pesos each, ¼ of them at 300 pesos each, 1/6 in 400 pesos and ¼ in 500 pesos each, by which, he earned a profit of 8,000 pesos in the end,

Then, we are required to calculate the number of tires Luis bought in that lot.

To solve this question, let us assume that there were "x" tires in that lot. Now, we will need to form a linear equation in one variable (x) as per the conditions mentioned above, and solving for "x", we will obtain our desired answer.

Since Luis bought a lot tires for 24,000 pesos, and earned a profit of 8,000 pesos by selling them, then he sold that lot of tires for

$(24000 + 8000) = $32000

Now, as he sold 1/3 of the tires at 200 each, ¼ in 300, 1/6 in 400 and ¼ in 500 pesos, and already assumed that there were "x" tires in that lot,

[{(1/3)x * 200} + {(1/4)x * 300} + {(1/6)x * 400} + {(1/4)x * 500}] = 32000

Or, [{(200x/3) + (300x/4) + (400x/6) + (500x/4)} = 32000]

Or, [100{(2x/3) + (3x/4) + (4x/6) + (5x/4)} = 32000]

Or, [100{(2x/3)+ (3x/4) + (2x/3) + (5x/4)} = 32000]

Or, [{(2x/3)+ (3x/4) + (2x/3) + (5x/4)} = (32000/100)]

Or, [{(8x + 9x + 8x + 15x)/12} = 320]

Or, [(40x/12) = 320]

Or, [x = {(320 * 12)/40}]

Or, [x = (8 * 12)]

Or, [x = 96]

That is, If Luis bought a lot tires for 24,000 pesos, sold 1/3 of the tires at 200 each, ¼ in 300, 1/6 in 400 and ¼ in 500 pesos each and earned a profit of 8,000 pesos in the end, then Luis had bought a lot of 96 tires.

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With the help of the given Venn diagram, the answer of n(A∪B) is 44 respectively.

A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects.

Circles that overlap share certain characteristics, whereas circles that do not overlap do not.

Venn diagrams are useful for showing how two concepts are related and different visually.

When two or more objects have overlapping attributes, a Venn diagram offers a simple way to illustrate the relationships between them.

Venn diagrams are frequently used in reports and presentations because they make it simpler to visualize data.

So, we need to find:

A ∪ B

Now, calculate as follows:

The collection of all objects found in either the Blue or Green circles, or both, is known as A B. Its components number is:

8 + 7 + 14 + 6 + 1 + 8 = 44

n(A∪B) = 44

Therefore, with the help of the given Venn diagram, the answer of n(A∪B) is 44 respectively.

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Answer:

theres the answers. hope this helps!

Step-by-step explanation:

Answer:

What are the dimensions, a, b, and c, of the net?

a = ✔ 5 cm

b = ✔ 13 cm

c = ✔ 15  cm

Step-by-step explanation:

I took it!

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

15,659,568

Step-by-step explanation:

To calculate the expression 2308208 * 12 - 12038928, we can follow the order of operations (PEMDAS/BODMAS):

1. Multiply: 2308208 * 12 = 27698496

2. Subtract: 27698496 - 12038928 = 15659568

Therefore, 2308208 * 12 - 12038928 equals 15,659,568.

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Answer:

B. 50% is the answer.

Step-by-step explanation:

that's the answer.

Answer:

the 2nd part is b. and c.

Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

The value of the expression (-2)(3)º(4) - 2 is -164.

Based on the answer choices provided, none of the options matc.

To solve the expression (-2)(3)º(4)-2, we need to follow the order of operations, which is parentheses, exponents, multiplication, and subtraction.

Let's break down the expression :

(-2)(3)º(4) -2

First, we calculate the exponent:

(-2)(81) - 2

Next, we perform the multiplication:

-162 - 2

Finally, we subtract:

-164

Therefore, the value of the expression (-2)(3)º(4) - 2 is -164.

Based on the answer choices provided, none of the options match the value of -164.

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