Find the perimeter of the shape below. Each grey square has a side
length of 1.

Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.

To determine how far Jonah swam from one corner of the pool to the opposite corner, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.

Using the Pythagorean theorem:

\(Hypotenuse^2 = Length^2 + Width^2\)

\(Hypotenuse^2\) =\(21^2 + 20^2\)

\(Hypotenuse^2\)= 441 + 400

\(Hypotenuse^2\)= 841

Taking the square root of both sides, we find:

Hypotenuse =\(\sqrt{841\)

Hypotenuse = 29

Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.

According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

The two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.

Using the Pythagorean theorem:

\(Hypotenuse^2 = Length^2 + Width^2\\Hypotenuse^2 = 21^2 + 20^2\\Hypotenuse^2 = 441 + 400\\Hypotenuse^2 = 841\)

Taking the square root of both sides, we find:

Hypotenuse = \(\sqrt841\)

Hypotenuse = 29

Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.

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Answer:

possible

Step-by-step explanation:

Step-by-step explanation:

Pythagoras's rule:  \(a^2 + b^2 = c^2\)  becomes  \(x^2 + 10^2 = y^2\)

If we say b = 10: \(b = 10 = \sqrt{c^2 - a^2} = \sqrt{y^2 - x^2}\)

You only need to look at the left triangle

Which of the options follows Pythagoras's rule?

Let's try the options until we get the right one (in no particular order)

If we try: 3) x = 4 y = \(29\sqrt{2}\)...

\(\sqrt{(29\sqrt{2})^2 - 4^4} = 7\sqrt{34} \neq 10\)

If we try: 4) x = 16 y = 116...

\(\sqrt{116^2 - 16^2} = 20\sqrt{3} \neq 10\)

If we try: 2) x = 16 y = 29...

\(\sqrt{29^2 - 16^2} = 3\sqrt{65} \neq 10\)

If we try: 1) x = 4 y = \(2\sqrt{29}\)...

\(\sqrt{(2\sqrt{29})^2 - 4^2} = 10\)

Answer:

a. The number of units which will minimize average cost is approximately 5,130 units.

b. The firm should produce 12,500 items, x, for maximum profit.

c. The number of items, x, that will produce a maximum profit is 60 items.

Step-by-step explanation:

Note: This question is not complete as there are some signs are omitted there. The complete question is therefore provided before answering the question as follows:

1. If the total cost function for a product is C(x) = 200(0.02x + 6)^3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?

2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total venue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?

3. If the profit function for a product is P(x) = 3600x + 60x2 - x3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?

The explanation to the answer is now given as follows:

1. If the total cost function for a product is C(x) = 200(0.02x + 6)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?

Given;

C(x) = 200(0.02x + 6)^3 ……………………………………….. (1)

We first simplify (0.02x + 6)^3 as follows:

(0.02x + 6)^3 = (0.02x + 6)(0.02x + 6)(0.02x + 6)

First, we have:

(0.02x + 6)(0.02x + 6) = 0.004x^2 + 0.12x + 0.12x + 36 = 0.004x^2 + 0.24x + 36

Second, we have:

(0.02x + 6)^3 = 0.004x^2 + 0.24x + 36(0.02x + 6)

(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 7.20x + 0.0024x^2 + 1.44x + 216

(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 0.0024x^2 + 7.20x + 1.44x + 216

(0.02x + 6)^3 = 0.00008x^3 + 0.0504x^2 + 8.64x + 216

Therefore, we have:

C(x) = 200(0.02x + 6)^3 = 200(0.00008x^3 + 0.0504x^2 + 8.64x + 216)

C(x) = 0.016x^3 + 10.08x^2 + 1,728x + 43,200

Therefore, the average cost (AC) can be calculated as follows:

AC(x) = C(x) / x = (0.016x^3 + 10.08x^2 + 1,728x + 43,200) / x

AC(x) = (0.016x^3 + 10.08x^2 + 1,728x + 43,200)x^(-1)

AC(x) = 0.016x^2 + 10.08x + 1,728 + 43,200x^(-1) …………………………. (2)

Taking the derivative of equation (2) with respect to x, equating to 0 and solve for x, we have:

0.032x + 10.08 - (43,300 / x^2) = 0

0.032x + 10.08 = 43,300 / x^2

X^2 * 0.32x = 43,300 – 10.08

0.32x^3 = 43,189.92

x^3 = 43,189.92 / 0.32

x^3 = 134,968.50

x = 134,968.50^(1/3)

x = 51.30

Since it is stated in the question that x represents the number of hundreds of units produced, we simply multiply by 100 as follows:

x = 51.30 * 100 = 5,130

Therefore, the number of units which will minimize average cost is approximately 5,130 units.

2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?

P(x) = R(x) - C(x) ……………. (3)

Where;

P(x) = Profit = ?

R(x) = 450x-1/100x^2

C(x) = 500 + 200x

Substituting the equations into equation (3), we have:

P(x) = 450x - 1/100x^2 - (500 + 200x)

P(x) = 450x - 0.01x^2 - 500 - 200x

P(x) = 450x - 200x - 0.01x^2 - 500

P(x) = 250x - 0.01x^2 – 500 …………………………………. (4)

Taking the derivative of equation (4) with respect to x, equating to 0 and solve for x, we have:

250 - 0.02x = 0

250 = 0.02x

x = 250 / 0.02

x = 12,500 items

Therefore, the firm should produce 12,500 items, x, for maximum profit.

3. If the profit function for a product is P(x) = 3600x + 60x2 – x^3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?

Given;

P(x) = 3600x + 60x2 – x^3 - 72,000 …………………………. (5)

Taking the derivative of equation (5) with respect to x, equating to 0 and solve for x, we have:

3600 + 120x - 3x^2 = 0

Divide through by 3, we have:

1200 + 40x – x^2 = 0

1200 + 60x – 20x – x^2 = 0

60(20 + x) – x(20 + x) = 0

(60 – x)(20 + x) = 0

Therefore,

x = 60, or x = - 20

The negative value of x (i.e. x = - 20) will be will be ignored because it has no economic significance. Therefore, the number of items, x, that will produce a maximum profit is 60 items.

Answer:

The anwser is 258 legs are there in the field

Step-by-step explanation:

can i be brainliest plz

Answer:

For this case we want to find the probability that a senior is chosen at random not planning to attend college after graduation so then we can use the complement rule given by:

\( P(A') = 1-P(A)\)

Where A is the vent of interest and replacing we got:

\( P(A') = 1-0.85= 0.15\)

So then the probability that a senior is chosen at random not planning to attend college after graduation is 0.15 or 15%

Step-by-step explanation:

For this case we know that the sample size if n =240 and we also know that the probability that in the Evan's class the any student are planeed to attend collge after graduation is:

\( P(A) =0.85\)

For this case we want to find the probability that a senior is chosen at random not planning to attend college after graduation so then we can use the complement rule given by:

\( P(A') = 1-P(A)\)

Where A is the vent of interest and replacing we got:

\( P(A') = 1-0.85= 0.15\)

So then the probability that a senior is chosen at random not planning to attend college after graduation is 0.15 or 15%

Answer:

a = –2, b = 4, c = – 3

Step-by-step explanation:

We are given the following quadratic equation in the question:

-2x^2 + 4x - 3 = 0−2x

2

+4x−3=0

General form of quadratic equation:

ax^2 + bx + c = 0ax

2

+bx+c=0

Comparing the given equation to general quadratic equation, we get,

a = -2, b = 4, c = -3a=−2,b=4,c=−3

Thus, the correct answer is

Option D) a = –2, b = 4, c = – 3

The values of a, b, and c in the given quadratic equation are a = -2, b = 4, c = -3

The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given is a quadratic equation -2x²+4x-3 = 0, we need to find the values of a, b, and c in the given quadratic equation.

The standard equation of a quadratic equation is ax²+bx+c = 0,

Comparing the given equation with the standard equation,

We get, a = -2, b = 4, c = -3

Hence, the values of a, b, and c in the given quadratic equation are a = -2, b = 4, c = -3

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Answer:

0.5 feet left

Step-by-step explanation:

12 inches = 1 foot

36 inches = ? feet

36 × 1 = 36

12 × ? = 12?

36 = 12?

? = 36/12

? = 3 feet

18 inches = x feet

18/12 = 1.5 feet

3 + 1.5 = 4.5 feet total used

5(total) - 4.5(feet used) = 0.5 feet left

Answer:

0

Step-by-step explanation:

Answer:

X equals 4

11 times 4 equals 44

Answer:

x = 4

Step-by-step explanation:

you multiply 11 by 4, and get 44

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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he will need to score 32 points per game he wil; beat the record by 3 points with 190,meaning the new median is greater than the older median so your answer is C.

Answer:

Step-by-step explanation:

Answer:

A^n = [4^n 4^n

0 1]

Step-by-step explanation:

To find the solution for the 2x2 matrix A:

[4 4

0 1] to the nth power = [ ]

We can use matrix multiplication to raise A to the nth power. Let's start with n = 1:

A^1 = [4 4

0 1]

Now, let's solve for A^2 by multiplying A^1 by A:

A^2 = A x A^1

= [4 4 [4 4

0 1] 0 1]

= [16 16

0 1]

Next, let's solve for A^3:

A^3 = A x A^2

= [4 4 [16 16

0 1] 0 1]

= [64 64

0 1]

We can see a pattern emerging:

   A^1 = [4 4

   0 1]

   A^2 = [16 16

   0 1]

   A^3 = [64 64

   0 1]

We can generalize this pattern as follows:

A^n = [4^n 4^n

0 1]

Therefore, the solution for the 2x2 matrix A raised to the nth power is:

A^n = [4^n 4^n

0 1]

Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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Answer:

8x^2y^3

Step-by-step explanation:

L = A/W

L = 48x^3y^5 : 6xy^2

48 : 6 = 8

x^3 : x = x^(3-1) = x^2

y^5 : y^2 = y^(5-2) = y^3

Answer:

8x²y³ inches

Step-by-step explanation:

Area of rectangle is Length times Width, so 6xy²·W = 48x³y⁵

Divide both sides by 6xy² using rules of exponents:

48/6 = 8

x³/x = x²

y⁵/y² = y³

REMEMBER your units!!

Answer:

Answer the question yourself and stop being lazy!

Step-by-step explanation:

Answer:

7x+10

Step-by-step explanation:

2x(3x)+1x(x+10)

6x+1x+10

7x+10

The equation of the line in the graph with points on the line of (-2, 7), and (0, -3), found by finding the slope and the y-intercept is presented in slope-intercept form as follows;

y = -5·x - 3

The slope-intercept form of the equation of a line is in the form; y = m·x + c, where;

m = The slope

c = The y-intercept

The points on the line are; (-2, 7), and (0, -3)

The slope, m, of a line with points, (x₁, y₁), and (x₂, y₂) can be presented as follows;

\(m = \frac{y_2-y_1}{x_2-x_1}\)

Therefore, the slope of the line is, m = (-3 - 7)/(0 - (-2)) = -5

The coordinates of the y-intercept of the line is; (0, -3)

Therefore, the equation of the line is; y = -5·x - 3

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Answer:

1

-

10

0.1

Step-by-step explanation:

Answer:

Step-by-step explanation:

36 - 4

Step-by-step explanation:

(6x - 2)(6x + 2)

= (6x)(6x) + (6x)(-2) + (2)(6x) + (-2)(2)

= 36 - 12x + 12x - 4

= 36 - 4

The function rule for g(x) is h(x) = (x - 0)² - 7.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex (0, -7) and other points (-3, 2), we can determine the value of a as follows:

f(x) = a(x - h)² + k

2 = a(-3 - 0)² - 7

2 + 7 = 9a

9 = 9a

a = 1

Therefore, the required quadratic function in vertex form is given by:

h(x) = a(x - h)² + k

h(x) = (x - 0)² - 7

h(x) = x² - 7

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The length of the ladder is 58.31 inches and the angle made by the ladder with the ground is θ = 59.04°.

The distance between the ladder and the wall is 30 inches.

The height at which the ladder touches the wall is 50 inches from the ground.

Let x be the slant height when the ladder touches the wall.

Then, by using a Pythagorean theorem:

(Base)² + (Altitude)² = (Hypotenuse)²

(30)² + (50)² = x²

x² = 900 + 2500

x² = 3400 inches²

x = √[ 3400 inches²]

x = 10√34 inches

x = 58.31 inches

Then the angle made by the ladder with gound is :

tan (θ) = opposite / adjacent

tan (θ) = 50/30

tan (θ) = 5/3

θ = tan⁻¹ ( 5/3 )

θ = 59.04°

Therefore, the ladder is 58.31 inches long and the angle between the ground and the ladder is 59.04°.

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Answer:

no of course yes its no yes

Step-by-step explanation:

Answer:

B. 19

Step-by-step explanation:

A triangle has three angles that add up to 180°.

86 + 32 = 118°

180 - 118 = 62°

The third angle has to equal 62°.

3x + 5 = 62°

3x = 57

x = 19°

Hope that helps.

Answer:

\(86 + 32 + 3x + 5 = 180 \\ 123+ 3x = 180 \\ 3x = 57 \\ x = 19\)

Answer:

x=0, 2.

Step-by-step explanation:

(x-2)x=0

x=0, x-2=0,

x=0+2=2

Answer:  the answer is 6.375% because I just took the test

Step-by-step explanation:

Answer: BC = 24

Step-by-step explanation:

Given:

AB = x+33

AC = 3x - 15

BC = x

<B = <C

Solution:

Because <B = <C, you can say the corresponding sides AB and AC are equal as well

AB = AC

x + 33 = 3x -15  

48 = 2x

x = 24

Since x = BC

BC = x

BC = 24

The amount that needs to be deposited in the account today is 4,097.72.

We are to determine the present value of $5000 given quarterly compounding with an interest rate of 4%.

Present value is the discounted value of a cash flow.

Present value = FV ÷ [1 + r]^nt

Where:

P = 5,000 ÷ [1 + 0.01]^(5 x 4)

P = 5000 ÷ [1.01^20]

P = 4,097.72

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The Value of x is 2/3.

The value of x, we need to determine the mean of the given values and set it equal to the expression for the mean.

The mean (average) is calculated by adding up all the values and dividing by the number of values. In this case, we have five values: x, x+3, x-5, 2x, and 3x.

Mean = (x + x+3 + x-5 + 2x + 3x) / 5

Next, we simplify the expression:

Mean = (5x - 2 + 3x) / 5

Mean = (8x - 2) / 5

We are given that the mean is also equal to x:

Mean = x

Setting these two expressions equal to each other, we have:

(x) = (8x - 2) / 5

To solve for x, we can cross-multiply:

5x = 8x - 2

Bringing all the x terms to one side of the equation and the constant terms to the other side:

5x - 8x = -2

-3x = -2

Dividing both sides by -3:

x = -2 / -3

Simplifying, we get:

x = 2/3

Therefore, the value of x is 2/3.

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Answer:

Step-by-step explanation:

Hi there!  

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I believe your answer is:  

\(B)\text{ } G(x)=x^3-5\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\boxed{g(x)=x^3-5}\)

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.