graph each equation using the slope and the y intercept​

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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a) Approximate Doubling Time Dappx = 70/r, where r is the annual interest rate in percentage terms.Assuming that r = 5%, 10%, 20%, 40%, and 60%Doubling time for 5% = 70/5 = 14 yearsDoubling time for 10% = 70/10 = 7 yearsDoubling time for 20% = 70/20 = 3.5 yearsDoubling time for 40% = 70/40 = 1.75 yearsDoubling time for 60% = 70/60 = 1.1667 yearsb) Exact Doubling Time Dexact = ln2/r where r is the annual interest rate in decimal terms.

Assuming that r = 5%, 10%, 20%, 40%, and 60%For 5%: ln2/0.05 ≈ 13.86 yearsFor 10%: ln2/0.1 ≈ 6.93 yearsFor 20%: ln2/0.2 ≈ 3.47 yearsFor 40%: ln2/0.4 ≈ 1.73 yearsFor 60%: ln2/0.6 ≈ 1.16 yearsc)

The percentage error is given by:(Dexact − Dappx)/Dexact × 100%For 5%: (13.86 - 14)/13.86 x 100% ≈ 1.18%For 10%: (6.93 - 7)/6.93 x 100%

≈ 1.15%For 20%: (3.47 - 3.5)/3.47 x 100%

≈ -0.86%For 40%: (1.73 - 1.75)/1.73 x 100%

≈ -1.15%For 60%: (1.16 - 1.1667)/1.16 x 100%

≈ -0.60%Note that the percentage error is small for lower values of interest rates but increases as the interest rate increases.

Also, the percentage error is negative for 20%, 40%, and 60%, which means that the approximate doubling time is actually larger than the exact doubling time.

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The dimensions of the rectangle are length and width are 6 and 11.6      respectively.

L = 3w - 11 ,

where,

L = length of the rectangle and

W =width of the rectangle

A=LW

Here A is Area of the Rectangle which is product of its dimensions i.e., length and breadth.

LW = 42

substituting for l:-

(3W-11)W= 42

3W^2 - 11W - 42 = 0

(3W + 10)(W - 6) = 0

W = 6 or -10/3  (ignore the negative root)

So the width is 6 and the length is 70/6= 11.6

The rectangle's length and width are therefore 6 and 11.6, respectively.

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Answer:

d

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

multiply the volume by 48

48 x 3=144

Answer:

\(2r-2s\)

Step-by-step explanation:

Start by removing the parentheses:

\((r-s)-(s-t)-(t-r)\\r-s-(s)-(-t)-t-(-r)\)

Note that two negatives make a positive.

\(r-s-s+t-t+r\)

Combine like terms

\(r+r-s-s+t-t\\2r-2s\)

The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) \(\sqrt{x + 5}\)

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)

\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)

\(\dfrac{5}{x} }=14^2=196\)

\(x = \dfrac{5}{196}\)

9e) \(\sqrt{\dfrac{4}{x} } = 1\)

\(\dfrac{4}{x} } = 1^2\)

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) \(\sqrt{\dfrac{0.6}{36} }\)

\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)

9h) \(\sqrt{\dfrac{4-10}{0.01} }\)

\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6

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Answer:

x={-2,-5,4}

Step-by-step explanation:

Isolate the X

Divide both sides by the coefficient: x= -2,-5,4

The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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Answer: 2m -7

Step-by-step explanation:

Answer:

2m -7

Step-by-step explanation:

The growth rate of the function f(x) = [15/(1+4\(e^{(-0.2x)\))] is always increasing over its entire domain, which is the set of all real numbers (-∞, +∞).

To determine the interval over which the growth rate of the function is increasing, we need to find the derivative of the function and analyze its sign.

Let's differentiate the function f(x) with respect to x:

f'(x) = d/dx [15/(1+4\(e^{(-0.2x)\))]

To simplify the process, we can rewrite the function as follows:

f(x) = 15(1+4\(e^{(-0.2x)\))⁻¹

Using the chain rule, we can differentiate f(x):

f'(x) = -15(1+4\(e^{(-0.2x)\))⁻² × d/dx (1+4\(e^{(-0.2x)\))

Now, let's compute the derivative of the term d/dx (1+4\(e^{(-0.2x)\)):

d/dx (1+4\(e^{(-0.2x)\)) = \(4(-0.2)e^{(-0.2x)\) = \(-0.8e^{(-0.2x)\)

Plugging this back into f'(x), we have:

f'(x) = -15(1+4\(e^{(-0.2x)\))⁻² × \(-0.8e^{(-0.2x)\)

Simplifying further:

f'(x) = 12\(e^{(-0.2x)\) / \((1+4e^{(-0.2x)})^2\)

To find the interval where the growth rate of the function is increasing, we need to analyze the sign of f'(x).

Since the denominator  \((1+4e^{(-0.2x)})^2\) is always positive, we can focus on the numerator, 12\(e^{(-0.2x)\).

For the numerator to be positive, \(e^{(-0.2x)\) must be positive. Since the exponential function \(e^x\) is always positive, \(e^{(-0.2x)\) is also positive for all values of x.

Therefore, the growth rate of the function f(x) = [15/(1+4\(e^{(-0.2x)\))] is always increasing over its entire domain, which is the set of all real numbers (-∞, +∞).

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The statement that non-normality of the residuals from a regression can best be detected by looking at the residual plots against the fitted y values is a false statement.

We have a statement and we need to find out if it is true. A negative residual indicates that the model did not fit. This means that the error produced by the model is not the same between variables and observations (that is error is not random). The content is not regular, that is, the content is distributed regularly and we can conclude that the linear model is the appropriate model. If the subject sees a curvilinear pattern such as a U-shaped pattern, we can conclude that a linear pattern is not suitable and a non-linear pattern would be better. These charts are useful for identifying inconsistencies, inconsistencies in error variance, and inconsistencies. Two well-known tests for normality of residues are the Kolmogorov Smirnov test and the Shapiro-Wilk test. So, residual plot can't be used to check the non-normality of the residuals from a regression. Therefore, it is false statement.

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Answer:

-54

Step-by-step explanation:

\(8(-9) - 6(-3)\\\)

Multiply 8 by -9 and 6 by -3

\(-72 - (-18)\)

Subtract\(Value = -54\)

Hope this helps

plz mark brainliest

The given two-way Frequency table, there are 33 left-handed students who are not in the music program.

The number of left-handed students who are not in the music program, we need to examine the data presented in the two-way frequency table.

From the table, we can see that the number of left-handed students in the music program is 15, and the total number of left-handed students is 48.

the number of left-handed students not in the music program, we subtract the number of left-handed students in the music program from the total number of left-handed students.

Number of left-handed students not in the music program = Total number of left-handed students - Number of left-handed students in the music program

Number of left-handed students not in the music program = 48 - 15

Calculating this, we find that the number of left-handed students not in the music program is 33.

Therefore, there are 33 left-handed students who are not in the music program, based on the data provided in the two-way frequency table.

In conclusion, based on the given two-way frequency table, there are 33 left-handed students who are not in the music program.

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Answer:

(465-249) / 9 = Square Feet

Step-by-step explanation:

You do whatever is in the parenthases 1st

Answer: 105

Step-by-step explanation:

Given

The ratio of men to women working for a company is 4:7

There are total of 165 employees

Suppose, there is  4x men and 7x women such that the ratio remains constant

\(\therefore 4x+7x=165\\\Rightarrow 11x=165\\\Rightarrow x=15\)

\(\text{Men= }4\times 15=60\\\text{Women= }7\times 15=105\)

Convert USD to THB, multiply amount of USD by the current exchange rate between USD and THB, which can be found on financial news or currency exchange websites, to get the equivalent amount in THB.

To convert US dollars (USD) to Thai baht (THB), you need to use the current exchange rate between the two currencies. Here are the steps to convert USD to THB:

Find the current exchange rate between USD and THB. This information can be found on financial news websites, currency exchange websites, or by contacting a bank or currency exchange service.

Multiply the amount of US dollars you want to convert by the current exchange rate to get the equivalent amount in Thai baht. For example, if the current exchange rate is 1 USD = 31.50 THB and you want to convert 100 USD to THB, the calculation would be:

100 USD x 31.50 THB/USD = 3,150 THB

Therefore, 100 USD is equal to 3,150 THB.

Note: The exchange rate between USD and THB can fluctuate over time, so make sure to use the current exchange rate for the most accurate conversion.

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Answer:

  x = 9

Step-by-step explanation:

You want the value of x that satisfies 6/40 = x/60.

This equation can be solved in one step: multiply by the inverse of the coefficient of x.

The coefficient of x is 1/60. Its inverse is 60/1 = 60. Multiplying the equation by 60 gives ...

  60(6/40) = 60(x/60)

  360/40 = x

  9 = x

__

Additional comment

Often, you will be advised to "cross multiply" as the first step in solving a proportion. Doing this would give you ...

  6(60) = 40(x)

Now, you would need to divide by the coefficient of x (or multiply by its inverse).

  6(60)/40 = (40x)/40

  360/40 = x = 9

This accomplishes in two steps what we did above in one step.

The nth term of the sequence (c) is f(n) = 5 * (3)ⁿ ⁻ ¹

The nth term of the sequence (d) is f(n) = 2 * (7)ⁿ ⁻ ¹

Sequence (c)

The table shows that the sequence is a geometric sequence with the following features

First term, a = 5

Common ratio, r = 15/5 = 3

So, we have the following representation

f(n) = a * rⁿ ⁻ ¹

So, we have

f(n) = 5 * (3)ⁿ ⁻ ¹

So, the sequence is f(n) = 5 * (3)ⁿ ⁻ ¹

Sequence (d)

The table shows that the sequence is a geometric sequence with the following features

First term, a = 2

Common ratio, r = 14/2 = 7

So, we have the following representation

f(n) = a * rⁿ ⁻ ¹

So, we have

f(n) = 2 * (7)ⁿ ⁻ ¹

So, the sequence is f(n) = 2 * (7)ⁿ ⁻ ¹

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The statements that are true according to the dot plot given are -

In descriptive statistics, a box plot is a method for graphically demonstrating the locality, spread and skewness groups of numerical data through their quartiles.

Given is a box plot summarizing data for the number of books that students read over the summer.

The statements that are true according to the dot plot given are -

Therefore, the statements that are true according to the dot plot given are -

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Answer: 61

Step-by-step explanation:

You should break the figure into separate shapes, find the area, and add them together.

\( \frac{1}{6} + \frac{2}{3} + (-1 \frac{1}{3} )\)

\( \frac{1}{6} + \frac{4}{6} + ( - \frac{4}{3} )\)

\( \frac{5}{6} - \frac{8}{6} \)

\( \frac{ - 3}{6} \)

\( - \frac{1}{2} \)

The answer is 3 ft-lb.

Beyond its natural length:

Work done to strech the spring to a lentgh x = 0.5 * k * x^2

Now;

12  = 0.5 * k * 9

k = 8/3 = 2.667

9 in = 1.5 ft

Work needed to stretch it 9 in. beyond its natural length = 0.5 * 2.667 * 1.5*1.5 = 3 ft-lb

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Answer:

The car's value is depreciating by $2,990 per year.

Step-by-step explanation:

To solve this problem, we just need to subtract the cars value this year, or $25,510, from the car value of last year, or $28,500.

28,500 - 25,510 = $2,990

Since the car value was $2,990 more just last year, the car's value is depreciating by $2,990 per year.

Hope this helps! :D

Answer:

Check picture

Step-by-step explanation:

The solution is Option B.

The system of equations is solved and the value of x and y is ( 3 , 7 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

-2x + 3y = 15   be equation (1)

Let the first equation be represented as B

Now , the value of B is

x + y = 10   be equation (2)

On simplifying the equation , we get

Subtracting y on both sides of the equation , we get

x = 10 - y   be equation (3)

Substituting the value of x from equation (3) in equation (2) , we get

-2 ( 10 - y ) + 3y = 15

On simplifying the equation , we get

-20 + 2y + 3y = 15

Adding 20 on both sides of the equation , we get

5y = 35

Divide by 5 on both sides of the equation , we get

y = 7

Substitute the value of y in equation (3) , we get

x = 10 - 7

x = 3

Hence , the value of x and y is 3 and 7 respectively

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Answer:

Option B: (3, 7)

Step-by-step explanation:

i took the test xx

The equation in polar form:

r⁴ = (14cos² θ) / (3cos⁴θ + 2)

The correct answer is: d. r² = 7cos² θ

To convert the given rectangular equation to polar form, we need to express it in terms of the polar coordinates r (radius) and θ (angle). Let's go through the conversion step by step:

Given equation: (x² + y²)² = 7(x² - y²)

Express x and y in terms of r and θ.

x = r cos θ

y = r sin θ

Substituting these values into the equation:

(r² cos² θ + r² sin² θ)² = 7(r² cos² θ - r² sin² θ)

Step 2: Simplify the equation.

(r⁴(cos⁴ θ + 2cos² θ sin² θ + sin⁴ θ)) = 7(r²(cos² θ - sin² θ))

Step 3: Cancel out r² from both sides.

r⁴(cos⁴ θ + 2cos² θ sin² θ + sin⁴ θ) = 7(cos² θ - sin² θ)

Step 4: Divide both sides by cos⁴ θ + sin⁴ θ.

r⁴ = 7(cos² θ - sin² θ) / (cos⁴ θ + sin⁴ θ)

Step 5: Divide both sides by cos⁴ θ.

r⁴ / cos⁴ θ = 7(cos² θ - sin² θ) / (cos⁴ θ + sin⁴ θ)

Step 6: Substitute tan² θ for sin² θ / cos² θ.

r⁴ / cos⁴ θ = 7(cos²θ - tan²θ) / (cos⁴ θ + tan⁴ θ)

Step 7: Simplify using the trigonometric identity: tan² θ + 1 = sec² θ.

r⁴ / cos⁴ θ = 7(cos² θ - tan² θ) / (cos⁴ θ + (tan² θ + 1)²)

Step 8: Simplify further.

r⁴ / cos⁴ θ = 7(cos² θ - tan² θ) / (cos⁴ θ + tan⁴θ + 2tan² θ + 1)

Step 9: Substitute sin² θ = 1 - cos² θ and tan² θ = sin² θ / cos² θ.

r⁴ / cos⁴ θ = 7(cos² θ - (1 - cos² θ) / cos² θ) / (cos⁴ θ + (1 - cos² θ)² / cos⁴ θ + 2(1 - cos² θ) / cos² θ + 1)

Step 10: Simplify further.

r⁴ / cos⁴θ = 7(cos² θ - (1 - cos² θ) / cos² θ) / (cos⁴ θ + (1 - 2cos² θ + cos⁴ θ) / cos⁴ θ + 2(1 - cos² θ) / cos² θ + 1)

Step 11: Simplify using common denominators.

r⁴ / cos⁴ θ = 7(cos² θ - (1 - cos² θ) / cos² θ) / ((cos⁴ θ + 1 - 2cos² θ + cos⁴ θ) / cos⁴ θ + 2(1 - cos² θ) / cos² θ + 1)

Step 12: Simplify further.

r⁴ / cos⁴ θ = 7(cos² θ - 1 + cos² θ) / (2cos⁴ θ + 2(1 - cos² θ) + cos⁴ θ + 1)

Step 13: Simplify the numerator.

r⁴ / cos⁴ θ = 7(2cos² θ) / (2cos⁴ θ + 2 - 2cos² θ + cos⁴ θ + 1)

Step 14: Simplify further.

r⁴ / cos⁴ θ = 14cos² θ / (3cos⁴ θ + 2)

Finally, we can rewrite the equation in polar form:

r⁴ = (14cos² θ) / (3cos⁴θ + 2)

Therefore, the correct answer is:

d. r² = 7cos² θ

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Answer:

slope of line AB = 5

Let the required line be 'l'.

since AB is parallel to 'l'.

so slope of 'l' = slope of AB = 5.

So, the required equation of line which passes through (4,5) and having slope 5 is given by

y - 5 = 5(x - 4).........[using slope point form]

y = 5x - 20 + 5

y = 5x - 15.

Step-by-step explanation: