The dot plot shows the height, in feet, of a group of trees being studied. How many trees are being studied? Enter the answer in the box. ​

Answer:

Sure. Here are the steps on how to find an equivalent expression to 2-4(x+1)-18:

1. Expand the parentheses:

```

2-4(x+1)-18 = 2-4x-4-18

```

2. Combine like terms:

```

2-4x-4-18 = -4x-14

```

Therefore, the equivalent expression to 2-4(x+1)-18 is -4x-14.

2 - 4(x + 1) - 18 can be simplified as follows:

= 2 - 4x - 4 - 18 [distribute -4]

= -20 - 4x [combine like terms]

Therefore, an equivalent expression to 2-4(x+1)-18 is -20 - 4x.

Answer: To calculate the amount of money you will have in the account after 40 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money in the account after t years, P is the principal (the initial amount of money deposited), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $2000, r = 0.02 (since the interest rate is 2%), n = 12 (since the interest is compounded monthly), and t = 40. Plugging these values into the formula, we get:

A = 2000(1 + 0.02/12)^(12*40)

A = $5,837.85

So you will have $5,837.85 in the account after 40 years.

Two quadratic functions that contains the points (5, 3) and (8, 0) are

In this problem we must find two possible quadratic functions that contains two points: (x, y) = (5, 3), (x, y) = (8, 0). The factor form of the quadratic function is now introduced:

y = a · (x - r₁) · (x - r₂)

Where:

If we know that (x₁, y₁) = (5, 3) and (x₂, y₂) = (8, 0), then the two possible quadratic functions are:

3 = a · (5 - r₁) · (5 - r₂)

3 = a · [25 - 5 · (r₁ + r₂) + r₁ · r₂]

0 = a · (8 - r₁) · (8 - r₂)

0 = 64 - 8 · (r₁ + r₂) + r₁ · r₂

0 = 64 - 8 · r₁ - 8 · r₂ + r₁ · r₂

0 = 64 - 8 · r₁ + (r₁ - 8) · r₂

Now we clear r₂:

r₂ = (8 · r₁ - 64) / (r₁ - 8)

And we eliminate r₂ in the first equation:

3 = a · [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]

And variable a is now cleared:

a = 3 / [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]

The function is graphed and two possible solutions are introduced below:

(r₁, a) = (6, 1), (r₁, a) = (10, 0.2)

And the values of r₂ are, respectively:

(r₁, a) = (6, 1):

r₂ = (8 · 6 - 64) / (6 - 8)

r₂ = - 16 / (- 2)

r₂ = 8

(r₁, a) = (10, 0.2):

r₂ = (8 · 10 - 64) / (10 - 8)

r₂ = 16 / 2

r₂ = 8

Finally, we complete and graph the resulting quadratic functions.

Case 1:

y = (x - 6) · (x - 8)

y = x² - 14 · x + 48

Case 2:

y = 0.2 · (x - 10) · (x - 8)

y = 0.2 · (x² - 18 · x + 80)

y = 0.2 · x² - 3.6 · x + 16

The graphs of the two quadratic functions are shown in the second image.

To learn more on quadratic functions: https://brainly.com/question/1863222

#SPJ1

The volume and surface area of a triangular prism is 1,848 cubic meters and 1,694 square meters.

What is surface area?

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

the volume and surface area of a right triangular prism with base dimensions of 24 m and 7 m height and a length of 22 m.

The volume of a right triangular prism is given by the formula:

V = (1/2) * b * h * l

where b is the base width, h is the height, and l is the length. Plugging in the given values, we get:

V = (1/2) * 24 m * 7 m * 22 m = 1,848 m³

Therefore, the volume of the right triangular prism is 1,848 cubic meters.

The surface area of a right triangular prism is given by the formula:

SA = 2 * (b * h + l * h + b * l)

Plugging in the given values, we get:

SA = 2 * (24 m * 7 m + 22 m * 7 m + 24 m * 22 m) = 1,694 m²

Therefore, the surface area of the right triangular prism is 1,694 square meters.

Hence, the volume and surface area of a triangular prism are 1,848 cubic meters and 1,694 square meters.

To know more about surface area visit :

https://brainly.com/question/16519513

#SPJ1

Given:

[tex]\vec F_{1} =27 \ N[/tex]

[tex]\vec F_{2} =24 \ N[/tex]

[tex]\vec a_{1} = 9 \ m/s^2[/tex]

Find:

[tex]\vec a_{2} = ?? \ m/s^2[/tex]

We know that [tex]\vec F= m \vec a[/tex]. Use [tex]\vec F_{1}[/tex] and [tex]\vec a_{1}[/tex] to find mass, m.

[tex]\Longrightarrow \vec F_{1} = m \vec a_{1} \Longrightarrow 27= m(9) \Longrightarrow m= \frac{27}{9} \Longrightarrow m= \boxed{ 3 \ kg }[/tex]

We now know the mass of the moving object we can now find [tex]\vec a_{2}[/tex].

[tex]\Longrightarrow \vec F_{2} = m \vec a_{2} \Longrightarrow 24= (3) \vec a_{2} \Longrightarrow \vec a_{2}= \frac{24}{3} \Longrightarrow \vec a_{2}= \boxed{ 8 \ m/s^2 } \ \therefore \ Sol.[/tex]

The volume of the cone is 288π m³. Hence, the answer is option C, 288π m³.

A cone is a shape created by connecting all the points of a circular base (which does not contain the apex) to a common point known as the apex or vertex using a series of line segments or lines. The height of the cone is determined by measuring the distance between its vertex and base.

The formula for the volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height.

Substituting the given values, we get:

V = (1/3)π(6²)(24)

V = (1/3)π(36)(24)

V = (1/3)(864π)

V = 288π

Therefore, the volume of the cone is 288π m³.

Hence, the answer is option C, 288π m³.

Learn more about cone on:

https://brainly.com/question/3393150

#SPJ1

the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.

How to solve the question?

To find the mean absolute deviation (MAD) for the high temperatures in Julia's town, we first need to find the mean temperature for the week.

To do this, we add up all the temperatures and divide by the number of temperatures:

(49 + 55 + 42 + 46 + 47 + 42 + 38) ÷ 7 = 43.3

The mean temperature for the week is 43.3 degrees.

Next, we need to find the distance of each temperature from the mean. To do this, we subtract the mean from each temperature:

|49 - 43.3| = 5.7

|55 - 43.3| = 11.7

|42 - 43.3| = 1.3

|46 - 43.3| = 2.7

|47 - 43.3| = 3.7

|42 - 43.3| = 1.3

|38 - 43.3| = 5.3

We take the absolute value of each difference to ensure that the distances are positive.

Now, we find the mean of the distances by adding up all the distances and dividing by the number of temperatures:

(5.7 + 11.7 + 1.3 + 2.7 + 3.7 + 1.3 + 5.3) ÷ 7 = 4.9

Therefore, the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.

In conclusion, the mean absolute deviation is a measure of the variability of a set of data. It is calculated by finding the mean of the absolute distances of each data point from the mean. In this case, the MAD is 4.9 degrees, indicating that the temperatures for the week were relatively close to the mean.

To know more about temperature visit :-

https://brainly.com/question/26866637

#SPJ1

The confidence interval can be expressed as a trilinear inequality: 82.9% < p < 95.7%.

The confidence interval in interval form is (0.1864, 0.3026).

The given confidence interval, 89.3% ± 6.4%, means that we are 89.3% confident that the true value of the population parameter lies within a range of 6.4% above and below the sample estimate.

To express this in the form of a trilinear inequality, first find the upper and lower bounds of the interval.

Upper bound = 89.3% + 6.4% = 95.7%

Lower bound = 89.3% - 6.4% = 82.9%

Therefore, the confidence interval 89.3% ± 6.4% can be expressed in the form of a trilinear inequality as:

82.9% < p < 95.7%

Find out more on confidence interval here:

#SPJ1

Answer:3-7=5

Step-by-step explanation: 3-7=5

George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months.

George's first mistake was in Step 1 where he tried to find the total number of cars he needs to sell in the next month to have a mean number of sales per month of 24. To find this value, George should have multiplied the desired mean number of sales per month (24) by the total number of months (7) to get the total number of cars needed to have a mean of 24 over 7 months. However, it seems that George skipped this step and directly assumed that the total number of cars needed for a mean of 24 in the next month is simply 24.

Let's go through each step to explain

Step 1 Find the total cars needed to have a mean of 24

To find the total number of cars George needs to sell over the next 7 months to have a mean of 24 cars sold per month, he should multiply the desired mean (24) by the number of months (7)

Total cars needed = 24 * 7 = 168

Step 2  Find the total cars sold

To find the total number of cars George sold over the past 7 months, he should add up the individual sales for each month:

Total cars sold = 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142

Step 3 Subtract the total cars sold from the total cars needed

To find the number of cars George needs to sell in the next month to meet his target mean of 24 cars sold per month over the past 8 months, he should subtract the total number of cars sold from the total cars needed

Cars needed in the next month = Total cars needed - Total cars sold

Cars needed in the next month = 168 - 142 = 26

Step 4 State the answer

George needs to sell 26 cars next month to have a mean of 24 cars sold per month over the past 8 months.

Therefore, George's mistake was in Step 1 where he did not correctly calculate the total number of cars he needs to sell over the next 7 months to have a mean of 24 cars sold per month.

To know more about sold here

https://brainly.com/question/29180467

#SPJ1

The condensed form of the expression abc x abc x abc is (abc)^3

When we have the same base raised to different exponents that are being multiplied together, we can simplify or condense the expression by adding the exponents.

In this case, we have the same base "abc" being raised to the exponent of 1 three times, so we can write it as:

abc x abc x abc

To condense this expression, we add the exponents 1+1+1=3, and write it as:

(abc)^3

So, the condensed form of the expression "abc x abc x abc" is "(abc)^3".

This is an example of the exponent rule for multiplying powers with the same base.

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

Answer:

10 hours

Step-by-step explanation:

[tex] \frac{28}{7} = \frac{40}{h} [/tex]

[tex]28h = 280[/tex]

[tex]h = 10[/tex]

Answer:

a) The common difference between consecutive terms is 9. Thus, the nth term can be expressed as:

n(9)+(-3)

b) To find the 10th term, we substitute n=10 in the expression we just found:

10(9) + (-3) = 87

Therefore, the 10th term of the sequence is 87.

Answer:

A. m∠X = 50°, AC = 3 cm

Step-by-step explanation:

If ABC is congruent to XYZ then the corresponding angle and sides are congruent so:

∠A = ∠X

∠B = ∠Y

∠C = ∠Z

and

AB = XY

BC = YZ

AC = XZ

Because we know m∠A is 50° and ∠A and ∠X are congruent then m∠X is also 50°

And because we know XZ is equal to 3 cm and XZ and AC are congruent  then AC is also 3 cm

The total number of 6 tickets will be earned when 54 points are earned.

Given that the total number of tickets earned for 9 points was earned = 1 ticket

the tickets earned when every 18 points are earned = 2 tickets

the tickets earned when every 27 points are earned = 3 tickets

Let's divide the points by tickets to find out how many points are earned for each ticket.

9/1 = 18/2 = 27/3 = 9

This shows for every ticket 9 points are earned. So, to find out the no. of tickets for 54 points, we can divide the 54 by 9.

no. of tickets earned for 54 points = 54/9 = 6 tickets.

From the above analysis, we can conclude that the 6 tickets are earned for 54 points.

To know more about mathematical patterns,

https://brainly.com/question/28580633

#SPJ1

After answering the presented question, we may conclude that  As a percentage result, around 74.43 grammes of the drug will remain after 18 hours.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also used on occasion. However, it is commonly indicated using the percent symbol "%." The % amount has no dimensions. Percentages are just fractions with a denominator of 100. Place a percent sign (%) next to a number to indicate that it is a percentage. For example, if you answer 75 out of 100 questions properly on a test (75/100), you score a 75%. Divide the money by the total and multiply the result by 100 to calculate percentages. The percentage is derived by multiplying (value/total) by 100%.

A substance's radioactive decay rate is expressed as a percentage per unit time. This indicates that the amount of material left after each unit of time will be lowered by the set percentage.

We may use the exponential decay formula to this problem:

[tex]N(t) = N_0 * e^{(-kt)}[/tex]

where:

N₀  = starting drug quantity

N(t) = the amount of material that remains after time. t k = decay constant (related to decay rate)

t = the amount of time that has passed

To calculate the amount of material left after 18 hours, we must first determine the value of k. Using the rate of decay stated in the issue, we may accomplish the following:

[tex]3.75% = k * 1 hour\\k = 0.0375/hour\\N(18) = 150 * e^{(-0.0375*18)}\\N(18) = 74.43 grams \\[/tex]

As a result, around 74.43 grammes of the drug will remain after 18 hours.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

The evaluation of the expression consisting of surds indicates that we get;

(9·x + 42 - 69·√x)/(x - 49)

A surd is a value under a square root sign, which can not be further simplified into fractions or whole numbers.

The expression (9·√x - 6)/(√x + 7), can be simplified by using the rationalization of surds technique as follows;

(9·√x - 6)/(√x + 7) = ((9·√x - 6)/(√x + 7)) × ((√x - 7)/(√x - 7))

(√x + 7) × (√x - 7) = ((√x)² - 7²) = (x - 49)

(9·√x - 6) × (√x + 7) = 9·x + 42 - 69·√x

Therefore; (9·√x - 6)/(√x + 7) = (9·x + 42 - 69·√x)/(x - 49)

Learn more on the rationalization of surds here: https://brainly.com/question/30458209

#SPJ1

a) The break-even point for the division is: 4000 units

b) The level of sales for 10% profit is: 4681 units

The break-even point is defined as the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. In other words, you've reached the level of production at which the costs of production equals the revenues for a product.

a) We are told that:

Selling price for income tax app = $8

Monthly fixed cost = $20000

Variable cost producing each app = $3

Thus:

8x = 3x + 20000

5x = 20000

x = 4000 units

b) 8x = 1.1(3x + 20000)

8x = 3.3x + 22000

4.7x = 22000

47x =220000

x = 4681 units

Read more about Break even point at: https://brainly.com/question/15281855

#SPJ1

Missing questions are:

(a) Find the break-even point for the division.

(x,y)=

(b) What should be the level of sales in order for the division to realize a 10% profit over the cost of making the income tax apps? (Round your answer up to the nearest whole number.)

The summary of the 3 rules on segments are written below.

The three rules on segments in circles are:

1. When two chords intersect inside a circle, they create four line segments.

The product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the other chord.

2. When two secants intersect outside a circle, they create four line segments.

The product of the length of the secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

3. When one secant and one tangent intersect outside a circle, they create three line segments.

The product of the length of the secant segment and its external segment is equal to the square of the length of the tangent segment.

Learn more about segments on:

https://brainly.com/question/2437195

#SPJ1

The mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]

A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.

The mass of a 2D region with variable density can be calculated using the double integral formula:

m = ∬R ρ(x,y) dA

where R is the region of integration, ρ(x,y) is the density function, and dA is the area element.

In this case, we have a triangular region with vertices (0, 0), (4, 0), and (0, 2), and the density function is ρ(x,y) = [tex]x^2 + y^2.[/tex]To set up the double integral, we need to determine the limits of integration for x and y.

Since the triangular region is bounded by the lines y = 0, y = 2, and x = (2/5)y, we can set up the integral as follows:

m = ∫0 ∫[tex]0^[/tex](2/5)y ([tex]x^2 + y^2)[/tex] dxdy

Integrating with respect to x first, we get:

m = ∫[tex]0^2 [(x^3/3) + xy^2]_0^(2/5[/tex])y dy

m = ∫[tex]0^2 [(8/375)y^5 + (4/15)y^3][/tex]dy

Evaluating the integral, we get:

m = [tex][(2/1875)y^6 + (2/5)y^4]_0^2[/tex]

m = (64/1875) + (16/5)

m = 136/375

Therefore, the mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]

To know more about triangle visit:

https://brainly.com/question/1058720

#SPJ1

Answer:

To solve the expression 2 + 7 • (-3)^2, we follow the order of operations, also known as PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we evaluate the exponent: (-3)^2 = 9 (because squaring a number means multiplying it by itself).

Next, we perform multiplication: 7 • 9 = 63.

Finally, we perform addition: 2 + 63 = 65.

So, the value of the expression 2 + 7 • (-3)^2 is 65.

Dear Editor,


I am writing to express my concern about the issue of leakages in Zambia. The constant leakages of natural resources such as oil, gas and minerals have been a major setback to the country's economic growth and development.


It is disheartening to note that despite the country being rich in natural resources, the benefits of these resources have not been fully realized due to leakages. This has led to a loss of revenue that could have been used to improve the lives of citizens through investments in education, healthcare, and infrastructure.


Furthermore, leakages also have negative environmental impacts, which can affect the health and wellbeing of communities living in the vicinity of these resources.


As a concerned citizen, I urge the government to take decisive action to curb leakages and ensure that the country's natural resources are utilized for the benefit of all Zambians.


Sincerely, [Your Name]

Answer:

Step-by-step explanation:

The equation for the height h of the object after t seconds is given by:

h = -16t^2 + 145t + 2

To find when the height will be 230 feet, we can set h = 230 and solve for t:

230 = -16t^2 + 145t + 2

We can simplify this equation by moving all the terms to one side:

16t^2 - 145t + 228 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 16, b = -145, and c = 228. Plugging in these values, we get:

t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)

t = (145 ± sqrt(21025 - 14592)) / 32

t = (145 ± sqrt(6433)) / 32

t ≈ 0.56 seconds or t ≈ 9.17 seconds

Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.

To find when the object will reach the ground, we can set h = 0 and solve for t:

0 = -16t^2 + 145t + 2

Again, we can simplify this equation by moving all the terms to one side:

16t^2 - 145t - 2 = 0

Using the quadratic formula again, we get:

t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)

t = (145 ± sqrt(21249)) / 32

t ≈ 9.51 seconds or t ≈ 0.15 seconds

Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.

~~~Harsha~~~

The inequality that represents the sentence that the absolute value of x is greater than 6 is given as follows:

|x| > 6.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The absolute value of x is represented as follows:

|x|.

The inequality that represents the absolute value being greater than six is gjven as follows:

|x| > 6.

More can be learned about inequalities at brainly.com/question/25275758

#SPJ1

Answer:

|x| > 6

Step-by-step explanation:

The correct statement is: |x| > 6.

This means that the distance between x and 0 on the number line is greater than 6 units, so x can be any number greater than 6 or less than -6.

The options given are:

Therefore, the correct statement is |x| > 6.

here's how to express the statement |x| > 6 as an inequality part 10a^2

| x | > 6

x^2 > 6^2

x^2 > 36

10x^2 > 360

10x^2 - 360 > 0

10x^2 - 360 > 0

Note that this inequality does not directly involve "a," as it is not mentioned in the original statement.

A. The current flowing through the inductor at time T is given by i(T) = (2/250) * (1 -[tex]e^{-4t}[/tex])A B. The total stored energy in the inductor from t = 0 to t = T is given by W(T) = 2( [tex]e^{-4t}-e^{-8t}[/tex]) J.

Finding the region beneath a curve or the entire accumulation of a quantity over a given period is the goal of the mathematical procedure known as integration. It is the inverse operation of differentiation and is frequently employed in a number of scientific, mathematical, and engineering disciplines.

Finding an antiderivative—a function that, when separated from the original function being integrated—is a necessary step in the integration process. The symbol for this antiderivative is frequently ∫f(x) dx, where f(x) is the function being integrated and dx denotes an incredibly minute change in x. The outcome of the integration is a family of functions that differ from one another by a constant quantity called the integration constant.

A. We know that v(t) = L di(t)/dt, where L is the inductance of the inductor and i(t) is the current flowing through it at time t. We can rearrange this equation to get di(t)/dt = v(t)/L, and then integrate both sides with respect to time from t = 0 to t = T to get:

∫[0, T] di(t)/dt dt = ∫[0, T] v(t)/L dt

After integrating the left side, we get:

i(T) - i(0)

This becomes i(T) as the starting current is zero. When the right side is integrated, we get:

(1/L) ∫[0, T] v(t) dt

When we replace the given phrase for v(t), we obtain:

(1/L) ∫[0, T] 8 -[tex]e^{-4t}[/tex] dt

When we incorporate this expression, we get:

(1/L) * (-2  [tex]e^{-4t}[/tex] ) |[0, T]

When the integration and simplification limitations are swapped out, we obtain:

i(T) = (2/L) * (1 -  [tex]e^{-4t}[/tex] ) A

As a result, the current through the inductor at time T can be calculated as follows:

i(T) = (2/250) * (1 -  [tex]e^{-4t}[/tex] ) A

B. As of time T, the inductor's total stored energy is given by:

W(T) = (1/2) L i²(T)

We obtain the following by substituting the expression for i(T) from section A:

W(T) = (1/2) * 250 * [(2/250) * (1 -  [tex]e^{-4t}[/tex] )]²

Simplifying, we get:

W(T) = 2.5 * [(1 -  [tex]e^{-4t}[/tex] )²] J

We integrate this expression with regard to time from t = 0 to t = T to determine the total energy stored from t = 0 to t = T:

W(T) = ∫[0, T] 2.5 * [(1 -  [tex]e^{-4t}[/tex] )²] dt

We can rewrite this integral as follows by replacing the supplied expression for p(t):

W(T) = (1/8) ∫[0, T] p(t) dt

Integrating p(t) in relation to time results in:

p(t) = 64 ( [tex]e^{-4t}-e^{-8t}[/tex])

∫[0, T] p(t) dt = 16 ( [tex]e^{-4t}-e^{-8t}[/tex]) J.

When we use this expression to solve for W(T), we obtain:

W(T) = 1/8 * 16 ( [tex]e^{-4t}-e^{-8t}[/tex]) J.

Simplifying, we get:

W(T) = 2 ( [tex]e^{-4t}-e^{-8t}[/tex]) J.

As a result, the formula for the total energy stored in the inductor from t = 0 to t = T is as follows:

W(T) = 2 ( [tex]e^{-4t}-e^{-8t}[/tex]) J.

To know more about current, visit:

https://brainly.com/question/1100341

#SPJ1

The measure of the value of x in the circle given is calculated as equal to: x = 12.

A semicircle is a two-dimensional shape that is half of a circle, consisting of a curved boundary or arc and a diameter or straight line segment that connects the two endpoints of the arc. This is always equal to 180 degrees.

Therefore, we have the equation:

12x + 6 + 3x - 6 = 180

Combine like terms:

15x = 180

Divide both sides by 15

x = 180/15

x = 12

Learn more about a circle on:

https://brainly.com/question/28108430

#SPJ1

The value of the expression when x = -1 and y = 4 is 41.

Evaluating the expression [tex]x^2[/tex]+7y+12 when x = -1 and y = 4, we get:

[tex]x^2[/tex]+7y+12 = [tex](-1)^2[/tex] + 7(4) + 12 = 1 + 28 + 12 = 41

Therefore, the value of the expression when x = -1 and y = 4 is 41.

Here is the step-by-step solution:

Substitute x = -1 and y = 4 into the expression.

Evaluate the exponent.

Multiply 7 by 4.

Add 1, 28, and 12.

The answer is 41.

To learn more about expression here:

https://brainly.com/question/34132400

#SPJ2

The value for the trigonometric expression cos(A+B) is (5√7 - 288)/325

Explain trigonometry.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It includes the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or sides of a triangle. Trigonometry has many practical applications in fields such as engineering, physics, and navigation.

According to the given information

We can use the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find cos(A + B).

Since cos(A) = -5/13 and A is in Quadrant II, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin(A). Solving for sin(A), we get sin²A = 1 - cos²A = 1 - (-5/13)² = 144/169. Since A is in Quadrant II, sin(A) is positive, so sin(A) = √(144/169) = 12/13.

Similarly, since sin(B) = 24/25 and B is in Quadrant II, we can use the Pythagorean identity to find cos(B). Solving for cos(B), we get cos²B = 1 - sin²B = 1 - (24/25)² = 7/625. Since B is in Quadrant II, cos(B) is negative, so cos(B) = -√(7/625) = -√7/25.

Substituting these values into the identity for cos(A + B), we get:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

          = (-5/13)(-√7/25) - (12/13)(24/25)

          = (5√7)/(13*25) - (12*24)/(13*25)

          = (5√7 - 288)/(13*25)

          = (5√7 - 288)/325

To know more about trigonometry visit

brainly.com/question/26719838

#SPJ1