What is the area of the triangle below (in square units)?

Remember, the formula for the area of a triangle is

where
represents the length of the base of the triangle and
represents its height.

A triangle with a base of 30 centimeters and a height of 4 centimeters.What is the area of the triangle below (in square units)?

Remember, the formula for the area of a triangle is

where
represents the length of the base of the triangle and
represents its height.

A triangle with a base of 30 centimeters and a height of 4 centimeters.

Answer:

5x+3

Step-by-step explanation:

(f+g)(x) = f(x)+g(x)

= 2x−6 + (3x+9)

= 5x+3

Answer:

\( \cos(o) = \frac{12}{13} \)

Step-by-step explanation:

cos O = adjacent / hypotenuse

cos O = 12/13

I hope I helped you^_^

Answer:

Cos 0 = 12/13

Step-by-step explanation:

Adyacent side/hypotenuse

Cos 0 = 12/13

The function will have a maximum value at the vertex (3, -54).Thus, the local maximum is 0.

Determine whether g is even, odd, or neither

To determine whether g is even, odd, or neither, we will use the formula given below:Even function: f(-x) = f(x)Odd function: f(-x) = -f(x)Neither: f(-x) ≠ f(x) and f(-x) ≠ -f(x)Let's plug in the given function: g(x) = x°-27xNow, we will find f(-x) and f(x) by replacing -x in place of x:f(-x) = (-x)°-27(-x) = x°+27xf(x) = x°-27xAs f(-x) ≠ f(x) and f(-x) ≠ -f(x)Thus, the given function g(x) is neither even nor odd.

There is a local minimum of - 54 at 3. Determine the local maximum.

Given that there is a local minimum of - 54 at 3.To determine the local maximum, we will check the end behavior of the function.Let's rewrite the function: g(x) = x°-27x => g(x) = x(x-27)When x < 0, both x and (x-27) will be negative, thus g(x) > 0.When x > 27, both x and (x-27) will be positive, thus g(x) > 0.

When 0 < x < 27, x will be positive, and (x-27) will be negative. Thus, the product x(x-27) will be negative. Therefore, the function will have a maximum value at the vertex (3, -54).Thus, the local maximum is 0.

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S (curl F) · N dS is the notation for evaluating the surface integral, which is the equation for a function on a surface, in this case, the surface being the top of a cylindrical container.

The surface integral is given by the formula:S (curl F) · N dS,Where S is the upper surface of the cylindrical container, F is the velocity field, curl is the curl operator, N is the unit normal to S and dS is the element of surface area.The velocity field is given byF(x, y, z) = (− 1/6) y3 i + (1/6) x3 j + 2k

To find the curl of F, we use the formula for the curl operator, which iscurl F = (∂Q/∂y − ∂P/∂z) i + (∂R/∂z − ∂P/∂x) j + (∂P/∂y − ∂Q/∂x) kwhere P = -1/6 y^3, Q = 1/6 x^3, and R = 2.

Substituting these values in the formula, we getcurl F = (0 − 0) i + (0 − 0) j + (x^2 − (− y^2)) k= (x^2 + y^2) k

Hence, we havecurl F = (x^2 + y^2) k.

Now, we need to evaluate the surface integral, which is given byS (curl F) · N dSWe are given that the container is cylindrical, and its radius is 3. Since the upper surface of the cylindrical container is a circle with radius 3, the unit normal to the surface is simply the z-axis, i.e.,

N = k.So, we haveS (curl F) ·

N dS = S (x^2 + y^2) dSwhere dS is the element of surface area.

To evaluate the surface integral, we need to parameterize the surface. Since the surface is a circle, we can use the polar coordinates r and θ, with r = 3 and 0 ≤ θ ≤ 2π.

Thus, the element of surface area is given bydS = r dθ dr

Substituting r = 3 and dS = 3 dθ dr, we haveS (curl F) ·

N dS = ∫[0,2π]∫[0,3] (r^2) (3 dθ dr)

= 3 ∫[0,2π]∫[0,3] (r^2) dr dθ= 3 (2π) [(3^3)/3]= 54π

Therefore, S (curl F) · N dS = 54π.

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Answer:

Step-by-step explanation:

The no of different ways in which these restaurants can be visited

= ¹⁵P₁₅

= 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 1.30 x 10¹²

b ) Each combination takes 1 week and 50 weeks in  a year to work

No of years to take to try all the combination

= 1.30 x 10¹² / 50

= 2.615 x 10¹⁰ years .

Using the information provided, no triangle will be formed.

This is shown by, summing the angles

The number of triangles to be formed considering the given angles is achieved knowing the basic properties of triangle which is:

With this knowledge, we sum the angles of the triangle

= 112 + 54 + 16

= 182

No triangle is formed as the sum is not equal to 180 degrees

If the angles are summed to 180 degrees, this is a criterion of formation of unlimited number of triangle

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We introduce artificial variables and create an auxiliary objective function to convert the inequality constraints into equality constraints. Then, we apply the simplex method to maximize the objective function while optimizing the original variables. If the optimal solution of the auxiliary problem has a non-zero value for the artificial variables, it indicates infeasibility.

Introduce artificial variables:

Rewrite the constraints as 3x₁ + 4x₂ + s₁ = 6 and -x₁ - 3x₂ - s₂ = -2, where s₁ and s₂ are the artificial variables.

Create the auxiliary objective function:

Maximize zₐ = -M(s₁ + s₂), where M is a large positive constant.

Set up the initial tableau:

Construct the initial simplex tableau using the coefficients of the auxiliary objective function and the augmented matrix of the constraints.

Perform the simplex method:

Apply the simplex method to find the optimal solution of the auxiliary problem. Continue iterating until the objective function value becomes zero or all artificial variables leave the basis.

Check the optimal solution:

If the optimal solution of the auxiliary problem has a non-zero value for any artificial variables, it indicates that the original problem is infeasible. Stop the process in this case.

Remove artificial variables:

If all artificial variables are zero in the optimal solution of the auxiliary problem, remove them from the tableau and the objective function. Update the tableau accordingly.

Solve the modified problem:

Apply the simplex method again to solve the modified problem without artificial variables. Continue iterating until reaching the optimal solution.

Interpret the results:

The final optimal solution provides the values of the decision variables x₁ and x₂ that maximize the objective function z.

In this way, we can solve the given linear programming problem using the M-method.

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Answer:

8n-4

Step-by-step explanation:

combine like terms

:)

Answer: 8 −4

That should be your answer unless you need to do it in simplest form then this should be your answer

(2- 1 + 7 )n - 4 = 8n-4

or 4( 2n-1 )

I hopes this helps

The form of the exponential equation is

a is the initial amount

r is the annual rate in decimal

Since the number of rabbits increases by 250% each year, then

Since the farm started with 12 rabbits, then

Substitute them in the form of the equation above

We need to find the time for the rabbits to be 250

Then substitute y by 250 and solve the equation to find x

Divide both sides by 12

Insert log to both sides

Use the rule of the exponent with log

Divide both sides by log(3.5) to find x

It will take about 2.42 years to be 250 rabbits

It should be noted that in the equation y = -3x² + x + 12, there are two real solutions.

It should be noted that the number of real solutions of a quadratic equation is represented by y = ax² + bx - c.

In the equation, equation y = -3x² + x + 12, the coefficients are a = -3, b = 1 and c = 12. The discriminant will be:

= 1² - 4(-4)(12)

= 145

It is positive, therefore, it has two solutions.

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Two plus x divided by twelve equals one divided by three

Case 1 :

Rewrite into numbers : 2 + x /12 = 1/3

-> x/12 = 1/3 - 2 = -5/3

-> x = -5/3 x 12 = -20

Case 2 :

Rewrite into numbers : (2 + x)/12 = 1/3

-> 2 + x = 1/3 x 12 = 4

-> x = 4 - 2 = 2

i dont know if you meant it the right way or the wrong way but ill just put them both

x=2

Step-by-step explanation:

(2+x)/12=1/3

3(2+x)=12

2+x=4

x=4-2

x=2

A straight line is represented by a linear function.

The equation of the line is \(y = -\frac 14 x\)

From the coordinate plane, the line passes through the following points

\((x,y) =(0,0)\ (4,-1)\)

The slope of the above points is calculated using:

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

So, the above equation becomes

\(m = \frac{-1 - 0}{4-0}\)

This gives

\(m = \frac{-1}{4}\)

Rewrite as:

\(m = -\frac{1}{4}\)

The line equation is then calculated as:

\(y = m(x-x_1) + y_1\)

So, we have:

\(y = -\frac 14 (x-0) + 0\)

This gives

\(y = -\frac 14 (x)\)

Remove bracket

\(y = -\frac 14 x\)

Hence, the equation of the line is \(y = -\frac 14 x\)

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The total sample size that is needed is 402.

Given that,

South :

Proportion, p = 0.189

Alpha = 1 - 95%

        = 0.05

Z Critical value = 1.96

[ UseExcel Function : " =NORMSINV(1-(0.05/2)) " ]

Margin of Error should be less than 0.05

Sample Size Formula is

Sample Size, n = (Z2)*p*(1-p)/(E2)

                      = (1.962)*0.189*(1-0.189)/(0.052)

                      = 235.53

                      = 236

Northeast :

Proportion, p = 0.123

Alpha = 1 - 95%

        = 0.05

Z critical value = 1.96

[ UseExcel Function : " =NORMSINV(1-(0.05/2)) " ]

Margin of Error should be less than 0.05

Sample Size Formula is

Sample Size, n = (Z2)*p*(1-p)/(E2)

                      = (1.962)*0.123*(1-0.123)/(0.052)

                      = 165.75

                      = 166

Therefore, total sample Size needed is 236 + 166 = 402

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Answer:

(0,-2.3) or (5.111,0)

Step-by-step explanation:

Grandma's house is 6 miles farther than Aunt Millie's house.

Given:

Thus, Grandma's house is 15-9 = 6 miles farther than Aunt Millie's house, by basic subtraction.

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Answer: The answer is 15.

Step-by-step explanation:

The range is the difference between the smallest and highest numbers in a list or set. In this case, the highest is 172 and the smallest 157. Subtract these two numbers to get 15, and there you go your range.

The marginal cost function is given as:MC = 2q + 6For a certain quantity, q, the marginal cost is the cost of producing one additional unit.

It's the change in total cost over the change in quantity. The total cost when q = 8 is given as 212. We are to determine the total cost when q = 14.To find the total cost, we need to integrate the marginal cost function over the range of quantities we are interested in.

So, we will integrate MC from q = 8 to q = 14. Then, we add the result to the total cost when q = 8 (212).Here is the calculation: Total cost = ∫(2q + 6)dq + 212 = [q^2 + 6q] from q = 8 to q = 14+ 212= [(14^2 + 6(14)) - (8^2 + 6(8))] + 212= [196 + 84 - 64 - 48] + 212= 380Hence, the total cost when q = 14 is 380.

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Answer:

Area = 96 square cm

Step-by-step explanation:

Area of the figure = (2 x Area of triangles) + Area of square

\(Area \ of \ triangle = \frac{1}{2} \times base \ height = \frac{1}{2} \times 8\times 4 = 16cm^2\\\\Area \ of \ square = side \times side = 8 \times 8 = 64cm^2\)

Therefore, \(Area \ of \ the\ figure = (2 \times 16) + 64 = 32 + 64 = 96cm^2\)

the BEST statement is: The serving costs about 40 cents.

To determine the cost of the optimal serving, we need to calculate the cost per serving based on the quantities of chicken and tomatoes used.

Given that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes, we can calculate the cost as follows:

Cost of chicken =\(0.89 ounces * $0.40/ounce\)

Cost of tomatoes = \(0.52 ounces * $0.08/ounce\)

Total cost = Cost of chicken + Cost of tomatoes

Total cost =\((0.89 * $0.40) + (0.52 * $0.08)\)

Total cost =\($0.356 + $0.0416\)

Total cost ≈\($0.3976\)

Rounding to the nearest cent, the cost of the optimal serving is about 40 cents.

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The table provided above shows the values that satisfy the equation d = 10,000 - 270t.

The table that shows only values that satisfy the equation d = 10,000 - 270t is:

t   |  d
------------
0   |  10,000
37  |  0
45  |  -2,700
52  |  -5,040

To find the values that satisfy the equation, we substitute different values of t into the equation and calculate the corresponding value of d. If the calculated value of d matches the given value, then it satisfies the equation.

For example, when t is 0, the equation becomes d = 10,000 - 270(0) which simplifies to d = 10,000. This matches the given value of 10,000, so it satisfies the equation.

Similarly, when t is 37, the equation becomes d = 10,000 - 270(37) which simplifies to d = 0. This matches the given value of 0, so it satisfies the equation.

When t is 45, the equation becomes d = 10,000 - 270(45) which simplifies to d = -2,700. This matches the given value of -2,700, so it satisfies the equation.

Lastly, when t is 52, the equation becomes d = 10,000 - 270(52) which simplifies to d = -5,040. This matches the given value of -5,040, so it satisfies the equation.

Therefore, the table provided above shows the values that satisfy the equation d = 10,000 - 270t.

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To find the perimeter of triangle formed by the tangents to the circles, find radii of circles and side lengths of triangle. The perimeter of triangle formed by the tangents to the circles is 12 times the radius of each circle.

Let's denote the radius of each circle as r. Since the circles are externally tangent to each other, the distance between their centers is equal to the sum of their radii, which is 2r.

When a triangle is formed by connecting the points of tangency on each circle, it creates three isosceles triangles. Each of these isosceles triangles has two congruent sides, which are the radii of the circles.By drawing the triangle, we can observe that the base of each isosceles triangle is equal to 2r, which corresponds to the diameter of one of the circles. The height of each isosceles triangle is equal to r, which is the radius of the circle.

Therefore, each side of the triangle formed by the tangents has a length of 4r.Since the triangle has three equal sides, its perimeter is given by 3 times the length of one side, which is 3 * 4r = 12r.The perimeter of the triangle formed by the tangents to the circles is 12 times the radius of each circle.

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Answer:

Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = \(\frac{1}{2}bh\)

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =  \(\frac{1}{2}*4*2.24 =\) 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2

For the rectangular sections of the roof, area is

A = \(lh\)

where \(l\) is the length of the rectangle = 5 ft

h is the height of the rectangle = 3 ft

A = 5 x 3 = 15 ft^2

For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2

For the bottom face, area is

A = \(lw\)

where \(l\) is the length of the house = 5 ft

w is the width of the house = 4 ft

A = 5 x 4 = 20 ft^2

Surface area of the roof of the dog kennel is

8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2

Answer:

  an = -3·2^(n-1)

Step-by-step explanation:

The first term is a1 = -3.

The common ratio is r = -6/-3 = 2.

The given formula tells you the formula for this sequence is ...

  an = -3·2^(n-1)

Answer:

x = -2

y = -11

i don't know

Answer:

Step-by-step explanation:

I got 900000

Answer:

900000

Step-by-step explanation:

10^5 is 100000

100000*5 is 900000

It took Amy a total of 18 1/4 minutes (or 18 minutes and 15 seconds) to run her slowest and fastest miles combined, rounded to the nearest 1/4 of a minute.

To find out how long it took for Amy to run her slowest and fastest mile combined, we need to first determine her slowest and fastest mile times.

From the frequency table, we can see that the slowest mile time recorded is 9 2/4 (which can be simplified to 9 1/2) and it occurred once. The fastest mile time recorded is 8 3/4 and it occurred twice.

To find the total time it took for Amy to run her slowest and fastest miles combined, we need to add these two times together.

9 1/2 + 8 3/4 = 18 1/4

Therefore, it took Amy a total of 18 1/4 minutes (or 18 minutes and 15 seconds) to run her slowest and fastest miles combined, rounded to the nearest 1/4 of a minute.

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Here is the complete question:

Amy ran 8 miles. She recorded how long it took her to run each mile, rounded to the nearest 1/4 of a minute?

TIME                                                  FREQUENCY

8 3/4                                                     2

9                                                            3

9 1/4                                                      2

9 2/4                                                      1

How long did it take army to run her slowest and fastest mile combined?

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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Answer: 1/3

Step-by-step explanation:

7/21=1/3

Answer:

A Rhombus

Step-by-step explanation:

it's a quadrilateral, but its sides aren't congruent