A garden is sodded in the shaded portion below. How many square feet were covered in the sod?

Circle A can be made similar to circle B by dilating circle A by scale factor 4.

Circles can be made similar by performing transformations such as dilations, translation, etc.

The given parameters are:

Circle A

[tex](x,y)=(6,7)[/tex] --- center

[tex]r=4[/tex] --- radius

Circle B

[tex](x,y)=(2,4)[/tex] --- center

[tex]r=16[/tex] --- radius

To do this, we simply make both circles have the same radius.

Given that:

[tex]r_A=4[/tex] --- radius of A

[tex]r_B=16[/tex] --- radius of B

Dilating the radius of A by 4 will make both circles have the same radius.

i.e.

[tex]R=r_A\times4[/tex]

[tex]R=4\times4[/tex]

[tex]R=16[/tex]

Now, the new radius of A is 16; same as B

Both circles now have the same radius, means that the circles are similar.

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Answer:

Step-by-step explanation:

Approach: If four numbers a, b, c and d are in proportion then a:b = c:d. The solution is to sort the four numbers and pair up the first 2 together and the last 2 together and check their ratios this is because, in order for them to be in proportion, the product of means has to be equal to the product of extremes.

The equation of the line on which the initial path of the ball lies is y = (-1/2)x + 5/2.

Let's call the point where the ball is initially released from the string "Q".

Since the ball is being twirled at the end of the string, its initial path will be tangent to the circle at point Q, and this tangent line will be perpendicular to the radius that passes through Q.

Since the center of rotation is the origin of the coordinate system, the radius of the circle passes through the origin and point Q. The equation of the radius can be found using the slope-intercept form:

slope of the radius = (y-coordinate of Q - y-coordinate of the origin) / (x-coordinate of Q - x-coordinate of the origin)

= (2 - 0) / (1 - 0) = 2

The radius also passes through the origin, so we can use the point-slope form of the equation:

y - y-coordinate of origin = slope of the radius * (x - x-coordinate of origin)

y - 0 = 2(x - 0)

y = 2x

Since the initial path of the ball is perpendicular to the radius at point P(1,2), its slope will be the negative reciprocal of the slope of the radius. The slope of the radius is 2, so the slope of the initial path is -1/2.

Using the point-slope form of the equation, we can find the equation of the line:

y - y-coordinate of P = slope of the initial path * (x - x-coordinate of P)

y - 2 = (-1/2)(x - 1)

y = (-1/2)x + 5/2

Therefore, the equation of the line on which the initial path of the ball lies is y = (-1/2)x + 5/2.

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Answer:

28

Step-by-step explanation:

a = b * h

a = 4 * 7 = 28

After applying the row operations, the matrix is obtained as [tex]\left[\begin{array}{c c c | c}1 & 1 & 1 & 3\\0 & 1 & -6 & -4 \\0 & 0 & -13 & -8\end{array}\right] \\[/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

The augmented matrix is given as -

[tex]\left[\begin{array}{c c c | c}1 & 1 & 1 & 3\\2 & 3 & -4 & 2 \\-1 & -4 & 4 & 1\end{array}\right][/tex]

The first row operation is -

[tex]R_2=-2r_1+r_2[/tex]

After applying the row operation the matrix will be -

[tex]\left[\begin{array}{c c c | c}1 & 1 & 1 & 3\\0 & 1 & -6 & -4 \\-1 & -4 & 4 & 1\end{array}\right] \\[/tex]

The second row operation is -

[tex]R_3=1r_1+r_3[/tex]

After applying the row operation the matrix will be -

[tex]\left[\begin{array}{c c c | c}1 & 1 & 1 & 3\\0 & 1 & -6 & -4 \\0 & -3 & 5 & 4\end{array}\right] \\[/tex]

The third row operation is -

[tex]R_3=3r_2+r_3[/tex]

After applying the row operation the matrix will be -

[tex]\left[\begin{array}{c c c | c}1 & 1 & 1 & 3\\0 & 1 & -6 & -4 \\0 & 0 & -13 & -8\end{array}\right] \\[/tex]

Therefore, the matrix is obtained as [tex]\left[\begin{array}{c c c | c}1 & 1 & 1 & 3\\0 & 1 & -6 & -4 \\0 & 0 & -13 & -8\end{array}\right] \\[/tex].

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Answer:C

Step-by-step explanation:

Answer:

The lower limit and upper limits of the athlete's height can be calculated by subtracting and adding the absolute error, respectively.

Lower Limit = 165.5 cm - 0.1 cm = 165.4 cm

Upper Limit = 165.5 cm + 0.1 cm = 165.6 cm

Therefore, the athlete's height lies between 165.4 cm and 165.6 cm, inclusive.

Answer:

$1141

Step-by-step explanation:

The general formula for compound interest is:

[tex]A(t)=P(1+r/n)^n^t[/tex], where A is the amount in dollars, P is the principal (i.e., amount invested), r is the interest rate, n is the number of compounding periods, and t is the time in years.

For Brandon's account (and equation), P = $9200, r = 0.0325, n = 4 and t = 19.

Explanations for r and n:

Now, we can simply plug in everything to find the amount Brandon would have in 19 years and round to the nearest dollar (i.e., nearest whole number):

[tex]A_{Brandon}(19)=9200(1+0.0325/4)^(^4^*^1^9^)\\ A_{Brandon}(19)=9200(1.008125)^7^6\\ A_{Brandon(19)}=17016.92431=17017[/tex]

For Lamonte's account (and equation), P = $9200, r = 0.02875, n = 12, and t = 19

Explanations for r and n:

We can again plug in the values into the general equation to find the amount Lamonte would have in 19 years and round to the nearest dollar/whole number:

[tex]A_{Lamonte}(19)=9200(1+0.02875/12)^(^1^2^*^1^9^)\\ A_{Lamonte}(19)=9200(1.002395833)^2^2^8\\A_{Lamonte}(19)=15875.86592=15876[/tex]

Now we can subtract Lamonte's amount (15875) from Brandon's (17017) to find how much more Brandon would have in his account than Lamonte in 19 years:

17017 - 15876 = $1141

**If you didn't do any intermediate rounding and waited until the very last subtraction to round, you'd still get a similar answer

17016.92431 - 15875.86713 = 1141.05718 = $1141

Simply enter the equations into the calculator and use the graphing option to visualize these equations.

A mathematical assertion that two expressions are equal is known as an equation. One or more variables, or values that can change within a specific range, are frequently present in equations. The equal sign (=) is frequently used in equations to denote that the expressions on each side of it have the same value. For instance, the formula x + 2 = 5 states that the product of x and 2 equals 5. When we solve for x in this equation, we get x = 3, which is the value of x that causes the equation to hold true.

given

Follow these steps to graph y = 2x - 1 and y = -x + 3:

To plot, pick a set of x-values. For instance, you could select -5 x 5.

For each equation, enter x values to determine the associated y values. You can create a table to aid with work organization:

Draw a coordinate plane and plot the points from your table there. For instance, the first row of the table is represented by the point (-5, -11).

For each equation, draw a straight line to join the points. The slope of the line for y = 2x - 1 will be positive, whereas the slope of the line for y = -x + 3 will be negative.

Use a graphing calculator to double-check your work and make sure your graph matches the one in the image.

Simply enter the equations into the calculator and use the graphing option to visualize these equations.

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So, if the minuend increases by 128 units, then the subtrahend does not need to increase in order to decrease the difference by 67 units.

An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign (=) between two expressions, with one expression on each side of the equals sign. Equations can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to determine the value of the variable that makes both sides of the equation equal. Equations are an important tool in mathematics and are used in various fields such as physics, engineering, finance, and economics to model and solve problems.

Here,

Let's denote the minuend by M, the subtrahend by S, and the difference by D.

In a subtraction, we have: D = M - S

If the minuend increases by 128 units, then the new minuend M' is given by: M' = M + 128

We want to find how much the subtrahend must increase, let's call it x, so that the difference decreases by 67 units. This means that the new difference D' is given by: D' = D - 67

Substituting the expressions for D, M, and M' in terms of S, we get:

D' = (M + 128) - (S + x) - 67

Simplifying this expression, we get:

D' = (M - S) + 61 - x

But we know that D = M - S, so we can substitute it in the above expression:

D' = D + 61 - x

Now, we can substitute the values we know:

D' = D - 67 (since we want the difference to decrease by 67 units)

Therefore, we get:

D - 67 = D + 61 - x

Simplifying this expression, we get:

x = 128 - 67 - 61

x = 0

In other words, the difference will automatically decrease by 67 units when the minuend increases by 128 units.

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Complete question:

In a subtraction, if the minuend increases by 128 units, find by how much the subtrahend must increase so that the difference decreases by 67 units.

To determine the number of milliliters (mLs) of Erythromycin sup 500mg/10mL needed to administer Erythromycin 0.4g bid for infection, we can use the following formula:

To calculate the adecuated dose of Erythromycin we have to follow the following procedure:

Where:

First, we need to convert the ordered dose from grams to milligrams (mg), as the concentration of Erythromycin sup is given in milligrams. 0.4g is equal to 400mg.

Next, we can substitute the values into the formula:

Therefore, the number of mLs of Erythromycin sup 500mg/10mL needed to administer Erythromycin 0.4g bid for infection is 8 mLs. It is important to note that the medication should be administered as prescribed by a healthcare provider, and the patient should complete the entire course of treatment, even if symptoms improve.

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The surface area of the given triangular prism having an isosceles triangle   base with sides 40,41 and 43 cm, is 2274 cm².

Area is a measure of the size of a two-dimensional shape or surface, such as a rectangle, triangle, circle, or any other shape that has length and width. It is usually expressed in square units, such as square meters, square centimeters, square feet, or square inches.

To find the surface area of a triangular prism, we need to find the area of each face of the prism and add them up.

The triangular base of the prism is an isosceles triangle with sides of 40 cm, 41 cm, and 43 cm.We may use Heron's formula to determine the area of this triangle:

s = (40 + 41 + 43) / 2 = 62

A = √(s(s-40)(s-41)(s-43)) = √(622221*19) = 798

Therefore, the area of the triangular base is 798 cm².

The height of the prism is given as 18 cm, which is also the length of the rectangular side of the prism.

The two other faces of the prism are rectangles with lengths equal to the base of the triangle (41 cm), and widths equal to the height of the prism (18 cm). The area of each rectangle is:

A = lw = 4118 = 738

Therefore, the area of both rectangles is 2*738 = 1476 cm².

The total surface area of the prism is the sum of the area of the base and the area of both rectangular sides:

Total surface area = Area of base + 2*(Area of rectangle)

Total surface area = 798 + 2*738

Total surface area = 2274 cm².

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Answer: length is 325 and width is 137

Step-by-step explanation:

924=2L+2w

L= 188+w

924=2(188+w)+2w

924=376+2w+2w

924=376+4w

w=137

plug back into equation

L=188+w

^^ w=137

L=188+137

L=325

Answer:

1. E, 2. C, 3. A, 4. D

Step-by-step explanation:

The negative sign means a that the image is on the opposite side.

The positive sign means a that the image is on the same side.

The magnitude of any factor between [0,1[ means that the image is contracted.

The magnitude of any factor equal to 1 means that the image is not dilated.

The magnitude of any factor between ]1,infinity[ means that the image is expanded.

To solve the problem, we need to multiply the distance each runner will run by the number of runners and get the total distance of the race. So we have:

distance per runner = 3/8 mile

number of runners = 4

total distance = distance per runner x number of runners

total distance = 3/8 x 4

total distance = 12/8 miles

To simplify the answer, we can divide both the numerator and denominator by 4, which gives us:

total distance = 3/2 miles

Therefore, the race is 3/2 miles long.

Answer:

[tex]\frac{12}{8}[/tex] or 1 [tex]\frac{4}{8}[/tex] or 1 [tex]\frac{1}{2}[/tex]  These are all the same answer.

Step-by-step explanation:

Helping in the name of Jesus.

The smallest sail, A, has a base length of 6 m and a height range of 5 to 8 m. The largest sail, sail C, has a smaller area than double that of sail A.

The table of possible dimensions and areas of the sails is:

Base Height Area

Sail A 6 m 5 m 15 m²

Sail B 6.14 m 7 m 21.5 m²

Sail C 14 m 4 m 28 m²

Let's assume that sail A has a height of 5 meters, then its area would be:

Area of Sail A = 1/2 x Base x Height = 1/2 x 6 x 5 = 15 square meters

If sail C has an area less than twice the area of sail A, then its area must be less than 2 x 15 = 30 square meters. Let's assume that sail C has an area of 28 square meters.

To find the dimensions of sail A and sail C, we can use the formula for the area of a triangle:

Area = 1/2 x Base x Height

For sail A, we already know the base and the area, so we can solve for the height:

15 = 1/2 x 6 x Height

Height = 5 meters

So sail A has a base of 6 meters and a height of 5 meters.

For sail C, we know the area and we have assumed a base length of 14 meters (to keep the height reasonable). Solving for the height:

28 = 1/2 x 14 x Height

Height = 4 meters

So sail C has a base of 14 meters and a height of 4 meters.

To find the dimensions of sail B, we can assume a height between 5 and 8 meters (since sail A has a height between 5 and 8 meters), and then solve for the base and the area using the formula for the area of a triangle:

Area = 1/2 x Base x Height

Let's assume sail B has a height of 7 meters:

Area of Sail B = 1/2 x Base x 7

Area of Sail B = 1/2 x (Area of Sail A + Area of Sail C)

Area of Sail B = 1/2 x (15 + 28)

Area of Sail B = 21.5 square meters

Solving for the base:

21.5 = 1/2 x Base x 7

Base = 6.14 meters (rounded to two decimal places)

So sail B has a base of 6.14 meters and a height of 7 meters.

Therefore, the table of possible dimensions and areas of the sails is:

Base Height Area

Sail A 6 m 5 m 15 m²

Sail B 6.14 m 7 m 21.5 m²

Sail C 14 m 4 m 28 m²

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Answer:

133

Step-by-step explanation:

Therefore, the values of angles B and C in pentagon ABCDE are 163 degrees and 205 degrees, respectively.

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The two rays are usually represented by lines or line segments, and they can be positioned in various ways relative to each other, creating different types of angles. Angles are typically measured in degrees or radians and can range from 0 degrees (a zero angle, where the two rays coincide) to 360 degrees (a full rotation of one ray around the vertex). Angles are used in many areas of mathematics, physics, and engineering, and they are important for understanding geometric concepts such as shape, symmetry, and proportion.

Here,

In a regular pentagon, all angles have the same measure of 108 degrees. However, in this problem, the angle measures of pentagon ABCDE are not given to be regular, and only the measures of angles A, E, and D are specified to be 90 degrees. To find the value of x, we can use the fact that the sum of the interior angles of a pentagon is equal to 540 degrees. Therefore, we can set up an equation based on this fact:

A + B + C + D + E = 540

Substituting the given values, we have:

90 + (6x + 1) + (8x - 11) + 90 + 90 = 540

Simplifying and solving for x, we get:

14x + 160 = 540

14x = 380

x = 27

Now that we have the value of x, we can use it to find the measures of angles B and C:

B = 6x + 1

= 6(27) + 1

= 163 degrees

C = 8x - 11

= 8(27) - 11

= 205 degrees

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1. The probability that an infected patient’s length of stay will be greater than 7 days is 0.3085.

2. The 70th percentile in stay length for a patient given that they have a

post-operative infection is 7.04.

3. The probability that the average stay length of the next 2 infected patients is less than 5.5 days is 0.3632.

4. The probability that a patient is infected and then stays for 3 to 4 days is  0.1587.

1. Probability of an infected patient staying more than 7 days:

We can standardize the normal distribution using the formula: Z = (X - μ) / σ, where X is the length of stay, μ is the mean length of stay, and σ is the standard deviation of the length of stay.

So, Z = (7 - 6) / 2 = 0.5.

Using a standard normal distribution table or calculator, we can find the probability that a patient will stay longer than 7 days as:

P(Z > 0.5) = 0.3085.

2. The 70th percentile in stay length for an infected patient:

We can use the inverse standard normal distribution function to find the Z-score corresponding to the 70th percentile.

Using a standard normal distribution table or calculator, we find that the Z-score corresponding to the 70th percentile is approximately 0.52.

So, Z = 0.52 = (X - 6) / 2.

Solving for X, we get:

X = 6 + 0.52 * 2 = 7.04.

3. Probability that the average stay length of the next 2 infected patients is less than 5.5 days:

The average length of stay of 2 infected patients can be modeled by a normal distribution with a mean of 6 days (the mean of a single infected patient's length of stay) and a standard deviation of σ/√2, where σ is the standard deviation of the length of stay of a single infected patient.

So, the standard deviation of the average length of stay of 2 infected patients is:

σ/√2 = 2/√2 = 1.414 days.

Using the standardized normal distribution formula, we get:

Z = (5.5 - 6) / 1.414 = -0.3536.

Using a standard normal distribution table or calculator, we can find the probability that the average stay length of the next 2 infected patients will be less than 5.5 days as:

P(Z < -0.3536) = 0.3632.

4. Probability that a patient is infected and then stays for 3 to 4 days:

We can standardize the normal distribution as before using the formula:

Z = (X - μ) / σ, where X is the length of stay, μ is the mean length of stay, and σ is the standard deviation of the length of stay.

For X = 3 days, Z = (3 - 6) / 2 = -1.5.

For X = 4 days, Z = (4 - 6) / 2 = -1.

Using a standard normal distribution table or calculator, we can find the probability that a patient is infected and then stays for 3 to 4 days as:

P(-1.5 < Z < -1) = P(Z < -1) - P(Z < -1.5) = 0.1587

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To determine the cost of carpeting the room, we first need to calculate the area of the room that needs to be carpeted.

The area of the room is:

A = l × w

A = 6 m × 4 m

A = 24 square meters

Next, we need to determine the area of the carpet required. Since the carpet has a width of 1.5 m, we can think of the room as being covered by a series of strips of carpet, each of width 1.5 m. We need to calculate the length of each strip and then multiply that by the width of the carpet.

The length of each strip is equal to the length of the room, which is 6 m. So, the area of each strip of carpet is:

A_strip = l × w_carpet

A_strip = 6 m × 1.5 m

A_strip = 9 square meters

To cover the entire room, we will need to use several strips of carpet. The number of strips required is the total area of the room divided by the area of each strip:

Number of strips = A / A_strip

Number of strips = 24 square meters / 9 square meters

Number of strips = 2.6667 strips

Since we cannot use a fractional number of strips, we will need to round up to 3 strips of carpet.

The total area of carpet required is the area of each strip multiplied by the number of strips:

Total area of carpet = A_strip × Number of strips

Total area of carpet = 9 square meters × 3

Total area of carpet = 27 square meters

Finally, we can calculate the cost of carpeting the room at the given rate of rupees 200 per meter:

Cost of carpeting = Total area of carpet × Cost per meter

Cost of carpeting = 27 square meters × Rs. 200 per meter

Cost of carpeting = Rs. 5,400

Therefore, the cost of carpeting the rectangular room of 6 m long and 4 m wide with the carpet of width 1.5 m at rupees 200 per meter would be Rs. 5,400.

The answer is A. (x-1)²/16-(y-1)²/4=1. The standard form of the equation that describes the hyperbola is (x-1)²/16-(y-1)²/4=1.

A hyperbola is a two-dimensional, closed-curve shape with two branches, each of which is a mirror image of the other.

This equation is in the standard form of a hyperbola equation, which is

(x-h)²/a² - (y-k)²/b² = 1, where (h,k) is the center of the hyperbola and a and b are the distance from the center to the vertices of the hyperbola.

In this case, the center of the hyperbola is (1,1).

This can be determined by taking the average of the coordinates of the two vertices, (1,-1) and (1,3), which is (1,1).

The distance from the center to the vertices of the hyperbola is 8 for the x-coordinate, and 4 for the y-coordinate.

This can be determined by taking the difference of the coordinates of the vertices, which is 8 for the x-coordinate and 4 for the y-coordinate.

Therefore, the standard form of the equation that describes the hyperbola is (x-1)²/16-(y-1)²/4=1.

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Answer:

Step-by-step explanation:

a) 2x-6 is equivalent to 1) -6+2x

b) 5/3-x+1/3 is equivalent to 4) x-3+x

c) 2x-3 is equivalent to 3) -6.9++4.9

d) 3x+0 is equivalent to 2) 3x

e) 3/5-13/5 is equivalent to 5) 3/2x+2+1/2x

Answer: We can simplify the given equation as follows:

sin(x/2) = sqrt(2) - sin(x/2)

2sin(x/2) = sqrt(2)

sin(x/2) = sqrt(2)/2

x/2 = pi/4 or x/2 = 3pi/4 (using the standard angles for sin)

x = pi/2 or x = 3pi/2

However, we need to check if these solutions satisfy the original equation since we simplified it along the way.

For x = pi/2, we have:

sin(pi/4) = sqrt(2) - sin(pi/4)

sqrt(2)/2 = sqrt(2) - sqrt(2)/2

sqrt(2)/2 = sqrt(2)/2

This is true, so x = pi/2 is a solution.

For x = 3pi/2, we have:

sin(3pi/4) = sqrt(2) - sin(3pi/4)

-sqrt(2)/2 = sqrt(2) - (-sqrt(2)/2)

-sqrt(2)/2 = sqrt(2)/2

This is not true, so x = 3pi/2 is not a solution.

Therefore, the only solution in the interval [0, 2pi) is x = pi/2.

Step-by-step explanation:

Answer:

Your answer will be y=4 I believe

Please mark me brainliest if that is correct :)

We must determine the voltage's rate of change with regard to time. The voltage changes sinusoidally with time in an AC circuit. the current flow in the circuit is [tex]3.817[/tex] Amperes.

To calculate the current flow in the circuit, we need to use the formula:

[tex]I = C x dV/dt[/tex]

Where:

I is the current flow in the circuit (in Amperes)

C is the capacitance of the capacitor (in Farads)

dV/dt is the rate of change of voltage with respect to time (in Volts per second)

First, we need to calculate the rate of change of voltage with respect to time. In an AC circuit, the voltage varies sinusoidally with time. The formula for voltage in an AC circuit is:

[tex]V = Vm sin(ωt)[/tex]

Where:

Vm is the maximum voltage (in Volts)

ω is the angular frequency (in radians per second)

t is the time (in seconds)

We know that the voltage is 240 V and the frequency is 60 Hz. We can use these values to calculate Vm and ω:

[tex]Vm = √2 x Vrms = √2 x 240 = 339.4 V[/tex]

[tex]ω = 2πf = 2π x 60 = 377 rad/s[/tex]

Now, we can calculate [tex]dV/dt:[/tex]

[tex]dV/dt = ω Vm cos(ωt)[/tex]

At  [tex]t = 0[/tex] (i.e. when the voltage is at its maximum), [tex]cos(ωt) = 1. Therefore, dV/dt = ω Vm = 127,234 V/s.[/tex]

Finally, we can calculate the current flow:

[tex]I = C x dV/dt = 30 x 10^-6 F x 127,234 V/s = 3.817 A[/tex]

Therefore, the current flow in the circuit is 3.817 Amperes.

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The measure of arc LQ (m∠LQ) is equal to 34 degrees.

In Mathematics and Geometry, a chord of circle can be defined as a line segment that typically join any two (2) points of a circle.

Generally speaking, the inscribed angle of a circle is equal to half of the central angle of a circle. Mathematically, this is represented by the following mathematical expression:

m∠U = 1/2(m∠WC - m∠LQ)

37 = 1/2(108 - m∠LQ)

74 = 108 - m∠LQ

m∠LQ = 108 - 74

m∠LQ = 34 degrees.

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The vertices of net that represents a container is 8 vertices.

A cuboid is a three-dimensional geometric shape that is formed by six rectangular faces or sides. It is also known as a rectangular prism. A cuboid has six faces, twelve edges, and eight vertices. The opposite faces of a cuboid are congruent and parallel to each other.

A cuboid can be defined by its length, width, and height, which are the three dimensions of the cuboid. The length is the longest side, the width is the shorter side, and the height is the distance between the two parallel faces.

Cuboids are common in many everyday objects, such as boxes, buildings, and books. They are also important in geometry and engineering as they have a simple shape that is easy to work with and can be used to represent more complex shapes.

The figure which is shown below is a cuboid. Net has 12 edges, 6 faces and 8 vertices.

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The complete question is:

The net below represent a container. What solid figure does it show?

How many vertices does the container have?