The net below shows a square pyramid. What is the lateral surface area?

The length of the perpendicular from Q to PR is approximately 3.86 units.

slope of PR = (y2 - y1) / (x2 - x1)

slope of PR = (15 - 3) / (5 - 1)

slope of PR = 3

Using the point-slope form of a line, we have:

y - y1 = m(x - x1)

y - 3 = 3(x - 1)

y - 3 = 3x - 3

y = 3x

The equation of the line perpendicular to PR and passing through Q is y = (-1/3)x + (17/3).

Finally, we can find the point where this line intersects PR by solving the system of equations:

y = 3x

y = (-1/3)x + (17/3)

Substituting the first equation into the second equation, we have:

3x = (-1/3)x + (17/3)

10/3 x = 17/3

x = 1.7

Substituting x = 1.7 into the first equation, we have:

y = 3(1.7)

y = 5.1

the point where the line perpendicular to PR intersects PR is (1.7, 5.1).

Now we can find the distance between Q and (1.7, 5.1) using the distance formula:

d = ✓((x2 - x1)² + (y2 - y1)²)

d = ✓((5 - 1.7)² + (4 - 5.1)²)

d = ✓(14.89)

d = 3.86

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The measurement closest to the total surface area of the triangular prism is J) 393.6  .

To find the surface area of a triangular prism, we need to find the area of all its faces and add them up.

Looking at the net of the triangular prism, we can see that it has two congruent triangles and three rectangular faces.

The area of each triangular face can be found using the formula for the area of a triangle:

Area of a triangle = (1/2) x base x height

In this case, the base of each triangle is 12 inches and the height is 4 inches. So, the area of one triangular face is:

(1/2) x 12 x 4  = 24  

The area of each rectangular face can be found using the formula:

Area of a rectangle = length x width

In this case, the length and width of the rectangular faces are:

12 in. x 10.4 in.

12 in. x 12 in.

4 in. x 10.4 in.

So, the area of each rectangular face is:

12  x 10.4 = 124.8  

12  x 12  = 144  

4  x 10.4  = 41.6  

Therefore, the total surface area of the triangular prism is:

2 x 24  + 124.8  + 144  + 41.6  = 393.6

So, the measurement closest to the total surface area of the triangular prism in square inches is J) 393.6   .

Correct Question :

The net of a triangular prism and its approximate dimensions are shown in the diagram, 4 in, 12 in, 10.4 in, 12 in, 12 in, 12 in. Which measurement is closest to the total surface area of the triangular prism in square inches?

F) 268.8  

G) 432  

H) 288  

J) 393.6  

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Answer:

P = (1/2)(6)(8)/(π(5^2))

= 12/(25π)

= .31 (about 31%)

The expressions 1 and 4 are having values less than 1.

Given are the expressions, we need to solve them,

1) -7 · 1/2 - 4

= -7/2-4

= -7-8 / 2

= -15/2

= -7.5 < 1

2) -7 · (1/2 - 4)

= -7 · -7/2

= 49/2

= 24.5 > 1

3) -7 · 1/2 · (- 4)

= -14/2 · (- 4)

= 56/2

= 28 > 1

4) -7 + 1/2 · (- 4)

= -7 -4/2

= -7 -2

= -9 < 1

5) -7 ÷ 1/2 · (- 4)

= -7 × 2 × -4

= -14 × -4

= 56 > 1

Hence, the expressions 1 and 4 are having values less than 1.

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Answer:

Question 3 : Less than one

Question 4 : Starting value

Step-by-step explanation:

Answer:

less than one + Starting value

Step-by-step explanation:

The answer for #3 is less than one because any number greater than one when multiplied increases the value of the number,

and #4 is starting value because it is what you are multiplying the change by. Please mark brainliest + enjoy the night!

When writing a proof , by copying the “given” statement(s) from the original problem

Given data ,

A true assertion that is provided in the problem or is known to be true should be the first statement in a proof. The subsequent logical argument has this as its foundation.

We can provide the groundwork for the proof and proceed to the desired conclusion by duplicating the "given" statement(s) from the original problem.

Once the first statement is established, we can move on to writing additional statements that are each logically supported by the first statement.

The logical evolution of the preceding assertions demonstrates that the last statement should be the intended conclusion.

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Answer:

Step-by-step explanation:

To compare the minimum y-values of the given functions, we need to find the minimum point of each function and compare their respective y-values.

For the function f(x) = 4 sin(2x-1) - 11, we know that the sine function oscillates between -1 and 1, and is multiplied by a factor of 4, which will change the amplitude of the function. We can find the minimum point of the function by setting its derivative equal to zero:

f'(x) = 8 cos(2x-1) = 0

cos(2x-1) = 0

2x-1 = (2n+1/2)π, where n is an integer

x = (2n+1/4)π + 1/2, where n is an integer

The minimum point will occur at x = (2n+1/4)π + 1/2, and the corresponding y-value can be found by substituting this value of x into the original function:

f(x) = 4 sin(2x-1) - 11

f((2n+1/4)π + 1/2) = 4 sin(2[(2n+1/4)π + 1/2]-1) - 11

f((2n+1/4)π + 1/2) = 4 sin(2nπ + π/2) - 11

f((2n+1/4)π + 1/2) = 4 (-1)^n - 11

We can see that the y-value of the minimum point alternates between -15 and -7 as n changes. Therefore, the smallest minimum y-value for the function f(x) is -15.

For the function h(x) = (x-2)² + 4, we know that it is a quadratic function with a minimum point at x=2. The y-value of the minimum point can be found by substituting x=2 into the function:

h(2) = (2-2)² + 4

h(2) = 4

Therefore, the smallest minimum y-value among the two given functions is 4, which is the minimum y-value of the function h(x) = (x-2)² + 4.

The volume of a cube is 6859 cubic inches if the side of the cube is 19 inches.

The given function = V(x) = [tex]x^{3}[/tex]

Side of cube = 19 inches

The cube has six faces with 12 edges. That means three faces are visible at a time. That means the product of the three faces of a cube gives the volume of a cube.

In the question, it is stated that the length of the cube is to be substituted in the value of x in order to calculate the volume of a cube.

The volume V of a cube = V = [tex]x^{3}[/tex].

Substituting x = 19,

The volume of the cube = [tex]19^3[/tex]

Volume of cube = 6859

Therefore, we can conclude that the volume of a cube is 6859 cubic inches.

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Answer:

250.75

Step-by-step explanation:

Peak time cost = 0.85 × 45 = 38.25

Off peak time cost = 0.75 × 150 = 112.5

Monthly payment = R100

Total monthly bill = 100+112.5+38.25 = R 250.75

The coordinates of the new figure are:

A' = (-1, 4)

B' = (-3, 2)

C' = (1, 1)

We have,

The coordinates are in the form of an ordered pair as (x, y).

Where x is the x-axis value and y is the y-axis value.

From the figure,

We see that,

A' = (-1, 4)

B' = (-3, 2)

C' = (1, 1)

Thus,

The coordinates are:

A' = (-1, 4)

B' = (-3, 2)

C' = (1, 1)

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The slope of Line B would have to be -1/2.

Two lines are perpendicular to each other if the product of their slopes is -1. The slope of Line A is given as 2. Therefore, the slope of Line B would have to be the negative reciprocal of 2, which is -1/2. This ensures that the product of the slopes of Line A and Line B is -1, satisfying the condition for perpendicularity.

In general, if the slope of Line A is m, then the slope of a line perpendicular to Line A would be -1/m. This relationship holds because perpendicular lines form right angles, and the slopes of perpendicular lines are negative reciprocals of each other.

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The tuxedo was rented for 4 days.

Let's start by assigning variables to the unknowns. Let "x" be the number of additional days rented, and "d" be the total number of days rented (including the first day).

From the given information, we know that the flat fee for the rental is $150, so the cost of the additional days is the total cost minus the flat fee, which is $300 - $150 = $150. We also know that the cost for each additional day is $50. Therefore, we can set up the equation:

$150 + $50x = $300

Subtracting $150 from both sides, we get:

$50x = $150

Dividing both sides by $50, we get:

x = 3

So the tuxedo was rented for 3 additional days, making the total number of days rented:

d = 1 + 3 = 4

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The Perimeter of the walkway is 18√5 ft.

Explanation:-

The perimeter of the rectangular walkway is the sum of the lengths of its four sides. If the width of the walkway is √5 ft and the length is 8√5 ft, then we can label the sides as follows:

Width = √5 ft

Length = 8√5 ft

Width = √5 ft

Length = 8√5 ft

The perimeter P is given by:

P = Width + Length + Width + Length

= 2(Width + Length)

= 2(√5 + 8√5)

= 2(9√5)

= 18√5 ft

Therefore, the perimeter of the walkway is 18√5 ft.

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The ordered pairs for t = 1 and t = 2 are (1, 1200) and (2, 2,400).

An equation to represent the relationship between the time t and the number of hard drives produced p is p = 1200t.

In Mathematics, a proportional relationship can be represented by the following mathematical expression:

p = kt

Where:

In order to have a proportional relationship and equivalent ratios, the variables p and t must have the same constant of proportionality. Therefore, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = p/t

Constant of proportionality (k) = 1,200/1

Constant of proportionality (k) = 1,200.

Therefore, the required equation is given by;

p = kt

p = 1,200t.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:Xmin:

-10

Xmax:

10

Ymin:

-10

Ymax:

10

Step-by-step explanation:

The next step in the construction of a regular hexagon is A. Use a compass and straightedge to continue drawing an equilateral

A circle with the required radius must first be drawn in order to make a regular hexagon. Draw a second circle whose centre is one of the spots on the first circle using the same radius. These two circles' intersection points will form the vertices of an equilateral triangle. Three of these equilateral triangles, with their vertices on the circle, must be drawn inside a circle. At the circle's centre, these three triangles will have a common vertex.

Drawing three more equilateral triangles, each of which shares a side with one of the previously drawn triangles, is necessary to finish the building of a regular hexagon. Drawing equilateral triangles keeps on until there are six of them, each of which has a side in common with a preceding triangle.

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Answer:

f : u = 12 : 9, so f : u : w = 12 : 9 : 5.

The sides of the triangle can be identified as follows:

6. The longest side is PR  7. The shortest side is QR

Based on the relationship between the sides of a triangle and its relative angle measures, we recall that the longest side will be opposite the largest angle measure and vice versa.

Therefore, we have the following:

m<Q = 83 degrees

m<P = 48 degrees

m<R = 180 - 83 - 48 = 49 degrees.

Angle Q is the largest angle, while angle P is the smallest.

Thus, we can conclude that:

6. The side that is the longest is PR

7. The side that is the shortest is QR

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Answer:

c.-5.81

Step-by-step explanation:

=-13/4 -2.56

=-581/100

=-5.81

Answer:

A = (1/2)(5.5)(8.5 + 12.5) = 57.75 m^2

The type of the conic basic x² - 4x + y² + 2y = 4 is a circle

From the question, we have the following parameters that can be used in our computation:

x² - 4x + y² + 2y = 4

The above equation has the following features

Using the above as a guide, we have the following:

A conic section that has the above features is a circle

This means that the type of the conic basic is a circle

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Answer:

12 ft

Step-by-step explanation:

See image

Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

;>

The equations of the three mediators of triangle ABC are:

x = 3 (the mediator of AB)

y = (-1/2)x + 5 (the mediator of AC)

y = (1/2)x + 2 (the mediator of BC)

The coordinates of A are (1,2) and the coordinates of B are (5,2), so the midpoint of AB is:

((1+5)/2, (2+2)/2) = (3,2)

The coordinates of A are (1,2) and the coordinates of C are (3,6), so the midpoint of AC is:

((1+3)/2, (2+6)/2) = (2,4)

The coordinates of B are (5,2) and the coordinates of C are (3,6), so the midpoint of BC is: ((5+3)/2, (2+6)/2) = (4,4)

The slope of BC is: (6-2)/(3-5) = -2

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Answer:

87

Step-by-step explanation:

I am not sure but try (143-104=39)39+21+27 you get 87

Answer:

Natural numbers are a set of positive integers (whole numbers greater than zero) that are used for counting and ordering things. They are denoted by the symbol "N" and the set of natural numbers includes 1, 2, 3, 4, 5, 6, 7, 8, 9, and so on.

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The value of m∠Q as shown in the right-angled triangle is 54.718°.

The Formula used is:

m∠Q = cos⁻¹(s/r)........................ (1)

Where:

a = 8 m

b = 8√3 m

Now, Substitute these values into equation 1

m∠Q = cos⁻¹(8/8√3)

m∠Q = cos⁻¹(1/√3)

m∠Q = 54.718.

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The relationship between Dani's time and Candice's time, taking into account the fact that Dani took 5 minutes longer to run the course. it is Reasonable time to assume that the runners' rates were constant. Option C is the correct answer.

Let "t" be the time it took Candice to run the course.

Then, according to the problem statement, Dani took 5 minutes longer than Candice to run the course. Therefore, Dani's time is equal to Candice's time plus 5 minutes, which can be expressed as:

D = C + 5

where D is Dani's time and C is Candice's time.

This equation represents the relationship between Dani's time and Candice's time, taking into account the fact that Dani took 5 minutes longer to run the course. It can be used to solve problems related to the two runners' times, such as finding their individual times or comparing their rates. Option C is the correct answer.

It is important to note that this equation assumes that both runners ran the course at a constant rate. If the runners' rates varied throughout the course, then the equation would not accurately represent their times. However, for the purposes of this problem, it is reasonable to assume that the runners' rates were constant.

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The quotient is 2x² + 3x + 2 and the remainder is -32x - 13.

We have,

We can use long division to divide f(x) by p(x) as follows:

x² - 3 | 2x^4 - x³ - 7x² + 7x - 13

           - (2x^4 - 0x³ + 6x²)

               ---------------------

                       - 13x² + 7x

                       - (-13x² + 39x)

                           -----------------

                                     -32x - 13

The quotient is 2x² + 3x + 2 and the remainder is -32x - 13.

We can write the division in the form:

f(x) = p(x) x q(x) + r(x)

where p(x) is the divisor, q(x) is the quotient, and r(x) is the remainder. In this case, we have:

f(x) = (x² - 3) x (2x² + 3x + 2) - (32x + 13)

This means that we can write f(x) as the product of p(x) and q(x), plus the remainder r(x).

Thus,

The quotient is 2x² + 3x + 2 and the remainder is -32x - 13.

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Answer:

Step-by-step explanation:

To find the order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3, we need to calculate the average rate of change of each function over that interval and compare them.

For f(x), we have:

average rate of change = [f(3) - f(-1)] / (3 - (-1))

= [(3+3)^2 - 2 - ((-1)+3)^2 + 2] / 4

= 23

For g(x), we have:

average rate of change = [g(3) - g(-1)] / (3 - (-1))

= [0 - (-3/2)] / 4

= 3/8

For h(x), we have:

average rate of change = [h(3) - h(-1)] / (3 - (-1))

= [(62-14)/(3-(-1))]

= 12

Therefore, the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3 is:

g(x), f(x), h(x)

So the answer is option (b).