Given: ∠2 and ∠4 are vertical angles.
Prove: m∠2=m∠4
Fill in the correct reason for the statements below by dragging and dropping the correct reason from the bank.

Answer:

t = 6

Step-by-step explanation:

-(t+2) = -31 +23

Solve for t.

Combine like terms on the right.

-(t+2) = -8

Divide each side by -1.

t+2 = 8

Subtract 2 from each side.

t+2-2 = 8-2

t = 6

Based on the total area of the floor, the cost to cover the floor is $1569.75.

The area of the floor is calculated as follows:

Area of floor = Area of the trapezium + Area of rectangle

Area of the trapezium = (a + b)/ * h

a = 30 - 20 ft or 10 ft

b = 35 ft

h = 15 ft

Area of the trapezium = (10 + 35)/2 * 15

Area of the trapezium = 337.5 ft²

Area of rectangle = 40 * 20

Area of rectangle = 800 ft²

Area of floor = 800 ft² + 337.5 ft² or 1137.5 ft²

The cost to cover the floor = 1137.5 * $1.38

The cost to cover the floor = $1569.75

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Answer:

27 weeks

Step-by-step explanation:

first you would figure out how long one oz. of hair gel would last her. You would do this by dividing 21 by 14. 21/14 is 1.5. Next, if 1 oz. lasts 1.5 weeks, and there is a 18 oz bottle, then all you need to do is multiply 18 by 1.5. 18 times 1.5 is 27. Therefore, an 18 oz. bottle of hair gel would last Emily 27 weeks.

On solving the provided question, we can say that The function that can be made are f(x)= INT (x) + 5 and g(x)= INT (x) + 8

Quantities and their variations, equations and related structures, shapes and their placements, and locations where they can be found are all included in the study of mathematics.

The relationship between a group of inputs, each of which has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a codomain, often known as a scope. F is typically used to denote functions (x).

An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

The function that can be made are -

Let x = dollar spent

coffee shop rewards program offered 1 point for every whole dollar spent and an additional 5 points for each purchase

⇒ f(x)= INT (x) + 5

the shop changes the points offered to an additional 8 points for each purchase and 1 point for every whole dollar spent

⇒ g(x)= INT (x) + 8

The graph of g will be a vertical translation and 3 units up from the graph of f.

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(c) When x is 2.3, the predicted value is 0.02 less than the actual value first from database (d). When x is 3 and the predicted value is compared to the actual figure from the table, the residual is -1.27.

For instance, rounding these values with two decimal places to one nearest tenth (3.4 + 5.5) would result in an approximate reply of 8.9. The estimated result would be 9, but they might potentially be increased to the next full number (3 + 6). The correct response is 8.91.

(c). Nearly 6.2 Minus 6.18 = 0.02 separates the projected result from the actual value. As a result, there is hardly any change. The residual is thus 0.02

(d). Y Equals 4.47 whenever x = 3 because 2.45 × 3 + 11.82. Since the true value is 3.2 and the anticipated value is 4.47, the differences between the two is 1.27. The residual is thus 1.27.

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The triangle that's created has angles of 90°, 45° and 45°.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

The triangle is attached.

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The angles m∠w and m∠y are supplementary angles and their measures are 50° and 130° respectively.

If two angles add up to 180°, they are considered supplementary angles, we can observe that the positions of the angles formed by the transversal cutting the parallel lines makes the two angles on a straight line which are supplementary so;

4x + 6 + 12x - 2 = 180

16x + 4 = 180°

16x = 180 - 4 {subtract 4 from both sides}

16x = 176

x = 176/16 {divide through by 16}

x = 11.

m∠w = 4(11) + 6 = 50°

m∠y = 12(11) - 2 = 130°

Therefore, the supplementary angles m∠w and m∠y have their measures as 50° and 130° respectively.

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At the end of 24 hours, 48 cupcakes will have grown. Every 8 hours, two cupcakes are grown, so after 24 hours, 24 sets of two cupcakes have been grown. Therefore, 48 cupcakes have grown.

At the end of 24 hours, 48 cupcakes will have grown. This is because every 8 hours, two cupcakes are grown. After 24 hours, 24 sets of two cupcakes have been grown. This means that in the 24 hours, two cupcakes were grown a total of 24 times. When this total is multiplied by two, it results in 48 cupcakes being grown. Therefore, after 24 hours, 48 cupcakes have grown. It is important to note that this is only the number of cupcakes that have grown in the 24 hour period, and not the total number of cupcakes. This number includes any cupcakes that were already present at the beginning of the 24 hour period, so the total number of cupcakes at the end of the 24 hour period could be higher than 48.

1. Calculate the number of sets of cupcakes grown in 24 hours: 24 hours divided by 8 hours = 3 sets

2. Calculate the number of cupcakes grown in 24 hours: 3 sets multiplied by 2 cupcakes = 6 cupcakes

3. Calculate the total number of cupcakes grown in 24 hours: 6 cupcakes multiplied by 4 sets = 24 cupcakes

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Answer:

- 3cos²Θ

Step-by-step explanation:

using the identity

sin²Θ + cos²Θ = 1 , then

sin²Θ = 1 - cos²Θ

given

3sin²Θ - 3

= 3(1 - cos²Θ) - 3

= 3 - 3cos²Θ - 3

= - 3cos²Θ

Answer:

f(-4) = -18

Step-by-step explanation:

So we have f(x) and we have f(-4). The X is where the -4 is so that means x = -4.

Since we know that, we plug it into the equation. Everywhere we see an X

So instead of 5(x) + 2, it will be 5(-4)+2.

5 times -4 is -20, which makes it -20 + 2

-20 + 2 = -18. Giving us our answer

Answer:

[tex]-18[/tex]

Step-by-step explanation:

f is a function of x. f depends on x. For every value of x, a certain value of f(x) is obtained.

This question requires us to determine the value of f(x) for x = [tex]-4[/tex]:

Substitute x = [tex]-4[/tex] into the provided function:

[tex]f(-4) = 5(-4) +2[/tex]

         = [tex]-20 + 2[/tex]

         = [tex]-18[/tex]

Answer:

The leading coefficient is -1. The degree of the polynomial is cubic.

Step-by-step explanation:

The leading coefficient is the number in front of the variable showcasing the biggest exponent. The degree of the polynomial is considered by looking at the biggest exponent, and identifying which one it is. In this case, it's a cubic polynomial.

The table shows a proportional relationship is:

Number of Necklaces         2        4       6      8

Number of Beads                20     40     60    80

As per the data given:

The tables show the number of necklaces made and the number of beads used.

Number of Necklaces         2        4       6      8

Number of Beads                20     40     60    80

From the table:

2 : 20 = 1 : 10

4 : 40 = 1 : 10

6 : 60 = 1 : 10

8 : 80 = 1 : 10

As there is a common ratio between each value there will be a proportional relationship

Number of Necklaces         2       4        6       8

Number of Beads                10     15      20     25

From the table:

2 : 10 = 1 : 5

4 : 15

6 : 20 = 3 : 10

8 : 25

As there is no common ratio between each value there will not be any proportional relationship

Number of Necklaces        2       4         6        8

Number of Beads               14      21      28      35

From the table:

2 : 14 = 1 : 7

4 : 21

6 : 28 = 3 : 14

8 : 35

As there is no common ratio between each value there will not be any proportional relationship

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Answer: The area of right triangle ABC can be found using the formula (1/2)bh, where b is the length of the base and h is the height. Since the base of the triangle is 5 units and the area is 12.5 square units, the height must be 2.5 units.

Knowing that point C is on the line x = -2, we can use the height of 2.5 units to find the y-coordinate of point C.

Starting from the line y = 2, moving 2.5 units down will give us a y-coordinate of y = 2 - 2.5 = -0.5.

So, a possible y-coordinate of point C is -0.5.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

A = 1/2 (b)(h)

12.5 = 1/2 (5)(h)

Multiply both sides by 1/2 or 2 to cancel out the fraction

2 x 12.5 = 1/2 (5)(h) x 2

25 = 5h

Divide both sides by 5 to get h on its own

25/5 = 5h/5

h = 5

HOWEVER, 5 is not our answer because we started on y = 2.

So,

5 + 2 = 7

The area of the parallelogram that has a width of 32.2 units and a height of 12.6 units will be 405.72 square units.

Let H be the height and W be the width of the parallelogram. Then the area of the parallelogram will be given as,

Area of the parallelogram = H × W square units

The width of the parallelogram is 32.2 units and the height of the parallelogram is 12.6 units. Then the area of the parallelogram is given as,

A = 32.2 x 12.6

A = 405.72 square units

The area of the parallelogram that has a width of 32.2 units and a height of 12.6 units will be 405.72 square units.

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Answer:

Step-by-step explanation:

There are 6 possible outcomes for each of the two rolls, so there are 6 x 6 = 36 possible outcomes for the sum of two rolls.

Event A: The sum is greater than 8.

There are five possible ways to achieve a sum greater than 8: (3, 6), (4, 5), (4, 6), (5, 4), and (6, 3). Each of these outcomes has a probability of 1/36. Therefore, the probability of event A is:

P(A) = 5/36

Event B: The sum is an even number.

There are three possible ways to achieve an even sum: (1, 1), (2, 2), and (3, 3). Each of these outcomes has a probability of 1/36. There are also three possible ways to achieve a sum of 4: (1, 3), (2, 2), and (3, 1). Each of these outcomes has a probability of 1/36. Similarly, there are three possible ways to achieve a sum of 6, 8, 10, and 12. Therefore, the probability of event B is:

P(B) = (3 + 3 + 3 + 3 + 3 + 3)/36

P(B) = 18/36

P(B) = 1/2

Therefore, the probability of event A is 5/36 and the probability of event B is 1/2.

The period of the function is 1.57 s.

The amplitude of the function is 6.

The equation of the midline, y = 6 sin 4x + 0.

The general form of a sinusoidal function is y = A sin(Bx - C) + D,

where:

For the given function y = 6 sin 4x, we can see that:

A = 6 (the amplitude is the absolute value of the coefficient of the sine function)

B = 4 (the coefficient of x inside the sine function determines the period)

C = 0 (there is no horizontal shift)

D = 0 (there is no vertical shift, so the midline is the x-axis)

Therefore, the period T is given by:

T = 2π/B = 2π/4 = π/2 = 1.57 s

The midline is the x-axis, so its equation is y = 0.

The amplitude is A = 6.

Therefore, we can write the equation of the function in the general form as:

y = 6 sin 4x + 0

or

y = 6 sin(4x)

Note that since the midline is the x-axis and there is no vertical shift, the sine function will oscillate between -6 and 6.

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Answer:

The system of equations are solved by eliminating a variable and solving for the remaining variable. Add the two equations together to eliminate the y, then solve for x.

In Step 3, Mike made an error. He incorrectly calculated his value for m by multiplying 2 by 22 instead of 2 by (22 + 4). The correct equation should have been m = 2(22 + 4).

Sally's formula for calculating b is correct:

b = 11

Sally's formula for calculating m is also correct:

m = 2(11) + 4 = 26

Mike's formula for calculating b is correct:

b = 22

However, Mike's formula for calculating m is incorrect. Instead of using the formula m = 2(b + 4), he used the formula m = 2(22 + 4), which gives him a value of 50 instead of the correct value of 50.

Therefore, Mike made a mistake in Step 3. He computed his answer for m erroneously by multiplying 2 by 22 rather than 2 by (22 + 4). The proper formula would have been m = 2(22 + 4).

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Jesse's ranking is 25th percentile.

Jesse's ranking can be calculated using the following formula:

Percentile = (Jesse's ranking / Total number of students in class) x 100

In this case, Percentile = (45/180) x 100 = 25th Percentile

Therefore, Jesse's ranking is 25th percentile.

To calculate percentile, we divide the rank of the student with the total number of students in the class and then multiply the result with 100. In this case, Jesse was ranked 45th in a class of 180 students and so his percentile is 25%. Percentile is a measure that helps us to compare individuals in a group. It helps us to know the relative performance of a person in a given group of people. Generally, a higher percentile indicates better performance than the other students in the group.

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Answer:

she can buy 2 outfits

Step-by-step explanation:

Answer:

Step-by-step explanation: have u tried turning off and back on again

There is no possible way that you can add a single bridge so that there is a path that uses each bridge once and only once.

Hence, the answer is no solution.

The seven bridges problem was seven bridges linking the various land masses of the town of Königsberg which straddles the Pregel River and that contained two islands.

The challenge was coming up with a route through the city that would only cross each of those bridges once. blatantly inappropriate. Euler demonstrated that the issue cannot be solved.

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Answer:

(i) 38.9%

(ii) 33.3%

(iii) 0%

Step-by-step explanation:

The total number of sweets is 18.  The probability of picking a color can be determined by dividing the number of each color by the total:

Blue:      5/18 or 27.8%

Red:       7/17 or 38.9%

Green:   6/18 or 33.3%

Yellow:  0/18 or 00.0%

Totals    18/18   100%

Note that the question askes for Yellow sweets, but there are none.

Divergence and curl are two important concepts in vector calculus. They are used to describe the behaviour of vector fields, which are functions that assign a vector to each point in space.

Divergence is a scalar function that describes the extent to which a vector field is spreading or contracting at a given point. If the vector field is spreading, the divergence at that point is positive; if it is contracting, the divergence is negative.

If the vector field is unchanged in size, the divergence is zero. The formula for the divergence of a vector field is given by the dot product of the gradient of the field with the unit normal vector at a point.

Curl, on the other hand, is a vector function that describes the rotational aspect of a vector field. It is defined as the cross-product of the del operator and the field. Curl measures the rate at which the vectors in a field are rotating about a point. If the curl is zero, the field is said to be irrotational. If the curl is non-zero, the field is said to be rotational.

Divergence and curl cannot be defined for a scalar function because a scalar function assigns a single scalar value to each point in space, while divergence and curl describe the behaviour of vector fields.

A scalar function has no direction or rotational component, so there is no way to describe the spreading or contracting behaviour or the rotational behaviour of the function.

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The new coordinates of A would be (3, -2)

Answer:

A prime = (3,-2)

x=3

y=-2

As per unitary method,

a) The length of the rope left after tying the parcel 260 cm

b) The initial length of the rope was 305cm.

The unitary method is a mathematical tool used to solve problems involving the partition of a whole into parts.

(a) To find the length of the rope left after tying the parcel, we subtract the length of the rope used to tie the parcel from the initial length of the rope. The length of the rope left is:

=> Initial length of the rope - Length of rope used to tie the parcel = Length of rope left

We are told that Ravi used 45cm of the rope to tie a parcel. Therefore, the length of rope left can be expressed as:

Initial length of the rope - 45 = Length of rope left

(b) To find the initial length of the rope, we add the length of the rope used to tie the parcel to the length of the rope left.

We know that the length of the rope left is divided into 4 pieces of 65cm each. Therefore, the total length of the rope left is

=> 4 x 65 = 260cm.

We can now use this information to find the initial length of the rope:

Length of rope left + Length of rope used to tie the parcel = Initial length of the rope

260 + 45 = 305cm

Complete Question:

Ravi had a rope. He used 45cm of the rope to tie a parcel. He then cut the remaining rope equally into 4 pieces. Each piece was 65cm long.

(a) Find the length of the rope left after tying the parcel.

(b) How long was the rope at first?

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The volume of the 14 cylindrical pillars made of concrete is 8.8 m³

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The volume of a cylinder is:

Volume = π * radius² * height

A temple has 14 cylindrical pillars made of concrete. If the radius of base of each pillar is 20 cm and height is 5 m.

Radius = 20 cm = 0.2 m

Volume of each cylindrical pillar = π * 0.2² * 5 = 0.628 m³

Volume of 14 cylindrical pillar = 14 * 0.628 m³ = 8.8 m³

The volume of the pillars is 8.8 m³

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