I had block the instructions but basically it said State what additional information is required in order to know that the triangles in the image below are congruent for the reason given.

Answer:

Keith p = 6d

Tameka p = 5d + 15

p=p so the following is also true:

6d = 5d + 15

let's do the same thing on both sides of the equation, subtract 5d

d = 15

after 15 days the will be on the same page

you could also say that Tameka is slowly catching up with a rate of 1 page per day

Answer:

children = 67

Step-by-step explanation:

two equations can be derived from this question

x + y = 85 equation 1

3x + y = 121 equation 2

where x = number of adults

y = number of children

subtract equation 1 from 2

2x = 36

x = 18

substitute for x in equation 1

y = 85 - 18 = 67

Therefore , the solution of the given problem of speed comes out to be

he needs to drive at 77.77 mph.

How quickly something is traveling is determined by its speed from a distance. How far an object moves in a certain length of time depends on its speed. Speed is calculated as follows: velocity = range x time. The most used units for expressing speed are meters per second (m/s), kilometers per hour (km/h), and kilometers per second (mph) (mph).

Here,

70 + 50 = 120 miles is indeed the total distance.

You would need 2.4 hours to travel the 120 miles at such an approximate speed of 50 mph.

However, you are already on the road for 1.5 hours, so you must finish the trip in 0.9 hours.

You need to travel at a speed of 77.77 mph to complete the final 70 miles approximately 0.9 hours.

Therefore , the solution of the given problem of speed comes out to be

he needs to drive at 77.77 mph.

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Rectangles can never be a regular polygon as there is difference between two figures.

Regular polygon: The flat, closed, straight-sided shape known as a regular polygon must also possess some additional characteristics. In the regular polygon, each interior and exterior angle is equal to every other interior and exterior angle, and each side is the same length as every other side.

Rectangle: Rectangle is a four-sided polygon in geometry with internal angles that are all 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square in that its opposite or parallel sides are of equal length.

According to the properties of a rectangle, only parallel or opposite sides are equal, however all of the sides of a regular polygon must have the same or equal length.

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The length of the diagonal distance, x, of his smaller bookend is 7.2.

The diagram of the books is given below:

The length of first triangle is 10 and diagonal distance is 12.

The length of second triangle is 6 and diagonal distance is x.

The shape of both triangle is same.

To determine the slant height of second triangle, we use the similar triangle theorem.

Using the theorem

The height of first triangle/The diagonal distance of first triangle = The height of second triangle/The diagonal distance of second triangle

10/12 = 6/x

Multiply by 12 on both side, we get

10 = 72/x

Multiply by x on both side, we get

10x = 72

Divide by 10 on both side, we get

x = 7.2

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(2x + 3) (x^2 - 6x + 9)

Answer:

y=9x-45

Step-by-step explanation:

9x-y=45

-y=45-9x

y=9x-45

Paul Sharkey, the owner of Sharkey's Fun Centre, wishes to expand the facility by constructing a water slide in the compound. The addition of this new feature is aimed at drawing more customers to the premises and increasing revenues.

The management understands that the implementation of such a project can be expensive. Still, the investment is necessary for the continued success of the business. Sharkey's Fun Centre already has a miniature golf course, various rides, and a range of electronic games.

However, the water slide will provide an additional attraction to customers. The facility is in an ideal location with excellent visibility and easy access, making it convenient for families with children to visit.

The addition of a water slide will make Sharkey's Fun Centre a one-stop-shop for families.

The construction of a water slide in Sharkey's Fun Centre is a necessary investment to attract more customers to the facility. The management understands that this project will require significant capital investment.

However, the business will benefit in the long run from increased revenues. Sharkey's Fun Centre is in a prime location with easy access and high visibility. The addition of a water slide will make it an even more popular destination for families with children.

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Answer:

POKEMON YEAH!

Okay, so you first want to take 2485, and subtract it from 4500, because that is the amount of money he has already collected.

4500 - 2485 = 2015

Now you need to find out how many time you can multiply 155, to get 2015, or higher. In this case, I am just gonna divide:

2015/155 = 13

It will take him 13 more weeks to have enough for the Pokemon cards!

Step-by-step explanation:

Hope it helps! =D

Answer: 36 square units.

Step-by-step explanation:

First, you can separate the figure into a 4x6 rectangle and a 6x4 isosceles triangle. You can find the area of the rectangle by using the rectangle area formula, A = l x w .

4 x 6 = 24 units

Then, to find the area of the triangle, you can use the triangle area formula, A = \(\frac{1}{2}\) b x h .

1/2 x 4 x 6 = 12 units

Finally, you can simply add 24 + 12 to get the total area of 36 units. Since the area is the measure found, you would use the square symbol (²) at the end of the units:

36 units²

I hope this helps!

The geometric description of the set of points in space whose coordinates satisfy the given pair of equations y=0 and z=0 is the x-axis, which is a straight line that passes through the origin of the Cartesian coordinate system.

The geometric description of the set of points in space whose coordinates satisfy the given pair of equations y=0 and z=0 is the x-axis. Thus, the correct answer is option G.A Cartesian coordinate system is a graph that uses geometric concepts to represent points in the plane using two-dimensional or three-dimensional space. Each point on the Cartesian plane is identified by its x-coordinate and its y-coordinate, where the x-coordinate refers to the horizontal position of the point, and the y-coordinate refers to the vertical position of the point.In the given pair of equations y=0 and z=0, the value of y is zero and the value of z is zero. Thus, the only value that could be other than zero is x, and all possible values of x would result in a point that is on the x-axis only. Therefore, the set of points in space whose coordinates satisfy the given pair of equations y=0 and z=0 is the x-axis.The x-axis is a single, straight line running horizontally through the Cartesian plane. The x-axis has an infinite number of points, each with its own unique x-coordinate and a y-coordinate of 0, as well as a z-coordinate of 0 in the case of the three-dimensional Cartesian coordinate system. Thus, the geometric description of the set of points in space whose coordinates satisfy the given pair of equations y=0 and z=0 is the x-axis, which is a straight line that passes through the origin of the Cartesian coordinate system.

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To find the components of the vector PQ and the coordinates of point P, we are given that PQ⋅P = (-3,-2) and Q = (5,-4). Additionally, we know that PR has components (-3,0) and R = (1,-2). By solving the equations, we can determine the values of PQ and P.

Let's start by finding the components of PQ. We can use the dot product formula, which states that the dot product of two vectors A and B is equal to the product of their corresponding components, added together. In this case, we are given that PQ⋅P = (-3,-2). Since the dot product of two vectors is equal to the product of their magnitudes multiplied by the cosine of the angle between them, we can set up the equation: PQ * P = ||PQ|| * ||P|| * cosθ, where θ is the angle between PQ and P. However, we are not given the angle or the magnitudes of the vectors, so we cannot directly solve for PQ and P.

Moving on to the second part of the problem, we are given that PR has components (-3,0) and R = (1,-2). To find point P, we need to determine its coordinates. We can use the fact that the components of a vector can be represented as the differences between the corresponding coordinates of two points. In this case, we have PR = P - R, where P is the unknown point. By substituting the given values, we get (-3,0) = P - (1,-2). Solving this equation, we can find the coordinates of point P.

To Conclude, we have a system of equations involving the dot product and vector subtraction. By solving these equations, we can determine the components of PQ and find the coordinates of point P.

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Answer: 6/8 or 3/4

Step-by-step explanation:

so you get (-20,-4) and (-12,-10) you do -4-10 witch is 6 then you do -20-12 witch is 8 you put 6 up top its your numerator and 8 on the bottom because its you denominator

Answer:

100

Step-by-step explanation:

Answer:

D.) 100

Step-by-step explanation:

Answer:

A) 1/13

Step-by-step explanation:

In a deck of 52 cards, there are 13 clubs. Out of those 13 clubs, there is 1 ten.

Since a club was drawn, the probability of the card being a ten is:

1 ten out of 13 clubs = 1/13

Answer:

10 visits

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Rewards for signing up = 80 points

Reward per visit = 2.5 points

Total points needed = 105

Let, number of visits = x

So, we can calculate number of visits by using following formula,

80 + (2.5 × X) = 105

2.5X = 105 - 80

2.5X = 25

X = 25 ÷ 2.5

X = 10 visits.

Hence, Olivia needs to make 10 visits in order to earn a free movie ticket.

Answer:

≈ 19.1 feet

Step-by-step explanation:

A right triangle is formed by the building , the ground and the ladder , that is the hypotenuse.

let x be the distance foot of ladder is from the building.

using Pythagoras' identity in the right triangle

x² + 34² = 39²

x² + 1156 = 1521 ( subtract 1156 from both sides )

x² = 365 ( take square root of both sides )

x = \(\sqrt{365}\) ≈ 19.1 feet ( to the nearest tenth )

Answer:

\(1.5\; \rm s\).

Step-by-step explanation:

The person in this question is in the air whenever the height is greater than \(0\).

The graph of \(y = -16\, t^{2} + 24\, t\) is a parabola opening downwards. Rearrange and find values of \(t\) that would set this expression to \(0\).

\(\begin{aligned}y &= -16\, t^2 + 24\, t \\ &= t\, (-16\, t + 24) = -8\, t\, (2\, t - 3)\end{aligned}\).

The first factor, \(t\), suggests that \(t = 0\) would set this expression to \(0\)- quite expected, since the person is on the ground right before jumping.

The second factor, \((2\, t - 3)\), suggests that \(2\, t = 3\) (in other words, \(t = 3/2 = 1.5\)) would also set this expression to \(0\). Hence, this person would be once again on the ground \(1.5\) seconds after jumping.

Hence, this person is in the air between \(t = 0\) and \(t= 1.5\) for a total of \(1.5\; \rm s\).

Answer: 28282

Step-by-step explanation:

I think

Answer:

option c

volume of right circular cone=1/3 *(pi)* r*r *h

The following statements are true:

The general least-squares problem is to find an x that makes Ax as close as possible to b.

If b is in the column space of A, then every solution of Ax = b is a least-squares solution.

Any solution of \(A^TAX = A^Tb\) is a least-squares solution of Ax = b.

What is matrix?

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used in many areas of mathematics, including linear algebra, calculus, and statistics.

The first statement is false. A least-squares solution of Ax = b is a vector x that minimizes the Euclidean norm ||b - Ax||, not necessarily making it smaller than any other norm.

The second statement is true. If b is in the column space of A, then Ax = b has at least one solution, and any solution is also a least-squares solution.

The third statement is true. Any solution of \(A^TAX = A^Tb\) can be written as \(x = (A^TA)^{-1}A^Tb\), and it is a least-squares solution of Ax = b because \((A^TA)^{-1}A^T\) is the left-inverse of A (if A has full column rank), and \((A^TA)^{-1}A^Tb\) is the projection of b onto the column space of A.

The fourth statement is false. A solution of \(A^TAX = A^Tb\) is not necessarily a solution of Ax = b, so it cannot be a least-squares solution of Ax = b.

The fifth statement is false. A least-squares solution of Ax = b is a vector x that satisfies the normal equation \(A^TA x = A^Tb\), not necessarily Ax = b. Moreover, x is the orthogonal projection of b onto Col A only if A has full column rank, in which case the projection matrix is \(A(A^TA)^{-1}A^T.\)

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Complete question : let a be an m x n matrix and b be a vector in rm. which of the following is/are true? (select all that apply)

A least-squares solution of Ax = b is a vector such that ||b - Ax|| ≤ b - Ax|| for all x in Rº.

The general least-squares problem is to find an x that makes Ax as close as possible to b.

If b is in the column space of A, then every solution of Ax = b is a least-squares solution.

Any solution of\(A^TAX = A^Tb\) is a least-squares solution of Ax = b.

A least-squares solution of Ax = b is a vector x that satisfies Ax = b, where is the orthogonal projection of b onto Col A.

Answer:

Step-by-step explanation:

338.33 ft

Answer:

hello louser your a very crazy man

Step-by-step explanation:

If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.

This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.

If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.

Then, we have:

0 ≤ Sn ≤ M1 for all n (Sn is bounded)

0 ≤ Tn ≤ M2 for all n (Tn is bounded)

Now, let's consider the partial sums of the series ∑an∑bn:

Pn = a1(T1) + a2(T2) + ... + an(Tn)

Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.

Using the properties of the partial sums, we have:

0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)

Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.

Therefore, the given statement is True.

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Answer:

974

Step-by-step explanation:

Let assume that:

The set of student that took part in Calculus be = C

Those that took part in discrete mathematics be = D

Let those that took part in data structures be = DS; &

Those that took part in Programming language be = P

Thus;

{C} = 507

{D} = 292

{DS} = 312

{P} = 344

For intersections:

{C ∩ DS} = 14

{C ∩ P} = 213

{D ∩ DS} = 211

{D ∩ P}  =43

{C ∩ D} = 0

{DS ∩ P} = 0

{C ∩ D ∩ DS ∩ P} = 0

According to principle of inclusion-exclusion;

{C ∪ D ∪ DS ∪ P} = {C} + {D} + {DS} + {P} - {C ∩ D} - {C ∩ DS} - {C ∩ P} - {D ∩ DS} - {D ∩ P} - {DS ∩ P}

{C ∪ D ∪ DS ∪ P} = 507 + 292 + 312 + 344 - 14 - 213 - 211 - 43 - 0

{C ∪ D ∪ DS ∪ P} = 974

Hence, the no of students that took part in either course = 974

1. The sequence (n+4)/n converges to 1 as n approaches infinity.
2. The sequence (n+8)/(n^2) converges to 0 as n approaches infinity.
3. The sequence tan((n(pi))/(4n+3)) oscillates and does not converge.
4. The sequence ln(3n/(n+1)) converges to ln(3) as n approaches infinity.
5. The sequence n^2/(sqrt(8n^4+1)) converges to 1/(sqrt(8)) = 1/4 as n approaches infinity.
6. The sequence (1+(1/n))^(5n) converges to e^5 as n approaches infinity.

1. The sequence converges. As n approaches infinity, (n+4)/n approaches 1.
2. The sequence converges. As n approaches infinity, (n+8)/(n^2) approaches 0.
3. The sequence converges. As n approaches infinity, tan((n*pi)/(4n+3)) approaches 0 since tan(n*pi) is 0 for all integer values of n.
4. The sequence converges. As n approaches infinity, ln(3n/(n+1)) approaches ln(3) as the leading terms dominate.
5. The sequence converges. As n approaches infinity, n^2/(sqrt(8n^4+1)) approaches 0 since the denominator grows faster than the numerator.
6. The sequence converges. As n approaches infinity, (1+(1/n))^(5n) approaches e^5 using the limit definition of e.

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Hence, there are 725,760 ways to seat the ten people together in a row, taking into account the two individuals who insist on sitting side-by-side.

If two of the ten people insist on sitting side-by-side, we can consider them as a single entity or a pair. So, essentially, we have nine entities (including the pair) to be seated in a row.

The number of ways to arrange these nine entities in a row is 9!, which is the factorial of 9.

However, within the pair, the two individuals can be arranged in 2! = 2 ways.

Therefore, the total number of ways to seat the ten people together, considering the pair as one entity, is 9! * 2!.

Simplifying this expression:

9! * 2! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * 2 = 725,760

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0.02 and 2 are rational numbers and √2 and √12 are irrational numbers

As a general rule;

Using the above as a guide,

0.02 and 2 are rational numbers because they can be represented as fractions i.e. 2/100 and 2/1

√2 and √12 are irrational numbers because they cannot be represented as fractions

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