A student claims that he can solve 12x+8y= 40 and 4x+5y=18 for x and y by adding the first Equation to a multiple of the second Equation. He can then use the new Equation and the first Equation to create a new system that has the same solution as the original system. The student begins by listing four different Equations.

Determine whether the student can use that Equation to replace the second Equation and create a new system that has the same solution. Select Yes or No for each Equation. ​

Answer: 7.5 miles per hour

Step-by-step explanation:

First speed was 3 miles per hour.

Second speed was 12 miles per hour.

To do an average, add both speeds and divide by two, which is the number of trips made.

= (3 + 12) / 2

= 15 / 2

= 7.5 miles per hour

It must rotate to get to its sideways position but it needs to move down to get to its location.

We have given that, transformations must be applied to object A to place it in the position of object B.

Rotation is the circular movement of an object around an axis of rotation. A three-dimensional object may have an infinite number of rotation axes.

Rotation and translation.

It must rotate to get to its sideways position but it needs to move down to get to its location.

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The algebraic expression that represents the total cost of signing the lease is as follows:

Total cost = r(2) + r(1) + D + C + r(12) * 0.07

Explanation: Given that Larry is renting an apartment that will cost r dollars per month. He must pay a D dollars application fee and C dollars for a credit application. His security deposit is two months rent and he must also pay the last month's rent upon signing the lease. His broker charges 7% of the total year’s rent as the fee for finding the apartment. Larry must pay the first month's rent and the last month's rent upon signing the lease. Therefore, the total cost of signing the lease will be:

r(2) + r(1) + D + C + r(12) * 0.07

r(2) represents the security deposit of two months rent, r(1) represents the last month's rent that he must pay upon signing the lease, and r(12) represents the yearly rent payable.

r(12) * 0.07 is the broker's fee for finding the apartment.

Conclusion: The algebraic expression that represents the total cost of signing the lease is as follows:

Total cost = r(2) + r(1) + D + C + r(12) * 0.07

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The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

106

Step-by-step explanation:

180-74=106

You can find x by looking at the corresponding angle under it and we know a straight line is 180 degrees and the other side of the x is 74 degrees then we just subtract to find the x angle

Hopes this helps please mark brainliest

Answer:

The v with arrow is for vector so you find the slope and apply it to each of the vertices

Step-by-step explanation:

The complex cube roots of 1 + i are:

z0 = (sqrt(2))^(1/3) [cos(π/12) + i sin(π/12)]

z1 = (sqrt(2))^(1/3) [cos(7π/12) + i sin(7π/12)]

z2 = (sqrt(2))^(1/3) [cos(11π/12) + i sin(11π/12)]

To find the complex cube roots of 1 + i, we can express 1 + i in polar form and use De Moivre's theorem.

Step 1: Convert 1 + i to polar form.

We have:

r = sqrt(1^2 + 1^2) = sqrt(2)

θ = tan^(-1)(1/1) = π/4 (45 degrees)

So, 1 + i can be written as:

1 + i = sqrt(2) (cos(π/4) + i sin(π/4))

Step 2: Apply De Moivre's theorem.

De Moivre's theorem states that for any complex number z = r(cos(θ) + i sin(θ)) and any positive integer n, the complex nth roots of z are given by:

z0 = r^(1/n) [cos(θ/n + 2πk/n) + i sin(θ/n + 2πk/n)]

In this case, we are finding the cube roots (n = 3) of 1 + i.

For the first cube root (k = 0):

z0 = (sqrt(2))^(1/3) [cos((π/4)/3) + i sin((π/4)/3)]

= (sqrt(2))^(1/3) [cos(π/12) + i sin(π/12)]

For the second cube root (k = 1):

z1 = (sqrt(2))^(1/3) [cos((π/4 + 2π)/3) + i sin((π/4 + 2π)/3)]

= (sqrt(2))^(1/3) [cos(7π/12) + i sin(7π/12)]

For the third cube root (k = 2):

z2 = (sqrt(2))^(1/3) [cos((π/4 + 4π)/3) + i sin((π/4 + 4π)/3)]

= (sqrt(2))^(1/3) [cos(11π/12) + i sin(11π/12)]

Therefore, the complex cube roots of 1 + i are:

z0 = (sqrt(2))^(1/3) [cos(π/12) + i sin(π/12)]

z1 = (sqrt(2))^(1/3) [cos(7π/12) + i sin(7π/12)]

z2 = (sqrt(2))^(1/3) [cos(11π/12) + i sin(11π/12)]

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Answer:

You could simply go to your course selection book (if there is one) and see if it's there. If not, then ask your guidance counselor for help or if you can automatically advance.

Step-by-step explanation:

Answer: 26 + 13 + 26 + 13 + x =180

Step-by-step explanation:

Answer:

-39

Step-by-step explanation:

 12 - {1+2[-1(3-8)]²}

=12 - {1+2[-1(5)]²}     solve the parenthesis first

=12 - {1+2[5]²}         multiple the 5 by -1

=12 - {1+2[25]}        then square the 5

=12 - {1+50}            multiple 25 by 2

=12 - 51                  solve the curly bracket

= -39                      finally solve it

(a) A = 1/2 (bh)

(b) b = P/R

(c) 8?

Answer:

14-16=2

Step-by-step explanation:

2÷5=0.4

probability is 0.4

If a long run athlete can run 1/2 km in 3 minutes then he can run 10 km in an hour.

Given, a long distance athlete can run 1/2 kilometer in 3 minutes.

How much distance can he cover in an hour = ?

How quickly something or someone is moving is determined by their speed. If you know how far an object has traveled and how long it has taken, you can calculate its average speed. Speed equals distance times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

Time = 60 minutes.

we know that 3 minutes = 1/2 km

therefore, distance covered in an hour = 1/2 ÷ 3/60

= 1/2 × 60/3

= 1/2 × 20

= 10

distance covered in an hour = 10 km.

hence we get the distance covered by the athlete in an hour as 10 km.

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The axis of symmetry divides a shape into congruent halves, such as a parabolic curve or a quadratic function's graph. It is determined by the vertex or calculated using the formula -b/2a. The rank of the three functions are h(x), g(x), and f(x).

The axis of symmetry is a line that divides a two-dimensional shape or a three-dimensional object into two congruent halves.

The axis of symmetry is a line that divides a parabolic curve into two equal sections.

If the quadratic function's equation is given in vertex form, f(x) = a(x - h)2 + k, where the vertex is (h, k) and "a" is a coefficient, the axis of symmetry is the line x = h.

The graph of a quadratic function is symmetric about the axis of symmetry. A graph of a parabola is symmetrical about its axis of symmetry, which passes through its vertex.

For the quadratic function g(x) = 2x2 - 8x + 6, the axis of symmetry can be found using the formula x = -b/2a; the axis of symmetry is x = 2.

The axis of symmetry of f(x) = -3(x - 4)2 - 1 is x = 4, and the axis of symmetry of h(x) = x2 + 2x + 3 is x = -1 (Note: vertex form and standard form).

To sum up, based on the order of the axis of symmetry, the rank of the three functions is as follows: h(x), g(x), and f(x).

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Answer:

Option B, \((48x^{8}y^{5})\)

Step-by-step explanation:

Step 1:  Simplify the exponent

\((12x^{2}y^{3})(2x^{3}y)^{2}\)

\((12x^{2}y^{3})(2^{2}x^{3*2}y^{1*2})\)

\((12x^{2}y^{3})(4x^{6}y^{2})\)

Step 2:  Simply the expression

\((12x^{2}y^{3}*4x^{6}y^{2})\)

\((48x^{2+6}y^{3+2})\)

\((48x^{8}y^{5})\)

Answer: Option B, \((48x^{8}y^{5})\)

Answer:

24

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

2/3 of 36 is 24 so he sold 24 tickets which leaves him with 1/3 or 12 tickets left

At the production level of 40 units, profit is maximized and the profit at this production level is $64,000.

Revenue is given by R(q) = 600q and cost is given by C(q) = 10,000 + 5q2. Profit is given by P(q) = R(q) - C(q).Therefore, P(q) = 600q - (10,000 + 5q2) or P(q) = -5q2 + 600q - 10,000. The profit is maximized at the production level where the derivative of P(q) is equal to zero.The derivative of P(q) is given by P'(q) = -10q + 600. Setting this to zero, we get -10q + 600 = 0 or q = 60. However, this is the maximum point of the revenue function R(q) and not the profit function P(q).To determine the maximum point of P(q), we need to find the second derivative of P(q) which is given by P''(q) = -10. Since P''(q) is negative, the maximum point of P(q) occurs at the production level q = 40. At q = 40, P(q) = -5(40)2 + 600(40) - 10,000 = $64,000.

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The area of the shaded region is equal to the area of the circle minus the area of the rectangle. To determine the said area, you have to calculate the area of the circle and the area of the rectangle first:

Area of the circle

The area of the circle can be determined using the following formula:

The radius of the circle is r=4cm, then the area can be calculated as follows:

Area of the rectangle

The area of the rectangle is equal to the product of its width and length:

The width of the rectangle is w=2cm and the length is l=3cm, so the area can be determined as follows:

Area of the shaded region(S)

The area of the shaded area is equal to the difference between the area of the circle and the area of the rectangle:

The area of the shaded region is 44.27cm²

Answer:

2(23)+29

2(23)+29

=528

Step-by-step explanation:

The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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According to the given angle of elevation, she now ascend to get back to sea level at 111.6 feet.

The term in angle of elevation in math is defined as an angle that is formed between the horizontal line and the line of sight.

Here we have given that  a scientist uses a submarine to study ocean life.

Here we also know that She begins at sea level, which is an elevation of o feet.

As we all know that she descends 28.7 feet and then She ascends 9.9 feet.

Finally she descends a second time, 92.8 feet.

Now, she is at the level of,

In first stage, she is at the level of

=> 28.7 - 9.9

=> 18.8

Then she descends at the level of

=> 18.8 + 92.8

=> 111.6

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Answer:

z = 2 x + 3 y

Step-by-step explanation:

Answer:

B. 12x^2 + 31x + 20

Step-by-step explanation:

Use FOIL (First, Outer, Inner, Last)

(3x + 4)(4x + 5)

12x^2 + 15x +16x + 20

12x^2 + 31x + 20

Answer:

B

Step-by-step explanation:

You are going to want to use the FOIL method. First outer inner last. Multiply 3x*4x to get 12x^2 then multiply 3x*5 to get 15x then multiply 4*4x to get 16x and last multiply 4*5 to get 20. Since 15x and 16x are like terms we add them together to get 31x

Since ε is positive, |xₙ - x| + |yₙ - y| < ε. This implies that |xₙ - x| < ε and |yₙ - y| < ε. Therefore, xₙ → x and yₙ → y. The converse of the claim made in (8.1) is not necessarily true.

(8.1) The claim that if zₙ → z, then xₙ → x and yₙ → y is true.

To prove this claim, let's consider the definition of convergence in complex numbers. For a sequence z_n to converge to z, it means that for any positive ε, there exists a positive integer N such that for all n ≥ N, |zₙ - z| < ε.

Now, let's consider the real and imaginary parts of z_n and z.

We have zₙ = xₙ + iyₙ and z = x + iy.

Since |zₙ - z| < ε, we can express it as |(xₙ - x) + i(yₙ - y)| < ε.

Using the triangle inequality, we can say that |xₙ - x| + |yₙ - y| ≤ |(xₙ - x) + i(yₙ - y)| < ε.

Since ε is positive, |xₙ - x| + |yₙ - y| < ε.

This implies that |xₙ - x| < ε and |yₙn - y| < ε.

Therefore, xₙ → x and yₙn → y.

(8.2) The converse of the claim made in (8.1) is: If xₙ → x and yₙ → y, then zₙ → z.

(8.3) The converse of the claim made in (8.1) is not necessarily true.

A counter-example to this converse is when xₙ = (-1)ⁿ and yₙ = 0 for all n.

In this case, xₙ → x = 1 and yₙ → y = 0, but z_n does not converge as it oscillates between -1 and 1.

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\(\text{Given that,}\\\\x^2 + \dfrac1{x^2} = 38\\\\\\(i)\\\\\left(x-\dfrac 1x \right)^2 = x^2 + \dfrac 1{x^2} - 2 \cdot x \cdot \dfrac 1x\\\\\\\implies \left(x-\dfrac 1x \right)^2 = 38 -2 = 36\\\\\implies x - \dfrac 1x = \pm\sqrt{36} = \pm 6 \\\\\\(ii)\\\\x^2 + \dfrac 1{x^2} = 38\\\\\\\implies \left(x^2 + \dfrac 1{x^2} \right)^2 = 38^2\\\\\\\implies x^4 + \dfrac 1{x^4} + 2\cdot x^2 \cdot \dfrac 1{x^2} = 1444\\\\\\\implies x^4 + \dfrac 1{x^4} + 2 = 1444\\\\\\\)

\(\implies x^4 +\dfrac 1{x^4} = 1444-2 = 1442\)

Answer:

826,783

82*6* (we go up)

826,783 is rounded to 830,000

Step-by-step explanation:

Answer: 3/K

Step-by-step explanation:

From the question, we are informed that Mary bought K stamps for 3 dollars and we are told to find the cost of one stamp.

Number of stamps bought = K

Cost of K stamps bought = 3 dollars

Cost of ones stamp = Cost of stamps bought ÷ Number of stamps bought

= 3/K

Therefore, the cost of one stamp is 3/K

Answer:

Here is your answer

((9 * 7) ^ 8) ^ 6 =

(63 ^ 8) ^ 6 =

248155780267521 ^ 6 = 233531986596828998799172199566520716360870650059740845218613277797210219279668591621121

Step-by-step explanation: