Solve the system of equations by elimination:
3x+y=5
2x-2y=-2

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Two positive angles that have a sum of π/2 radians are complementary angles, whereas two positive angles that have a sum of π radians are supplementary angles.

Complementary angles are two angles whose measures add up to a right angle, which is equal to π/2 radians or 90 degrees. In other words, if α and β are complementary angles, then α + β = π/2.

Supplementary angles, on the other hand, are two angles whose measures add up to a straight angle, which is equal to π radians or 180 degrees. If α and β are supplementary angles, then α + β = π.

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Answer: (0.5, 8.5)

Step-by-step explanation: (9+-8/2) is 1/2 and (7 + 10/ 2) is 8.5. After plugging it into the equation, I checked with a graphing site.

Solution

We will draw a diagram to illustrate the information

Using the concept of SOHCAHTOA

We are given adjacent and we want to find opposite

Therefore, the answer is

Answer:

4

Step-by-step explanation:

the nth term of a geometric sequence is

\(a_{n}\) = a₁ \(r^{n-1}\)

where a₁ is the first term and r the common ratio

here a₁ = 2 and r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{4}{2}\) = 2

then

a₂₈ = 2 \((2)^{27}\)

a₂₆ = 2 \((2)^{25}\)

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{(m-n)}\) , then

\(\frac{a_{28} }{a_{26} }\)

= \(\frac{2(2)^{27} }{2(2)^{25} }\) ( cancel 2 on numerator/ denominator )

= \(\frac{2^{27} }{2^{25} }\)

= \(2^{(27-25)}\)

= 2²

= 4

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

Given that,

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

Whether the claim is true or false must be determined.

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.

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The height of the pole is approximately 64 feet when rounded to the nearest tenth.

To determine the height of the pole, we can use the concept of a right triangle formed by the pole and the two cables. Let's denote the height of the pole as 'h'.

In the given scenario, one cable is 48 feet long and the other is 63 feet long. The ground distance between them is 80 feet. We can visualize this as follows:

      A

     /|

    / |

 h /  | 63

  /   |

 /    |

/     |

/______C

  48    B

Here, A represents the top of the pole, B represents the point where the 48-foot cable touches the ground, and C represents the point where the 63-foot cable touches the ground.

Using the Pythagorean theorem, we can establish the following relationship:

\(AB^2 + BC^2 = AC^2\)

Substituting the given values, we get:

\(h^2 + 48^2 = 80^2\\h^2 + 2304 = 6400\\h^2 = 6400 - 2304\\h^2 = 4096\)

Taking the square root of both sides, we find:

h =\(\sqrt{4096}\)

h ≈ 64

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The image of trapezoid JKLM under the transformation (x,y) → (x+7,y-3) is a trapezoid with vertices J' (1, 3), K' (4, 4), L' (6, 0), and M' (-1, -3).

To find the image of J, we add 7 to the x-coordinate and subtract 3 from the y-coordinate. Thus, J' has coordinates (Jx + 7, Jy - 3) = (-6 + 7, 6 - 3) = (1, 3).

Similarly, for K, we add 7 to the x-coordinate and subtract 3 from the y-coordinate. So, K' has coordinates (Kx + 7, Ky - 3) = (-3 + 7, 7 - 3) = (4, 4).

For L, we add 7 to the x-coordinate and subtract 3 from the y-coordinate. Therefore, L' has coordinates (Lx + 7, Ly - 3) = (-1 + 7, 3 - 3) = (6, 0).

Lastly, for M, we add 7 to the x-coordinate and subtract 3 from the y-coordinate. Hence, M' has coordinates (Mx + 7, My - 3) = (-8 + 7, 0 - 3) = (-1, -3).

Therefore, the image of trapezoid JKLM under the given transformation is a trapezoid with vertices J' (1, 3), K' (4, 4), L' (6, 0), and M' (-1, -3).

When graphing and transforming figures, it is essential to understand the impact of coordinate transformations on the original shape. In this case, we are given the trapezoid JKLM with vertices J(-6,6), K(-3,7), L(-1,3), and M(-8,0), and we need to determine its image under the transformation (x,y) → (x+7,y-3).

To find the image of each vertex, we apply the transformation to its coordinates. For J, we add 7 to the x-coordinate (-6 + 7) and subtract 3 from the y-coordinate (6 - 3), resulting in J' with coordinates (1, 3). This means that the image of point J is located at (1, 3) on the graph.

Similarly, for K, we add 7 to the x-coordinate (-3 + 7) and subtract 3 from the y-coordinate (7 - 3), giving us K' with coordinates (4, 4). Thus, the image of point K is situated at (4, 4) on the graph.

Moving on to point L, we perform the same transformation by adding 7 to the x-coordinate (-1 + 7) and subtracting 3 from the y-coordinate (3 - 3), resulting in L' with coordinates (6, 0). Therefore, the image of L is positioned at (6, 0) on the graph.

Lastly, for point M, we add 7 to the x-coordinate (-8 + 7) and subtract 3 from the y-coordinate (0 - 3), which yields M' with coordinates (-1, -3). Thus, the image of M is located at (-1, -3) on the graph.

In summary, the image of trapezoid JKLM under the transformation (x,y) → (x+7,y-3) is a trapezoid with vertices J' (1, 3), K' (4, 4), L' (6, 0), and M' (-1, -3). By applying the given transformation, we have shifted the original trapezoid 7 units to the right and 3 units down, resulting in the new positions of the vertices.

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The correct answer is: A) The standard error decreases and the confidence interval narrows.

As the sample size increases, the standard error of the sample mean decreases. The standard error measures the variability or spread of the sample means around the true population mean. With a larger sample size, there is more information available, which leads to a more precise estimate of the true population mean. Consequently, the standard error decreases.

Moreover, with a larger sample size, the confidence interval for the true mean becomes narrower. The confidence interval represents the range within which we are confident that the true population mean lies. A larger sample size provides more reliable and precise estimates, reducing the uncertainty associated with the estimate of the population mean. Consequently, the confidence interval becomes narrower.

Therefore, statement A is the most accurate description of the change in the standard error of the sample mean and the size of the confidence interval for the true mean as the sample size increases.

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Answer:

Step-by-step explanation:

C

First of all, stop thinking on the number 1000 and turn your attention to the number 990 instead. If you solve the problem for 990 you just have to add 993,995,996 & 999 to it for the final answer. This sum is (a)=3983

Count all the #s divisible by 3: From 3... to 990 there are 330 terms. The sum is 330(990+3)/2, so (b)=163845

Count all the #s divisible by 5: From 5... to 990 there are 198 terms. The sum is 198(990+5)/2, so (c)=98505

Now, the GCD (greatest common divisor) of 3 & 5 is 1, so the LCM (least common multiple) should be 3×5=15.

This means every number that divides by 15 was counted twice, and it should be done only once. Because of this, you have an extra set of numbers started with 15 all the way to 990 that has to be removed from (b)&(c).

Then, from 15... to 990 there are 66 terms and their sum is 66(990+15)/2, so (d)=33165

The answer for the problem is: (a)+(b)+(c)−(d)=233168

Simple but very fun problem.

we have that

A quadratic equation that will have a solution of only x = 0 is given by the equation

Answer:

y=-x-6

Step-by-step explanation:

First step is to put y=-x-6

Second step is to replace the y with x and the x with y:

x=-y-6

Now solve for y:

-y=x+6

y=-x-6

In this case the inverse is the same as the equation

Answer:

-8

Step-by-step explanation:

substitute x with 3

-4(3) + 4

simplify (multiply)

-12+4

simplify

-8

Answer:

g(3) =  -8

Step-by-step explanation:

g(3) = -4x + 4 Substitute 3 for X:

g(3) =  -4(3) + 4

-4 * 3 = -12

g(3) = -12+4

g(3) =  -8

The number represented by each point on the number line is:

Point A: 1 2/3

Point B: 2

A number line is a visual representation of the real number system, where each point on the line corresponds to a specific real number.

Looking at the given number line, you will notice that there are 3 spaces between 0 and 1. This implies:

3 spaces = 1 unit

1 space =  1/3 unit

Thus, we can say the value of the points are:

Point A: 1 2/3

Point B: 2

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Answer:

The piece-wise function is;

\(f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}\)

Step-by-step explanation:

The flat rate for renting the car = $35 per day

The amount charged as insurance fee per day for renting the car for 3 days or less = $10

The insurance fee charged per day when the car is rented for more than 3 days = $5

Let the number of days = x

Therefore, we have;

For x ≤ 3, f(x) = 35 × x + 10 × x = x × (35+10) = 45·x

For x > 3, f(x) = 35 × x + 5 × x = x × (35+5) = 40·x

Therefore;

The charge rate for renting the car for less than or equal to 3 days = 45·x

The charge rate for renting the car for more than 3 days = 40·x

The piece-wise function can be presented as follows;

\(f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}\)

Since tan m = 1/2 and tan n = -6, the precise value of tan (m+n) will be 3.51.

The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle. The law of tangent is another name for tan. The ratio of a triangle's opposing side to its adjacent side is known as the tangent formula for a right-angled triangle. The angle's sine to cosine ratio can also be used to represent the angle.

Here,

tan m= 1/2

tan n= -6

m=tan inverse(1/2)

n=tan inverse(-6)

m=26.565 degrees

n= -80.537 degrees

n=360-80.537

n=279.463 degree

tan (m+n)=tan(26.565+279.463)

tan 306.028=3.51

The exact value of tan (m+n) will be 3.51 as the value of tan m= 1/2 and tan n= -6.

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The lower bound and upper bound for Helen's value would be;  3.165, and 3.065.

The circumference is the perimeter of the circle.

Given that the circumference of circle C, at 405 mm to three significant numbers.

Helen correctly estimates the diameter of circle, d, to be 130 mm to two significant numbers.

She wants to find the value of Pi using the formula π=C/D

We have, the circumference of the circle, C = 405 mm

The diameter of the circle, d = 130 mm

π=C/D

π= 405 mm / 130 mm

= 405 / 130

π= 3.115 measured to the nearest 0.1.

The degree of accuracy is nearest 0.1.

Then;

0.1/2 = 0.05

Therefore, Upper bound = 3.115 + 0.05 = 3.165

Lower bound = 3.115 - 0.05 = 3.065

Therefore, the lower bound and upper bound for Helen's value would be;  3.165, and 3.065.

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The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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There are a total of 8 people going on the trip, 4 of which are not members of the French club.

$284 - (8.11 * 4) = 284 - 32.44 = 251.56

251.56/x = 8.11

x = 251.56/8.11 = 31

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Answer:

a^2+a-6

Step-by-step explanation:

i have attached your answer

Answer:

203,549 !!!

Step-by-step explanation:

In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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Answer:

I think it is neither

Step-by-step explanation:

I am not sure but I know it isn't a function

Answer: D Because it does not pass the vertical line test

hope this helps :)

Answer:

10 4/5

Step-by-step explanation:

9514 1404 393

Answer:

  irrational

Step-by-step explanation:

If we assume the decimal fraction continues indefinitely without repeating, then the number is irrational.

__

The pattern that seems to have been established is an increasing number of repetitions of the digit 3, with each set followed by the digit 2. This pattern can continue indefinitely without repeating.

1727.88 cm³/sec is the volume of the cone .

How much volume do a cone and a cylinder have?

Volume of cone V = 1/3πr²h

               r/h = 15/20 = 3/4

            V = 1/3πr²h

dv/dt = 1/3 [π[r²dh/dt + 2rhdr/dt]

   dr/dt = dh/dt = 2cm/sec

   r = 15 cm  h = 20 cm

 dv/dt = π/3[15² × 2 + 2 × 15 × 20 × 2 ]

   550π  = 1727.88 cm³/sec

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