The sum of two numbers is 18. Their difference is -8. Find the two numbers.
Part A
Write a system of equations that represents the situation.
x + y =
x-y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.

The type of graph that represents a system of linear equations that has multiple common coordinate pairs as a solution is called a line of best fit.

A line of best fit is a line drawn through data points that are scattered on a graph in order to illustrate a relationship between the data.

This line helps identify patterns in the data, and when plotted, multiple points can exist on the same line, which in this case represents the multiple common coordinate pairs.

To create a line of best fit, you will need to calculate the slope and the intercept for the equation that models the data. Then, you can plot the points onto the graph and draw a line through them.

The resulting line will be the line of best fit, which represents the multiple common coordinate pairs that are solutions for the system of linear equations.

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Answer:

(5 x 5 = (25) + 1 = (26) + 6 = ?)

Step-by-step explanation:

You're welcome.

Answer: 32

Step-by-step explanation:

5x5 is 25 +1=26 so 26+6=32

Answer:

r - s = (4 - 8, 6 - (-3)) = (-4, 9)

The mistake made by the student is (c) incorrect sign was used for the first term.

When using the distributive property, the expression 7(y-5) should be expanded as 7y - 35, not y - 35. The student incorrectly distributed the 7 to the second term only, while ignoring the first term, which led to an incorrect expression.

Therefοre, the sοlutiοn οf the given prοblem οf angles cοmes οut tο be  m∠1 + m∠6 = 180°.

The largest and smallest walls οf a skew are determined by the intersectiοn οf lines that create its ends. There is a chance that twο lines will cοme tοgether at a junctiοn. Anοther result οf twο οbjects interacting is an angle. They mοst clοsely resemble dihedral fοrms. Twο line beams can be arranged in different ways between their extremities tο fοrm a twο-dimensiοnal curve.

Here,

=> m∠1 + m∠2 = 180° (interior angles on the same side of the transversal and between the parallel lines)

=> m∠4 + m∠5 = 180° (interior angles on the same side of the transversal and between the parallel lines)

Other views shown in the figure include:

=> m∠3 = 75° (given)

=> m∠1 = m∠6 (corresponding angles)

Vertical angles: m2 = m6 x - 15° (alternate interior angles)

Angles corresponding to m4 are m5 (vertical angles)

So let's assess each assertion:

Since they are corresponding angles, m1 = m6 is correct.

This is also accurate because the angles are vertical: m2 = m6.

M1 + M6 = 180°: Since they are linear pairs, this is correct.

=> x = 90°: According to the data in the illustration, this isn't always the case.

=> x = 120°: Based on the data shown in the illustration, this is also not always the case.

Thus, the following assertions are true:

=> m∠1 = m∠6

=> m∠2 = m∠6

=> m∠1 + m∠6 = 180°

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Answer:30 gallons

Step-by-step explanation:

Answer:

30 gallons of tea

Step-by-step explanation:

Step 1:

First, before we do anything, let's convert 2 hours into minutes. There are 60 minutes in an hour, so we would multiply 60 and 2 to get 120 minutes.

Step 2:

Since we know that 4 cups of tea are poured every minute, we must multiply 4 by 120 because it is poured every 1 minute, and 4 × 120 = 480.

Step 3:

We also know that there are 16 cups of tea in one gallon, so we would divide 480 by 16 because we are trying to get how many gallons there are. 480 ÷ 16 = 30, so there are 30 gallons of tea poured in two hours.

three and seven tenths times five

This problem is a classic example of applying the stars and bars combinatorial method.

To solve this problem, we need to distribute 23 identical objects into 7 distinct containers so that none of the containers is empty. Let's start by assuming that each container has at least one object. This means we have distributed 7 objects, leaving 16 objects to be distributed.

We can now use the stars and bars method to distribute these 16 objects. Imagine placing all 16 objects in a line, and placing 6 dividers between them to separate them into 7 groups (one for each container). Each group will then receive the objects that are to the left of the divider.

For example, if we have the sequence OO|OOO|O|OOO|OO|OO|O, this corresponds to 2 objects in the first container, 3 objects in the second container, 1 object in the third container, and so on.

The number of ways to place the 6 dividers in the sequence of 16 objects is the same as the number of ways to choose 6 positions out of 16 to place the dividers. This can be computed using the formula for combinations:

$${16 \choose 6} = \frac{16!}{6!(16-6)!} = 8008$$

Therefore, there are 8008 ways to distribute 23 identical objects into 7 distinct containers so that no container is empty.

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The given statement regarding the GDP of major economies of the world is False.

To determine the accuracy of this statement, we would need to gather data on the real GDP per capita growth rates of major economies between 1982 and 2009 and compare them. Without this data, we cannot definitively say whether the statement is true or false. However, based on historical trends and current economic data, it is unlikely that Italy had the highest growth rate of real GDP per capita during this time period.

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The total time that it took the fireman to be ready and aboard the firetruck can be obtained by summing all of the time spent. When summed, the total figure will be 32 seconds.

The total time taken to board the firetruck can be calculated by summing all the time given in seconds. We start by getting the time it took the firefighter to reach the fire pole which is 9.5 seconds.

Next is the time it took him to slide down the pole which is 3.2 seconds. Next is 13.6 seconds for sliding down the pole and 5.7 seconds for climbing aboard. The sum of all these is 32 seconds.

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The equation of the quadratic function that passes through these points is:

[tex]y = -3x^2 - 12x - 8.[/tex]

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, which means it contains one variable with an exponent of 2. The general form of a quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

Using polynomial interpolation with these 5 points, we can find a quadratic polynomial that passes through all the points. Let the equation of the polynomial be [tex]y = ax^2 + bx + c[/tex].

Using the point (0, -8), we get:

[tex]-8 = a(0)^2 + b(0) + c[/tex]

c = -8

Using the point (-1, 1), we get:

[tex]1 = a(-1)^2 + b(-1) - 8[/tex]

a - b = 9

Using the point (-3, 1), we get:

[tex]1 = a(-3)^2 + b(-3) - 8[/tex]

9a - 3b = 27

Using the point (-4, -8), we get:

[tex]-8 = a(-4)^2 + b(-4) - 8[/tex]

16a - 4b = 0

Using the point (-2, 4), we get:

[tex]4 = a(-2)^2 + b(-2) - 8[/tex]

4a - 2b = 12

Solving this system of equations, we get:

a = -3

b = -12

c = -8

Therefore, the equation of the quadratic function that passes through these points is:

[tex]y = -3x^2 - 12x - 8.[/tex]

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Answer: B

Step-by-step explanation:

because I did it and it was right lol

We will need to place three tablets of hydroxyzine 10 mg in Mrs. Stevens' med cart drawer for a 24-hour supply because her prescriber has instructed her to take it every eight hours.

Mrs. Stevens will need to take 10 mg of hydroxyzine three times per day (every eight hours) to comply with the prescription. We will need to figure out how many tablets of hydroxyzine 10 mg she will need for those three daily doses because we need to fill the drawer for 24 hours.

We will require a total of 30 mg per day for three doses, each of which contains 10 mg. Since we are filling it for 24 hours, that means we will need

for the entire day. There are 10 mg of hydroxyzine in each tablet., therefore,

However, as we are only using the drawer for three doses, we will require three 10 mg hydroxyzine tablets.

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The value of the double integral is 128/27 - 32/9 + 8ln2/3. From triangular region with vertices (0, 1), (1, 2), (4, 1) d.

To evaluate the double integral, we first need to set up the limits of integration. Since the region D is a triangle, we can use the following limits:

0 ≤ x ≤ 1

1 + x ≤ y ≤ 4 - x

The integral then becomes:

∫0^1 ∫1+x^4-x 8y^2 dy dx

Evaluating the integral with respect to y first, we get:

∫0^1 ∫1+x^4-x 8y^2 dy dx = ∫0^1 [(8/3)(y^3)]1+x^4-x dx

= ∫0^1 [(8/3)(1+x^3)^3 - (8/3)(1+x^2)^3] dx

= 128/27 - 32/9 + 8ln2/3

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Answer:

Step-by-step explanation: Since the rectangle sits within the larger circle, let's look at it this way:

Area of Shaded Region = Area of Circle - Area of Rectangle

OR

(X) =( pi * r^2 ) - (rectangle length * rectangle width)

Now we fill in the numbers where we know the numbers:

(X) = (pi * (12 cm)^2) - (3cm * 10cm)

(X) = (pi * 144cm^2) - (30 cm^2)

(X) = 144pi - 30

(X) = 452.39 - 30

(X) = 422.39 cm^2

In a sampling distribution of means, the distribution will approximate the normal distribution, the mean of the sampling distribution will equal the mean of the population and the standard deviation of the sampling distribution is based on Central Limit Theorem, option A.

The central limit theorem (CLT) of probability theory states that, under the assumption that all samples are of equal size and regardless of the population's actual distribution shape, the distribution of a sample variable approaches a normal distribution (i.e., a "bell curve") as the sample size increases.

In other words, the central limit theorem (CLT) is a statistical assumption that, given a sufficiently enough sample size from a population with a limited degree of variance, the mean of all sampled variables from the same population will be roughly equal to the mean of the entire population. According to the law of large numbers, these samples also resemble a normal distribution, with their variances almost equaling the variation of the population as the sample size increases.

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Complete question:

In a sampling distribution of means... 1. the distribution will approximate the normal distribution (bell curve). 2. the mean of the sampling distribution will equal the mean of the population 3. the standard deviation of the sampling distribution is called the standard error. This is based on the...

Central Limit Theorem

Standardization of Transformation

Z-Score Distribution Table

Relative Frequency of Probability

Answer: 100000

Step-by-step explanation:

Answer:

The possible coordinates of point A are (−8,1) or (8,1).

The correct statement regarding the best measure of the variability is given as follows: The IQR is the best measure of variability, and it = 6. The Interquartile Range (IQR of a data-set. As it not affected by outliers, it is the best measure of variability of a data-set. The quartiles for this problem are given as follows: First quartile: Q1 = 15. Third quartile Q3 = 21. Hence the IQR is obtained as follows: IQR = 21 - 15 IQR = 6

Answer: The IQR is the best measure of variability, and it equals 6.

IQR is the best way to measure the variability in this question and its also equal to six. I took the test just now and got it right i cant really explain anything else.

Your gross pay per month including tips is $533.00. The answer is A) $533.00.

First, let's calculate your hourly wage including tips:

Hourly wage including tips = $6.75 + $3.50 = $10.25

Next, let's calculate your total earnings per week:

Total earnings per week = hourly wage including tips x hours worked per week

= $10.25 x 13 hours

= $133.25

Now let's calculate the deductions from your earnings:

FICA deduction = 7.56% x $133.25 = $10.08

Federal tax withholding = 9.6% x $133.25 = $12.80

State tax withholding = 6.7% x $133.25 = $8.92

Total deductions = $10.08 + $12.80 + $8.92 = $31.80

Finally, let's calculate your gross pay per month:

Gross pay per month = total earnings per week x 4 weeks - total deductions

= ($133.25 x 4) - $31.80

= $533.00

Therefore, your gross pay per month including tips is $533.00. The answer is A) $533.00.

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The perimeter of a rectangle is equal to twice the length plus twice the width. Therefore, 18 cm = 2(length + 5) + 2(width). This equation can be solved by subtracting 2(width) from both sides, resulting in 18 - 2(width) = 2(length + 5). Finally, dividing both sides by 2 gives us 9 - width = length + 5. Therefore, width = 4 cm and length = 9 cm.

In this problem, we were given the perimeter of a rectangle, and asked to find its dimensions. We used the formula for the perimeter of a rectangle to set up an equation and solve for the length and width. The width of the rectangle turned out to be 4 cm, and the length was 9 cm, with the length being 5 cm greater than the width.

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As per the concept of combination method, there are 22,100 different ways to draw three cards from a standard deck of 52 cards without replacement, where the order of the cards does not matter.

The number of ways to draw three cards from a deck of 52 cards without replacement can be calculated using combinations. A combination is a way of selecting a subset of objects from a larger set, where the order of selection does not matter. The number of combinations of r objects chosen from a set of n objects is given by the formula:

ⁿCₓ = n! / x!(n-x)!

Where n! (read as n factorial) is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

In our case, we want to find the number of combinations of three cards chosen from a set of 52 cards. Using the formula above, we have:

⁵²C₃ = 52! / 3!(52-3)!

= (52 x 51 x 50) / (3 x 2 x 1)

= 22,100

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The solution of the system 2 -1 5 with -2 -1 in real form is (x, y) = (7/4, 7/2).

To solve the system with the given coefficients, first, let's rewrite it as a linear system of equations:

2x - y = 5
-2x - y = -2

Now, let's solve this system step-by-step:

Step 1: Solve for y in the first equation:
y = 2x - 5

Step 2: Substitute the expression for y from Step 1 into the second equation:
-2x - (2x - 5) = -2

Step 3: Simplify and solve for x:
-2x - 2x + 5 = -2
-4x = -7
x = 7/4

Step 4: Substitute the value of x back into the expression for y:
y = 2(7/4) - 5
y = 7/2

The solution in real form is (x, y) = (7/4, 7/2).

Regarding the ellipse with counterclockwise orientation, the trajectory can be described as a smooth, closed curve in the shape of an ellipse. The ellipse will have a major and minor axis, with the points on the ellipse moving continuously in a counterclockwise direction along the curve.

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Answer:

The Factor Theorem and Synthetic Division are not the same. The Factor Theorem states that if a polynomial f(x) has a root c, then x - c is a factor of f(x). Synthetic Division is a way of dividing a polynomial by a binomial.

Step-by-step explanation:

To use Synthetic Division, you first need to find the coefficients of the polynomial. Then, you set up the synthetic division table with the binomial on top and the coefficients of the polynomial on the bottom. Starting with the first coefficient, you multiply it by the first term of the binomial and write the product below the coefficient. Then, you add the two numbers below the product and write the sum below that. Continue until you reach the end of the binomial. The remainder at the bottom of the table is the remainder when f(x) is divided by x - c.

If the remainder is 0, then x - c is a factor of f(x).

The area of triangle TUV with vertices T(-8,2), U(-2,8), and V(-9,9) are 13.4 units.

A triangle is a closed two-dimensional plane figure that has three sides, three angles, and three vertices. The sum of the angles of a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles. Some common types of triangles include equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are a fundamental concept in geometry and are used in many areas of mathematics and science.

Here,

To find the area of triangle TUV, we can use the formula:

Area = 1/2 * base * height

We can choose any two sides of the triangle as the base and the corresponding height. Let's choose TU as the base and the perpendicular distance from V to TU as the height.

First, let's find the length of TU:

TU = √[(8 - 2)² + (-2 - (-8))²]

= √[6² + 6²]

= 6√(2)

Next, let's find the slope of TU:

mTU = (8 - 2) / (-2 - (-8))

= -3/2

The line perpendicular to TU passing through V has a slope equal to the negative reciprocal of mTU:

mVQ = 2/3

The equation of the line passing through V and perpendicular to TU is:

y - 9 = (2/3)(x + 9)

Solving for x and y at the point where this line intersects TU, we get:

y = (2/3)x + 19

(2/3)x + 19 = -3x/2 + 7

x = -8/7

y = 94/21

The perpendicular distance from V to TU is the absolute value of y - 8:

|94/21 - 8| = 2/21

So, the area of triangle TUV is:

Area = 1/2 * TU * (2/21)

= (1/21)√(2)

To find the area of rectangle QRS, we need to find the length and width. We can use the distance formula to find the length QR and the width QS:

QR = √[(9 - (-8))² + (9 - 2)²]

= √[289]

= 17

QS = √[(9 - (-9))² + (2 - 2)²]

= √[324]

= 18

So, the area of rectangle QRS is:

Area = QR * QS

= 17 * 18

= 306

Area of triangle QRS = Area of rectangle QRS - Area of triangle TUV

= 306 - (1/21)√(2)

≈ 13.4 units

So, the answer is (C) 13.

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Complete question:

Triangle TUV, with vertices T(-8,2), U(-2,8), and V(-9,9), is drawn inside a rectangle. What is the area, in square units, of the triangle TUV?

A. 7

B. 10

C. 13

D. 18

Answer:

26

Step-by-step explanation:

One example of a quadrilateral that is not a rectangle or a rhombus is a trapezoid. A trapezoid has one pair of opposite sides that are parallel, but the other pair of sides are not. (the figure is attached is attached below)

Yes, there are many other shapes that could have been drawn, such as a kite, parallelogram, or irregular quadrilateral. The possibilities are endless, as long as the shape has four sides.

A trapezoid is a quadrilateral with one pair of opposite sides parallel, but the other pair of sides are not. It can be visualized as a shape that resembles a ladder. Unlike a rectangle or rhombus, a trapezoid does not have equal side lengths or equal angles. It can be used in various mathematical contexts, such as finding the area or perimeter of a geometric figure. Additionally, there are many other shapes that could have been drawn instead of a trapezoid, as long as they have four sides. The shapes could have different angles and side lengths, leading to different properties and applications.

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Divide your single screen window into four equal quadrants. You can do this by drawing two perpendicular lines that intersect in the center of the window.

To create the following four distinct drawings in a single screen window, with each occupying one quadrant of the window, follow these steps:

. Divide your single screen window into four equal quadrants. You can do this by drawing two perpendicular lines that intersect in the center of the window.

. In the first quadrant, draw a logarithmic spiral with a given value for k. To do this, start at the center of the quadrant and draw the spiral outwards, increasing the distance between the spiral lines as you move away from the center, according to the formula r = a * e^(k * theta), where r is the distance from the center, a is a constant, e is the base of the natural logarithm, k is the given value, and theta is the angle.

. In the second quadrant, create a distinct drawing that is different from the logarithmic spiral. This can be any other type of curve, shape, or pattern that you would like.

. In the third quadrant, create another distinct drawing that is different from the first two. Again, this can be any curve, shape, or pattern that you choose.

. In the fourth quadrant, create a final distinct drawing that is different from the first three. Make sure to choose a different curve, shape, or pattern for this quadrant as well.

By following these steps, you will have created four distinct drawings in a single screen window, each occupying one quadrant of the window, with the first quadrant featuring a logarithmic spiral with the specified value for k.

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Answer:

290

Step-by-step explanation: