Solve the system using linear combination. Show all work.

{3x+4y=21

{5x+4y=11

The equation of the line 2x + 3y + 1 = 0 after it has been reflected across y = -1 and rotated about O(2,3) by 180 degrees is -2x + y = 15.

To reflect the line 2x + 3y + 1 = 0 across the line y = -1, we need to subtract twice the y-coordinate of each point on the line from the equation of the line.

This is because the reflection of a point across a line is obtained by reflecting it across the line's perpendicular bisector, which is also the line with the same x-coordinates and twice the distance from the point to the line.

Subtracting twice the y-coordinate, we get:

2x + 3(-2y - 1) + 1 = 0

Simplifying the equation, we get:

2x - 6y - 5 = 0

Now, to rotate the line about the point O(2,3) by 180 degrees, we can use the rotation formula:

x' = 2a - x

y' = 2b - y

where (x,y) are the coordinates of a point on the original line, and (x',y') are the coordinates of the same point after rotation about the point (a,b).

Substituting the coordinates of two points on the line, we get:

(0,-1) → x' = 2(2) - 0 = 4, y' = 2(3) - (-1) = 7

(-1/2,0) → x' = 2(2) - (-1/2) = 4 1/2, y' = 2(3) - 0 = 6

Now, we can use the two points (4,7) and (4 1/2,6) to find the equation of the rotated line using point-slope form:

slope = (6-7) / (4 1/2 - 4) = -2

y - 7 = -2(x - 4)

y = -2x + 15

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The exponential function to represent the number of new participants of the challenge as a function of the day number, is f(x) = 12 × 4ˣ.

Let f(x) be the number of new participants on day x.

On day 0 (today), Aliyah, Kim, and Reese are the only participants. They each send selfies to 4 friends, so there will be 3 x 4 = 12 new participants on day 1.

From day 1 onwards, each new participant will send selfies to 4 friends. Therefore, the number of new participants will quadruple each day. This gives us an exponential growth function:

f(x) = 12 × 4ˣ

where f(x) represents the number of new participants on day x.

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Answer: 77

Step-by-step explanation: You could set up a proportion for this question. 1.5 centimeters = 3.5 meters x centimeters = 180 meters 1.5 x 180 / 3.5 Rounded to the nearest whole number, the answer is 77.

Each person would receive 10.67π square inches of pizza.

If 12 friends shared 8 small pizzas equally, we need to determine the amount of pizza each person would receive. To do this, we can start by calculating the total amount of pizza in all 8 small pizzas.

Assuming that each small pizza has the same size, we can divide the total amount of pizza by the number of people sharing it to get the amount of pizza each person would get.

Let's assume that each small pizza has an area of 10 square inches, for a total area of 80 square inches for 8 small pizzas. Dividing this area equally among 12 people, each person would receive approximately 6.67 square inches of pizza.

Alternatively, if we assume that each small pizza has a diameter of 8 inches, we can use the formula for the area of a circle to calculate the total area of each small pizza:

Area = π x (radius)^2

Area = π x (4 inches)^2

Area = 16π square inches

For 8 small pizzas, the total area would be:

Total area = 8 x 16π = 128π square inches

Dividing this area equally among 12 people, each person would receive approximately 10.67π square inches of pizza.

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Answer:

[tex]x=[/tex] ±[tex]\sqrt{10wy} - t[/tex]

Step-by-step explanation:

[tex](x+t)^2=10wy[/tex]

[tex]x+t=[/tex] ±[tex]\sqrt{10wy}[/tex]

[tex]x=[/tex] ±[tex]\sqrt{10wy} - t[/tex]

Using the above information, we can calculate the missing figures in the table and this is shown on the table attached.

For the "Shorts" row: It's given that 42 people were wearing shorts.

Therefore, the "Close-Toed Shoes" column in the "Shorts" row is also 42, and the "Total" column is the sum of open-toed and closed-toed shoes, which is 84.

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See text below

30 people surveyed were wearing open-toed shoes.

1/3 of the people with open-toed shoes were wearing

pants.

• 42 people were wearing shorts.

Twice as many people were wearing closed-toed shoes

than open-toed shoes.

Complete the table using the information given.

                   Open-Toed Shoes              Close-Toed Shoes         Total

Shorts                     -------                           ------                               --------

Pants                         ------                           ----------                            ------

Total                          ------                           ----------                            ---------

Therefore, angles ZACB and ZAXB are congruent, and since they are complementary to angles ZAO and ZBO, respectively, they must be supplementary.

The Circumscribed Angle Theorem states that an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs. More formally, if two chords of a circle intersect at point P, then the measure of the angle formed by the chords (let's call it angle ABC) is equal to half the sum of the measures of the arcs intercepted by the angle.

Here,

To prove that ZAXB and ZACB are supplementary, we need to show that the sum of their measures is 180 degrees. Here's the proof:

Given: ZAXB is a circumscribed angle of circle C.

To Prove: ZAXB and ZACB are supplementary.

Proof:

Draw circle C with center O and circumscribed angle ZAXB.

Draw radii OA, OB, and OC to the points of intersection A, B, and C.

Since XA and XB are tangent to circle C at points A and B, respectively, we know that angles OAX and OBX are right angles.

Therefore, angles ZAO and ZBO are complementary to angles ZAC and ZBC, respectively.

By the Inscribed Angle Theorem, we know that angles ZAO and ZBO are congruent to angle ZAXB.

Therefore, angles ZACB and ZAXB are congruent, and since they are complementary to angles ZAO and ZBO, respectively, they must be supplementary.

Thus, we have proven that ZAXB and ZACB are supplementary.

Therefore, the proof is complete.

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The walking distance that is saved by cutting across the lot is 55.

A right triangle, also known as a right-angled triangle, is a triangle that has one angle that measures 90° (a right angle). The remaining two angles are acute, or less than 90°

Apply right angle triangle rules;

⇒ 38² = (x+14)² + x²

⇒ 1444 = x² + 196 + 28x + x²

⇒ 2x² + 28x - 1248 = 0

⇒  x = 19 and x = -33

Therefore, the walking distance that is saved by cutting across the lot is:

⇒ x + x + 14

⇒ 19 + 19 + 14

⇒ 52

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The way Lucy used the statistics from her survey is not valid as the sample size she used (three of her classes at GTCC) is too small to accurately represent the entire population of college students nationwide.

In order to draw valid conclusions about the entire population, the sample size should be representative and large enough to minimize sampling errors. Lucy's sample size is too small and limited to her own classes, which may not be representative of the entire college student population. Therefore, her conclusion that nearly a third of college students plan to continue their education further is not necessarily accurate or reliable. A larger and more representative sample size would be required to obtain more accurate and reliable results.

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The circumference of the circle given the radius as 11 cm in terms of π is 22π cm.

Circumference of a circle = 2πr

Where,

Radius, r = 11 cm

Circumference of a circle = 2πr

= 2 × π × 11

= 22π cm

Ultimately, the circumference in terms of π is 22π.

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The trigonometry functions when calculated are sin(A) = 18/34 and cos(A) = 30/34

From the question, we have the following parameters that can be used in our computation:

The right triangle

Where we have

Using the above as a guide, we have the following:

sin(A) = 18/34

cos(A) = 30/34

Hence, the values are sin(A) = 18/34 and cos(A) = 30/34

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The volume of sand in the rectangular prism is 80 percent of the total volume, which can be written as:

0.8 x V = 0.8(L x W x H) cubic inches

A three-dimensional object with six faces, including two at the top and bottom and four lateral faces, called a rectangular prism. The prism's faces are all rectangular in shape. There are three sets of identical faces as a result.

We need to know the dimensions of the rectangular prism to solve the problem. Let's assume the dimensions are length = L inches, width = W inches, and height = H inches.

The volume of the rectangular prism is given by V = L x W x H cubic inches.

If the rectangular prism is filled 80 percent with sand, then 20 percent of the volume is empty space. So, the volume of sand in the rectangular prism is 80 percent of the total volume, which can be written as:

0.8 x V = 0.8(L x W x H) cubic inches

Therefore, we need to know the dimensions of the rectangular prism to find the volume of sand.

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The complete question is:

James fills the rectangular prism 80 percent with sand. How many cubic inches of sand are in the rectangular prism?

Therefore, the measure of angle XOB is 60 degrees.

The radius is the distance around a circle from its centre to its edge. For instance, if the circle's radius is 7 cm, its diameter will be 7 x 2, or 14 cm. You can find the diameter of a circle if you know its circumference and divide it by a certain number.

Since O is the circle's center, the inscribed angle theorem states that the length of the arc XOY is twice the length of the angle XOB.

We know that the measure of the arc XOY is 120, so:

2 * measure of angle XOB = measure of arc XOY

2 * measure of angle XOB = 120

measure of angle XOB = 60

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The measure of angle ZCOD is 27°.

Since A, O, and B are collinear, angles AOC and COB form a linear pair, which means their sum is 180°. Therefore:

x + 50° = 180°

Solving for x, we get:

x = 130°

Next, we can use the fact that angles AOC and BOA are vertical angles, which means they are congruent. Therefore:

x = 103°

Substituting x with 130°, we get:

130° = 103° + COD

Solving for COD, we get:

COD = 27°

Finally, since angles AOD and COB are alternate interior angles, they are congruent. Therefore:

77° = 50° + ZCOD

Solving for ZCOD, we get:

ZCOD = 27°

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--The complete question is, Given that points A, O, and B are collinear, find the measure of angle ZCOD, where:

Angle AOC is denoted by x and measures 90°

Angle BOA measures 103°

Angle AOD measures 77°

Angle COB measures 50°.

Please note that point O is located between points A and B.--

Ricardo used w/100 Ccf of water.

Given that, Ricardo household used w cubic feet of water in a month of summers,

we need to express the number of ccf of water they used algebraically,

Ccf = A CCF is a unit of measurement of volume.

The CCF is used to measure gas consumption, used in the billing of natural gas and water delivered to households.

1 CCF = 100 cubic feet

CCF means Centum Cubic Feet.

1 cubic feet = 0.01 Ccf

Therefore,

w cubic feet = 0.01 × w Ccf

= w / 100

Hence, Ricardo used w/100 Ccf of water.

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Therefore , the solution of the given problem of unitary method comes out to be to the water's surface on Tuesday is -55/1.

To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.

Here,

The scuba diver goes four times as deep on Tuesday than he did on Monday, which was -13.75 feet.

Let's determine the depth of the Tuesday dive by the scuba diver:

=> Depth on Tuesday equals 4 times Monday's depth.

=>  Tuesday's depth = 4 * (-13.75)

=>  Tuesday's depth = -55.

So, on Tuesday, the scuba diver goes down to a depth of -55 feet.

The diver's position with respect to the water's surface can be expressed as a rational number by writing it as -55/1 as -55 is already a whole number.

The rational number corresponding to the diver's position with respect to the water's surface on Tuesday is therefore -55/1.

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A congruence transformation that maps triangle RST to triangle UVW is a reflection along the line y = 1, followed by a translation 2 units right and down by 1 units.

A congruence transformation that maps triangle RST to triangle UVW is a rotation of 180°, followed by a translation 2 units left and down by 5 units.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-images underwent a sequence of congruence transformations to produce the images.

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Answer:

A(-6,0) B(-1,0) C(0,6)

Step-by-step explanation:

(A) When x=4, (AB)(4) = 2(4)³ + 3(4)² - 5(4) - 5 = 91. This means that the area of the rectangular tile when x=4 is 91 square inches.

(B) The expression (AB)(x) represents the area of the rectangular tile in square inches.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots.

A(x) represents the length of the rectangular tile in inches, and B(x) represents the width of the rectangular tile in inches.

A)

To find (A+B)(x), we add the expressions A(x) and B(x):

(A+B)(x) = A(x) + B(x)

= x² + 5 + 2x - 1

= x² + 2x + 4

When x=4, (A+B)(4) = 4² + 2(4) + 4 = 24. This means that the sum of the length and width of the tile when x=4 is 24 inches.

To find (AB)(x), we multiply the expressions A(x) and B(x):

(AB)(x) = A(x) * B(x)

= (x² + 5)(2x - 1)

= 2x³ + 3x² - 5x - 5

When x=4, (AB)(4) = 2(4)³ + 3(4)² - 5(4) - 5 = 91. This means that the area of the rectangular tile when x=4 is 91 square inches.

B)

The expression (AB)(x) represents the area of the rectangular tile in square inches. This is because the product of the length (A(x)) and width (B(x)) of a rectangle gives its area. So (AB)(x) is the formula for the area of the rectangular tile, which is a quadratic function of x.

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The percentage of the large pizza they ate is 100%

To calculate the percentage of pizza they both ate we have to add and then covert the fractions to percentage.

Given from the question

Frank ate 20% of the large pizza and Joey ate 4/5 portion of the large pizza

Converting 4/5 into percentage

For converting into percentage we have to multiply 100 to the fraction

= 4/5 x 100

= 80%

Now, let us proceed by adding the collected two percentages to find out the total percentage of pizza consumed by Frank and Joey

20% + 80%

= 100%

The percentage of the large pizza they ate is 100%.

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The value of test statistic is 2.553089.

A test statistic is a numerical summary of a sample that is used to make inferences about the population from which the sample was drawn. It is often used in hypothesis testing to determine whether a null hypothesis should be rejected or not.

The test statistic is calculated from the sample data and is compared to a distribution of the test statistic under the null hypothesis. If the test statistic falls in a region of the distribution that is unlikely to occur by chance, then the null hypothesis is rejected in favor of an alternative hypothesis.

Value of test Statistic = 1.34457321/0.526645738

= 2.553089

So, value of test statistic is 2.553089

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Step-by-step explanation:

There are 4 tens in a deck of 52  

    so  4/52   of getting  ten

       then 1 /52 for the ace of hearts

4/52 * 1/52 = 4/ 2704  = 1/676 =  .001  (rounded)  

We reject the null hypothesis relationally and come to decide that there is ample proof at the 0.05 importance threshold that suggests the average reading level of the work is below 5.

Plugging our values into the equation, we acquire t = (4.8 - 5) / (0.8 / ✓(40)) = -1.8257; where the degrees of freedom for this experiment is 39.

Turning to a t-distribution table or calculator, the p-value amounts to 0.0392 when making a one-tailed exam with 39 degrees of freedom.

Significantly, the p-value is lesser than the significance level of 0.05; thus, we reject the null hypothesis relationally and come to decide that there is ample proof at the 0.05 importance threshold that suggests the average reading level of the work is below 5.

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The surface area and volume of a cube with different edge length are

When a cube with edge length 4inches ,

Surface area = 96 square inches and Volume =64 cubic inches.

Cube dilated by scale factor 0.25 ,  

Surface area = 6 square inches and Volume =1 cubic inches.

The surface area of a cube is = 6 times the area of one face.

Each face of this cube has an area equals to

= (4 inches) x (4 inches)

= 16 square inches,

So the total surface area is,

Surface area

= 6 x 16 square inches

= 96 square inches

The volume of a cube =  length of one edge cubed.

Here, the edge length is 4 inches,

Volume

= (4 inches)^3

= 64 cubic inches

When a cube is dilated by a scale factor of 0.25, all of its edges are multiplied by 0.25.

This implies,

The edge length of the image cube is

0.25 x 4 inches = 1 inch.

Surface area of the image cube =  6 times the area of one face.

Each face of the image cube has an area of

= (1 inch) x (1 inch)

= 1 square inch,

So the total surface area is,

Surface area

= 6 x 1 square inch

= 6 square inches

Volume of the image cube = length of one edge cubed.

Here, the edge length is 1 inch,

Volume

= (1 inch)^3

= 1 cubic inch

Therefore, the surface area and volume for the given dimensions are

For edge length 4inches , Surface area = 96 square inches and Volume =64 cubic inches.

For scale factor 0.25 ,  Surface area = 6 square inches and Volume =1 cubic inches.

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Answer:

Step-by-step explanation:

the 32 pack because it costs just slightly more

The Pythagorean theorem to make problem-solving more accessible and efficient.

By incorporating technology into mathematical problem-solving, these tools help students and professionals alike in understanding and applying the theorem in various scenarios.

The Pythagorean theorem or provide a workaround. Here are a few tools that you might find useful:
GeoGebra:

GeoGebra is a dynamic geometry software that allows users to create, manipulate, and visualize geometric constructions.

It heavily relies on the Pythagorean theorem to explore and prove various geometric relationships.

GeoGebra can be accessed online or through its app, making it convenient and easy to use.
Desmos Graphing Calculator:

Desmos is an advanced graphing calculator that helps visualize and solve problems involving the Pythagorean theorem.

By plotting points, lines, and curves, you can explore the theorem's applications in various contexts, such as distances, vectors, and trigonometry.
Microsoft Math Solver:

This app allows you to input a math problem and receive step-by-step solutions.

It can solve problems related to the Pythagorean theorem, including finding side lengths and proving whether a triangle is a right triangle.
Wolfram Alpha:

Wolfram Alpha is a computational knowledge engine that can process queries and provide answers.

It is particularly helpful for solving problems based on the Pythagorean theorem. \

A problem, and Wolfram Alpha will provide a step-by-step solution, helping you understand the process better.

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There are indeed modern tools that help solve problems related to the Pythagorean theorem. Some of these tools include computer software, smartphone applications, and online calculators. These tools often provide a workaround or rely heavily on the Pythagorean theorem to solve various geometric and trigonometric problems, such as finding the length of a side in a right-angled triangle or determining the distance between two points in a coordinate system. By using these tools, users can easily and accurately apply the Pythagorean theorem to solve real-life problems or mathematical challenges.

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Part - A: For Sky View School has a mean is 50.8, a median is 50 and a mode is 25.

Riverside School has a mean is 9.93, a median is 20.5 and a mode is 20.

Part B: For Sky View School has a 1,298.16 is variance and For Riverside School has a variance is 477.0

Part C: Riverside School is a better choice because it has a higher maximum class size 57 compared to Sky View School 69.

Given that,

In the stem-and-leaf plot, information gathered about the composition of 15 classes at two separate schools is in the picture.

We know that,

Part - A:

For Sky View School has

The mean is  = 50.8.

The median is  = 50.

The mode is 25.

For Riverside School has

The mean is  = 9.93.

The median is  = 20.5.

The mode is 20.

Part B:

For Sky View School:

The range is 96 - 12 = 84.

The 25th percentile is the 4th value when the data is arranged in ascending order, which is 20. The 75th percentile is the 12th value, which is 60.

So, the IQR is 60 - 20 = 40.

Square of mean = -38.8, -33.8, -28.8, -25.8, -25.8, -25.8, -23.8, -20.8, -9.8, -7.8, 11.2, 11.2, 14.2, 21.2, and 45.2.

Now summation of the square of mean is 19,472.4

Now, dividing by 15 we have

= 1,298.16 is variance

For Riverside School:

The range is 25 - 2 = 23.

The 25th percentile is the 4th value when the data is arranged in ascending order, which is 5. The 75th percentile is the 11th value, which is 21.

So, the IQR is 21 - 5 = 16.

The deviations from the mean are: -19.7, -9.7, -9.7, -9.7, -9.7, -9.7, -9.7, -9.7, 0.3, 0.3, 10.3, 20.3, 20.3, 20.3, 27.3.

The sum of squared deviations is 6678.7.

Variance =  = 477.0

Part C:

Riverside School is a better choice because it has a higher maximum class size of 57 compared to Sky View School 69.

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Terrell hit 0.8 of his home runs during the first half of the baseball season, which is the decimal equivalent of the fraction (4)/(5).

A fraction is a way of representing a part of a whole, where a whole is divided into equal parts and the fraction represents the number of those equal parts that are being considered.

A decimal number is a number expressed in the base-ten positional system, where each digit can take one of ten possible values and the value of each digit is determined by its position relative to the decimal point.

To write a fraction as a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). In this case, the fraction is (4)/(5), which means Terrell hit 4 out of 5 home runs during the first half of the season

(4)/(5) = 0.8

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The given question is incomplete, the complete question is:

Terrell hit a total of 10 home runs during the baseball season. He hit (4)/(5) of the home runs during the first half of the season. Write the fraction of home runs hit during the first half of the season as a decimal.

The optimal measure of variability is the IQR, which equals 4. The proper measure of variability for the data is C.

The difference among the third and the first quartile is defined by the interquartile range. The entire series is divided into four equally sized pieces by the partitioned values referred to as quartiles. Three quartiles are present.

The spread of the middle 50% of the data, which is less susceptible to outliers than the range, is measured by the interquartile range (IQR), which is the best measure of variability for these data.

The IQR is calculated by deducting the third quartile ([tex]Q_3[/tex]) from the first quartile ([tex]Q_1[/tex]). We can see from the box plot that [tex]Q_1[/tex] is roughly

17 and [tex]Q_3[/tex] is roughly 21.

Therefore,

[tex]IQR=Q_3-Q_1\\\\IQR=21-17\\\\IQR=4[/tex]

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Answer:

The center of the circle is at (-6, 14), and the radius is 15, so we have this equation:

[tex] {(x + 6)}^{2} + {(y - 14)}^{2} = 225 [/tex]