Draw a triangle with vertices A(0, 4), B(2, -2), and C(-2, -2). Apply a dilation centered at the origin with scale factor to this triangle and draw the resulting triangle,A'B'C'. In complete sentences, describe the following:

a,The relationship between corresponding sides in terms of their lengths.
b.The relationship between corresponding sides in terms of their orientations.
c.The relationship between corresponding angles in terms of their measures.

Answer:

We can use the triangle inequality theorem to determine the possible lengths of the third side of the triangle. According to the theorem, the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

So, for a triangle with sides of length 16 and 17, the length of the third side must satisfy the following inequality:

17 - 16 < third side < 17 + 16

1 < third side < 33

Therefore, the length of the third side must be described by the expression:

1 < third side < 33

Step-by-step explanation:

The dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.

The area of Rectangle is length times of width.

Area of rectangular pool = 6x² − 11x + 3

To factor the trinomial, we need to find two binomials that multiply together to give the trinomial 6x² − 11x + 3.

We use product-sum method of factoring to find the two binomials.

We need to find two numbers that multiply to 6 (the coefficient of the x² term) and add to -11 (the coefficient of the x term).

6x² − 11x + 3

6x² −2x-9x + 3

(2x − 1)(3x − 3)

Hence, the dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.

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x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

[tex]y=b_1x+b_0[/tex]

There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.

Given a collection of pairs (x,y) of numbers, there is a line [tex]y=b_1x+b_0[/tex] that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.

[tex]b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)[/tex]

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

[tex]y=b_1x+b_0[/tex]

specifying the least squares regression line is called the least squares regression equation.

Example,

Find the least squares regression line for the five-point data set

x = 2  2  6  8  10  

y=  0  1   2  3  3.

compute the table,

x   y     x2         xy

2  0     4           0

2  1      4            2

6   2   36       12

8   3   64        24

10  3   100    30

28  9   208    68   (sum)

[tex]S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125[/tex]

The regression line is y=0.34375x-0.125

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The value of the length, x is 5√3

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

Rise = 11

Length = x

Hypotenuse = 14

The value of the length , x is calculated as

x^2 = Hypotenuse^2 - Rise^2

Substitute the known values in the above equation, so, we have the following representation

x^2 = 14^2 - 11^2

So, we have

x^2 = 75

Take the square root of bpth sides and evaluate

x = 5√3

Hence, the value of x is 5√3

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Answer:

Area = 452 cm²

Step-by-step explanation:

[tex] = \frac{\pi }{4} {d}^{2} [/tex]

[tex] = \frac{\pi}{4} {(24)}^{2} = 452.39 \: cm²[/tex]

Answer:no

Step-by-step explanation:

if it was then it supposed to be like 4*20=5*15 which is not right equation

Answer:

1. S = 20w + 100

2. M = -400w + 3,500

Step-by-step explanation:

1. Since Mateo is starting with a balance of $100, we can set this as our constant term (the 'b' in y = mx + b). Every week, he earns $20, so we can set this as the coefficient on the variable w (which represents how many weeks have passed).

2. Emily is spending money in this situation, so the coefficient on w is negative, as the amount of money she has left is getting smaller. The exact amount that she spends each week is $400, so the negative of that is going to be the coefficient of w in the equation. We can set the constant term in this equation to $3500, as Emily starts with that much money when no weeks have passed (when w = 0).

Answer:

The mass of 3.5 moles of Ca (Sodium)  is 140 g to two significant figures.

The value of x for the given circle is 115°.

Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and properties of objects in space. It includes the study of points, lines, planes, angles, curves, surfaces, and solids.

Using the Angles of Intersecting Chords Theorem,

When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

So, angle x = (190° + 40°)/2  = 115°

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The solution to the simultaneous equation given is (3, 4)

Given the system of equation below

2x+y=10

3x-y=5

From equation 2, the value of y is expressed as:

y = 3x - 5

Substitute the result into equation to have:

2x + 3x - 5 = 10

5x - 5 = 10

5x = 15

x = 3

Since y = 3x - 5

y = 3(3) - 5

y = 4

Hence the solution to the system of equation is (3, 4)

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The Credit Score is 4274274274274274.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

A phrase is used to describe each number in the series.

Given:

The sum of any three adjacent digits is 13.

The  second digit is 2 and the tenth digit is 4.

So, _2_ _ _ _ _ _ _ 4 _ _ _ _.

Now, the 2nd, 5th, 8th, 11th, 14th digits are equal and so are the 3rd, 6th, 9th, 12th, 15th.

So, the credit card number is 4274274274274274 and the last three digits are 274 which shows the sum is 13.

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The weighted average of the numbers is 0.1.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

Given that, average of the numbers -3 and 5 with 3/5

The weight of first number and 2/5 of second number.

Here, -3(3/5)+5(2/5)/2

= (-1.8+2)/2

= 0.2/2

= 0.1

Therefore, the weighted average of the numbers is 0.1.

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Answer:

Step-by-step explanation:

75%

the matches are

-2(2x+5) ≤ -7(x+4)         x<=-6

4x-3x-1                          x<=-1

5(x-3)9(x+1)                   x>=-6

3(x-4)+5 2x-9                x>=-2

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

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The correct matching of the inequalities can be shown from the calculations below

Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.

Using the principle of inequalities we have;

1) -2(2x + 5) ≤ - 7(x + 4)

-4x -10 ≤ -7x -28

-4x +7x ≤ -28 + 10

3x ≤ -18

x ≤ -6

2) 4x - 6/2 ≥ 3x - 1

4x - 6 ≥ 6x - 2

4x - 6x ≥ -2 + 6

-2x ≥ 4

x  ≤ -2

3) 5(x - 3) ≤ 9(x + 1)

5x - 15  ≤ 9x + 9

5x - 9x  ≤ 9 + 15

-4x  ≤ 24

x ≥ -6

4) 3(x - 4) + 5 ≥ 2x - 9

3x - 12 + 5≥ 2x - 9

3x - 2x ≥ -9 + 12 -5

x ≥ -2

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skiing for 5 hours will make the cost of skiing at both ski resorts equal.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, Bunny Hill Ski Resort charges $50 for ski rentals and $5 per hour of skiing, while Black Diamond Ski Resort charges $25 for rentals and $10 per hour of skiing.

Let's define:

x as the number of hours of skiing

C₁ as the total cost of skiing at Black Diamond ski resort

C₂ as the total cost of skiing at Bunny Hill ski resort

At Black Diamond ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:

C1 = 25 + 10x

At Bunny Hill ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:

C₂ = 50 + 5x

We want to find at what point C₁ = C₂, so we set the two equations equal to each other:

25 + 10x = 50 + 5x

Simplifying the equation, we get:

5x = 25

Dividing both sides by 5, we get:

x = 5

Therefore, skiing for 5 hours will make the cost of skiing at both ski resorts equal.

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From the sum of the interior angles, it is possible to find x=70°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square, all angles are 90° and all sides present the same value.

The sum of the interior angles of a quadrilateral is equal to 360°.

The question gives a trapezoid and its respective angles. Thus,

x+85+150+55= 360

x+140+150=360

x+290=360

x=360-290

x=70°

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Answer:

b) 70°

Step-by-step explanation:

We know that,

→ The sum of all interior angles in a quadrilateral is 360°.

Now we have to,

→ Find the required value of x.

Forming the equation,

→ 85° + 150° + 55° + x = 360°

Then the value of x will be,

→ 85° + 150° + 55° + x = 360°

→ 290° + x = 360°

→ x = 360° - 290°

→ [ x = 70° ]

Hence, the value of x is 70°.

60 kilometers per hour (kph) is equal to  roughly 37.28  long hauls (miles) per hour( mph).

To convert kilometers per hour to long hauls per hour, you can use the following conversion formula:

long hauls per hour =  kilometers per hour x0.621371.

Plugging in 60 kilometers per hour, we get,

long hauls per hour =  60 x0.621371  

long hauls per hour ≈37.28.  

Thus, 60 kilometers per hour is roughly 37.28 long hauls per hour.  

A kilometer (km) is a unit of length or distance used in the metric system. It is roughly original to 0.621  long hauls.

Mile is a unit of length or distance used in the customary system of dimension, primarily in the United States and United Kingdom. One afar is original to 280 bases or 760 yards, which is  roughly 1.609 kilometers in the metric system.

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The percentage of decrease is 20%

First, if we have an initial value A, and we increase it by x (a percentage in decimal form) then the new value will be:

A' = A*(1 + x)

Whle a decrease is written as:

A' = A*(1 - x)

In this case we have an increase of the 25%, it is written as:

A' = A*(1 + 0.25)

A' = A*1.25

IF we pass the factor to the other side, will get:

(1/1.25)*A' =  A

(0.8)*A' = A

Now we want to write the coefficient on the left in the form (1 - x)

We will get:

0.8 = 1 - 0.2

0.2 is the percentage (in decimal form) decreased  from A' to get A. Then the answer is 20%.

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In a case whereby two planes, which are 2235 miles apart, fly toward each other. Their speeds differ by 45 mph. If they pass each other in 3 hours, the speed of slower is 350mph and faster is 395mph.

The concept here is simplification.

Let represent the speed of the slower plane using the( x),

Let us represent the speed of the faster to be ( x + 45)

The distance traveled  that can be associated to the slower plane ( 3x).

then the distance that can be attributed toi that of the faster plane = 3(x + 45).

given that the  total distance=(2235 miles).

[3x + 3(x + 45) ]= 2235

3x + 3x + 135= 2235

[6x ]= 2235-135

6x = 2100

x=350

hence,  the speed of the slower plane is 350

the speed of the faster= x + 45 = 350+45= 395

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The speed of first plane is 350 miles/hour and the speed of second plane is 395 miles/hour .

Given, Distance between the planes = 2235 miles

Let, the speed of the first plane be 'x' miles/hour.

Let, the speed of the second plane be 'x+45' miles/hour.

Since, they are flying towards each other, their speed will get added.

The collective speed of both the planes = (2x + 45) m/h.

A/Q, they pass each other in 3 hours, i.e. they collectively covers the distance of 2235 miles in 3 hours.

We know Distance = Speed × Time

Given, Distance = 2235 miles , Time = 3 hours , Speed = (2x + 45) m/h

                      2235 = 3  × (2x + 45)

                       745 = 2x + 45

                        x = 350 miles/hour.

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A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

Mixture word problems require you to combine two or more separate items, and then calculate some quantity of the resulting mixture (such as a percentage, price, or number of liters, for example). There will always be some type of "rate," like miles per hour or price per pound. Mixtures are substances that contain two or more distinct substance categories. To separate them, utilize physical tools. Examples include air, different gases, a mixture of sugar and water, a solution of salt and water, and so on.

here, we have,

Given,

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution.

Equation:

X + y = 119

y = 119 - x

0.40x + 0.12y = 119 of 0.32

0.40x + 0.12y = 38.08

Using y = 119 -x

0.40x + 0.12(119 - x) = 38.08

0.40x + 14.28 - 0.12x = 3808  Eq(2)

0.28x = 23.8

x = 85

and,

y = 119 - 85

y = 119 - 85

y = 34

Equating values in equation (2),

=0.40(85) + 0.12(34)

=34 + 4.08

=38.08

A pharmacist wants to mix a 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

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Answer:

7/10

Step-by-step explanation:

Here ya go!

The coordinates of A' in triangle A'B'C' which was produced after reflection with condition y =x is equal to option d. ( 1, 2).

Graph is attached.

Triangle A'B'C' is produced after reflection of the triangle ABC over the line y = x.

From the graph we have ,

Coordinates of A is ( 2 , 1)

Coordinates of B is (-1, 4)

Coordinates of C is ( 0, -2)

Condition of reflection of triangle ABC over the line y = x.

x-coordinates replace by y and y replace by x.

Coordinates of triangle A'B'C' are

Coordinates of A' is ( 1, 2)

Coordinates of B' is (4, -1 )

Coordinates of C' is ( -2, 0 )

Therefore, if the coordinates of point A in triangle ABC are (2, 1), the coordinates of point A' in triangle A'B'C' would be option d. (1, 2).

The above question is not complete , the complete question is:

Triangle ABC is reflected over the line y = x to produce triangle A'B'C'. What will be the coordinates of A'? Graph is attached.

a.  (2,−1)            b.  (−2,−1)                 c.  (2,1)                d.  (1,2)

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Answer:

180 - 119.4 = 60.6

So the answer is 60.6

Answer:

60.6°

Step-by-step explanation:

Supplementary angles equal 180 degrees. So we can show this with the following equation:

119.4 + x = 180

where x is the measure of the other supplementary angle.

If we subtract 119.4 from both sides, we get the the value of x, which is 60.6.

The value of x is  15√2

The value of the side y is 30

The sum of angles in a rectangle is 360 degrees

To determine the value of the variable, x

Let's use the trigonometric identity, cosine

cos = adjacent/hypotenuse

substitute the values

cos 45 = 15/x

Find the value

1/√2 = 15/x

cross multiply

x = 15√2

For y, we have;

sin 45 = y/15√2

1/√2 = y/15√2

Make y subject

y= 15√2 /√2

y = 60/2

y = 30

Hence, the values are 30 and 15√2

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90 degrees Fahrenheit is equal to approximately 32.2 degrees Celsius using conversion formula method.

To convert Fahrenheit to Celsius, the following formula can be used:

Celsius = (Fahrenheit - 32) x 5/9

Plugging in 90 degrees Fahrenheit, we get:

Celsius = (90 - 32) x 5/9

Celsius = 58 x 5/9

Celsius = 290/9

Celsius ≈ 32.2

Therefore, 90 degrees Fahrenheit is approximately 32.2 degrees Celsius.

Fahrenheit is a temperature measurement system developed by the German physicist Daniel Gabriel Fahrenheit in 1724.

The Celsius scale is widely used throughout the world for measuring temperature, and it is the standard unit of temperature used in most scientific research and international trade. In addition to measuring air temperature, Celsius is used to measure temperature in a variety of fields, including chemistry, biology, and engineering.

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The length of the slide shown is 15 feet

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let l represent the length of the slide, hence:

sin(53) = 12/l

l = 12/sin(53)

l = 15 feet

The length is 15 feet

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In linear equation, $869,776  will her total payment for the home be .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.

The number is $6.74.

That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.

2. Amount borrowed

You will make a 22% down payment:

Thus the amount borrowed is $426,000 - $93,720 = $332,280

3. Monthly payment

Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:

4. Total monthly payments:

Multiply the number of payments by the monthly payment.

Number of payments = 20 years × 12 payments /year = 240 payments.

5. Total payment for the home.

The total payment for the home will be the down payment plus the amount paid to the bank:

$322,280 + $537,496 = $869,776

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Answer:

Step-by-step explanation:

Put ' - 3' whre 'x' is and compute the answer

f(-3) = 3 (-3) - 7

      = -9 - 7 = - 16

The solution is, B = 245, is a Reflex Angle., when it is given that A=65.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

We know that, a ray is a line that continues on forever inn one direction with a point at it's start.

here, we have,

A = 65°

now,  B is a Reflex Angle ,

so, we know that Reflex Angle means the angle with value >180 to <270.

now, we get,

B = 180 + 65

  = 245

Hence, The solution is, B = 245, is a Reflex Angle.

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