what are the two related linear equations for |x – 2| = 5.

Step-by-step explanation:

[tex] {x}^{2} + 5x + 6[/tex]

[tex] {x}^{2} + 6x - x + 6[/tex]

[tex]x(x + 6) - 1(x + 6)[/tex]

[tex](x - 1)(x + 6)[/tex]

Answer: love=an intense feeling of deep affection

Step-by-step explanation:

a) 49 square tiles are needed to make pattern number 7

b) 84 circular tiles are needed to make pattern number 20

c) When the pattern number is odd, the total number of tiles (square

and circular) needed to make the pattern is B) always odd

A sequence in mathematics is an enumerated collection of objects in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the sequence is defined as the number of elements (which could be infinite). Unlike a set, the same elements can appear multiple times in a sequence at different positions, and the order does matter. Formally, a sequence can be defined as a function from natural numbers (the sequence's positions) to the elements at each position. The concept of a sequence can be extended to include an indexed family, which is defined as a function from an arbitrary index set.

a) Squares tiles needed for 7 pattern =n²

n²=7²

n²=49

b) Circular tiles for 20th pattern=4(n+1)

=4(20+1)

=4(21)

=84

c) Total tiles(square and circle)

=n²+4(n+1)

for n=odd (let n=1,3,5)

n=1; 1+4(1+1)=9

n=2;  9+4(3+1)=25

n=5;  25+4(5+1)=49

Therefore, It is always odd

So, the answer is option B

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Answer:

Step-by-step explanation:

Down payment = $150

Monthly Payment = $48.5

Buyer price = $1250

Number of months = 30  (2 1/2 years)

The total amount of monthly payments = Monthly payments × Number of months

                                                                  = 48.5 × 30

                                                                  = 1447.50

The total cost = Total amount of monthly payments + Down payments

                       = 1447.50 + 150

                       = 1597.50

Finance charge =  Total cost  - Buyer price

                          = 1597.50 - 1250

                          = 347.50

The smallest positive integer a such that the intermediate value theorem guarantee a zero exist between 0 and 1

given that

polynomial f(x) = 2[tex]x^{3}[/tex] - [tex]x^{2}[/tex]- 4x+4

first derivation of f(x)

f'(x) = 6[tex]x^{2}[/tex] - 2x - 4

      = 6[tex]x^{2}[/tex] - 6x +4x -4

      = 6x(x-1) + 4(x-1)

     = (6x+4)(x-1)

x = -0.6,1

second derivation of f(x)

f''(x) = 12x-2

now substitute x values in f''(x)

x=1

f"(x) = 12(1) - 2 = 12-2= 10

x= -0.61

f"(x) = 12(-0.61) -2 = -7.32-2= -9.32

a=1

the intermediate value theorem guarantee a zero exist between 0 and 1

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Using ratios we know that 40 hamburgers will be served.

So, a number of hamburgers that will be served are:

So, the number of hamburgers will be:

Therefore, using ratios we know that 40 hamburgers will be served.

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Correct question:
A concession stand serves hot dogs and hamburgers at a ratio of 3 to 2. Based on this ratio, how many hamburgers will be served if there are a total of 60 hot dogs served?

Relay exchanges will not take place at any of the 0.25-mile markers

The calculated relay exchanges are

The number of team members which is 9 is equal to the number of relay exchanges in the 4-mile race.

This will result to the relay exchanges occurring at  every 4/9, and repeated addition of 4/9 will give the  other points, and the list is

4/9, 8/9, 4/3, 16/9, 20/9, 8/3, 20/9, 32/9, and 4 in fraction

In decimal form this will be listed in four decimal place

0.4444

0.8889

1.3333

1.7778

2.2222

2.6667

3.1111

3.5556

4

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After solving the exponential function y = 12.5ˣ, the value of y = 1.

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0.

The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

So, the exponential function:

y = 12.5ˣ

We know that x is 0.

The exponential function rule states that when the power is 0, the answer is always 1.

y = 12.5ˣ

y = 12.5⁰

y = 1

Therefore, after solving the exponential function y = 12.5ˣ, the value of y = 1.

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Correct question:

For this exponential function, what is the output value (y), when the input value (x) is O?

y = 12.5ˣ

Answer: -10/6

Step-by-step explanation:

Using the Slope Formula which is, [tex]\frac{y_{2} -y_1}{x_2-x_1}[/tex] you can substitute the numbers. This leads to [tex]\frac{-1 -9}{-1-(-7)}[/tex] which will get you, [tex]\frac{-10}{6}[/tex].

Answer: try a c and e

Step-by-step explanation:

Answer:87,600

Step-by-step explanation:

Answer: it’s a vertical line going through the point (6,0)

Step-by-step explanation: this is because when you only have an x value the line is going to be vertical line through the x value on that axis

The least angle at which given figure maps onto itself is 180°. This can be understand by using magnitude of symmetry.

What is symmetry?

In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more precise definition of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Although these two interpretations of "symmetry" can occasionally be distinguished from one another, they are intricately linked and are therefore discussed jointly in this article. Aspects of mathematical symmetry can be seen in abstract objects like theoretical models, language, and music, as well as in the passage of time, as a spatial relationship, through geometric transformations, and in other types of functional transformations.

A figure in the plane has rotational symmetry if the figure can be mapped into itself by a rotation between 0° to 360° about the center of figure.

The given figure has one line of symmetry,

figure is divided into two parts that can overlap

angle will be = 360/2=180° .

So, the smallest angle is 180°.

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Answer:

115°

Step-by-step explanation:

They are the same angle because we know the lines are parallel.

Answer:

115°

Step-by-step explanation:

alternate exterior, they're the same

The amount of time it takes for the cannonball to strike the ground is equal to 6.516 seconds.

Based on the information provided, we can logically deduce that the height (h) in meters, of this cannonball during above the​ ground is related to time by the following function:

h(t) = - 4.9t² + 30.5t + 9.3.

Generally speaking, the height of this cannonball would be equal to zero (0) when it strikes the ground. Therefore, we would equate the height function to zero (0):

0 = - 4.9t² + 30.5t + 9.3.

4.9t² - 30.5t - 9.3 = 0

Next, we would solve the quadratic equation by using the quadratic formula:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-30.5)\; \pm \;\sqrt{(-30.5)^2 - 4(4.9)(-9.3)}}{2(4.9)}\\\\x = \frac{30.5\; \pm \;\sqrt{930.25\; + \;182.28}}{9.8}\\\\x = \frac{30.5\; \pm \;\sqrt{1112.53}}{9.8}[/tex]

Time, x = (30.5 ± 33.3546)/9.8

Time, x = (30.5 + 33.3546)/9.8

Time, x = 63.8546/9.8

Time, x = 6.516 seconds.

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Answer:

Step-by-step explanation:

24

The slopes are similar in each segment of the line because the ratios, 8/2 and 4/1 are similar.

The first step to understanding slope of a line is that; it represents the rate of change in the vertical axis to that in the horizontal axis.

Consequently, it follows that the slope of the first segment can be computed by drawing a triangle with vertical side length of 4 and a horizontal side length of 1.

Hence, the slope of the first segment (from the triangle is) 4 / 1.

Also, for the second segment; a triangle with vertical length; 8 and a horizontal length, 2. Hence, the slope of the segment is; 8 / 2.

Ultimately, since the ratios, 8 / 2 and 4 / 1 are similar, it follows that the two triangles are similar and consequently, the slope is same in each segment of the line.

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The equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1

The line is passing through the y intercept = (0, 1)

Here at x = 0, the values of y = 1

Then the y intercept of the line is 1

The slope of the line = 4

The slope of the line is the change in y coordinate with respect to the change in x coordinates of the function

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

x is the x coordinate

y is the y coordinate

Then the equation in the slope intercept form

y =4x + 1

Hence, the equation in slope intercept form of the line that passes through the y-intercept (0, 1) and has a slope of 4 is y = 4x + 1

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Answer:

x = 4 or x = 6

Step-by-step explanation:

to solve the inequality

solve both

x - 3 = 9 - 2x OR x - 3 = - (9 - 2x)

x - 3 = 9 - 2x ( add 2x to both sides )

3x - 3 = 9 ( add 3 to both sides )

3x = 12 ( divide both sides by 3 )

x = 4

OR

x - 3 = - (9 - 2x)

x - 3 = - 9 + 2x ( subtract 2x from both sides )

- x - 3 = - 9 ( add 3 to both sides )

- x = - 6 ( multiply both sides by - 1 )

x = 6

The erosion occurs at a rate of 2/1000 m/years. Over 1,000,000 years, the erosion will be 2,000 meters.

Rate is a ratio between one quantity to another quantity. Rate is also a measure of how fast a quantity changes when another quantity changes. For instance, velocity is a rate to measure the change of distance per amount of travelled time.

Suppose we have two quantities: x and y, with rate of change in y per change in x is denoted by dy/dx, then

y = dy/dx · x

In the given problem:

y = length of erosion

t = time

dy/dt = 2 meters / 1000year = 2/1000 meters/year

Then,

y = dy/dt · t

  = 2/1000 · 1,000,000 = 2,000 meters

Hence, over  1,000,000 years, the regional erosion = 2,000 meters

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Answer:150 minutes easy?

Step-by-step explanation:

The product of two rational numbers is always rational because (ac/bd​) is the ratio of two integers, making it a rational number.

We need to prove that the product of two rational numbers is always rational. A rational number is a number that can be stated as the quotient or fraction of two integers : a numerator and a non-zero denominator.

Let us consider two rational numbers, a/b and c/d. The variables "a", "b", "c", and "d" all represent integers. The denominators "b" and "d" are non-zero. Let the product of these two rational numbers be represented by "P".

P = (a/b)×(c/d)

P = (a×c)/(b×d)

The numerator is again an integer. The denominator is also a non-zero integer. Hence, the product is a rational number.

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Answer:

scalene acute

Step-by-step explanation:

scalene = 2 sides are the same and one is different

acute = all three angles are smaller than 90

Answer:

Step-by-step explanation:

5.8, 5.8042, 5.84, 6.328

The length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.

According to the question,

We have the following information:

The perimeter of an isosceles triangle is 48 inches. Each leg is 6 inches less than two times the base.

We know that in an isosceles triangle two sides are equal.

Let's take the base of the triangle to be x inches.

Other sides = (2x-6) inches

So, we have the following expression:

2x-6+2x-6+x = 48

5x-12 = 48

5x = 48+12

5x = 60

x = 60/5

x = 12 inches

Now, the other two sides of triangle:

2*12-6

24-6

18 inches

Hence, the length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.

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The cost of one pound is $3.3 or the rate of per pound fruits is $3.3.

What is meaning of one pound?

Pound is an unit to measure mass of an object. The plural form of pound is pounds.

What is the unitary method?

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that Miranda buys 5.1 pounds of avocados at the local store. The cost of the fruits is $16.83.

Apply unitary method to calculate the cost of 1 pound:

The cost 5.1 pounds fruit is $16.83.

The cost 1 pound fruit is $16.83/5.1 = $3.3.

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Three betas will be in our model aside from the y-intercept.

In the given question, we have to find how many betas will be in your model aside from the y-intercept.

You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day.

While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear.

You decide not to test for interactions.

From the given question,

We have y intercept that means our model well be

[tex]y=\beta_{0}+x_{1}\beta _{2}+x_{2}\beta _{2}+x_{1}x_{2}\beta _{12}[/tex]

where [tex]\beta _{1}[/tex] is for temperature and [tex]\beta _{2}[/tex] is day of the week.

3 betas are there aside intercept of y.

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-4 is the absolute value of -3.5 and three fifths.

An expression is combination of variables, numbers and operators.

negative absolute value of negative three fifths.

−3.5-3/5

Three fifths means three by five

-3.5-3/5

(-5(3.5)-3)/5

Minus seventeen point five minus three divided by five

-17.5-3/5

Minus twenty point five divided by five

-20.5/5

Minus four point one

-4.1

-4

Hence -4 is the absolute value of -3.5 and three fifths.

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Answer:

  11 mi/h

Step-by-step explanation:

You want the speed of the boat when it travels 12 miles upstream against a current of 5 mph in the same time it travels 32 miles downstream with the current.

The relation between time, speed, and distance is ...

  time = distance/speed

If b represents the speed of the boat, the times upstream and downstream are the same, so we have ...

  (12 mi)/(b -5) = (32 mi)/(b+5)

Multiplying by the product of the denominators gives ...

  12(b+5) = 32(b-5) . . . . . . also divided by "mi"

  12b +60 = 32b -160 . . . . multiply by (b+5)(b-5)

  220 = 20b . . . . . . . . . . . . add 160 -12b

  11 = b . . . . . . . . . . . . . . . . . divide by 20

The speed of the boat in still water is 11 miles per hour.

__

Additional comment

Each trip took 2 hours.

Answer:

750 miles

Step-by-step explanation:

20 gallons -------------- 300 miles

1 gallon ---------------- 300/20 = 15 miles

50 gallons -------------- 15x50 = 750 miles