Find the distance between each pair of parallel lines with the given equations).
y=2 x-3
2 x-y=-4

Yes, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5  ,both are equals to (-1/5).

As given in the question,

Given number is 5

Case 1 : First find reciprocal of 5

Reciprocal of 5 =1/5

Then, opposite of the reciprocal of 5 =(-1/5)

Case 2. First find the opposite of 5

Opposite of 5 =-5

Reciprocal of the opposite of 5 =(1/ -5)

                                                =(1/-5) × (-1/-1)

                                                =(-1/5)

Therefore, the opposite of the reciprocal of 5 is same as the reciprocal of the opposite of 5  ,both are equals to (-1/5).

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Answer:

Step-by-step explanation:

solve by factoring

you get x=3/2

The value of A in the 4-digit number, 3A5A is 5.

The 4-digit number provided in the question has to be a multiple of 15 given the information in the question. A multiple of a number is divisible by that number. A multiple of 10 is 100 because when 100 is divided by 10 , the value gotten is 10.

A multiple of a number is the product of an integer and that number. For example, a multiple of 2 is 100. This is because 2 multiplied by 50 is equal to 100.

The multiplies of 15 either have a unit value of 5 or 0.

If A is 5, the number becomes 3555.

3555 / 15 = 237

If A is 0, the number becomes 3050

3050 / 15 = 203.33

Thus, the value of A is 5 because 3555 is divisible by 15.

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Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of an obtuse triangle (altitudes). Take note of how these three centers interact with one another.

An obtuse-angled triangle or obtuse triangle is one in which one of the angles is an obtuse angle or greater than 90°. The sum of the obtuse triangle's interior angles is only 180°. This means that the angle sum property of any triangle remains unchanged.

An obtuse-angled triangle is one in which one of the interior angles is greater than 90°. If one angle in an obtuse triangle measures more than 90°, the sum of the remaining two angles is less than 90°.

Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of an obtuse triangle (altitudes). Take note of how these three centers interact with one another.

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Answer:

Step-by-step explanation:

where?

Restaurant A offers the best value as one hamburger is $1.29

The first step is to calculate the price of one burger in restaurant A

11= 14.19

1= x

cross multiply

11x= 14.19

x= 14.19/11

x= 1.29

The next step is to calculate the price on one burger in restaurant B

2= 2.64

1= x

Cross multiply

2x= 2.64

x= 2.64/2

x= 1.32

Hence the price of the hamburger at Restaurant A is $1.29 and the price at Restaurant B is $1.32.

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Answer:

(A) Restaurant A for $1.29

Step-by-step explanation:

Got it right on my quiz.

Answer: M(-4.75,-6.25)

Step-by-step explanation:

C(-3,-8)    D(-6.5,-4,5)

Let the midpoint of C(-3,-8) and D(-6.5, -4.5) is M(x,y)

[tex]\displaystyle\\M(x,y)=(\frac{-3+(-6.5)}{2} ,\frac{-8+(-4.5)}{y} )\\\\M(x,y)=(\frac{-9.5}{2},\frac{-12.5}{2})\\\\M(x,y)=(-4.75,-6.25)\\\\Thus, \ M(-4.75,-6.25)[/tex]

Answer:

x=-9

Step-by-step explanation:

x=-9

Thank you so much!

By substitution, the solution of the system of equations, 3c + 2d = 2 and d = 4, is (c , d) = (-2 , 4).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in variables c and d,

3c + 2d = 2     (equation 1)

d = 4     (equation 2)

Since the second equation is already expressed in d in terms of a constant, substitute the second equation to the first equation.

3c + 2d = 2     (equation 1)

3c + 2(4) = 2

3c + 8 = 2

Combining all terms containing the variable c on one side and the constants on the other side of the equality, and solving for c.

3c + 8 = 2

3c = 2 - 8

3c = -6

c = -6/3

c = -2

Hence, the solution of the given system of equations is (c , d) = (-2 , 4).

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Answer:

26 and 32 are the two numbers, the product is 832

Step-by-step explanation:

Answer: 2n+5-3

Step-by-step explanation:

Break this quote down:

"three less than the product of a number and two, increased by five"

To this:

"three less than the product" ==> product-3

Now break this quote down

Product: "product of a number and two, increased by five"

To this:

"product of a number and two" ==> 2*n

"increased by five" ==> +5

"product of a number and two, increased by five" ==> 2*n+5

Product: 2*n+5

Product-3: 2*n+5-3=2n+5-3

The baseball field mark up its organic hotdogs from $2.00 to $6.50 each by 225%.

The markup on cost is defined as the amount added to the original cost of a product or service to arrive at the new selling price. It can also be a percentage of the original cost.

mark up = selling price - original price

If organic hotdogs at the grocery store cost $2.00 each and at a major league baseball game, an organic hotdog cost $6.50, then the mark up price is the difference between the two.

mark up = selling price - original price

mark up = $6.50 - $2.00

mark up = $4.50

To get the percentage of the mark up from the original price, divide the mark up price by the original selling price and multiply by 100%.

percent mark up = (mark up price/original price) x 100%

percent mark up = ($4.50/$2.00) x 100%

percent mark up = 2.25 x 100%

percent mark up = 225%

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answer=

Children =5

Adults = 3

3/8 are adults

It looks like you want to find

[tex]\displaystyle \int_1^4 x f''(x) \, dx[/tex]

Integrate by parts:

[tex]u = x \implies du = dx[/tex]

[tex]dv = f''(x) \, dx \implies v = f'(x)[/tex]

Then

[tex]\displaystyle \int_1^4 x f''(x) \, dx = x f'(x) \bigg|_{x=1}^{x=4} - \int_1^4 f'(x) \, dx[/tex]

By the fundamental theorem of calculus,

[tex]\displaystyle \int_1^4 f'(x) \, dx = f(4) - f(1)[/tex]

so that

[tex]\displaystyle \int_1^4 x f''(x) \, dx = 4 f'(4) - f'(1) - f(4) + f(1) = 12 - 7 - 8 + 4 = \boxed{1}[/tex]

The number of the text messages where it will result in the exact same charge from both companies is 500 messages

Number systems are mathematical systems that allow computers to understand and express numbers in various ways. A number is a mathematical value that is used to count and measure items as well as execute arithmetic calculations.

Natural numbers, whole numbers, rational and irrational numbers, and so on are all types of numbers. Similarly, different number systems with differing properties exist, such as the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.

Let the number calls be x where the messages will result in the exact same charge

So, Cell phone company A charges $20 per month plus $0.05 per text

message is 20 + 0.05x

And, Cell phone company B charges $10 per month plus $0.07 per text message is 10 + 0.07x

As we want the numbers to be equal, following equation is obtained

20 + 0.05x = 10 + 0.07x

Lets find x

20 + 0.05x = 10 + 0.07x

0.07x - 0.05 = 20 -10

0.02x = 10

x = 10/0.02

x = 500

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ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

The right angle triangle JKL with base JL and perpendicular KJ has been drawn.

Height = KJ = a

Since J(0,0) so K(0,a)

Hence "ΔJKL has been drawn such that its base JL is a unit long, vertex K is on the y-axis, and the height of the triangle is b units".

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The number falls between [tex]-\frac{25}{4}[/tex] and - 400 % is [tex]-\frac{43}{8}[/tex] = 5.375

first we convert fraction into decimal number

[tex]-\frac{25}{4}[/tex]  = - 6.25

and for remove percentage we divide by 100

- 400 % = - 4

from choose the option,

[tex]-\frac{43}{8}[/tex]  = 5.375

- 720 % = - 7.2

[tex]-\frac{20}{3}[/tex] = - 6.6

then, choose  [tex]-\frac{43}{8}[/tex]  

therefore, number lies between [tex]-\frac{25}{4}[/tex] and - 400 % is [tex]-\frac{43}{8}[/tex] = 5.375

A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0.

Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers). For example, 12/23, 10/32, 12/10, 4/21. A rational number can also be written in the form of a/b, where b is not 0 and a & b are integers. For example, 15/7, -18/13, 3/-7, -6/-12.

All fractions can be termed as rational numbers; however, all rational numbers cannot be termed as fractions. Only those rational numbers in which ‘p’ and ‘q’ are positive integers are termed as fractions. Let a/b be any fraction. Now, a and b are natural numbers. Since all natural numbers are also integers, a and b are also integers. Thus, the fraction a/b is the quotient of 2 integers such that b ≠ 0. Hence, a/b is a rational number. One of the examples in which a number is a rational number but not a fraction is:

Consider the fraction 12/-32. It is a rational number but not a fraction because its denominator (n) is not a natural number.

A fraction is expressed in the form of the ratio of whole numbers, a/b and b≠0.

A rational number is also expressed in the form of a ratio, p/q, where numerator and denominator are integers and q≠0.

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The sequence 1620,540,180,60,20, . . . .. is a geometric sequence with common ratio 1/3.

To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.

If it is an arithmetic sequence, then:

  a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric sequence, then:

  a(n) = a(n-1) . r

where r is the common ratio.

The given sequence is:

    1620,540,180,60,20, . . .  .

In this sequence:

a(1) = 1620

a(2) = 540

a(3) = 180

First we check the difference between 2 consecutive terms:

a(2) - a(1) = 540 - 1620 = -1080

a(3) - a(2) = 180 - 540 = -360

Since the difference is not constant, then the sequence  is not an arithmetic one.

Now we check the ratio,

a(2) : a(1) = 540 : 1620 = 1/3

a(3) : a(2) = 180 : 540 = 1/3

and so on

Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 1/3

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Answer:

the answer is D

hope this helps!

The result of the expression -5(x+2y)+15(x+2y) for the variable x=7 and y= -7 is -70

Given,

The expression = -5(x+2y)+15(x+2y)

The value of the variables

x=7 and y= -7

Substitute the values in the expression

-5(7+2(-7))+15(7+2(-7))= -5(7-14)+15(7-14)

=-5(-7)+15(-7)

=35-105

=-70

Hence, the result of the expression -5(x+2y)+15(x+2y) for the variable x=7 and y= -7 is -70

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If a cargo van delivers only 50-pound and 80-pound packages and the total weight of the packages cannot exceed 1,500 pounds, then a system of inequalities to determine the maximum number of 80-pound packages that the van can carry per trip is x + y ≥ 20; 80x + 50y ≤ 1,500.

A system of inequalities is a term used in mathematics that is a set of two or more than two inequalities in one or more than one variable.

Consider,

the number of 80-pound packages = x

the number of 50-pound packages = y

As the van can carry a minimum of 20 packages, the sum of x and y can be given as,

x + y ≥ 20

The weight of 80-pound boxes can be given as 80x and the weight of 50-pound boxes can be given as 50x. As the total weight of the packages cannot be more than 1500 pounds,

80x + 50y ≤ 1500

If we consider x to be 19,18 or 17 and the remaining to be y, it will exceed the limit of 1500 pounds. If x is considered to be 16,

80(16) + 50 (4) = 1480

Hence, the maximum number of 80-pound packages that the van can carry per trip is 16.

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Answer: f = 10

Step-by-step explanation:

        An undefined slope means it's graphed as a straight vertical line. There is no change in x, so the x value will be the same for both points.

       Here, f = x as coordinate points are written as (x, y);

       f = 10

Answer:

when sixteen times a number is decreased by seventeen the result is 26

Answer:

-1/10 - 7i/24

Step-by-step explanation:

The average rate of change between the given values of the variable is 21

A function can be defined as an expression or rule showing the relationship between a dependent and an independent variable.

Given the function;

h(t) = 2t^{2}[/tex] − t

For t =2

Substitute the value of t as 2 in the function, we have;

h(2) = 2 (2)² - (2)

Find the square

h(2) = 2(4) - 2

h(2) = 8 - 2

h(2) = 6

For t = 9

Substitute the value of t as 9 in the function, we have;

h(9) = 2(9)² - 9

Find the square

h(9) = 2(81) - 9

h(9) = 153

The average change = 153 - 6 = 147/ 9 -2 = 147/ 7 = 21

Thus, the average rate of change between the given values of the variable is 21

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Answer:

8, 26 and 19

Step-by-step explanation:

Perimeter is the length of all sides of a polygon. It is simply the length of the boundary around a closed shape. Perimeter of a triangle = Sum of all three sides.

Hence,

[tex]\Rightarrow[/tex] n + 3n + 2 + 4n - 13 = 69 (acc. to Q)

[tex]\Rightarrow[/tex] n + 3n + 4n + 2 - 13 = 69

[tex]\Rightarrow[/tex] 8n - 11 = 69

[tex]\Rightarrow[/tex] 8n = 80

[tex]\Rightarrow[/tex] n = 80/10

[tex]\Rightarrow[/tex] n = 8

Length of all three sides:

Answer:

The simplified answer would be: -22n

Please correct me if I am wrong, hope this helps! ;)

Answer:

-22n.

Step-by-step explanation:

'+-' = '-'   so,

– 8n+– 8n+– 6n

= -8n - 8n -6n

= -22n.

Question

The turtle population on an island is increasing at a rate of 1.4% per year. The population was 3800 in the year 2009.

What is the predicted population in the year 2014?

Answer:

3541