The perimeter of the quadrilateral below is 119 units. Find the length of side AB.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{ m}{\downarrow }}{\cfrac{1}{2}}x+5\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]

so, we're really looking for the equation of a line with a slope of -2 and that passes through (-2 , 3)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-2)})\implies y-3=-2(x+2) \\\\\\ y-3=-2x-4\implies y=-2x-1[/tex]

Answer:

12.2 km

Step-by-step explanation:

Here is ONE way :

7.6 mi * 5280 ft/mi * 12 in / ft   /   (39.37 in / m * 1000 m / km)  = 12.2 km  

The value of 50-cents coins is $21, the value of 10-cents coins is $15 and the value of the 20-cents coins is $14.

Percentage of the number:

Percentage is defined as the a number or ratio that can be expressed as a fraction of 100.

If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Given,

Roslan had a total of 50$ in 10-cents coins,20- cent coins and 50-cents coins.

The value of his 10- cents coins was 30% of the total value of all his coins.

The value of his 20-cents coins was 28% of the total value of all his coins.

Here we need to find the value of 50-cent coins.

We know that,

Total value = $50

So the value of 10-cent coins

=> 30% × $50 = $15

Then the value of 20-cent coins

=> 28% × $50 = $14

Through the known values of 10-cents and 20-cents we have calculate the value of 50-cents coins as,

=> $50 – $15 – $14 = $21

Therefore, the value of 50-cents coins is $21.

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This is because they are likely to report their favorite game as soccer or some other related game.

What is survey explain?

What three sorts of surveys are there?

Most studies fall into one of three categories: exploratory, descriptive, or causal. Each has a distinct function and can only be applied in specified ways.

The biased result would be provided by the -

Ask people attending a soccer game

This is because they are likely to report their favorite game as soccer or some other related game.

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Step-by-step explanation:

completing the square means finding an expression

(x + a)² = b²

or

(x - a)² = b²

(x + a)² = x² + 2ax + a²

(x - a)² = x² - 2ax + a²

because of the "+ 18x" in the original equation we know that we are looking for (x + a)².

now, let's compare the different terms :

x² = x²

18x = 2ax

18 = 2a

a = 9

so, the complete square would look like

(x + 9)² = x² + 18x + 81

but we have only "+ 79" in the original equation.

so, we add the missing 2 (to both sides to keep the equation true)

x² + 18x + 79 + 2 = 0 + 2

x² + 18x + 81 = 2

(x + 9)² = 2

x + 9 = ±sqrt(2)

x1 = sqrt(2) - 9

x2 = -sqrt(2) - 9

x = sqrt(2) - 9, -sqrt(2) - 9

yes, every quadratic equation has 2 solutions.

as every cubic equation has 3 solutions.

and so on.

Answer:

2,739 and 2,489

Step-by-step explanation:

There are many solutions to both problems:

(Rules)
If the number is 5 or higher round (up)
If the number is 4 or lower round (down)

2,739⇒3,000
  ↑↑↑
  Higher than 500 so round up to get 3,000

2,489⇒2,500
    ↑↑
    Higher than 50 so round up to get 2500

2,739 and 2500 are both possible solutions.

Answer:

1032x

Step-by-step explanation:

[tex]3x+4x+\cdots+43x=x(3+4+\cdots+45) \\ \\ =43x\left(\frac{45+3}{2} \right) \\ \\ =43(24x) \\ \\ =1032x[/tex]

The number of children who wore both orange and black will be 8.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

There are 46 children going to a party. 18 will wear black costumes, 12 will wear orange costumes and some will wear both black and orange.

Then the number of children who wear costumes and black & orange. Then we have

⇒ 46 - 18 - 12

⇒ 46 - 30

⇒ 16

Half of the guests will go in costumes that are neither black nor orange. Then we have

⇒ 16 / 2

⇒ 8

Then the number of the children who orange and black will be  

⇒ 16 - 8

⇒ 8

The number of children who wore both orange and black will be 8.

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Answer:

There is nothing positive or negative about zero. Zero is just zero. It is NEITHER positive NOR negative. To the right of zero on number line are positive numbers and on the left of zero, lie the negative numbers on the number line.

Answer:

Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and located to the left of 0 on a number line. The number zero is neither positive nor negative.

Answer: Reformatting the input :

Changes made to your input should not affect the solution:

(1): "c5"   was replaced by   "c^5".  1 more similar replacement(s).

STEP

1

:

           c4

Simplify   ——

           c5

Dividing exponential expressions :

1.1    c4 divided by c5 = c(4 - 5) = c(-1) = 1/c1 = 1/c

Final result :

 1

 —

 c

Step-by-step explanation: hope this helps

Answer: square root of 5 and square root of  9

Step-by-step explanation:

The another point is  (2,23) of the function y(x).

What does regression analysis mean?

The given Regression is -

y (X) = 30 - 3. 5 x .......................(1)

now   when x = 0 , y(x) = 30    ..........................(1)

thus ,   y- intercept  = 30

one point is    ( 0 , 30 )

Again taking   x = 0  we get

             y(x) =   30 - 3. 5  x 2    by (1)

               y(X) = 23

Thus the another point is  (2,23).

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Answer:

x = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

4x - 10 = - 6x - 2 ( add 6x to both sides )

10x - 10 = - 2 ( add 10 to both sides )

10x = 8 ( divide both sides by 10 )

x = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex]

The inference is that Ah Fo's reply to the magician giving him the three brass pennies is D.

Ah Fo tells the magician that he doesn't want a reward for his help.

It should be noted that the information is about how the character helped the magician. Despite the help, he didn't request for anything in return.

Therefore, the inference is that Ah Fo's reply to the magician giving him the three brass pennies is that Ah Fo tells the magician that he doesn't want a reward for his help.

In conclusion, the correct option is D.

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Read the excerpt from "The Three Brass Pennies."

“And what might your decision be?” asked the magician, as he spread out the three brass pennies before him.

“I would ask first,” went on Ah Fo, “for the power to read accurately the thoughts of others; secondly, for the power to foretell my own future at least a month in advance of any given moment; third, for the power to acquire all learning without any effort!”

When he had finished, the magician sat back with a gasp, took off his spectacles and wiped them, put them on once more, and stared at Ah Fo in astonishment and not a little dismay. “This is most unusual,” he stammered, “not to say somewhat dangerous! Have you duly considered, my son, the extent of all you ask?”

Answer:

it should be b.

Step-by-step explanation:

2 rare coins will make them $100 each month. There are 12 months in a year.

12 × 2 = 24 months

so $100 × 24 months will give us 2400.

Then Mario purchases 3 coins making it cost $150 ($50 + $50 + $50)

2400 + 150 = 2550

Brainliest plss :,)

The snail move at the pace in 1440in/hr.

Speed:

Speed is measured as the ratio of distance to the time in which the distance was covered.

Speed is a scalar quantity as it has only direction and no magnitude.

Given,

A snail moves at a pace of 2 ft/min.

Here we need to find how fast does the snail move in inches/hour.

We know that,

1 ft/min = 720.00 in/h

So, here we have 2 feet/minute.

That is equal to

=> 2 x 720.00 in/h

When we multiply it then we get the value of,

=> 1440 in/hr

Therefore, the snail move at the pace in 1440in/hr.

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Answer:

the answer of that is 16 x 5

Step-by-step explanation:

An equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power is 2d⁻³/11d⁻⁹

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

Translating the word problem into an algebraic expression, we have;

4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³

22 times d raised to the ninth power = (22 × d)⁻⁹ = 22d⁻⁹

Next, we would write the equation as a quotient:

Expression = 4d⁻³/22d⁻⁹

Expression = 2d⁻³/11d⁻⁹

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The solution for the expression {8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6 will be 1.

We are given the expression:

{8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6

We will solve this expression by using the property of PEMDAS:

Solving the expression , we get

{8 (29 - 28) / 11 - 8 + 1} - 3 (2) / 6

= (8 × 1) / 4  -( 6 / 6)

= 2 - 1

= 1

Therefore, the solution for the expression {8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6 will be 1.

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Answer:

Step-by-step explanation:

f(x) = 0

then x =

-2 and +2

f(x) = 5

then x = +3 and -3

The inequality which can be used to determine the number of gigabytes is 41.5 + 5x < 50 and the solution is  x < 1.7

The given parameters are

Flat cost = $41.50

Rate = $5 per gigabyte

Budget = Under $50

The equation is represented as:

Total cost = Flat cost + Rate * Number of gigabyte

So, we have

y = 41.5 + 5x

The budget is under 50

So, we have

41.5 + 5x < 50

Subtract 41.5 from both sides

5x < 8.5

Divide by 5

x < 1.7

Hence. the inequality which can be used to determine the number of gigabytes is 41.5 + 5x < 50 and the solution is  x < 1.7

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Answer:

Step-by-step explanation:

Comment

The key to this is to know what a remote angle is. A remote angle is one that has one leg in common with the exterior angle. Make this a little simpler.

The exterior angle is outside the triangle. In this case it is the 157 degree angle.

The two remote angles each contribute just one side to the exterior angle. <B contributes BC and <A

Theorem

The two remote angles = the exterior angle.

Equation

x + x - 21 = 157

Solution

x + x - 21 = 157                    Combine the left side

2x - 21 = 157                       Add 21 to both sides

2x - 21 + 21 = 157+21         Combine  

2x = 178                             Divide by 2

2x/2 = 178/2

x = 89

Answer

x = A = 88

89 - 21 = B =68

1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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The area of the parallelogram is [tex]\sqrt{132}[/tex].

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.

Given that,

vertices k(1, 1, 3), l(1, 3, 5), m(6, 9, 5), and n(6, 7, 3)

Area of Parallelogram = |KL × KN|

KL = (1, 1, 3) - (1, 3, 5) = (0, 2, 2)

KN = (1, 2, 3) - (3, 7, 3) = (2, 5, 0)

Area of the parallelogram = cross product of two vectors, represented by the adjacent sides.

Area of Parallelogram = |(0, 2, 2) × (2, 5, 0)|

                                    = |i(2 × 0 - 5 × 2) - j(0 × 0 - 2 × 2) + k(0 × 5 - 2 × 2)|

                                    = |i(-10) - j(-4) + k(-4)|

                                    = |-10i + 4j - 4k|

                                    = [tex]\sqrt{(-10)^{2}+(4)^{2}+(-4)^{2} }[/tex]

                                    = [tex]\sqrt{100+16+16}[/tex]

                                    = [tex]\sqrt{132}[/tex]

Hence, The area of the parallelogram is [tex]\sqrt{132}[/tex].

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Answer:

Your answer is 65

Step-by-step explanation:

f(x) = x² - 4x - 12

f(-7) = (-7)² - 4 x (-7) - 12

= 49 - (-28) - 12

= 49 + 28 - 12

= 77 - 12

= 65

Answer:

5 year

3 inches every year 48 minus 32 equals 16 3 Inches divided into 16 equal 5.333333 round it equals 5 years y = 5 years

Answer:

The distance between both points is 5 units

Step-by-step explanation:

The distance formula is: d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}