Find the area of the shaded region. All angles are right angles.
5m
30 m
20m
5m

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:

1/20

Step-by-step explanation:

hope this helps

Answer:

49/20

Step-by-step explanation:

Bye! ~ SunnyBunny <3

The algebraic expression is,

⇒ 10 + c/3 = 12

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

''ten more than the quotient of c and three is 12.''

Now, We can formulate;

⇒ ten more than the quotient of c and three is 12

⇒ 10 + c/3 = 12

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Complete question is this,

Ten more than the quotient of c and three is 12.

Adrianna's distance from her house increases from 60 yards to 180 yards, her distance from the bus stop varies from 340 yards to 220 yards.

What is the straightforward meaning of distance?

Adrianna walks from her house to a bus stop that is 400 yards away.

as Adrianna walks to the bus stop the distance between Adrianna and bus stop will b decreasing .  

Further As Adrianna's distance from her house is  60 yards then she is 400 -60 = 340 yards away from bus stop

Also As Adrianna's distance from her house is  180 yards then she is 400 -180 = 220 yards away from bus stop .

As Adrianna's distance from her house increases from 60 yards to 180 yards, her distance from the bus stop varies from 340 yards to 220 yards.

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[tex]\displaystyle\\Answer:\ y=\sqrt{\frac{x-1}{2} } \ \ \ \ (x\geq 1,\ \ \ \ y\geq 0)[/tex]

Step-by-step explanation:

[tex]y=2x^2+1\\[/tex]

We change the argument and the value:

[tex]\displaystyle\\x=2y^2+1\\\\x-1=2y^2+1-1\\\\x-1=2y^2\\[/tex]

Divide both parts of the equation by 2:

[tex]\displaystyle\\\frac{x-1}{2}=y^2\\\\ \sqrt{\frac{x-1}{2} }=y \ -\ the\ desired\ inverse\ function\\\\[/tex]

The restrictions are imposed on the inverse function by on x:

[tex]x-1\geq 0\\x\geq 1[/tex]

The restrictions are imposed on the inverse function by on y:

[tex]y\geq 0[/tex]

Then the original function is defined on the sets:

[tex]x\geq 1,\ \ \ \ y\geq 0[/tex]

The initial function, a parabola, is constrained because of the inverse function; only in this case the functions are reciprocal.

Answer:

10xto the power of 7

Step-by-step explanation:

Multiply x2x2 by x5x5 by adding the exponents.Tap for fewer steps...Move x5x5.5⋅2(x5x2)5⋅2(x5x2)Use the power rule aman=am+naman=am+n to combine exponents.5⋅2x5+25⋅2x5+2Add 55 and 22.5⋅2x75⋅2x7Multiply 55 by 22.10x710x7

The left over fabric area is; 0.03 m²

Now, if the radius of a circle is r, then the diameter is;

d = 2r

Now, there are 16 identical circles to be cut from a square sheet of fabric whose sides are 0.4 m long.

Thus, the height of the square will be the diameter of four circles.

Height of square = 4(2r) = 8r

Thus;

8r = 0.4

r = 0.4/8

r = 1/20 m

Left over fabric area = (0.4 * 0.4) - (π × (1/20)²)

Left over fabric area = 0.03 m²

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Using Trigonometric ratios, we can conclude the length of the indicated side is 12.70m.

It can be solved using Trigonometric ratios and Pythagoras theorem

Firstly using Trigonometric ratios

Using Sinθ,

Sinθ = perpendicular / hypotenuse(h)

Sin 39 = 8 / h

0.63 = 8 / h

h = 8 / 0.63

h = 12.70

∴ The length of indicated side is 12.70m

Secondly, using Pythagoras theorem,

(hypotenuse)² = (Altitude)² + (Base)²

⇒ (H)² = 8² + 10²

⇒ (H)² = 64 + 100

⇒ (H)² = 164

⇒ H = √164

⇒ H = 12.80

∴ The length of indicated side is 12.80m

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One of the solutions to the following linear inequality is the value x=-10.

What are linear inequalities?

Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. It's important to remember that if p < q, then p must be a number that is strictly less than q. If p ≤ q, then p is a number that is strictly smaller than q or exactly equal to q. The same is true for the other two inequality signs > (greater than) and ≥ (greater than or equal to).

What guidelines apply for resolving linear inequalities?

Given equation: 6x-4≤-28

Add 4 to both sides according to the addition rule:

(6x+4)+4 ≤ (−28)+4

6x-4+4≤ -24

6x≤-24

Now, divide both sides by 6 according to the division rule:

6x/6 ≤−24/6

x ≤ -4

Therefore, x ≤ -4 is the solution for the given linear inequality where, x ∈ (-∞,-4)

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The next minimum monthly payment is expected to be $145.24

What is the balance on the credit card before interest is computed?

First and foremost, we need to determine the credit card balance after the purchases and payment for next month are considered

balance after purchases and payment=$2,064.92-$185.00+$812.61

balance after purchases and payment=$2,692.53

interest for next month=$2,692.53*32.99%/12

interest for next month=$74.02

minimum monthly payment=($2,692.53+$74.02)*5.25%

minimum monthly payment=$145.24

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Answer:

60

Step-by-step explanation:

rid of precentage and zeros, multiply the numbers you have left.

Use 1/8*(whatever amount of days until fractions match)

it will take road x 44 days to repair (1/8*44)

road y will take 70 days to repair (1/8*70)

it will take road y 26 days longer to repair

Answer:

7 : 1.

Step-by-step explanation:

1 - 7/8 = 1/8 is syrup.

So, water to syrup

= 7/8 : 1/8

= 7 :1.

The ratio of water to syrup is 7:1

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here, 7/8 of a can of drink is water, the rest is syrup thus the fraction for syrup is 1/8 of the can. Therefore the ratio of water and syrup is

7/8:1/8=7:1

Hence, The ratio of water to syrup is 7:1

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The value modulus functions of x are found as 12 and -3.

A modulus function returns the magnitude of a number regardless of its sign.

The modulus function's value is always non-negative. Whenever f(x) is a modulus function, we get:

for the given function;

m(x) = |2x - 9|, where m(x) = 15.

then,

15 = |2x - 9|

Open the modulus function in its corresponding positive and negative values;

15 = 2x -9 and also 15 = -(2x - 9).

Solving both;

15 = 2x -9

2x = 15 + 9

2x = 24

x = 12

and, the second functions;

15 = -(2x - 9)

15 = -2x + 9

-2x = 15 - 9

x = -3

Thus, the solution for x are 12 and -3.

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The correct question is-

Given m(x) = |2x - 9|, find x when m(x) = 15.

Answer: the pattern grows by one square being added to the figure before it. I know because when I count the squares on figure one to three I count one block being added to each side.

Step-by-step explanation:

Regarding the quadrants, we have that:

Leila is correct, as most y-coordinates are also negative, meaning that most points are in quadrant 3.

There are four quadrants of points (x,y), and their signals are given as follows:

For this problem, we have that Leila is correct, as most y-coordinates are also negative, meaning that most points are in quadrant 3.

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The dimensions of the fence that will maximize the area are-

Multiply the width by the height of a rectangle to find its area. If we know the lengths of two sides of a rectangle, we can calculate the height and width.

Now, as per the question;

Let 'L'  be the length and,

'W' width of the rectangular

Also, let the river is running along L.

Perimeter to be covered by fence:

P = L + 2W

2700 = L + 2W

Thus, L= 2700 - 2W

Substitute the value of L in the area

Area, A= LW

A = (2700 - 2W)W

A = 2700W - 2W²

This is a quadratic equation;

Now, the vertex of the rectangular with the greatest area will have the greatest width.

(W,A), where W= -b/2a where b = 2700 and a = -2

Solve for W,

W = -2700/2×(-2)

   = -2700/-4

W = 675 ft.

Substitute the value of W in L to find it.

L= 2700 - 2W

 = 2700 - 2×675

L = 1350 ft

Thus, the maximum area will become;

Maximum area A = 1350 × 675

Maximum area A = 911250 sq. ft

Therefore, the maximum area is found to be 911250 sq. ft

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The complete question is-

A farmer has 2700 feet of fencing available to enclose a rectangular area bordering a river. if no fencing is required along the​ river, find the dimensions of the fence that will maximize the area. what is the maximum​ area

The below mentioned are the factors of given equations

Factorization:

In mathematics, factorization or factoring is the method of expressing a quantity or another numerical component as a product of many factors, typically small or easier components of the same kind.

In the case of integers, ancient Greek mathematicians were the first to consider factorization. They demonstrated the fundamental theorem of arithmetic, which states that any positive integer can be taken account into a prime number product , which cannot be factored into integers greater than 1. Furthermore, this factorization is unique until the order of the factors is changed.

1)[tex]9a^{2}-18a=9a(a-2)[/tex]

2)[tex]16a^{3}b^{3} +32ab=16ab((ab)^{2} +2)[/tex]

3) inappropriate question

4)[tex]3x^{5} +4x^{4} -5x^{2} =x^{2} (3x^{3} +4x^{2} -5)[/tex]

5)[tex]2x^{3} -x=2(x-1)(x+1)[/tex]

Therefore,The above mentioned are the factors of the given questions.

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Answer:

24

Step-by-step explanation:

18/3 = 6

6*4 = 24

hi

18 = 6*3

so  18* 4/3 =  6*3*4 /3 =   24

The result of diving 107 by 10⁻³ is (E) 107,000.

So, we know that 10⁻³ is 0.001.

Therefore, the result of diving 107 by 10⁻³ is (E) 107,000.

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The correct question is given below:

The result of dividing 107 by 10^-3 is?

a. 10-4.

b. 102.5.

c. 1010.

d. 104.

e. 107,000

I will use the example that they gave to describe the method

First, you need to find the difference between the new amount and the original amount. The new one is 30, while the original one is 24, so the original amount incrased by 6.

Now, you take the difference that you got, and divide it by the original amount. 6 : 24 = 1/4, or 25%. So, the percentage increase is 25%

Applying the same for the others :

32 -> 56 (increased by 24, 24:32 = 3/4 -> 75%)
15  -> 18  (increased by 3, 3:15 = 1/5 -> 20%)
30 -> 33 (increased by 3, 3:30 = 1/10 -> 10%)
150 -> 153 (increased by 3, 3:150 = 1/50 -> 2%)
120 -> 126 (increased by 6, 6:120 = 1/20 -> 5%)
200 -> 202 (increased by 2, 2:200 = 1/100 -> 1%)

The company's profit in the year 2003 is $3.1 million

Profit is defined as the amount of revenue generated after deduction of all the liabilities.

Given that in the year 2000 profit = $2.2 million

Each year increase in profit = 13% =0.13

Total number of year = 2003-2000=3 years

Profit is denoted by

[tex]profit=initial profit(1+each.year.increase)^{years}[/tex]

Substituting the values we get

profit=[tex]2.2(1+0.13)^3[/tex]

=[tex]2.2(1.13)^3=2.2*1.442897[/tex]

=3.174373

=3.1 million

Therefor , the company's profit in the year 2003 is $3.1 million

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After spending the money on oranges and apple, Sarah is left with 20p.

As per the given question;

Sarah spend the amount to buy the 3 oranges is 30p each.

Total spending on oranges = 3 x 30p = 90p.

For buying 1/2 kg of apple; Sarah spend the amount of  £1.20 per kg.

Cost for half kg of apples = 60p.

Total cost =  apple + oranges

Total cost = 60p + 30p = 90p.

Total cost = £1.50

Now, the only money Sarah has is one 50p coin and six 20p coins.

Sarah' money = 50p + (6 x 20)p

Sarah' money = 50p + £1.20

Sarah' money = £1.70

Money left = £1.70 - £1.50

Money left = £0.20 = 20p

Thus, the money left to Sarah is 20p.

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The correct question is -

Sarah wants to buy some fruit. She wants to buy and 3 oranges at 30p each 1/2kg apples at £1.20 per kg.

The only money Sarah has is one 50p coin and six 20p coins.

She pays for the fruit.

Work out how much money Sarah has left.

For the entire independent-measures experiment 24 individuals are participated.

Different participants are utilized in each condition of the independent variable in an experimental design known as an independent measures design, or between-groups. This indicates that a different group of participants is present for each condition of the experiment. A research strategy known as an independent measures design uses numerous experimental groups with subjects only being assigned to one group. Throughout the experiment, each participant is solely exposed to one independent variable condition. A drug trial for a novel medicine would serve as an example. This has the benefit of preventing order effects, which occur when participants behave differently as a result of the order in which conditions are done, often as a result of factors like boredom or exhaustion.

We are given the value  t(22) = 5.30, p < .01

So here degree of freedom (df) is 22 and it is independent so there is two samples,

so df= n₁+n₂-2

⇒ 22 =  n₁+n₂-2

⇒ n₁+n₂ = 24.

Thus for the entire experiment 24 individuals are participated.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

750 students are boys, 250 are girls.

Step-by-step explanation:

1/4 of 1000 is 250.

250 + 250 + 250 = 750 boys.

if 3/4 are boys, then 1/4 (the rest of the school population) are girls.

150 students are girls.