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trig

The intersection (2,2) (2,4) (8,4) (8,2) is  (5,3).

On the coordinate plane, the four points that are given together form a rectangle. We must first locate the midway of both diagonals in order to determine where the diagonals will connect.

The midpoint of the diagonal that passes through the points (2,2) and (8,4) is ((2+8)/2, (2+4)/2). (5,3).

The midpoint of the diagonal that passes through the points (2,4) and (8,2) is ((2+8)/2, (4+2)/2). (5,3).

Consequently, the diagonals' point of intersection is (5,3).

Due to the fact that a rectangle's two diagonals meet here in the middle, this location also serves as the rectangle's centre.

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The sides of the right triangle are 15 cm, 20 cm, and 25 cm.

What is triangle?

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

Let x be the length of the shorter leg of the right triangle.

Then, according to the problem statement, the longer leg is 5 cm more than the shorter leg, which means its length is x + 5 cm.

The hypotenuse is 10 cm more than the shorter leg, so its length is x + 10 cm.

By the Pythagorean theorem, we have:

x² + (x+5)² = (x+10)²

Expanding the squares and simplifying, we get:

x² + x² + 10x + 25 = x² + 20x + 100

Subtracting x² and simplifying further, we get:

x² - 10x - 75 = 0

Factorizing the left-hand side, we get:

(x - 15)(x + 5) = 0

Therefore, the possible solutions are x = 15 and x = -5, but x cannot be negative in this context, so we take x = 15 cm.

Then, the longer leg is x + 5 = 20 cm, and the hypotenuse is x + 10 = 25 cm.

Therefore, the sides of the right triangle are 15 cm, 20 cm, and 25 cm.

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Option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.

A pοlynοmial is a mathematical expressiοn cοnsisting οf variables, cοefficients, and the οperatiοns οf additiοn, subtractiοn, multiplicatiοn, and nοn-negative integer expοnents.

Pοlynοmials are an impοrtant part οf the "language" οf mathematics and algebra. They are used in nearly every field οf mathematics tο express numbers as a result οf mathematical οperatiοns. Pοlynοmials are alsο "building blοcks" in οther types οf mathematical expressiοns, such as ratiοnal expressiοns.

We have:

6x² − 8x

= 2(3x² −4x)

Then,

6x² - 3x + 8x -4

= 6x² +8x−3x−4

= 2x(3x+4) −3x −4

= 2x(3x+4)−(3x+4)

= (2x−1)(3x+4)

Thus, option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.

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The number of books that each kid in Mr. Johnson's sixth-grade class read during the summer was recorded. 5 books have been read on average by Mr. Johnson's students.

There are six students in Mr. Johnson's sixth-grade class, and their number of books read is 0, 2, 4, 6, 8, and 10.

To find the median, we need to find the middle value in the list of numbers. If there is an odd number of values, then the median is the middle number. If there is an even number of values, then the median is the average of the two middle numbers.

In this case, there are six numbers, which is an even number, so we need to find the average of the two middle numbers, which are 4 and 6.

The average of 4 and 6 is (4 + 6)/2 = 5.

Therefore, the median number of books read by Mr. Johnson's students is 5.

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The area of the shape, given the dimensions of the various parts of the shape, can be found to be 8, 100 ft ².

You can divide the shape into other shapes. Then you can find the areas of these shapes and then sum them up.

The area of the composite shapes would therefore be :

= ( 30 x 60 ) + ( 30 x 60 ) + ( ( 60 + 30 + 60) x 30 )

= ( 30 x 60 ) + ( 30 x 60 ) + ( 150 x 30 )

= 1, 800 + 1, 800 + 4, 500

= 8, 100 ft ²

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56 ounces is equal to 3 pounds and 8 ounces. So the answer is D: 3 lb 8 oz.

Pound is a unit of measurement for mass or weight commonly used in the United States and the United Kingdom. The symbol for pound is "lb".

In the English system of measurement, there are 16 ounces in one pound. To convert a weight in ounces to pounds, we need to divide the number of ounces by 16.

In this case, we have 56 ounces. So, by dividing 56 by 16, we obtain:

56 / 16 = 3 with a remainder of 8

This means that 56 ounces is equal to 3 pounds and 8 ounces. So the answer is D: 3 lb 8 oz.

In the US customary system, one pound is equal to 16 ounces, while in the imperial system used in the UK, one pound is equal to 14 ounces.

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Convert 56 ounces(oz) into pounds(Ib)

56 oz = ____lb ____oz

A. 2 lb 1 oz

B. 2 lb 3 oz

C. 2 lb 6 oz

D. 3 lb 8 oz

The loan's simple interest rate is 5.232% per quarter.

What is the formula for the future value of a loan with simple interest?

A = P(1 + rt)

where A is the future value, P is the principal, r is the simple interest rate per period, and t is the number of periods.

In this case, we have:

P = 4500

A = 4561.88

t = 3 months = 3/12 year =0.25 year

Substituting these values into the formula,

[tex]4561.88 = 4500(1 + 0.25r)[/tex]

Dividing both sides by 4500,

[tex]1.01308 = 1 + 0.25r[/tex]

Subtracting 1 from both sides,

[tex]0.01308 = 0.25r[/tex]

Dividing both sides by 0.25,

[tex]r = 0.05232 \: or \: 5.232\%[/tex]

Therefore, the loan's simple interest rate is 5.232% per quarter.

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Answer:

d= 90 Degrees

e= 97 Degrees

f = 83

Answer:

Step-by-step explanation:

To find:-

Answer:-

We can see that angles e and 97° are vertically opposite angles. So they will be equal as vertically opposite angles are equal .

Hence here ,

→ e = 97°

Secondly e and f form linear pair , and the sum of linear pair is 180° . Hence here ,

→ e + f = 180°

→ 97° + f = 180°

→ f = (180-97)°

→ f = 83°

Same goes with d and 90° . They both form linear pair. So that ,

→ 90° + d = 180°

→ d = 180°-90°

→ d = 90°

These are the required values of the unknown angles.

The measure of angle D is 100°

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°.

Since the the sum of angle in a triangle is 180°, then to get the value of angle D will subtract the sum of the known angles from 180.

Therefore,

angle D = 180-( 40+40)

= 180-80

= 100°

therefore the measure of angle D Is 180°

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Answer:

∠A=125° and ∠B=35°

Step-by-step explanation:

We know that, by angle sum property of triangles,

∠A +∠B+∠C=180°

⇒​ (6x−1)° ​+20°  +(x + 14)°=180°

⇒​ 6x−1 ​+20 +x + 14=180 [Open parenthesis]

⇒7x+33=180

⇒7x=180-33  [Subtracting 33  from both sides]

⇒7x=147  

⇒x=21  [Divide 7 from both sides]

Now substitute value of x in the expressions of ∠A and ∠B.

Therefore, ∠A=(6(21)-1)°=(126-1)°=125°

∠B=(21+14)°=35°

Answer:

The equation that represents the situation is: A = 200(1-0.025)^5 where A is the amount remaining after 5 years, 200 is the starting value, 0.025 is the decimal equivalent of the decay rate of 2.5%, and 5 is the number of years.

Parallelogram JKLM is a rectangle because it has four right angles.

The SSS (side-side-side) congruence theorem is one of the postulates of Euclidean geometry that states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Abigali wants to prove that a parallelogram is a rectangle if its diagonals are congruent.

Since, JKLM is a parallelogram, JK≅ML.

Also by the reflexive property, KL is congruent to itself. So, since JL≅KM as well, ΔJKL ≅ ΔMLK by the SSS congruence theorem.

Now because the corresponding angles in congruent triangles are congruent, ∠JKL ≅ ∠MLK.

Also, since parallelograms have JK//ML,

Consecutive Interior Angles are supplementary.

So, since m∠JKL and m∠MLK are equal, they must both be 90°. Because the opposite angles in parallelograms are congruent, m∠MJK and m∠JML are both 90°. So, parallelogram JKLM is a rectangle because it has four right angles.

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The measure of the angle x is 41.41° in the given triangle.

Triangle is a clοsed twο-dimensiοnal shape. It is a three-sided pοlygοn. All sides are made οf straight lines. The pοint where twο straight lines jοin is the vertex. Hence, the triangle has three vertices. Each vertex fοrms an angle.

Given that cos θ = side adjacent to angle x/hypotensive

Here, side adjacent to angle x = 6

hypotensive = 8

cos x = 6/8

x = arccos 6/8

x = 41.41°

Thus, the measure of the angle x is 41.41° in the given triangle.

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Answer:

378

Step-by-step explanation:

[tex]\frac{14}{x}[/tex] = [tex]\frac{1}{27}[/tex]  Cross multiply and solve for x

x = (14)(27)

x = 378

Helping in the name of Jesus.

Answer:

slope = 15

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 21) ← 2 ordered pairs from the table

m = [tex]\frac{21-6}{2-1}[/tex] = [tex]\frac{15}{1}[/tex] = 15

the linear relationship is then of the form

y = mx + c ( m is the slope and c the y- intercept )

from the table the point (0, - 9 ) crosses the y- axis at - 9 ⇒ c = - 9

y = 15x - 9 ← linear relationship

Answer: $13, 658 increase

First, we need to calculate the current total variable costs:

Total Variable Costs = Sales x Variable Costs as a % of Sales

Total Variable Costs = $603,000 x 0.63

Total Variable Costs = $380,490

Next, we can calculate the current operating income:

Operating Income = Sales - Total Variable Costs - Fixed Costs

Operating Income = $603,000 - $380,490 - $202,000

Operating Income = $20,510

If sales increase by $37,400, the new sales figure will be $640,400 ($603,000 + $37,400). We can then calculate the new total variable costs:

New Total Variable Costs = New Sales x Variable Costs as a % of Sales

New Total Variable Costs = $640,400 x 0.63

New Total Variable Costs = $404,232

Finally, we can calculate the new operating income:

New Operating Income = New Sales - New Total Variable Costs - Fixed Costs

New Operating Income = $640,400 - $404,232 - $202,000

New Operating Income = $34,168

Therefore, the operating income will increase by $13,658 ($34,168 - $20,510) if sales increase by $37,400.

The selling price of the DVD player after a 15% discount is applied can be found as follows:

Discount = 15% of the marked price = (15/100)*$320 = $48

Selling price = Marked price - Discount = $320 - $48 = $272

Therefore, the actual selling price of the DVD player after a 15% discount is $272.

Answer:

$272

Step-by-step explanation:

Formula:
Selling price = Marked price - Discount

We first find the discount by taking 15% off of $320 which is $48

We then insert the Maked price and the Discount into the formula which is:

Selling price = $320 - $48
Selling price = $272

Answer:

7x = 126 is the equation

She sold 18 t-shirts.

Step-by-step explanation:

Since she sold t-shirts for 7 each, we need to find how many T-shirts she sold. 126 dollars is how much she made, so we need to divide.

126/7 = 18.

The equation would be:

7x = 126.

Step-by-step explanation:

Mona had = 32 math problems.

Let math problems shw completed be x.

Before dinner: 3/4x maths.

remaining maths = x- 3/4x

= 4x-3x/4 = 1/3x.

The answer is failed to estimate number of rock songs on his MP3 player.

What is a MP3 player and how does it work?

It's a compressed digital audio file. A player stores these files on a memory chip so that you can play it back at your leisure. Contains a miniature hard disk drive, which can store huge quantities of data. MP3s usually contain music, but the format is also used for general audio files such as audiobooks and podcasts.

The statements that are true about Josiah's solution are:

He set up a proportion correctly using the information given.

He correctly solved for x, the number of rock songs on his MP3 player.

Therefore, he did not find the average of the number of rock songs in the sample to estimate the number of rock songs on his MP3 player.

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Answer:

The formula for finding the area of a triangle is:

Area = 1/2 x base x height

where "base" is the length of one of the sides of the triangle, and "height" is the distance from that side to the opposite vertex.

Step-by-step explanation:

let the third vertex=C

180-86.2=93.8°

angle near the satellite=180-(83.9+93.8)=180-177.7°=2.3°

angles of triangle are 83.9°,93.8°,2.3°

by sine formula

[tex]\frac{AC}{Sin~93.8} =\frac{AB}{Sin 2.3} \\\frac{AC}{Sin(180-93.8)} =\frac{68}{Sin~2.3} \\\frac{AC}{Sin~86.2} =\frac{68}{Sin~2.3} \\AC=\frac{Sin~86.2}{Sin~2.3} \times~68\\AC \approx 1690.69\\AC\approx1691~mile[/tex]

surface area of a refrigerator,

square feet (sq ft)

square inches (sq in)

the total area or the solid that the surface of the solid occupies.

we know that refrigerator have cuboid shape so,

surface area of cuboid =2(lb+bh+hl)

where l is length ,b is breath ,and h is height of cuboid .

The units generally  used to measure the surface area of a refrigerator are:

square feet (sq ft)

square inches (sq in)

Therefore, the options are square feet (sq ft) and square inches (sq in) correct.

Meters (m) and millimeters (mm) are typically not used for measuring the surface area of a refrigerator.

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the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.

Why it is and what does symmetry mean?

To find the axis of symmetry of the quadratic function f(x) = 7 - 4x + x²2, we can use the formula:

x = -b / 2a

where a and b are the coefficients of the x²2 and x terms, respectively, in the quadratic equation ax²2 + bx + c = 0.

In the given function, a = 1 and b = -4. Substituting these values into the formula, we get:

x = -(-4) / 2(1) = 2

Therefore, the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.

Symmetry is a property that describes a balanced and consistent arrangement of parts or elements that are similar in size, shape, and position. In mathematics, symmetry refers to the idea that a geometric object, function, or equation remains unchanged after some transformation, such as a reflection, rotation, or translation.

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Answer:

There are 26 letters in the alphabet, and 9 digits from 1 to 9.

The probability of choosing X as the letter is 1/26, since there is only one X in the alphabet.

The probability of choosing a prime number digit is 4/9, since there are 4 prime numbers among the digits 1-9 (2, 3, 5, and 7) and 9 total digits.

Therefore, the probability of choosing X followed by a prime number digit is:

P(X and prime) = P(X) × P(prime) = (1/26) × (4/9) = 4/234

So the probability of getting X followed by a prime number is 4/234, or approximately 0.017 or 1.7%.

The prοfit exceeds the cοst as y > 1000 + 15x. Sο, οptiοn 4 is cοrrect.

Gaining anything is knοwn as prοfit. When the Selling price ( SP ) οf the prοduct is mοre than the cοst price ( CP ) οf the prοduct, we gain prοfit. Oppοsite tο the prοfit is lοss i.e. lοsing anything is called lοss. When the Selling price ( SP ) οf the prοduct is less than the cοst price ( CP ) οf the prοduct, we get a lοss.

Prοfit can be calculated by the fοrmula,

Prοfit   =   Selling Price - Cοst price

     P   =   SP - CP

Lοss can be calculated by the fοrmula,

Lοss   =   Cοst price - Selling price

   L    =   CP - SP

As per the questiοn,

x  =    number οf units prοduced

expressiοn   =   1000 + 15x

⇒  When y > 1000 + 15x, then prοfit exceeds cοst:

x   =   50  & y   =   1750

x   =   100  & y   =   2500

x   =   150  & y   =   3250

x   =   200  & y   =   4000

x   =   0  & y   =   1000

Therefοre, the graph in the 1st οptiοn is cοrrect as the prοfit exceeds the cοst.

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Complete question:

The cost of a small business is given by the expression 1000 + 15x, where x is the number of units produced. the business will be profitable whenever its profit y exceeds its cost. if the profit region is shaded in blue, which of the following graphs corresponds to the given situation?

Using calculations based on a perpetual inventory system, the inventory balance that Altira Corporation would report in its August 31, 2024, balance sheet and the cost of goods sold it would report in the income statement, using the Average Cost Method are as follows:

The average cost method or the weighted-average cost method under the perpetual inventory system adds up all the cost of goods available for sale at each sales point and divides by the number of units available for sale in determining the average cost to be applied to the cost of goods sold.

Principally, the perpetual inventory system ensures that each inventory movement is separately recognized and the cost of goods sold determined, unlike the periodic inventory system.

August 14 for Sales of 6,000 units:

Average cost per unit = $5.46 ($54,600 ÷ 10,000)

Cost of goods sold  = $32,760 ($5.46 x 6,000)

August 25 for Sales of 7,000 units:

Average cost per unit = $5.54 ($21,840 + $33,600 ÷ 10,000)

Cost of goods sold  = $38,780 ($5.54 x 7,000)

Total cost of goods sold = $71,540 ($32,760 + $38,780)

Total cost of goods available for sale = $111,400 ($10,600 + $44,000 + $33,600 + $23,200)

Ending Inventory = $39,860 ($111,400 - $71,540)

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To estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].

What are the dimensions?

The given formula for estimating the number of square feet, A, of carpeting needed for a room x feet by y feet containing a stairway w feet by z feet with n stairs is:

A = xy + w[z(2n - 1) + 2n]

Let's break down this formula to understand the different parts:

The term w[z(2n - 1) + 2n] represents the additional area needed to cover the stairway. We add this to the area of the main part of the room, xy, to get the total area of carpeting needed, A.

So to estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].

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