What is the area of the PURPLE triangle below?

I will give you some intuitive remarks for some inspiration on the proofs.

For the first one, notice that if m divides n then n = pm where p is a integer.

Since n and m are both natural numbers p then must be a natural number as well.

Now we know that basically we want to prove that if a is congruent to b mod n then a is congruent to b mod "a factor of n" (this is cause n = pm).

Tell me if you need more clarification.

For the second proof, I would just draw a Venn diagram and prove that the two intersections cover identical regions.

The set of numbers arranged from greatest to least is:

OC) 2.7 x 105; 3.1 x 10¹; 2.4 x 10¹0

To see why, let's convert each number to scientific notation, which makes it easier to compare them:

OA) 2.4 x 10 = 24

2.7 x 105 = 270,000

3.1 x 105 = 310,000

OB) 3.1 x 10 = 31

2.4 x 10 = 24

2.7 x 105 = 270,000

OC) 2.7 x 105 = 270,000

2.4 x 10¹ = 24

3.1 x 10¹ = 31

OD) 3.1 x 103 = 3,100

2.7 x 105 = 270,000

2.4 x 10 = 24

As we can see, the set of numbers in option OC is arranged from greatest to least, with 2.7 x 105 being the largest number, followed by 3.1 x 10¹, and then 2.4 x 10¹0 as the smallest number

Answer:

−(3x2+−xx−5)

Step-by-step explanation:

Answer:

2000

Step-by-step explanation:

Formula = Number x 100/Percent = 600 x 100/3 = 2,000

Following shows the steps on how to derive this formula and find out 3% of what number is 60.

Step 1: If 3% of a number is 60, then what is 100% of that number? Setup the equation.

60/3% = Y/100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

3Y = 60 x 100

3Y = 6000

Y = 6000/100= 2000

Answer: a) The profit function can be written as:

P(x) = 5x - 400x + 600

To find the asymptotes, we can look at the denominator of the second term, which is (x - 3). This means that there is a vertical asymptote at x = 3. To find the intercepts, we can set P(x) = 0:

5x - 400x + 600 = 0

Solving for x, we get:

x = 1.5 and x = 2.5

Therefore, there are x-intercepts at (1.5, 0) and (2.5, 0). To sketch the graph, we can also note that the coefficient of x^2 is negative, which means that the graph is a downward-facing parabola.

b) The domain of the function is the set of all possible values of x, which in this context represents the amount of coffee sold. Since we cannot sell a negative amount of coffee, the domain is x ≥ 0.

The range of the function is the set of all possible values of P(x), which represents the profit. Since the coefficient of x^2 is negative, the maximum profit occurs at the vertex of the parabola. The vertex has x-coordinate:

x = -b/(2a) = -(-400)/(2(-200)) = 1

Therefore, the maximum profit occurs when x = 1. The vertex has y-coordinate:

P(1) = 5(1) - 400(1) + 600 = 205

Since the coefficient of x^2 is negative, the range is (-∞, 205].

c) The horizontal asymptote of the function is y = -400, which represents the long-term average profit per kilogram of coffee sold. This means that as x gets very large, the profit per kilogram approaches -400. This could happen, for example, if the cost of producing the coffee increased significantly while the price remained the same.

d) To find the amount of coffee that must be sold to make a profit of $4000, we can set P(x) = 4000 and solve for x:

5x - 400x + 600 = 4000

Simplifying, we get:

-395x = -3400

Dividing both sides by -395, we get:

x ≈ 8.61

Therefore, approximately 8.61 kg of coffee must be sold to make a profit of $4000.

Step-by-step explanation:

The unit price in dollars per pound is $4.75 (rounded to the nearest cent).

What is profit and loss?

Mathematicians use the profit and loss formula to calculate market prices for goods and to assess how lucrative a company is. There is a selling price and a cost price for every commodity. We can determine the profit made or loss suffered for a specific commodity based on the values of these prices. Cost price, fixed, variable, and semi-variable costs, selling price, marked price, list price, margin, etc. are some of the key words that are discussed in this article.

To find the unit price in dollars per pound, we need to divide the total cost by the total weight:

Unit price = Total cost / Total weight

In this case, the total weight is 3.8 pounds and the total cost is $18.05.

Unit price = $18.05 / 3.8 pounds

Unit price = $4.75 per pound (rounded to the nearest cent)

Therefore, the unit price in dollars per pound is $4.75 (rounded to the nearest cent).

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Answer:

The answer is 96

Step-by-step explanation:

2*(26+22)

2*48

96

The correct solution of given expression is C. (5 + 1 - 4) + (10/12 + 9/12 - 7/12) = 2 + 1 = 3.

What is expression?

In mathematics, an expression is a combination of symbols, numbers, and operators that represents a value or a relationship between values. Expressions can be composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and radicals.

We can simplify the expression inside the parentheses first and then subtract the fraction.

(5 5/6 + 1 3/4) - 4 7/12

= (33/6 + 7/4) - 55/12

= (11/2 + 7/4) - 55/12

= 22/4 + 7/4 - 55/12

= 29/4 - 55/12

To subtract these fractions, we need a common denominator of 12:

= (329)/(34) - (555)/(512)

= 87/12 - 275/60

= 87/12 - 11/4

= (29/4) - (33/12)

= (29/4) - (11/3)

To find the correct solution, we can simplify this expression:

(29/4) - (11/3) = (87/12) - (44/12) = 43/12

Therefore, the correct solution is C. (5 + 1 - 4) + (10/12 + 9/12 - 7/12) = 2 + 1 = 3.

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Answer:

316

Step-by-step explanation:

Answer:

Step-by-step explanation:

from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.

The value of x rounded to the nearest tenth is equal to 24.3 units.

In order to determine the value of x, we would apply basic trigonometry. From the information provided about this right angled triangle, we can logically deduce the following parameters:

Therefore, we would use the cosine trigonometry to determine the value of x as follows:

Cosθ = Adj/Hyp

Cos21 = x/26

x = 26cos21

x = 26(0.9336)

x = 24.3 units.

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Answer:

13sqrt{2}

Step-by-step explanation:

let's assume one side of square is a;

diognal which is BD=

[tex]a\sqrt{2}\\BE is BD/2=\frac{a\sqrt{2}}{2}=13\\a\sqrt{2}=26\\a=26/\sqrt{2}=13\sqrt{2}[/tex]

BC=CD=DA=AB=a=13sqrt{2}

Answer:

  5624.22 feet

Step-by-step explanation:

You want to know the distance from a skyscraper 1465 ft tall to a point where the angle of elevation to its top is 14.6°.

The tangent relation tells you ...

  Tan = Opposite/Adjacent

The distance between buildings is the side of the right triangle adjacent to the angle of elevation. The height of skyscraper B is the side opposite the angle of elevation. Using the tangent relationship, we can find the distance d between the buildings as ...

  tan(14.6°) = 1465/d

  c = 1465/tan(14.6°) ≈ 5624.22 . . . ft

The distance from A to B is about 5624.22 feet.

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Answer:

-0.63

1/7

15%

10%

Step-by-step explanation:

hope this helps

The APR when compounded semiannually and quarterly would be :

To find the APR when compounded semi - annually, we first need to find the periodic rate to be :

= Annual rate / 2 semi annual periods

= 3. 425 / 2

= 1.7125%

Then use the Effective Annual Rate (EAR) to find the APR to be:

= ( 1 + periodic rate ) ^ number of periods - 1

= ( 1 + 1. 7125 % ) ² - 1

= 3.4543%

For the APR when compounding quarterly, you can variate the EAR formula to the original version of:

= ( 1 + annual rate / number of periods ) ^ number of periods - 1

= ( 1 + 3. 425 / 4 ) ⁴ - 1

= 3.4692%

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Answer:

A

Step-by-step explanation:

Based on the employee contribution, the Traditional IRA is the better choice because the employee will be taxed at a lower rate on lower earnings in retirement than during employment. The Option A is correct.

The Traditional IRA allows the employee to make contributions on a pre-tax basis, which reduces the taxable income during the years of contribution. This reduces the tax liability during employment years in the 33% tax bracket. During retirement, the employee will be in the 15% tax bracket, which means they will pay a lower tax rate on the withdrawals from the Traditional IRA.

In contrast, the Roth IRA contributions are made with after-tax dollars, and the withdrawals during retirement are tax-free. Since the employee is currently in the 33% tax bracket, they will pay a higher tax rate on their current income than they would in retirement. Therefore, the Traditional IRA is a better choice for the employee in this scenario.

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Answer:

$1.39

Step-by-step explanation:

Robbie had 5.00 to start out with. The hamburger he bought was $1.26. The potato chips were $0.65 and the total of the 2 drinks would be $1.70. $0.85 x 2 = $1.70. If we add $1.26 + $0.65+ $1.70 it will equal = $3.61.  Now if we take Robbies $5.00 and minues that by $3.61 (total of all food and drinks) we would get $1.39. So, Robbie only had $1.39 left.

Hopefullly that helps you !

Answer:

3/4

Step-by-step explanation:

3/4 is larger because since they have the same denominator (the bottom value), you compare the numerators (the top value). Whichever numerator is bigger gives you the larger fraction.

Answer: 3/4 is larger, this is simply because 3/4 is = 75%

whereas 1/4 = 25%

let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

[tex]\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}[/tex]

The answer is x = 5±√61/2, I really hope this helps (:

Answer:

kamari

Step-by-step explanation:

Tashaun: [tex]\frac{74}{2}[/tex]= 32mph

kamari: 153/3=51mph

so we can see that kamari is speeding the speed limit is 50 and 51>50 brainliest?

Answer:

25

Step-by-step explanation:

Measure of the arc or angle indicated is 150.9 degrees.

In geometry, an arc is a portion of the circumference of a circle or any other curved shape. It is defined by two endpoints and all the points on the curve that lie between them. An arc is usually named by its two endpoints, with a small arc symbol above them to indicate that it is an arc.

The length of an arc can be calculated using the formula:

Arc length = (central angle/360) x 2πr

where r is the radius of the circle, and the central angle is the angle subtended by the arc at the center of the circle, measured in degrees.

The measure of an arc is the degree measure of the central angle subtended by the arc. A semicircle is an arc that subtends a central angle of 180 degrees, and a full circle is an arc that subtends a central angle of 360 degrees.

Since DE and PE are chords of the circle, and they intersect at point P, we can use the intersecting chords theorem to find the length of DP. Let x be the length of DP. Then:

DP * PE = DE * PC

x * (x + PE) = ([tex]\frac{CE}{2}[/tex]) * ([tex]\frac{CE}{2}[/tex])

x² + x(PE) - [tex]\frac{CE}{2}^{\frac{2}{4} }[/tex] = 0

Since angle DPE is 60 degrees, we can use the law of cosines to find PE. Let y be the length of PE. Then:

y² = DE² + DP² - 2 * DE * DP * cos(60)

y² = ([tex]\frac{CE}{2}[/tex])² + x^2 - ([tex]\frac{CE}{2}[/tex]) * x

Substitute this expression for y^2 into the equation for x and simplify:

[tex]x^{2} +x((\frac{CE}{2})^{2} + x^{2} -\frac{CE}{2} *x)^{0.5} -(\frac{CE}{2} ^{\frac{2}{4} } )=0[/tex]

Solve for x:

x = [tex]\frac{CE^{2} -4*(CE^{2} -3*\frac{CE}{2} ^{2} )^{0.5} }{4}[/tex]

x = [tex]\frac{3}{4} *\frac{CE^{2} }{CE^{2} -12}[/tex]

Now we can find the measure of the CD arc by using the formula for the central angle:

CD arc = [tex]2*arctan(\frac{DP}{CE})[/tex]

CD arc = [tex]2*arctan(\frac{x}{\frac{CE}{2} } )[/tex]

CD arc = [tex]2* arctan(CE^{2} -4*(CE^{2} -3*\frac{(\frac{CE}{2} ^{2})^{0.5}}{CE^{2}-12 } ))[/tex]

Simplifying this expression, we get:

[tex]CD arc=2*arctan(2*3^{\frac{1}{2} } -1)[/tex]

CD arc ≈ 150.9 degrees.

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Measure of the arc or angle indicated in the given figure is 150.9 degrees.

In geometry, an arc is a portion of the circumference of a circle or other curved shape. It is defined by his two endpoints and all midpoints of the curve. Arcs are usually named after their two endpoints, with a small arc symbol above them to indicate that they are arcs.

Arc Length = (Center Angle/360) x 2πr

where r is the radius of the circle and the central angle is the angle the arc makes at the center of the circle, measured in degrees.

The arc measurement is the angle of the central angle defined by the arc. A half circle is an arc that spans a central angle of 180 degrees, and a full circle is an arc that spans a central angle of 360 degrees.

Since DE and PE are chords of the circle and intersect at P, we can use the chord rule to find the length of DP. Let x be the length of DP.  Then:

DP × PE = DE × PC

x × (x + PE) = (CE/2) × (CE/2)

x² + x(PE) - [tex]\frac{CE}{2} ^{\frac{2}{4} }[/tex] = 0

Since angle DPE is 60 degrees, we can use the law of cosines to find PE. Let y be the length of PE. Then:

y² = DE² + DP² - 2 × DE × DP × cos(60)

y² = ([tex]\frac{CE}{2}[/tex])² + x² -  ([tex]\frac{CE}{2}[/tex]) × x

Substitute this expression for y² into the equation for x and simplify:

[tex]x^{2} +x((\frac{CE}{2} ^{2}) + x^{2} - \frac{CE}{2}*x)^{0.5} -[/tex] [tex]\frac{CE}{2} ^{\frac{2}{4} }[/tex] = 0

Solve for x:

x = [tex]\frac{CE^{2} - 4*(CE^{2}-3*\frac{CE}{2} ^{2})^{0.5} }{4}[/tex]

x = (3/4) × (CE²/CE²-12)

Now we can find the measure of the CD arc by using the formula for the central angle:

CD arc = 2arc tan(DP/CE)

CD arc = 2arc tan [x/(CE/2)]

CD arc = 2arc tan (CE² - 4 × (CE² - 3 × [tex]\frac{(\frac{CE}{2} ^{2}) ^{0.5} }{CE^{2}-12 }[/tex] )

Simplifying this expression, we get:

CD arc ≈ 150.9 degrees.

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The size of angle y in the quadrilateral is 130 degrees.

A quadrilateral is a polygon with 4 sides and angles. The quadrilateral above is a kite. The sum of angles in a quadrilateral is 360 degrees.

Therefore, let's find the angles in the quadrilaterals as follows:

y + y + 70 + 30 = 360(sum of angles in a quadrilateral)

2y + 100 = 360

2y = 360 - 100

2y = 260

divide both sides by 2

y = 260 / 2

y = 130 degrees

Therefore, the size of y is 130 degrees.

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Answer:

Since the prism is completely filled with 96 cubes that have an edge length of 1/2 cm, we can find the volume of the prism by multiplying the number of cubes by the volume of each cube.

The volume of each cube is (1/2 cm)^3 = 1/8 cm^3.

The number of cubes is 96.

Therefore, the volume of the prism is:

volume = (number of cubes) x (volume of each cube)

volume = 96 x (1/8 cm^3)

volume = 12 cm^3

So, the volume of the prism is 12 cubic centimeters.

Answer:

6 weeks and 840 hours

Step-by-step explanation:

There are 168 hours in one week.

24 hrs/day * 7 days = 168 hours

1008 hours ÷ 24 hours(1 day) = 42 days ÷ 7 days in a week = 6 weeks

168 hours/week * 5 weeks = 840 hours