what does a formal proof need to have

Answer:

The set notation for the diagram is P-Q

Step-by-step explanation:

Area of the trapezoid = height x average of bases

                 area = 4 x (8+13)/2) = 42 in^2

Area of triangle  = 1/2 base * height   = 1/2 (13-8) * 4 = 10 in^2

Answer:

P = side a + side b + side c

Step-by-step explanation:

The perimeter of any polygon is all sides added together.

Answer:

3 X sides please mark me brainlist

Answer:

\(m=\frac{5}{3}\\\\m =1\frac{1}{3}\)

Step-by-step explanation:

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(0,\:0\right),\:\\\left(x_2,\:y_2\right)=\left(3,\:5\right)\\\\m=\frac{5-0}{3-0}\\\\Simplify\\\\m=\frac{5}{3}\\\\m =1\frac{1}{3}\)

Answer:

------------------------

Find the slope of AB:

Use point-slope form and point A(2, 4) to determine the line:

Multiply both sides by 9 to clear fraction:

Open parenthesis and convert the equation into ax + by + c = 0:

The perimeter and the area of each composite figure are, respectively:

Case 1: p = 77.6 cm, A = 304 cm²

Case 2: p = 25.1 ft, A = 28 ft²

Case 3: p = 42 mi, A = 52.5 mi²

Case 4: p = 56.5 in, A = 179.424 in²

In this problem we need to determine the perimeter and the area of four composite figures, that is, figures formed by combining triangles and rectangles, whose area formulas are listed below:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we find the perimeter and the area of each figure:

Case 1

p = 2 · (18.8 cm) + 2 · (20 cm)

p = 77.6 cm

A = (15.2 cm) · (20 cm)

A = 304 cm²

Case 2

p = 10 ft + 8.1 ft + 7 ft

p = 25.1 ft

A = 0.5 · (10 ft) · (5.6 ft)

A = 28 ft²

Case 3

p = 17.5 mi + 6 mi + 18.5 mi

p = 42 mi

A = 0.5 · (17.5 mi) · (6 mi)

A = 52.5 mi²

Case 4

p = 20 in + 13.9 in + 15 in + 7.6 in

p = 56.5 in

A = (7.6 in) · (13 in) + 0.5 · √[(13.9 in)² - (13 in)²] · (13 in) + 0.5 · √[(15 in)² - (13 in)²] · (13 in)

A = 98.8 in² + 31.982 in² + 48.642 in²

A = 179.424 in²

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The airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

How to solve for the airplane's groundspeed

To determine the resultant velocity of the airplane, we need to break down the airplane's velocity and the wind's velocity into their respective components and add them. Let's assume that the angles are measured clockwise from true north.

Let's denote:

Vp = airplane's speed = 250 km/h

θp = airplane's heading = 075 degrees

Vw = wind's speed = 85 km/h

θw = wind's heading = 300 degrees

We can then find the eastward (x) and northward (y) components of the velocities:

For the airplane:

Vpx = Vp * cos(θp) = 250 * cos(75 degrees) = 64.95 km/h

Vpy = Vp * sin(θp) = 250 * sin(75 degrees) = 241.92 km/h

For the wind:

Vwx = Vw * cos(θw) = 85 * cos(300 degrees) = 73.60 km/h

Vwy = Vw * sin(θw) = 85 * sin(300 degrees) = -42.50 km/h

We then sum the x and y components of the two velocities to find the resultant velocity components:

Vrx = Vpx + Vwx = 64.95 km/h + 73.60 km/h = 138.55 km/h

Vry = Vpy + Vwy = 241.92 km/h - 42.50 km/h = 199.42 km/h

The magnitude of the resultant velocity, which represents the groundspeed (Vr), is found using the Pythagorean theorem:

Vr = sqrt((Vrx)^2 + (Vry)^2) = sqrt((138.55)^2 + (199.42)^2) = 242.25 km/h

The bearing (θr) of the resultant velocity (relative to north) can be found using inverse tangent:

θr = atan2(Vry, Vrx) = atan2(199.42, 138.55) = 55.04 degrees

Therefore, the airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

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Answer:

32 days

Step-by-step explanation:

make a rate time distance chart:

                   r             t         d

first 5         | y  |     5        | 5y

final days | y+6 | x-6        | (y+6)(x-6)

take y for planned rate and x for time till test

then make system of equations:

1. 5y+(y+6)(x-6) = 844

2. 768/y =x

/Henrietta knew the time till test, so we can assume that she planned in such a way that would mean she learned exactly 768 spells if she worked at the set rate. On this assumption we make 2

solve, and you get 2 options: x=-10/3 y =-144 (exclude, negative)

the second one is x=24 y=32 that works for us, so answer is she planned to learn 32 spells each day.

The number of magic Henrietta planned to learn each day is 32

Represent the number of magic learned each day in the first 5 days with x, and the total days with y.

So, the total number of magic learned in this time frame is:

Total = 5x

In the remaining days (i.e y - 5), she learned 6 more each day

i.e. x + 6

So, the total number of magic learned in this remaining days is:

Total = (x + 6)(y - 5)

So, we have the following system of equations:

\(5y+(x+6)(y-5) = 844\)

\(xy = 768\)

Using a graphing calculator, we have:

(x,y) = (32, 24)

Hence, the number of magic she planned to learn each day is 32

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Answer:

Options 1 and 4 are the only other parallel lines

Step-by-step explanation:

Plug the equation into a graphing calculator and observe your results.

Answer:

The answers are y = −4x, 16x + 4y = 9, and y = −4x + 15

Step-by-step explanation:

y=-4x has the -4 as slope so it parallel

y = −4x + 15 also has the -4 as a slope so it parallel

16x + 4y = 9 u have to solve.

4y=-16x+9 First step is to subtract -16 both sides (which just tosses -16 to the other side where the 9 is.

y=-4x+2.25 Divide everything by 4

REMEMBER TO MARK ALL THREE TO GET FULL CREDIT

The features related to vectors are listed below:

Case A: u' = (- 4√41 / 41, - 5√41/ 41)

Case B: Tip coordinantes of vector v: (x, y) = (10, 10)

Case C: r = 11.402

In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.

Case A - Unit vector

Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:

u' = u / ||u||

Where:

Please notice that the magnitude of the vector is determined by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

Where:

Thus, the unit vector of u is:

u' = (- 4, - 5) / √[(- 4)² + (- 5)²]

u' = (- 4, - 5) / √41

u' = (- 4 / √41, - 5 / √41)

u' = (- 4√41 / 41, - 5√41/ 41)

Case B - Definition of a vector

This can be found easily by vector subtraction:

v = Tip coordinates - Base coordinates

(3, 4) = (x, y) - (7, 6)

(x, y) = (3, 4) + (7, 6)

(x, y) = (10, 10)

Case C - Magnitude of a vector

The magnitude is found by means of Pyhtagorean theorem:

r = √[(- 4 - 3)² + (- 5 - 4)²]

r = √[(- 7)² + (- 9)²]

r = 11.402

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Answer:

  f(g(2)) = 51

Step-by-step explanation:

The expression f(g(2)) means you are to use g(2) as the argument for the function f(x).

__

The value of a function is found by substituting the argument value in the defining expression, then simplifying the result.

Here, we do that in steps, working outward from the innermost parentheses, as required by the Order of Operations.

  g(2) = 7(2^2) = 7·4 = 28 . . . . . put 2 where x is in g(x) = 7x^2, evaluate

  f(g(2)) = f(28) = 2(28) -5 = 56 -5 = 51 . . . . . . put 28 where x is in f(x) = 2x -5

  f(g(2)) = 51

_____

Many graphing calculators will let you define functions. You can use the calculator to compute the value for you. A spreadsheet can do the same thing.

Answer: voluntary response sampling

Step-by-step explanation:

Based on the information given in the question, the sampling technique that is being used is the voluntary response sampling.

A voluntary response sampling refers to a sample which is gotten when a researcher tells the members to join a particular sample and then the ones that are interested then joins. Such participants volunteer voluntarily and take part in the research studies and give their opinions on the topic.

Since the student organization at a local college posted a poll on its website and the interested students took part, it is a voluntary response sampling.

Given:

Charlie bought a new computer for $450 with his credit card.

He plans to pay the minimum payment  of $25 per month.

To find:

The rate of change.

Solution:

Let y be the remaining amount of loan after x months.

Initial amount of loan = $450

Payment of one month = $25

Payment of x months = $25x

Now,

Remining amount = Initial amount of loan - Payment of x months

\(y=450-25x\)     ...(i)

The slope intercept form is

\(y=mx+b\)     ...(ii)

where, m is slope and b is y-intercept.

From (i) and (ii), we get

\(m=-25\)

Therefore, the rate of change is -25 dollars.

Answer: The number 0.1453 belong to rational numbers and real numbers.

Step-by-step explanation:

Therefore,

The number 0.1453 belong to rational numbers and real numbers.

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Answer:

b

Step-by-step explanation:

9514 1404 393

Answer:

  A: -1, 3/5

  B: (-1/5, -3 1/5)

  2: plot the given points and draw a curve through them.

Step-by-step explanation:

The x-intercepts are most easily found from a graph of the function. I like the Desmos graphing calculator for this purpose. The x-intercepts are -1 and 3/5.

You can also find the x-intercepts by factoring the function.

  f(x) = 5x^2 +5x -3x -3 = 5x(x +1) -3(x +1) = (5x -3)(x +1)

The x-intercepts are the values of x that make the factors zero:

  5x -3 = 0   ⇒   x = 3/5

  x +1 = 0   ⇒   x = -1

__

The vertex is on the axis of symmetry, which is the vertical line at the value of x halfway between the zeros. (-1 +3/5)/2 = (-2/5)/2 = -1/5

The value of f(x) there is ...

  f(-1/5) = (5(-1/5) +2)(-1/5) -3 = (-1 +2)(-1/5) -3 = -1/5 -3 = -3 1/5

The vertex is (-1/5, -3 1/5).

__

The easiest step to take to graph the function is to type it into a graphing calculator (see attached).

If you're graphing this by hand, the three points given in parts A and B will be on the graph. The leading coefficient in the function is 3, so the x^2 parent function is vertically stretched by a factor of 3. This can make it a little more difficult to find points that lie on the graph.

Recognizing that the vertex form equation is ...

  f(x) = 3(x +1/5) -3 1/5

I might choose x-values that are -1/5 ± 1/2 to get y-values that are -3 1/5 + 3/4. And, x = -1/5 ± 1 ⇒ y = -3 1/5 +3.

Answer is (d). 1m & 4 m. The magnitude of the result of P + Q is between P + Q and P - Q. The magnitude of the resultant is between 3 and 5 meters when the displacement is between 1 and 4 meters.

A resultant displacement is produced when displacement vectors are added. However, as long as two vectors have the same vector amount, any two vectors can be added. A resultant velocity is produced when two or more velocity vectors are added. A resultant force is created when two or more force vectors are joined together.

S = x^2 + y^2 is the displacement formula that results. For displacement, use the letter "S." The object is moving in two directions at once: X in the first direction and Y in the second. Y = 0 if your object only moves in one direction.

verify option 1:

(1,1) = P+Q = 1+1=2

P-Q = 1-1 =0

Resultant R = 2+0 = 2 (so, we can add this Option)

verify option 2:

(1,2) = P+Q = 1+2=3

P-Q = 1-2 =-1

R= 3-1= 2 (so, we can add this Option)

verify option 3:

(1,3) = P+Q = 1+3=4

P-Q = 3-1 = 2

R= 4-2= 2 (so, we can add this Option)

verify option 4:

(1,4) = P+Q = 1+4=5

P-Q = 1-4 = 2

R= 5-2= 3 (so, we can't add this Option)

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The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

Here, we have,

we know that,

The sum of the angles in a triangle add to 180

x+2x+6x = 180

Combine like terms

9x= 180

Divide by 9

9x/9 = 180/9

x = 20.

Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

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complete question:

The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.

Answer:

4800 inches^3

Step-by-step explanation:

to find volume you must multiply the length width and depth

40 * 20 * 6

40 * 20 = 800

800 * 6 = 4800

your answer is 4800 inches cubed

Answer:

x = -3

Step-by-step explanation:

Axis of parabola is x axis so

Axis of symmetry is x co-ordinate i.e x=2

a) To maximize profits, 10 units should be sold in market 1 and 5 units in market 2.

b) The corresponding prices are $180 in market 1 and $160 in market 2.

c) If it becomes illegal to discriminate, the profit loss is $50.

d) The imposition of a tax of $5 per unit sold in market 1 would likely decrease the monopolist's profit and potentially lead to adjustments in prices and quantities sold in both markets.

a) To maximize profits, the monopolist should set marginal revenue equal to marginal cost in each market.

In this case, marginal revenue is equal to the derivative of the demand function with respect to quantity, and it can be calculated as MR = dP/dQ.

For market 1:

MR₁ = dP₁/dQ₁ = -2

For market 2:

MR₂ = dP₂/dQ₂ = -4

Setting MR equal to marginal cost, which is the derivative of the cost function with respect to quantity, gives:

MR₁ = -2 = dC/dQ₁ = 20

MR₂ = -4 = dC/dQ₂ = 20

Solving these equations, we find:

Q₁ = 10

Q₂ = 5

Therefore, the monopolist should sell 10 units in market 1 and 5 units in market 2 to maximize profits.

b) To determine the corresponding prices, we substitute the quantities obtained in part (a) into the demand functions:

For market 1:

P₁ = 200 - 2Q₁ = 200 - 2(10) = 180

For market 2:

P₂ = 180 - 4Q₂ = 180 - 4(5) = 160

Therefore, the corresponding prices are $180 in market 1 and $160 in market 2.

c) To calculate the profit lost if it becomes illegal to discriminate, we need to compare the profits under discrimination with the profits under non-discrimination.

Under discrimination, the monopolist charges different prices in each market, while under non-discrimination, the same price is charged in both markets.

Under discrimination:

Profit = Total revenue - Total cost

For market 1:

Total revenue₁ = P₁ \(\times\) Q₁ = 180 \(\times\) 10 = $1

For market 2:

Total revenue₂ = P₂ \(\times\) Q₂ = 160 \(\times\) 5 = $800

Total revenue = Total revenue₁ + Total revenue₂ = $1800 + $800 = $2600

Total cost = C = 20(Q₁ + Q₂) = 20(10 + 5) = $300

Profit = Total revenue - Total cost = $2600 - $300 = $2300

Under non-discrimination:

Since the same price is charged in both markets, we take the average price:

Average price = (P₁ + P₂) / 2 = (180 + 160) / 2 = $170

Total revenue = Average price \(\times\) (Q₁ + Q₂) = $170 \(\times\) (10 + 5) = $2550

Total cost remains the same at $300.

Profit = Total revenue - Total cost = $2550 - $300 = $2250

Therefore, the profit lost if discrimination becomes illegal is $2300 - $2250 = $50.

d) The imposition of a tax of $5 per unit sold in market 1 would increase the cost per unit for the monopolist.

This would affect the profit-maximizing quantity in market 1 and potentially lead to a change in prices.

The monopolist would compare the new marginal cost, which includes the tax, with the marginal revenue to determine the new profit-maximizing quantities and prices.

The tax would likely reduce the monopolist's profits and could potentially result in adjustments in production and pricing strategies.

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Answer: Here are the basic steps as to write any decimal with any amount of repeating digits as a fraction!

1. Create an equation such that x equals the decimal number.

2. Count the number of decimal places, y. Create a second equation multiplying both sides of the first equation by 10y.

3. Subtract the second equation from the first equation.

4. Solve for x.

5. Reduce the fraction.

Let's use the repeating decimal 0.6... with the digit 6 repeating as our example.

Hint: The six's in bold are repeating.

x = 0.6

10x = 6.6

10x - x = 6.6 - 0.6

9x = 6

x = 6/9 or 2/3

Answer:

rotation about Point a and  reflection across line M

Step-by-step explanation:

  got it right on edgentuinty dont know how to spell it lol

Answer:

The first transformation was a : rotated about point A

The second transformation was a : reflection across line M

Step-by-step explanation:

hope this helped <3

Answer:

64.29%

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

thank you

Step-by-step explanation:

:)

package of 25 (cards) = $5.25

1) Explain how you can tell that the unit price per card is less than $1.

if the price per card were 1 then the total price would be 25. The price has to be about a fifth of 1

2) Price per unit (card) = total price / number of cards

Price per unit (card) = $5.25/ 5

= 0.21

________________________

Answer

The price per card is 0.21

Answer:

I would say that the answer is D

Step-by-step explanation:

Hope this helps you:)

The result of the division of the two complex numbers is equal to z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)].

In this problem we find two complex numbers in rectangular form, whose division must be found. This can done by easily by means of complex numbers in polar form and definition of division:

Complex number (rectangular form)

z = r · (cos θ + i sin θ)

Complex number (polar form)

\(z = r\cdot e^{i\cdot \theta}\)

Where:

Division between two complex numbers in polar form:

\(\frac {z_{1}}{z_{2}} = \left(\frac{r_{1}}{r_{2}}\right)\cdot e^{i\cdot (\theta_{1}-\theta_{2})}\)

This number is equivalent to the following expression in rectangular form:

z₁ / z₂ = (r₁ / r₂) · [cos (θ₁ - θ₂) + i sin (θ₁ - θ₂)]

If we know that r₁ = 8, r₂ = 9, θ₁ = π / 10 and θ₂ = π / 12, then the division of the two complex numbers is:

z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)]

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The formula for the volume of a cone is:

V = (1/3)πr^2h

Solving for r:

V = (1/3)πr^2h

3V = πr^2h

r^2 = (3V)/(πh)

r = sqrt[(3V)/(πh)]

Given that V = 660cm^3, h = 14cm and π = 22/7:

r = sqrt[(3 × 660)/(22/7 × 14)] ≈ 7 cm

So the radius is approximately 7 cm.

To find the value of h:

V = (1/3)πr^2h

660 = (1/3)(22/7)(7^2)h

660 = (22/3)(49/7)h

660 = (22/3)(7)h

h = 660 / [(22/3)(7)]

h = 9.45 cm (rounded to two decimal places)

Therefore, the value of h when the volume of the cone is 660 cm^3 is approximately 9.45 cm.

Answer:

I would say A lmk if im wrong.

Step-by-step explanation:

Answer: A

Step-by-step explanation: You can use the pythagorean theorom to figure this one out. For all right traingles the sum of one of the smallest sides squared plus the sum of the other smallest side squared equal the biggest side squared or a^2+b^2=c^2. Which ever one of these doesnt fit the equation isnt a right traingle. 5^2+9^2=106, 11^2=121 106\(\neq\)121.