Find the area of the triangle whose vertices are (−2,3),(3,2) and (−1,−8) by using determinant method.

The Answer is approximately equal to 942.48 or 300π

(π=pi)

By using the speed fοrmula, the velοcity οf the wind is apprοximately 66.23 mph.

Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn. Mathematically, speed is calculated as fοllοws:

speed = distance/time

where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

Let's assume that the speed οf the wind is represented by the variable "v" (in mph). When the plane flies dοwnwind, the speed οf the plane relative tο the grοund is the sum οf its airspeed and the wind speed, οr (340 + v) mph. Similarly, when the plane flies upwind, the speed οf the plane relative tο the grοund is the difference between its airspeed and the wind speed, οr (340 - v) mph.

Nοw, lets use the fοrmula:

time = distance / speed

tο set up twο equatiοns and sοlve fοr the wind speed "v".

First, fοr the dοwnwind flight:

time = distance / speed

200 / (340 + v) = t

Secοnd, fοr the upwind flight:

time = distance / speed

140 / (340 - v) = t

Since the time taken fοr bοth flights is the same, we can equate the twο equatiοns:

200 / (340 + v) = 140 / (340 - v)

Nοw, we can sοlve fοr "v":

200(340 - v) = 140(340 + v)

68,000 - 200v = 47,600 + 140v

308v = 20,400

v ≈ 66.23

Therefοre, the velοcity οf the wind is apprοximately 66.23 mph.

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For the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

The opposing sides are equal and parallel. Angles on either side are equal. The subsequent or neighbouring angles are additional. All of the angles will be at right angles if any one of them is a right angle.

We know that the opposite sides of a parallelogram are parallel and equal thus,

8p + 6 = 9p – 2

6 + 2 = 9p – 8p

8 = p

Now, the value of side is:

UV = 8(8) + 6 = 70

The value of side VW is:

VW = 5(8) – 6 = 34

Hence, for the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.

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Answer:

1. To expand the polynomial f(x) = (x-3)(x+2)(x+3), we can use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x+3) using FOIL again.

2. To expand the polynomial g(x) = (x-3)(x+2)(x-2), we can also use the FOIL method twice, where we first multiply (x-3) and (x+2) using FOIL, then multiply the resulting binomial by (x-2) using FOIL again.

3. The polynomial f(x) has three linear factors, and so the degree of the polynomial will be 3, since we will have to multiply three binomials together. The polynomial g(x) has four linear factors, and so the degree of the polynomial will be 4.

If we were to expand a polynomial with five linear factors, the degree of the polynomial would be 5, since we would have to multiply five binomials together.

4. The degree of a polynomial is determined by the highest power of x in the polynomial, which is determined by the number of terms in the expanded polynomial expression.

(6 sentences to use):

1. To expand the polynomial (x-3)(x+2)(x+3), we use the distributive property and multiply each term of the first binomial by each term of the second binomial, then multiply the resulting trinomial by the third binomial.

2. To expand the polynomial (x-3)(x+2)(x-2), we use the same strategy as in the previous example, multiplying each term of the first binomial by each term of the second binomial, and then multiplying the resulting trinomial by the third binomial.

3. The polynomial f(x) has three linear factors, so its degree is 3, which means the highest exponent in the polynomial is 3.

4. The polynomial g(x) has four linear factors, so its degree is 4, which means the highest exponent in the polynomial is 4.

5. If we were to expand a polynomial using five linear factors, we would again use the distributive property to multiply each term of each binomial together, resulting in a polynomial with a degree of 5, which means the highest exponent in the polynomial would be 5.

6. This strategy for multiplying three binomials is a useful tool in algebraic manipulation, allowing us to expand and simplify polynomial expressions.

Hope this helped! Sorry if it didn't. If you need more help, ask me! :]

The solution to the linear system with repeated eigenvalues can be written in two forms: the exponential form and the Jordan form. In the Jordan form, the solution is written as:  [tex]x(t) = e^(J*t) * v_0[/tex]

In the exponential form, the solution is written as:
[tex]x(t) = e^(lambda*t) * (v + t*w)[/tex]
Where lambda is the repeated eigenvalue, v is the eigenvector, and w is the generalized eigenvector.

In the Jordan form, the solution is written as  :  [tex]x(t) = e^(J*t) * v_0[/tex]
Where J is the Jordan matrix, which is a matrix with the repeated eigenvalue lambda on the diagonal and a 1 on the superdiagonal, and v_0 is the initial condition vector.

Both forms of the solution give the same result, but the exponential form is simpler and easier to compute. The Jordan form is more general and can be used to find the solution for any linear system with repeated eigenvalues.

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Answer:

(x-1)(x+6)

Step-by-step explanation:

Yes, trigonometry only works on the right angled triangles.

The study of correlations between triangles' side lengths and angles is known as trigonometry.

Thus, the right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.

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The complete question is-

Right triangle and trigonometry:

Does trigonometry work on right triangles?

The conditional probability of drawing a heart on the fourth draw given that the first three cards are not hearts is 13/49.. The correct answer is D.

After drawing three cards without replacement, there are 52 - 3 = 49 cards remaining in the deck, of which 13 are hearts and 36 are not hearts.

If the first three cards are not hearts, then there are 36 cards remaining in the deck for the fourth draw, of which 13 are hearts and 23 are not hearts.

The conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, can be calculated using Bayes' theorem:

P(heart on 4th draw | first 3 not hearts) = P(heart on 4th draw and first 3 not hearts) / P(first 3 not hearts)

The probability of drawing a heart on the fourth draw and the first three not being hearts is:

P(heart on 4th draw and first 3 not hearts) = (36/52) * (35/51) * (34/50) * (13/49) = 0.0334

The probability of the first three cards not being hearts is:

P(first 3 not hearts) = (36/52) * (35/51) * (34/50) = 0.5764

Therefore, the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, is:

P(heart on 4th draw | first 3 not hearts) = 0.0334 / 0.5764 ≈ 0.058 or approximately 5.8%.

Therefore, the answer is 13/49. The correct answer is D.

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Answer: The volume of a cube is calculated by multiplying the edge length by itself three times, or V = l^3.

If the edge length of Jasmine's cube is doubled, the new edge length will be 4 inches x 2 = 8 inches.

Thus, the new volume of the cube would be V = 8^3 = 512 cubic inches.

Comparing this new volume to the original volume of the cube, V = 4^3 = 64 cubic inches, we can see that the new volume is multiplied by 8.

Therefore, the correct answer is D) The volume is multiplied by 8.

Step-by-step explanation:

There are approximately 2425 of those intervals that will contain the population means.

A confidence interval is a range of values that includes a parameter estimate with a certain degree of certainty. A confidence interval is a measure of uncertainty about an estimation procedure, rather than a statement about a parameter. A confidence interval is a specific value or a range of values in statistics that is used to estimate population characteristics.

This is because a 97% confidence interval means that if we were to repeat the sampling process many times, about 97% of the resulting intervals would contain the population mean. In other words, we would expect 97% of the intervals to be "correct" in the long run, while about 3% of them would not contain the population mean.

Therefore, out of the 2500 intervals we compute, we would expect approximately 0.97 x 2500 = 2425 intervals to contain the population mean, and about 0.03 x 2500 = 75 intervals not to contain the population mean. However, it's important to note that the actual number of intervals that contain the population means may vary from this expected value due to random sampling variability.

Where, [tex]\[\bar{x}\][/tex] is the sample mean

[tex]\[\frac{s}{\sqrt{n}}\][/tex] is the standard error of the mean

zα/2 is the z-score that covers α/2 in the tails of a normal distribution.

As we draw 2500 samples of size 100 from a population and compute a 97% confidence interval for each sample, the proportion of the sample will contain the population means.

Therefore, the number of intervals that will contain the population mean is approximately 2425.

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Step-by-step explanation:

The distributive property of multiplication over addition states that for any numbers a, b, and c, a × (b + c) = a × b + a × c.

Looking at Marta's work, we can see that the distributive property was used in line 1, where she distributed the 2 to both terms inside the parentheses:

2(x - 4) + 2x = x + 7

2x - 8 + 2x = x + 7

4x - 8 = x + 7

Therefore, the step in Marta's work that is justified by the distributive property is line 1, where she distributed the 2 to both terms inside the parentheses.

Answer:

The formula for the volume of a triangular prism is given by:

V = (1/2)bhL

where b is the base length of the triangle, h is the height of the triangle, and L is the length of the prism (i.e., the distance between the two triangular faces).

We are given the area of the rectangular surface of the prism, which is the product of the lengths of two adjacent sides of the rectangle, and we know that this area is equal to 864 cm^2. Therefore, we can use the Pythagorean theorem to find the length of the third side of the rectangle, which is also the base length of the triangular face:

17^2 = 9^2 + 10^2

289 = 81 + 100

289 = 181

So, the base length of the triangular face is 8 cm. Now we can plug in the known values into the formula for the volume of the prism:

864 = (1/2)(8 cm)(h)(L)

We are not given the length of the prism, L, but we know that it is equal to the base length of the triangle, which is 8 cm. Therefore, we can simplify the equation to:

864 = 32h

Solving for h, we get:

h = 864/32

h = 27

So the height of the prism is 27 cm.

The function f(x)= (x+4)(x-2)/(x+4)(x-2) passes through the origin with a constant slope of 1, and has two removable discontinuities at x=-4 and x=2.

The function that passes through the origin with a constant slope of 1 and has removable discontinuities at x=-4 and x=2 is given by:

f(x)= (x+4)(x-2)/(x+4)(x-2). This function can be written in its factored form as f(x)= 1.

The function has a constant slope of 1, which means that for any two points (x_1,y_1) and (x_2,y_2) the slope is given by

(y_2-y_1)/(x_2-x_1)=1.

The function has two removable discontinuities at x= -4 and x= 2. This means that at these points the function is undefined, and the derivative of the function is infinite.

Removable discontinuities can be resolved by factoring out a common factor from the numerator and denominator of the function. In the case of the given function, factoring out (x+4) and (x-2) resolves the discontinuities. The graph of the function is a straight line which passes through the origin. This is because the function is of the form y=mx, where m is the constant slope of 1, which makes the function pass through the origin.

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The first 5 terms of the sequence, whose general term is an = -9n - 9, would be the following: -18, -27, -36, -45, -54.

In mathematics, a sequence is an ordered list of numbers, called terms, that follow a particular pattern or rule. Each term in a sequence is identified by its position in the sequence, which is usually represented by an integer index or subscript.

To find the first 5 terms of the sequence with the general term an = -9n - 9, we can simply substitute the values of n from 1 to 5 into the formula and simplify:

a1 = -9(1) - 9 = -18

a2 = -9(2) - 9 = -27

a3 = -9(3) - 9 = -36

a4 = -9(4) - 9 = -45

a5 = -9(5) - 9 = -54

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Answer:

No

Step-by-step explanation:

14x + 2 ≠ 16x

Because 2 doesn't have an x variable, it can't be added with 14x!

7 times 5 shows the number of students in the four-square match. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

It is stated that the four fundamental operations, often known as "arithmetic operations," can explain all real numbers. Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.

We are given that there were 7 teams in the four-square match and each team was made of 5 third-graders.

Now, in order to find the total students, we will use the multiplication operation.

From this, we get 7 times 5 which represents the total students.

Hence, 7 times 5 shows the number of students in the four-square match.

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On a taxable income of $25,000, you must pay $3,358.75 in taxes.

To find how much tax you need to pay on a taxable income of $25,000, you will need to use the tax table given.

Since $25,000 falls in the third row of the table, which is for taxable income over $7,825 but not over $31,850, we will need to use the formula for this row:

Tax = $782.50 + 15% of the amount over $7,825

To calculate the tax, we need to first find the amount over $7,825, which is:

25,000 - 7,825 = 17,175

Now we can substitute this into the formula to get:

Tax = 782.50 + 0.15 x 17,175

Tax = 782.50 + 2,576.25

Tax = 3,358.75

Therefore, the amount of tax you need to pay on a taxable income of $25,000 is $3,358.75.

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The value of the vehicle 5 years after purchase will be $12,500. After we predict the depreciation of car values as time progresses.

Due to use, wear, and tear, or becoming obsolete, an asset loses value over time. Depreciation is the measurement of this decrease.

Using the given linear model y = -1100x + 25,000, we can substitute x = 5 (since we want to find the value after 5 years of purchase) and solve for y:

y = -1100(5) + 25,000

y = -5500 + 25,000

y = 19,500

Therefore, the value of the vehicle 5 years after purchase will be $19,500.

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The given complex numbers are 2 - 3i and -2 + 6i. We need to find the sum and product of the given complex numbers.

Sum of the complex numbers = (2 - 3i) + (-2 + 6i)

= 2 - 2 + (-3i + 6i)

= 4i

Therefore, the sum of the given complex numbers is 4i.

Now, let's find the product of the given complex numbers.

Product of the complex numbers = (2 - 3i) (-2 + 6i)

= -4 + 12i + 6i - 18i^2

= -4 + 18i + 18 (as i^2 = -1)

= 14 + 18i

Therefore, the product of the given complex numbers is 14 + 18i.

Hence, the sum of the given complex numbers is 4i and the product of the given complex numbers is 14 + 18i.

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A) the probability of winning a positive amount of money is approximately 0.000487.

B) the ticket would have to cost $0.0522 (or approximately $0.05) for this lottery to be fair, in the sense that the expected profit is $0.

(a) To calculate the probability of winning a positive amount of money, we need to add up the probabilities of winning each prize except for the $0 prize:

Probability of winning a positive amount
= Probability of winning $300,000 + Probability of winning $70,000 + Probability of winning $600 + Probability of winning $18 + Probability of winning $5 + Probability of winning $3

Probability of winning a positive amount

= 1/5,518,121 + 1/1,715,449 + 1/9,024 + 1/1,768 + 1/358 + 1/166

Probability of winning a positive amount

≈ 0.000487 (to two decimal places)

Thus, the probability of winning a positive amount of money is approximately 0.000487.

(b) To find the ticket cost that makes the lottery fair, we need to calculate the expected profit, which is the sum of the products of the probability of winning each prize and the amount of money won for that prize. Since there are six possible prizes, the expected profit can be written as:

Expected profit = (1/5,518,121)($300,000) + (1/1,715,449)($70,000) + (1/9,024)($600) + (1/1,768)($18) + (1/358)($5) + (1/166)($3) - Ticket cost

Simplifying the expression above, we get:

Expected profit
= $0.0522 - Ticket cost

For the lottery to be fair, the expected profit should be $0. Therefore, we can set the expected profit equal to $0 and solve for the ticket cost:

$0 = $0.0522 - Ticket cost

Ticket cost = $0.0522

Therefore, the ticket would have to cost $0.0522 (or approximately $0.05) for this lottery to be fair, in the sense that the expected profit is $0.

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In response to the query, we can state that Salim thereby covered a total fraction distance of about 3.83 miles.

To represent a whole, any number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of the numerator to the denominator. They can all be expressed as simple fractions as integers. In the numerator or denominator of a complex fraction is a fraction. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.

Salim therefore walked a total of:

4/3 Plus 5/2 miles

We must identify a common denominator in order to add these fractions:

Six is the least frequent multiple of 3 and 2.

We may therefore rephrase the following fractions with denominators of 6:

4/3 = (4/3) x (2/2) = 8/6

5/2 = (5/2) x (3/3) = 15/6

We can now combine the fractions:

8/6 + 15/6 = 23/6

Salim covered a distance of 23/6 miles in all.

This fraction can be simplified by dividing both the numerator and denominator by their largest common factor, which is 1:

3.83 miles, or 23/6 miles (rounded to two decimal places)

Salim thereby covered a total distance of about 3.83 miles.

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The amount that Jessica will earns if she sells 34 books is 86 dollars.

An earning refers to the income that a person  get from wages and salaries, security and other government benefits, dividends and interest, business ownership, other sources etc.

Our Equation to solve for earnings is:

A = 52 + (1)B

A = 52 + B

A(34) = 52 +34

A(34) = $86

Therefore, the total earned in one week if she sold 34 books is $86.

Missing words' Write an equation relating A to B. Then use this equation to find the amount of money Lena earns if she sells 34 books. Equation:  Amount Jessica earns is she sells 34 books: ____ dollars".

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Using the perimeter formula of a rectangle we can write an equation describing the values of x and y is as follows:

2y + 2x = 52 inches

The perimeter of a rectangle is the total length of its edges. It is expressed in linear units like centimetres, inches, and the like and can be taken to mean the total measurement of the rectangle's length and width. For instance, you may rapidly calculate how much ribbon you'd need if you needed to decorate the edge of your rectangular notebook. Similar to how calculating the perimeter will help you determine how much wire you'll need to erect a fence around your garden.

The formula P = 2(l + w), where l is the length and w is the width, determines the perimeter of a rectangle. Since we are aware that this rectangle's perimeter is 52 inches, we can write the following equation: 2l + 2w = 52 inches.

We can express the equation in terms of x and y to discover the potential values for x and y. We may substitute the width (x) and the length (y) into the equation to get 52 inches: 2y + 2x.

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Answer:

y = x/3 - 8/3 (OR) 3y = x - 8

Both of the above solutions are the same

Step-by-step explanation:

Using the form 'y=mx+c',

Since m = 1/3,

y = 1/3x + c

Substituting (5, -1) into the above equation:

-1  = 5/3 + c

c = -1 - 5/3

= -8/3

Hence,

y = x/3 - 8/3

(which is also the same as)

3y = x - 8

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The correct response is (f) 26 ft. The radius of the cylinder is approximately 26 ft.

To solve for the radius, we can use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. We can plug in the given values to get:

63,679 = πr²(30)

Dividing both sides by 30π gives:

r² = 676

Taking the square root of both sides gives:

r ≈ 26

Rounding to the nearest whole number gives the answer of 26 ft. Therefore, the correct response is (f) 26 ft.

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Complete Question:

A cylinder has a height of 30 ft and a volume of 63,679 ft³. what is the radius of the cylinder? round your answer to the nearest whole number. responses

a) 676 ft

b) 676 ft  

c)338 ft

d) 338 ft

e) 52 ft

f) 26 ft.  

Answer:

13 matches

Step-by-step explanation:

Notice 1st have 4 matches
then 2nd have 7 matches (since one is shared), this is 8-1

then 3rd have 10 matches (since two are shared) this is 12-2
Notice the pattern 4 matches per square minus one per aditional square from the first.
This give an equation
4n-1(n-1)= 3n+1
lets check
For n=1    matches= 3(1)+1=4

For n=2    matches= 3(2)+1=7

For n=3    matches= 3(3)+1=10
It works.
so

For n=4   matches= 3(4)+1=13

Step-by-step explanation:

Your monthly payments with taxes and insurance included would be $2,903.71. This is calculated by taking the loan amount of $450,000 and multiplying it by the simple interest rate of 6.00%. The result is $27,000, which is then divided by the length of the loan, 30 years. This gives you

the principal and interest portion of your monthly payment, which is $2,033.33. To that, you add your yearly taxes of $2,000 and insurance of $1,500, divided by 12 months, to get an additional $416.67 and $125, respectively. Adding these two numbers together gives you your total monthly payment of $2,903.71.