find the area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10).

The quotient is 3x²+5x+5.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

The given expressions are 3x³-x²-5x-10 and x-2.

Here, (3x³-x²-5x-10)/(x-2)

x-2|3x³-x²-5x-10|3x²+5x+5

  (-)3x³-6x²

____________

          5x²-5x-10

       (-)5x²-10x

   ____________

               5x-10

            (-)5x-10

      ____________

                   0

Therefore, the quotient is 3x²+5x+5.

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The value of expression y ' (-1) is, 24.

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

We have to given that;

The expression is,

⇒ y = (4x² - 5)³

Now, We can differentiate with respect t x as;

⇒ y (x) = (4x² - 5)³

⇒ y' (x) = 3(4x² - 5)² × (4×2x - 0)

⇒ y' (x) = 3 (4x² - 5)² × 8x

⇒ y' (x) = 24x (4x² - 5)²

Substitute x = 1, we get;

⇒ y ' (1) = 24 × 1 (4 × 1² - 5)²

⇒ y' (1) = 24 (- 1)²

⇒ y' (1) = 24

Thus, The value of expression y ' (-1) = 24

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The value(s) of x that satisfy the given solution is  (5, 7).

Power on both sides: (√4x-5)²-(2x-10)

2 Simplify using exponent power rule (a")=am

x²-4x-5-(2x-10) 2

Expand the expression using (a+b)

2-a2+2ab+

b2: 2-4x-5-(2x) 2-2×2×10+10²

Multiply the monomials: 2-4-5-(2) 2-40

+102 Calculate the power: 2-4-5-(2x) 2-40x+ 100

Simplify using exponent rule with same exponent

(ab)"a"-b" 2-4x-5-22-2-40x+100 Calculate the power: 2-4-5-4x-40+

100

equation: 2-4-5-4x²+40x-100-0 Combine like terms: -3x²+36-105-0

12r+35-0

Rearrange all nonzero terms to the left side of the Reduce the greatest common factor on both sides of the equation: -2+12-35-0 Multiply each term of the equation by -1: 2-

Find two integers: -7-5--12 1-7x (-5)=35

Rewrite the middle term: 2-7x-5x+35-0 Factor the first two terms and the last two terms respectively: (-7) -5(x-7)=0 Apply zero product property that at least one

Extract the common factor: (x-7)(x-5) =0

factor is zero: 2-7-0 or x-5-0 Rearrange unknown terms to the left side of the

equation: -7

Rearrange unknown terms to the left side

equation: =5

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Answer:

B. the area is d x pi its the solution

The average rate of change of the function f(x) on the interval [4,9] is equal to 23.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f(x) over the interval [4, 9]:

a = 4; f(a) = 97

b = 9; f(b) = 212

Substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (212 - 97)/(9 - 4)

Average rate of change = 115/5

Average rate of change = 23.

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Answer:

The new taxes would be $3300.

Step-by-step explanation:

The assessment value and tax rate determine how much a house will cost in taxes. The amount of taxes would increase if the assessment is raised from $108,000 to $128,000.

To find the new amount of taxes, you need to multiply the increased assessment value by the same tax rate:

$128,000 - $108,000 = $20,000 increase in assessment value

$20,000 * ($2700/$108,000) = $600 increase in taxes

Therefore, the new taxes would be $2700 + $600 = $3300.

97.75 - 85 = 12.75

This means the amount of tax was $12.75.

If we divide the amount of tax by the original price of the shirt, it gives us the percent of the tax:

      12.75 ÷ 85 = 0.15 = 15%

Sales tax is 15%.

The key in the calculation is to divide by the original price of the shirt.

Answer:

x = ±√13 - 8

Step-by-step explanation:

Move the constant term to the right side of the equation.

x² + 16x + 51 = 0

x² + 16x = -51

We complete the square by taking half of the coefficient, squaring it, and adding it to both sides of the equation. The formula is (b/2)².

x² + 16x = -51

here the formula would be (16/2)² = 64

x² + 16x + 64 = -51 + 64

Now just simplify by factoring the left side and adding up the right side.

(x + 8)² = 13

You have to isolate x to find what it equals. Here start by taking the square root of both sides

x + 8 = √13

Subtract 8 to both sides

x = ±√13 - 8

For the hours is she going to do studying per day is 10 hours.

The Lagrangian method is a mathematical technique used to find the maximum or minimum value of a function subject to constraints. It is used in optimization problems where the objective is to maximize or minimize a function, but there are some constraints that limit the possible values of the inputs.

The Lagrangian method works by combining the objective function and the constraints into a single function, called the Lagrangian, which is then optimized. The Lagrangian is defined as the original objective function minus the product of the constraints and a set of Lagrange multipliers, which represent the trade-off between the objective and the constraints.

To maximize Julie's utility subject to the constraint of 15 hours of waking time, we need to find the optimal level of s (study time) that satisfies the constraint and maximizes the utility function.

We can start by using the Lagrangian method to find the optimal solution. The Lagrangian is given by:

L(s,λ) = S^(1/3)I^(2/3) + λ(15 - s - I)

Where λ is the Lagrange multiplier, representing the marginal rate of substitution between s and I. To find the optimal solution, we need to find the values of s and λ that satisfy the first-order conditions:

∂L/∂s = (1/3)S^(-2/3)I^(2/3) - λ = 0

∂L/∂λ = 15 - s - I = 0

Solving the first-order conditions for s and λ, we get:

s = (15 * (2/3)) / (1 + (2/3)) = 10 hours

I = 15 - s = 5 hours

So, Julie will spend 10 hours per day studying.

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Answer:

2y-3

Step-by-step explanation:

GCF of 32 and 48=16

(32y-48)/16=2y-3

The solution of given trigonometric equation, 6sin²θ-13sinθ+7 = 0 is θ = π/2

A trigonometric equation is one that contains a trigonometric function with a variable.

Given is a trigonometric equation,

6sin²θ-13sinθ+7 = 0

Solving for θ

6sin²θ-6sinθ-7sinθ+7 = 0

6sinθ(sinθ-1)-7(sinθ-1) = 0

(6sinθ-7)(sinθ-1) = 0

sinθ = 1

θ = π/2

or,

6sinθ-7 = 0

sinθ = 7/6 [no solution]

Hence, the solution of given trigonometric equation, 6sin²θ-13sinθ+7 = 0 is θ = π/2

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Answer:

The table can't be completed as I can't see the table.

However, I can give you the values:

4 Oranges for every 1 Cup of Orange Juice

4, 1

8, 2

12, 3

16, 4

20, 5

Step-by-step explanation:

The equation of the linear function represented by the table below in slope intercept form is f(x) = 4x - 1.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

General equation of a linear function in slope intercept form is,

y = f(x) = mx + c

Here c is the y intercept and m is the slope.

y intercept is the point on the line when x coordinate equals zero.

Given four points on the line (-1, -5), (1, 3), (3, 11) and (5, 19).

Consider two points (1, 3) and (3, 11).

Slope, m = (11 - 3) / (3 - 1) = 8 / 2 = 4

So the equation is y = 4x + c.

Substitute (1, 3) in the above equation.

3 = (4 × 1) + c

c = 3 - 4

c = -1

So the equation is y = 4x - 1.

Hence the given function can be represented as f(x) = 4x - 1.

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Answer:

Chair: $2.50

Table: $8.50

Step-by-step explanation:

First, let's create equations with the information given to us:

x= cost of a chair

y= cost of a table

5x + 3y = $38

2x + 12y = $107

The next step is to solve for x in terms of y. To do this, I will be using the equation 5x + 3y = $38.

5x + 3y = $38   [Subtract 3y from both sides]

5x = -3y + 38   [Divide by 5]

x =(-3/5)y + 38/5

Now that we have found the value of x in terms of y, we will plug it into the equation 2x + 12y = $107.

2x + 12y = $107

2 ((-3/5)y + 38/5) + 12y = 107   [Distribute]

(-6/5)y + 76/5 + 12y = 107   [Combine like terms]

(54/5)y + 76/5 = 107   [Subtract 76/5 from both sides]

(54/5)y = 459/5   [Multiply both sides by 5/54]

y = 17/2 or 8.5

So, the cost of a table is $8.50.

Now that we have found the price of the table, let's plug it into the equation  5x + 3y = $38 to find the price of the chair.

5x + 3y = $38

5x + 3 ( 17/2 ) = 38   [Distribute]

5x + 51/2 = 38   [Subtract 51/2 from both sides]

5x = 25/2   [Divide both sides by 5]

x = 5/2 or 2.5

So, the cost of a chair is $2.50.

So, the chair costs $2.50 while the table costs $8.50.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer:

23.

Step-by-step explanation:

1) if 'G is the midpoint of DF and H is the midpoint of EF', then 0.5*DE=GH, and

2) it is possible to write: 0.5(18+4x)=3x+2, where x=7.

3) if x=7, then GH=3*7+2=23.

For Given Fraction 5/3, The total number of votes is 7648.

What is a fraction?

In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

For example, 5/10 is a fraction.

Here, 5 is a numerator and 10 is a denominator.

There are four different types of fractions. They are:

Unit Fraction – In a fraction, the numerator with 1 is called a unit fraction. For example, ½, ¼

Proper Fraction – If a numerator value is less than the denominator value, it is called a proper fraction. Example: 7/9, 8/10

Improper Fraction – If a numerator value is greater than the denominator value, then it is called an improper fraction. Example: 6/5, 11/10

Mixed Fraction – If a fraction consists of a whole number with a proper fraction, it is called a mixed fraction. Example 5 ¾, 10 ½

Now,

As given ratio is 5/3 for Yes votes to no votes

so total votes is 5x+38x

and also given that no votes i.e. 3x=2868

so, x=956

Hence,

            Total votes=8*956=7648

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Answer:To convert this to miles per hour, we need to first convert the distance to miles. We know that 1 mi = 5280 ft, so 98 ft = 98 / 5280 mi = 0.0184 mi.

Now we can use the formula speed = distance / time again, but this time using miles and hours as the units. So, speed = 0.0184 mi / (11.5 s / 3600 s/hr) = 0.0184 mi / 0.003194 hr = 5.8 mi/hr.

Step-by-step explanation:

Answer:

5.81 mph

Step-by-step explanation:

We want to first convert the number of feet to miles and then divide by the number of hours. Since we know that 5280 feet is one mile, we essentially want to find how many "groups" of 5280 are in some distance and that's the number of miles. We can do this by dividing.

[tex]\frac{98}{5280}\approx0.018561[/tex]

Now we want to find how many hours 11.5 seconds is. It's basically the same process as we divide this by the number of seconds in an hour 3600.

11.5/3600 = 0.00319

Now divide the distance over the time and this gives us approximately: 5.81 mph

Answer:

269

Step-by-step explanation:

big × square root 05 is Justin Beiber

Answer:

301/8200

Step-by-step explanation:

82 x (X) = 301/100

82x/1 = 301/100

now we cross multiply.

8200x = 301

x = 301/8200

it may be wrong, sorry if it is :(

The amount of money that Yolanda invested in the stock is x = $1600

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

To solve this problem we will only formulate two equations:

(a) The sum of the amount to invest in stocks and bonds will be $6000:

x + y = 6000

(b) The percentage of stocks 6% and bonds 11% for a profit of $580.

0.06x + 0.11y = 580

x + y = 6000 ----⇒ x = 6000 - y

0.06(6000 - y) + 0.11y = 580

360 - 0.06y + 0.11y = 580

0.05y = 220

y = $4400

x = 6000 - 4400

x = $1600

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The domain of the table below is {-3, 6, 12}

From the question, we have the following parameters that can be used in our computation:

The table of values

The domain of a function is the set of the input values

This means that the domain is

Domain =  {-3, 6, 12}

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The solution of the initial value problem xy' + y = 8e is equal to

log (x ) =  - log ( 8e - y ) .

Solution of the initial value problem is:

xy' + y = 8e

⇒ x (dy /dx ) + y = 8e

⇒ x (dy/dx ) = 8e -y

⇒  dx / x  = ( 1 / (8e -y ) ) dy

Integrate both the sides we get,

⇒ log (x ) =  - log ( 8e - y ) + c  ____(1)

Now , we have y ( 1 ) = -1 + 8e

Substitute the value  y ( 1 ) = -1 + 8e in (1) we get,

⇒ log ( 1 ) = - log ( 8e - ( -1 + 8e )) + c               ( value of log (1) = 0 )

⇒ 0 = - log ( 8e + 1 - 8e ) + c

⇒ 0 = log ( 1 ) + c

⇒ c = 0

Now substitute c =0 in (1) we get,

log (x ) =  - log ( 8e - y )

Therefore, the explicit solution of the initial value problem is equal to

log (x ) =  - log ( 8e - y ) .

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To make a tree diagram, start by writing out the given information and drawing a box around it. Then draw two branches off of the box representing the two possible outcomes of selecting a student, male or female. Then draw two more branches off of each of the first two branches, representing the two possible outcomes of receiving aid.

Then draw two more branches off of each of the second two branches, representing the two possible outcomes of receiving federal aid. This will create a tree diagram that looks like this (see the image).

From the tree diagram, we can calculate the probability of selecting a student from the given information as follows:

P(selecting a student) = P(selecting a male) + P(selecting a female) = (of male students/total students) + (of female students/total students) = (of male students + of female students)/total students =

Therefore, the probability of selecting a student from the given information is .

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The function that has the average rate of change of -4 over the  interval [-2, 2] is (D) p(x).

What is the Average Rate of Change?

Here, average rate of change of the function must be calculated over the interval [-2, 2].

(A) The average rate of change of the function m(x):

Here, a = -2, m(a) = -12, and b = 2, m(b) = 4

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{4-(-12)}{2-(-2)} \\\implies A(x)=4[/tex]

(B) The average rate of change of the function q(x):

Here, a = -2, q(a) = -4, and b = 2, q(b) = -12

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{q(b)-q(a)}{b-a}\\\implies A(x)=\frac{-12-(-4)}{2-(-2)} \\\implies A(x)=-2[/tex]

(C) The average rate of change of the function n(x):

Here, a = -2, n(a) = -6, and b = 2, n(b) = 6

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{n(b)-n(a)}{b-a}\\\implies A(x)=\frac{6-(-6)}{2-(-2)} \\\implies A(x)=3[/tex]

(D) The average rate of change of the function p(x):

Here, a = -2, p(a) = 12, and b = 2, p(b) = -4

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{-4-12}{2-(-2)} \\\implies A(x)=-4[/tex]

Therefore, the function that has the average rate of change of -4 over the  interval [-2, 2] is (D) p(x).

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Answer:

118°

Step-by-step explanation:

Answer:

a) The equation to solve this problem would be:

10 + 3.75h = 41.88

b) To solve for h, we first need to subtract 10 from both sides:

3.75h = 31.88

Then, divide both sides by 3.75:

h = 8.50 (rounded to the nearest tenth)

So Amanda rented the bike for 8.5 hours.

Step-by-step explanation:

Answer:  a) To solve the problem, we can use the equation:

Cost = 10 + 3.75h

Where h is the number of hours Amanda rented the bike.

b) We know that the cost is about $41.88, so we can plug that in for the cost and solve for h:

41.88 = 10 + 3.75h

31.88 = 3.75h

h = 31.88/3.75

h = 8.5 hours

So Amanda rented the bike for 8.5 hours. (rounding to the nearest tenth)

Step-by-step explanation:

Answer:

I think so.

Step-by-step explanation:

The probabilities for this problem are given as follows:

a) Moderate to high, given that it is an aerospace company: p = 4/9 = 0.4444.

b) Moderate to high, given that it is a food retailer: p = 6/11 = 0.5455.

c) As the probabilities are different, the company type is independent of the level of risk of the firm's stock.

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

Hence the probability is given as follows:

p = 8/18

p = 4/9.

For item b, the outcomes are given as follows:

Hence the probability is given as follows:

p = 30/55

p = 6/11.

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Answer:

The origin is the point (0,0)

(2,-2)  Start at the origin and move 2 unit right along the x axis, from there move down 2 units.  Place a point at that location.

(-2, 1.5) Start at the origin and move 2 units left along the x axis, from there move up 1.5 space and place a point.

(-1, 2/4)  Start at the origin and move left 1 unit along the x axis, from there move up 1/2 a unit and place a point.  2/4 is the same as 1/2

Step-by-step explanation:

$2.4 is the discount used to purchase a pair of sunglasses

percentage, a relative value indicating hundredth parts of any quantity.

Given that Alexandra bought a pair of sunglasses online for $24.

She used a coupon code to get a 20% discount.

The website also applied a 10% processing fee to the price after the discount.

20%-10%=10%

Now 10% of price is 24

10/100×24=x

2.4=x

24+2.4=26.4 is the actual price.

Hence, $2.4 is the discount used to purchase a pair of sunglasses

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