What is the sum of the polynomials? (8x2-9y2-4x)+(x2-3y2-7x)

Answer: In the picture below.

Step-by-step explanation:

The provided mathematical expressions represent the process of calculating Zhi's remaining tickets after playing 'g' games at a fair. '18 - 3g' symbolizes subtracting three times the number of games played from the initial total (18) tickets. '3(6 – g)', on the other hand, corresponds to multiplying the number of tickets per game (3) by the subtraction of already played games from total possible games (6).

The subject of this question is based on mathematical expressions and variables. In the case of Zhi's expression, 18 represents the total number of tickets she bought. 'g' corresponds to the number of games played, and 3 is the number of tickets required for each game. Therefore, '18 – 3g' means subtracting three times the number of games played (3g) from the total quantity of tickets (18), which would give us the number of tickets left.

Diego's expression, however, expresses the same idea differently. '6 – g' symbolises the number of games Zhi could play before she runs out of tickets (since 18 tickets divided by 3 tickets per game equals 6 games). The '3' outside the bracket is again the number of tickets each game requires. As such, '3(6 – g)' expresses the multiplication of the tickets needed per game (3) by the difference between the total games possible and the games already played (6-g). This, therefore, provides the same result—Zhi's remaining tickets after g games.

https://brainly.com/question/34902364

#SPJ11

Answer: Hello mate!

lets suppose you have (x -1) friends (then when you count yourself, there are x persons in the group) where x is a natural number.

you have two possible prices at the movie theater:

1) the $12.99 per person, then if you have x persons in the group, the total charge is $12.99*x

2) with the promotion they pay $8.99 per person and includes a $20 reservation, then the total charge is $8.99*x + $20

now, let's find the number x is where the second option is cheaper than the first.

in order to do this, we can regulate both equations in order to determine in which x₀ the costs are the same, then if x< x₀, the first option is cheaper and if x>x₀ the second option is cheaper.

$12.99*x₀ = $20 + $8.99x₀

$12.99x₀ - $8.99x₀ = $20

$4x₀ = $20

x₀ = 20/4 = 5

Then if in your group are less than 5 persons, took option 1.

if there are more than 5 persons, took the option 2

if there are exactly 5 persons, both options cost the same.

Answer:

60 marbles

Step-by-step explanation:

Given:  24 red marbles is 40% of how many marbles

Let number of marbles be x

"24 red marbles is 40% of how many marbles"

             24 = 40% of x

solve for x

First change % to decimal

    24 = 0.40x

Division property of equality, divide by 0.04 both sides

     x = 24÷0.40

     x = 60

Hence, 40% of 60 is 24

The equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.

The equation of a line with slope (m) passing through a point (x₁, y₁) is given by the point-slope form:

y - y₁ = m(x - x₁)

The slope (m) is 2, and the point (x₁, y₁) is (3, 9). Plug these values into the equation:

y - 9 = 2(x - 3)

Now, you can simplify this equation:

y - 9 = 2x - 6

To isolate y, add 9 to both sides:

y = 2x - 6 + 9

y = 2x + 3

Therefore, the equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.

learn more about slope here

brainly.com/question/31668066

#SPJ3

The solution to the problem involves setting up and solving a system of equations derived from the distance function in 3D. The minimum point of the distance function corresponds to the point in the plane that's closest to the origin.

To find the coordinates of the point (x, y, z) on the plane z = 3x + 4y + 4 which is closest to the origin, we need to find the minimum distance from origin (0,0,0) to any point on the plane. The distance equation is given by √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]. This is simply Euclidean distance in 3D.

In this case, we can define the distance function d = √(x² + y²+ (3x + 4y + 4)²). To find the minimum distance, we take the derivative of this distance function with respect to both x and y, set them to 0, and solve the resulting equations. The solutions to these equations yield x and y. We substitute x and y into z = 3x + 4y + 4 to get z.

Finally, solving these equations we obtain the coordinates of the point (x, y, z) on the plane that is closest to the origin.

https://brainly.com/question/32034725

#SPJ11

Answer:

  (-6/13, -8/13, 2/13)

Step-by-step explanation:

You want the point on the plane z = 3x +4y +4 that is closest to the origin.

When the plane equation is written in standard form, the variable coefficients comprise a vector that is normal to the plane. The line normal to the plane and passing through the origin can be written in terms of this vector. Solving for the variable in that equation lets us find the point on the plane where the line intersects.

The standard form equation for the plane is ...

  3x +4y -z = -4 . . . . . . . subtract 4+z from the given equation

Then the normal to the plane is ...

  N = (3, 4, -1)

and the vector equation of the line through the origin is ...

  L = (0, 0, 0) +tN = (3t, 4t, -t)

The value of t that makes a point on the line satisfy the plane equation is ...

  3(3t) +4(4t) -(-t) = -4

  26t = -4

  t = -4/26 = -2/13

Then the point tN is ...

  (-2/13)(3, 4, -1) = (-6/13, -8/13, 2/13)

The point on the plane closest to the origin is (-6/13, -8/13, 2/13).

Answer:

The correct answer is 49.1 minutes to 59.3 minutes

Step-by-step explanation:

The 99% confidence interval for the number of minutes that an adult spends surfing the Internet per day is [49.091, 59.308].

A confidence interval (CI) is a range of estimates for an unknown parameter.

The formula for confidence interval is mean ± (standard normal variate at α level of significance)*(standard deviation)/ (√sample size)

CI = 54.2 ± 2.58 * 14/√50

CI = 54.2 ± 5.1081

CI = [49.091, 59.308]

Learn more about confidence interval here:

https://brainly.com/question/13031032

#SPJ2

Answer:

[tex]bh=50[/tex] for b=5 and h=10.

Step-by-step explanation:

Given : The value of b=5 and h=10.

To find : Evaluate bh ?

Solution :

As we have given bh i.e. b and h are multiplied together,

So, [tex]bh=b\times h[/tex]

Substitute, b=5 and h=10

[tex]bh=5\times 10[/tex]

[tex]bh=50[/tex]

Therefore, [tex]bh=50[/tex] for b=5 and h=10.

Answer:

48 sq. in.

Step-by-step explanation:

Formula for finding trapezoid area: A = 1/2(h)(b1 + b2)

They said the median of a trapezoid is equal to half the sum of the bases, so multiply the median by 2 to get the sum of the bases.

Sum of the bases = 8(2) = 16

Now plug what you have into the equation to find the area: A = 1/2(6)(16)

Simplify to get: 48

Hope this helps!

Answer:

Net assest value of one share is $8 .

Option (c) is correct .

Step-by-step explanation:

As given

A mutual fund has total assets of 2.4 million dollars and 300,000 shares.

As 1 million = 1000000

Total assest value = $2.4 × 1000000

Thus

[tex]Net\ asset\ value\ of\ one\ share = \frac{2.4\times 1000000}{300000}[/tex]

Put all the values in the above

[tex]Net\ asset\ value\ of\ one\ share = \frac{24\times 1000000}{300000\times 10}[/tex]

[tex]Net\ asset\ value\ of\ one\ share = \frac{24}{3}[/tex]

Net asset value of one share = $8 .

Therefore net assest value of one share is $8 .

Option (c) is correct .

Final answer:

Solutions to a system of linear equations are represented graphically as the intersections of lines on a graph and can be unique, infinitely many, or none. Graphical representations are essential in various applications, like economic models, and software like R facilitates solving these systems.

Explanation:

Possible solutions to a system of linear equations can be one of three types: a unique solution, infinitely many solutions, or no solution. Graphically, these solutions are represented by the intersections of lines on a graph. In the case of a unique solution, the lines intersect at exactly one point.

For example, consider two linear equations of the form y = mx + b. Graphically, each equation is represented by a straight line. Where these lines cross is the solution to the system. If both equations produce the same line, they have infinitely many solutions since every point on the line satisfies both equations.

The drawing shows the friends ended up with 1/2 the pie.

Answer:

Let the probability of error-free transmission of a message over a communication channel is P.

Then the Probability of Retransmission  is =1-P

Now the question is Probability when no retransmission is required

                            = Probability of error free transmission in first attempt

                               =P

Now , suppose after first failure error free transmission takes place.

Since events are independent.

∵P[error free transmission after a failure ]= P[1-P]

If after two attempts error free transmission takes place

then P[ error free transmission after two failures]= P [1-P]²

So, For after n failures

P[error free transmission after n failure]=P[tex][1-p]^n[/tex]

Using the simple interest formula I = PRT, it is calculated that Akule borrowed $1500 at an annual interest rate of 12% for 1.5 years to pay $270 in interest.

The subject of this question is Mathematics, specifically focusing on simple interest calculation. To find out the period of time Akule borrowed money for, we can use the simple interest formula I = PRT, where I is the interest paid, P is the principal amount borrowed, R is the annual interest rate, and T is the time in years. Akule paid $270 in interest on a $1500 loan at 12% annual simple interest. Using the formula, we solve for T as follows:

T = I / (P × R)

T = $270 / ($1500 × 0.12)

T = $270 / $180

T = 1.5 years

Therefore, Akule borrowed the money for 1.5 years.

Akule borrowed the money for 0.18 years.

To find the period of time Akule borrowed the money, we can use the formula:

Interest = Principal × Rate × Time

Given that Akule paid $270 in interest and borrowed $1500 at an annual simple interest rate of 12%, we can plug in these values into the formula:

270 = 1500 × 0.12 × Time

Simplifying the equation, we get:

0.12 × Time = 270 / 1500

Time = (270 / 1500) / 0.12

Time = 0.18 years

Hence, Akule borrowed the money for 0.18 years.

1. Given gross salary is = $768

Federal tax withholding = $68

Social security = 6.2% or 0.062*765 = $47.43

Medicare tax = 1.45% or 0.0145*765 = $11.09

State tax = 22% or 0.22*68 = $14.96

Now net salary = gross salary - tax deductions

[tex]765-(68+47.43+11.09+14.96)[/tex] = $623.52 (option D)

2. [tex]\frac{33500-28600}{28600}*100[/tex] = 17.13% (option D)

3. Option B.II and III

4. B.Checks are deposited in ATM's, so some retailers will not accept checks from a bank without ATM service.

5. B.Bank E offers you a chocolate bar for filling out an application for checking and credit at the same time.

6. D.Make purchases or get cash now, and pay back the bank in monthly payments.

7. A point of sale transaction occurs when an ATM withdrawal is made- yes this is right.

8. The answer is Thursday.

9. No picture given.

Mike need to deposit approximately $22,815 in his money market account now, which has a 1.825% interest rate compounded daily, to have $25,000 in 4 years.

To find out how much Mike should invest now, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:  
 A = the amount of money accumulated after n years, including interest.
P = principal amount (the initial amount of money)
r = annual interest rate (in decimal)
n = number of times interest applied per time period
t = time the money is invested for in years

In this case, Mike wants to have A = $25,000 in t = 4 years. The interest rate r is 1.825% or 1.825/100 = .01825 in decimal form, and since it is compounded daily, n = 365. So, we can plug into the formula and solve for P:
$25,000 = P(1 + .01825/365)^(365*4)

By performing the calculation, we find that P is approximately $22,815. Mike will therefore need to invest this amount in his money market account now to achieve his goal.

https://brainly.com/question/14295570

#SPJ2

Final answer:

To calculate the probability of losing one or more friends, we need to calculate the probability that a friend does not get a red candy and multiply it by the number of friends. The probability is 0.458.

Explanation:

To answer this question, we need to calculate the probability that at least one friend will not get a red candy.

First, let's calculate the probability that a friend does not get a red candy. There are 42 candies in the bag and 6 of them are red. So, the probability that a friend does not get a red candy is (42-6)/42 = 36/42 = 6/7.

Since each friend gets 7 candies, the probability that one friend does not get a red candy is (6/7)^7, because each candy is independent. Finally, since there are 6 friends, we multiply the probability by 6 to get the probability that at least one friend does not get a red candy: 6 * (6/7)^7 = 0.458 (rounded to 3 decimal places).