What is the GCF of 14x^2 and 4xy? A. 10x B. 28x^2y C. 2x2 D. 2x

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:

tanA=2.6591

Step-by-step explanation:

[tex]tanA=\dfrac{sinA}{cosA} \\\\tanA=\dfrac{0.936}{0.352} \\\\tanA=2.6591[/tex]

Let

[tex]A(0,0)\\B(5,1)[/tex]

we know that

the formula to calculate the slope between two points is equal to

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

Substitute the values in the formula

[tex]m=\frac{(1-0)}{(5-0)}[/tex]

[tex]m=\frac{1}{5}[/tex]

therefore

the answer is the option b

the slope is equal to  [tex]\frac{1}{5}[/tex]

Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, BC. Using the definition of reflection, reflect BC over l. By the definition of reflection, C is the image of itself and A is the image of B. Since reflections preserve length, AC = BC.

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.

Answer:

  1..25a

Step-by-step explanation:

a + 25%·a = a(1 + 0.25) = 1.25a

_____

Comment on percentages

The symbol "%" is a shorthand way to write "/100", so 25% = 25/100 = 0.25.

Of course, 100/100 = 100% = 1.

Adding 25% of something to 100% of it gives 125% of it, the original amount multiplied by 125/100 = 1.25.

Answer:

1.25a

Step-by-step explanation:

a + 25%·a = a(1 + 0.25) = 1.25a

_____

Comment on percentages

The symbol "%" is a shorthand way to write "/100", so 25% = 25/100 = 0.25.

Of course, 100/100 = 100% = 1.

Adding 25% of something to 100% of it gives 125% of it, the original amount multiplied by 125/100 = 1.25.

Read more on Brainly.com - https://brainly.com/question/9011267#readmore

Answer:

4 + 0 = 4/2 = 2 would be the answer.

Step-by-step explanation:

Without additional data, such as the percentage of those surveyed who chose football, it's impossible to determine the total number of people surveyed from the information provided. The data given only specifies that 210 individuals selected football as their favored sport to watch.

Based on the provided question, there's not enough information to determine the total number of people who were surveyed. The information given only states that 210 people picked football as their favorite sport to watch, but it does not provide the overall total number of people surveyed.

To calculate the total number of respondents, you need to know the ratio or percentage of people who chose football. For example, if you knew that football was chosen by 70% of those surveyed, you could use that information to calculate the total number of people. In this case, the equation would be 210 = 0.70 * x. Solving for x (the total number of people surveyed) would give you x = 210 / 0.70, which comes out to approximately 300 people.

https://brainly.com/question/31801216

#SPJ12

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

Answer:

The correct options are 2 and 5.

Step-by-step explanation:

The general form of conics is

[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]

This equation represents the hyperbola if

[tex]B^2-4AC>0[/tex]

compare the given equations with the general equation.

In option 1,

[tex]A=2,B=0,C=2,D=16,E=14,F=-9[/tex]

[tex]B^2-4AC=(0)^2-4(2)(2)=-16<0[/tex]

This equation does not represents a hyperbola.

In option 2,

[tex]A=2,B=0,C=-5,D=4,E=-10,F=57[/tex]

[tex]B^2-4AC=(0)^2-4(2)(-5)=40>0[/tex]

This equation represents a hyperbola.

In option 3,

[tex]A=-1,B=0,C=-7,D=5,E=2,F=-81[/tex]

[tex]B^2-4AC=(0)^2-4(-1)(-7)=-28<0[/tex]

This equation does not represents a hyperbola.

In option 4,

[tex]A=0,B=0,C=-2,D=1,E=4,F=15[/tex]

[tex]B^2-4AC=(0)^2-4(0)(-2)=0[/tex]

This equation does not represents a hyperbola.

In option 5,

[tex]A=-1,B=0,C=3,D=12,E=7,F=11[/tex]

[tex]B^2-4AC=(0)^2-4(-1)(3)=12>0[/tex]

This equation represents a hyperbola.

Therefore the correct options are 2 and 5.

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 .

Answer:

60 degrees, 30 degrees

Explanation:

Sun angle = 90° - Zenith angle

On September 22, the sun passes over celestial equator. Equinox occurs.

Zenith Angle = Latitude of the place

Latitude of New Orleans, US = 29.95° ≈ 30°

Latitude of  Helsinki, Finland = 60.95° ≈ 60°

Thus, the Sun angle at noon at New Orleans would be 90° - 30° = 60°

and at Helsinki, Finland would be 90° - 60° = 30°

Answer:

For any value of P & Q except when both are equal , we get One solution of equation.

Step-by-step explanation:

Given: Linear Equation, Qx - 6 = Px - 103

           This equation has exactly 1 solution.

To find: Value of P and Q

First we solve the linear equation for value of x,

Qx - 6 = Px - 103

Transpose Px to LHS ( Left hand side ) we get,

Qx - Px - 6 = -103

Transpose 6 to RHS ( Right hand side ) we get,

Qx - Px = -103 + 6

Qx - Px = -97

taking x common in LHS, we get

( Q - P )  x =  -97

Traspose ( Q - P ) to RHS, we get

[tex]x=\frac{-97}{Q-P}[/tex]

[tex]x=\frac{-97}{-(P-Q)}[/tex]

[tex]x=\frac{97}{P-Q}[/tex]

Thus, we are get only 1 value of x but it exist if P ≠ Q

otherwise no solution exist for the given linear Equation.

Therefore, For any value of P & Q except when both are equal , we get One solution of equation.

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

27.5 if you divide 550by 5% you get 27.5

Janice will purchase 4 pounds of potatoes if she has $5.00. If she only has $3.00 to spend, she will purchase 3 pounds of potatoes.

To determine how many pounds of potatoes Janice will purchase, we need to subtract the cost of each pound of potatoes from her total budget until she no longer has enough money to purchase another pound. Let's go step by step:

Janice has $5.00 and the first pound of potatoes costs $1.50. After purchasing the first pound, she will have $5.00 - $1.50 = $3.50 left.

Therefore, Janice will purchase 4 pounds of potatoes.

If Janice only has $3.00 to spend, we can follow the same steps:

Therefore, if Janice has $3.00 to spend, she will purchase 3 pounds of potatoes.

https://brainly.com/question/30523995

#SPJ2

Answer:

True.

Step-by-step explanation:

We use law of sine to solve the triangle when two sides and angle (SSA) is given.There are different cases possible .

1)  If a < b sin A.

In this case  No possible triangles or we can say there will be zero solutions.

2) If a > b sin A.

In this case there are   Two triangles possible.In such cases at least one of the solutions will be an obtuse triangle.

3) If a = b sin A.

We have   Unique solution or one solution.This is true for a right triangle.

Hence the given statement  SSA triangle problems may have zero, one, or two solutions is True.

Answer: true

Step-by-step explanation:

Ap3x

Manuel's hourly rate of pay is calculated by dividing his total weekly earnings by the total hours he worked. He worked a total of 30 hours and earned $337.50, resulting in an hourly rate of $11.25.

The question asks us to calculate Manuel's hourly rate of pay based on the total amount he earned in a week and the number of hours he worked. To find the hourly rate, we need to divide the total earnings by the total number of hours worked.

Calculate the total number of hours worked in a week: 5 days a week times 6 hours each day equals 30 hours.

Divide Manuel's total earnings for the week by the total hours worked:
$337.50 divided by 30 hours equals an hourly rate of $11.25.

7 weeks until July 4.

Calculating the Number of Weeks Until July 4

To determine in how many weeks it will be until July 4, given that there are 49 days left:

We know there are 7 days in a week.

We need to divide the total number of days by the number of days in a week.

The calculation is: 49 days ÷ 7 days/week.

Doing the division: 49 ÷ 7 = 7 weeks.