Explain distributive property in your own words.

The equation of the tangent plane to the given surface at the specified point is 18x + 16y - 34.

Given: z = 3(x - 1)² + 2(y + 3)² + 7

We have to find the equation of the tangent plane to the given surface at the specified point.

We have a formula to find the equation of the plane tangent to z = f(x, y) at a point (a, b, c) as shown below:

z = c + \(f_x\)(a, b) (x - a) + \(f_y\) (a, b) (y - b)

Here, we need to find \(f_x\) (a, b) and \(f_y\) (a, b).

Differentiating z = 3(x - 1)² + 2(y + 3)² + 7 partially with respect to x, we get:

∂z/∂x = 6(x - 1)

Differentiating z = 3(x - 1)² + 2(y + 3)² + 7 partially with respect to y, we get:

∂z/∂y = 4(y + 3)

Therefore, at point (4, 1), we have a = 4,

b = 1,

c = 66,

\(f_x\) (a, b) = ∂z/∂x

= 6(4 - 1)

= 18

and \(f_y\) (a, b) = ∂z/∂y

= 4(1 + 3)

= 16

Now substituting these values in the plane equation, we get:

z = 66 + 18(x - 4) + 16(y - 1)

Simplifying the above equation, we get the equation of the tangent plane as shown below:

z = 18x + 16y - 34

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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The ratios are not equal. The ratio 11/2 is not equal to the ratio 11/12.No, the ratio 11/2 and 11/12 are not equal. To determine if two ratios are equal, we need to compare their simplified forms.

The ratio 11/2 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1 in this case. Therefore, 11/2 is already in its simplest form.

The ratio 11/12 can also be simplified. The greatest common divisor of 11 and 12 is 1. Dividing both the numerator and denominator by 1 gives us the simplified form of 11/12, which is also 11/12.

Comparing the simplified forms, we see that 11/2 is not equal to 11/12. The numerator and denominator of these ratios are different, with 2 in the denominator for 11/2 and 12 in the denominator for 11/12.

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Answer:

B

Step-by-step explanation:

B it's wrong because 8 is divided by a number not a number by 8

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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Third length of the triangle will be lies between 3cm < l < 11 cm if the two sides of the triangle are 7 cm and 4 cm.

Let the measure of third side of the triangle is ‘l’ cm

We know that the sum of two sides of a triangle is always greater than the measure of the third side.

We can say that,

l < 4 + 7

⇒ l < 11cm

It is also said that the measure of a side of a triangle is always greater than the difference of the other two sides of the triangle, concluding that

l > |7 - 4|

⇒ l > 3cm

From the above conditions, we can say that ‘l’ lies between 3 cm and 11 cm.

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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First, we'll need to determine what sort of relationship the given angles have. We can see that the two angles make a straight line, so they must be supplementary, or a linear pair.

Supplementary angles/Linear Pairs create a straight line, as seen here, which means that the sum of the angles is 180 degrees.

Therefore, the two given expressions/angles will add up to 180.

(5x - 16) + (x + 10) = 180

6x - 6 = 180

6x = 186

x = 31

Answer: x = 31

Hope this helps!

Answer:

51.5

Step-by-step explanation:

i think not sure if there's an odd number of numbers you get the 2 numbers add them up and divide them by 2! hope this helps! good luck.

The angle ACB is tan⁻¹(80/a), the range of tan⁻¹(x) is (0, 90) and the time taken to reach the shore is a/30

The measure of ACB can be calculated using the following tangent trigonometry ratio

tan(ACB) = Opposite/Adjacent

So, we have

tan(β) = 80/a

Take the arc tan of both sides

So, we have

β = tan⁻¹(80/a)

So, the angle is tan⁻¹(80/a)

Given that the angle is an acute angle

The range of tan⁻¹(x) for acute angles can be found by considering the values of the tangent function for angles between 0 and 90 degrees.

Since tan(0) = 0 and tan(90) is undefined, the tangent function takes on all positive values in this range.

So, the range of tan⁻¹(x) for acute angles is (0, 90) degrees.

Here, we have

Distance = a

Speed = 30 km/h

The time taken to reach the shore can be calculated using the formula:

time = distance / speed

Substituting the given values, we get:

time = a / 30 km/h

Simplifying this expression, we get:

time = a / 30 hours

Therefore, the time taken to reach the shore is a/30 hours, where a is the distance to the shore in kilometers.

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Answer: The number twelve carries religious, mythological and magical symbolism, generally representing perfection, entirety, or cosmic order in traditions since antiquity.

Step-by-step explanation: If you're not talking about this type of 12 correct me.

The single inequality:

y > |x + 2|

Can be rewritten into:

y > x + 2

y > -x - 2

So the second option is the correct one.

Remember that an absolute value equation like:

|x + a| = b

Can be rewritten as:

x + a = b

x + a = -b

So the inequality:

y > |x + 2|

Also can be rewritten into two equations, which are:

y > x + 2

-y < x + 2

The direction of the sign changes in the second one because the sign of the variable in the left changes.

Then if we multiply both sides by -1 of the second inequality, we get:

y > -x - 2

Then the two inequalities are:

y > x + 2

y > -x - 2

So the correct option is the second one.

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Answer: $140.48

Step-by-step explanation:

To solve the equation -2.5(e + 17.4) = -50, we can use algebraic techniques to isolate the variable e on one side of the equation.

First, we can simplify the left-hand side of the equation by distributing the -2.5 to the expression inside the parentheses:

-2.5e - 2.5(17.4) = -50

Next, we can simplify the expression on the left-hand side by multiplying:

-2.5e - 43.5 = -50

To isolate the variable e, we can add 43.5 to both sides of the equation:

-2.5e = -6.5

Finally, we can solve for e by dividing both sides of the equation by -2.5:

e = 2.6

Therefore, the solution to the equation -2.5(e + 17.4) = -50 is e = 2.6.

Answer: 12 only

Step-by-step explanation:

The value of f(0) from the graph of f(x) is (a) 12 only

Functions are used to represent graphs, equations, ordered pairs and relations.

To interpret the value of the function, we start by reading the graph.

From the graph, the value of the function when x = 0 is 12

This means that:

\(f(0) = 12\)

Hence, the value of f(0) from the graph of f(x) is (a) 12 only

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Answer:

see attached

Step-by-step explanation:

Answer:

Step-by-step explanation:

Try counting by qurter

Answer: A

Step-by-step explanation: If you fill in the x-intercept and the y-intercept and solve -4(2) + 20 = 12       And -4(3) + 20 = 8    

if you solve for those you would get your y-intercept

Answer: ≈39 ft

Step-by-step explanation: Pythagorean theorem= √40^2-8^2 ≈39.19!

To differentiate the function f(x) = x^5), we can use the power rule of differentiation. According to the power rule, if we have a function of the form f(x) = x^n), where (n) is a constant, then its derivative is given by:

[f(x) = nx^{n-1}]

Applying this rule to f(x) = x^5), we have:

[f(x) = 5x^{5-1} = 5x^4]

Therefore, the derivative of f(x) = x^5) is (f(x) = 5x^4).

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Answer:

Step-by-step explanation:

3x - 14 = [ 4(x-9)]

3x - 14 = 4x - 36

-14 + 36 = 4x - 3x

22 = x

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

check

3 x 22 - 14 = [4(22 - 9)

52 = 52

same value the answer is good

Answer:

-2 floor so underground

The weight of the piknits can be used to predict the number of goggles as there is a Linear equation in variables that may be defined as a linear courting among x and y, that is, variables.

In this case,  let x is the impartial variable, and y relies upon it, so y is called as the established variable.

linear courting (or linear association) is a statistical period used to explain a straight-line courting among variables. Linear relationships may be expressed both in a graphical layout or as a mathematical equation of the shape y = MX + b.

"There is no linear relationship between the weight and the number of glasses"

"There is a linear relationship.

A. Yes, because the scatterplot shows a linear pattern.

C. Yes, because a random sample was taken from Piknits for the scatterplots of the 4th and 5th residuals.

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Answer:

Let f = first number and s = second number.

f + s = 30

f = 2s

2s + s = 30

3s = 30, so s = 10 and f = 20.

The first number is 20, and the second number is 10.

Answer:

The answer is the given information is the SAS case, Evelyn is approximately 104 meters from the plane, and the angle of elevation of the plane is 12°.

Step-by-step explanation:

Edge

Two triangle are congruent when the shape and size of both the triangle are same. The given information is the SAS case.

To find the form of the case we need to know about the triangle congruence theorem.

Two triangle are congruent when the shape and size of both the triangle are same.

Triangle congruence theorem are-

Given information-

Evelyn is 104 meters from the take off.

The angle of elevation of the plane is 12°.

The plane is 100 meters away from the takeoff point.

The distance is 100 meters and 104 meters. The other two sides , as are same and the angle of elevation is also same for this case (12 degrees).

Thus the two triangle formed which are congruent.

As above discussed the case of SAS exists for the triangle congruence theorem.

Hence the given information is the SAS case.

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Answer:

Step-by-step explanation:

The last one: 79, 79, 79, 79, 79, 79, 79, 79, 79, 79 because there isn't any difference in the numbers.

S.D.: 0

Answer:

Width is 11 inches

Step-by-step explanation:

I am not sure what the question is.  I think you might be looking for the width length.  The perimeter is the distance around a rectangle.  If the whole distance around is 48.  We have 2 lengths and 2 widths.  They tell us that the length is 13.  We have two lengths so the lengths add up to 26.  We can subtract that from 48 and that leaves us with 22 (48-26)  This is the total for the 2 widths.  Since the 2 widths are the same length we divide that number by 2 to get 11.

11 + 11+ 13 + 13 = 48

The total amount of money that Johnny will have to pay is f(10) = 30.

What are expressions?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Given is that it costs Johnny $15 a month plus $1.50 per song to download music. This situation is represented by the expression →

1.5(x) + 15.

The expression is given by -

f(x) = 1.5(x) + 15

where [x] is the number of songs downloaded.

For [x] = 10 songs, the total amount of money that Johnny will have to

pay is -

f(10) = 1.5 x 10 + 15

f(10) = 15 + 15

f(10) = 30

Therefore, the total amount of money that Johnny will have to pay is f(10) = 30.

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The cost that Johnny has to pay to download 10 songs is 30$

as per given in the question,

johnny's  regular cost is 15$ a month

$1.50 is to be added for every song download

The cost to be find for 10 songs download

the equation which can be formed is

let x be the number of songs

1.5 times the number of songs + the cost of every month

therefore

1.5(x) + 15

the total number of songs to be downloaded is  10

so,

1.5(10) + 15

=> 15 +15

=> 30 $

Now the cost that has to pay by johnny after the downloading of 10 songs is 30 $

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