Find the minimum value of f (x,y,z) = 2x2 + y2 + 3z2 subject to
the constraint 2x – 3y - 4z = 49

The explicit rule for the sequence is f(n) = 6 - 4(n - 1)

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

a1 = 6

a(n) = a(n - 1) - 4

In the above sequence, we can see that -4 is added to the previous term to get the new term

This means that

First term, a = 6

Common difference, d = -4

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 6 - 4(n - 1)

Hence, the explicit rule isf(n) = 6 - 4(n - 1)

Read more about sequence at

brainly.com/question/30499691

#SPJ1

Answer:

b) 8 x - 21

Step-by-step explanation:

Apply the distributive property.

7

x

+

7

⋅

−

1

−

2

(

x

+

1

)

+

3

(

x

−

4

)

Multiply

7

by

−

1

.

7

x

−

7

−

2

(

x

+

1

)

+

3

(

x

−

4

)

Apply the distributive property.

7

x

−

7

−

2

x

−

2

⋅

1

+

3

(

x

−

4

)

Multiply

−

2

by

1

.

7

x

−

7

−

2

x

−

2

+

3

(

x

−

4

)

Apply the distributive property.

7

x

−

7

−

2

x

−

2

+

3

x

+

3

⋅

−

4

Multiply

3

by

−

4

.

7

x

−

7

−

2

x

−

2

+

3

x

−

12

Subtract

2

x

from

7

x

.

5

x

−

7

−

2

+

3

x

−

12

Add

5

x

and

3

x

.

8

x

−

7

−

2

−

12

Subtract

2

from

−

7

.

8

x

−

9

−

12

Subtract

12

from

−

9

.

8

x

−

21=

8

x

−

21

Answer:

m (Slope) = 3

Step-by-step explanation:

Slope formula:

m = (y2 - y1) / (x2 - x1)

= (24 - 3) / (9 -2)

= 21 / 7

=3

The required value of d in the given arithmetic operation is 9/10.

What are subtraction and addition?

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. To add, one must add two or more numbers or values to produce a new number. The inverse of addition is subtraction and vice versa.

For instance, 10 - 1 = 9 if 9 + 1 = 10. That demonstrates that adding 1 produces the number 10 when added to 9, but subtracting 1 from 10 produces the number 9.

Given, -1/3d + 4/5 = 1/2

\(\frac{-1}{3} d+\frac{4}{5} =\frac{1}{2} \\\\\frac{-1}{3} d =\frac{1}{2}-\frac{4}{5}\\\\\frac{-1}{3} d = \frac{5-8}{10}\\\\\frac{-1}{3} d = \frac{-3}{10}\\\\\frac{d}{3}=\frac{3}{10}\\\\d = \frac{9}{10}\)

So, the required value of d = 9/10.

To learn more about subtraction and addition

https://brainly.com/question/20460320

#SPJ1

Answer:

  £25,353.01

Step-by-step explanation:

You want to know the debt in 14 years if it is initially £800 and increases by 28% per year.

The amount with interest compounded is given by ...

  A = P(1 +r)^t

where P is the principal borrowed, r is the annual interest rate, and t is the number of years.

Bryn will owe ...

  A = 800·1.28^14 ≈ 25353.01

After 14 years Bryn will owe £25,353.01.

<95141404393>

Answer:

the answer is

-17-1/17-2=-18/15=Slope

Answer: 15.75

Step-by-step explanation: 4.5 x 3.5

The desirable heart rate for a 46 year old women is 115.1

Expression means a number, a variable, or a combination of numbers and variables and operation symbols.

Given:

The medical researchers has found the desirable heart rate of the person through the following expression

For men the expression is

r = 165 - 0.75a

For women the expression is

r = 145 - 0.65a

Here r represents the heart rate and a represents the person's age.

Here we need to find the desirable heart rate of the 46 year old women

So, the value of a is 46,

Now we have to apply the value on the given expression in order to solve it,

So,

r = 145 - (0.65 x 46)

r = 145 - 29.9

r = 115.1

To know more about expression here

https://brainly.com/question/13947055

#SPJ4

Answer:

First figure:

Faces--5

Edges--8

Vertices--5

Type--pyramid

Second figure:

Faces--6

Edges--12

Vertices--8

Type--rectangular prism

There is no angle (0) in degrees that answers the preceding equation since cos(0) = 3/2 is illogical.

To determine the angles of a right triangle, trigonometric ratios are ratios of the side lengths of the triangle. Sine (sin), cosine (cos), and tangent (tan) are the three fundamental trigonometric ratios, and their definitions are as follows:

Sine: The length of the angle's opposite side divided by the length of the hypotenuse is known as the sine of the angle.

Cosine: The length of the neighbouring side divided by the length of the hypotenuse is the angle's cosine value.

Angle's tangent is determined by dividing the length of the adjacent side by the length of the opposite side.

These ratios can be used to discover missing side lengths in right triangles and other situations with right triangles.

given

The number one is the value of cos(0).

There is no angle (0) in degrees that answers the preceding equation since cos(0) = 3/2 is illogical.

To know more about trigonometric ratios visit:

https://brainly.com/question/29002217

#SPJ1

The length of each side of the square is approximately 4.472 cm. To find the length of each side of the square, we can use the formula for the area of a square.

The area of Square is A = s², where A is the area and s is the length of each side.

Substituting A = 20 into the formula, we get:

20 = s²

Taking the square root of both sides, we get:

s = √(20)

Simplifying the radical, we get:

s = √(4*5)

s = 2√(5)

Therefore, the length of each side of the square is approximately 4.472 cm, rounded to three decimal places.

Learn more about Square:

https://brainly.com/question/25092270

#SPJ4

Using the equation x - 7 = 12, we can apply it to find the number of students in Mrs. Jones' class, where the girls are 12 and the boys are 7.

An equation is a mathematical statement that two or more expressions share equality or are equivalent in value.

The equation sign (=) is used when two expressions or values are equal.

x - 7 = 12

Where the number of girls = 12

And the number of boys = 7

x = 12 + 7

x = 19

Thus, we can conclude from the equation x - 7 = 12 that x is the total number of students in Mrs. Jones' class.

Learn more about equations at https://brainly.com/question/2972832

#SPJ1

Answer:

a = 35

c = 85

Step-by-step explanation:

85 + 60 + a = 180 as they are all supplementary angles (together they form an angle of 180°)

therefore a = 35.

a + ( 180 -(a+85)) + c =180 (as the angles of a triangle add up to 180°. our triangle is NMT, the angles are a, c and 180°-(a+85°) for a theorem about lines secant to parallel lines)

therefore c = 85

a=35°

Answer:

Solution given;

∡ZTN=85°

∡NTM=a

∡RTM=60°

∡ZTN+∡NTM+∡RTM=180°[since the sum of angle of a straight line is 180°]

substituting value

85°+a+60°=180°

a+145°=180°

a=180°-145°

a=35°

again

∡ZTN=∡TNM=85°[alternate angle]

Step-by-step explanation:

Answer:

soowwwyyy for bad handwriting;(

Answer:

Each friend would get 24 marbles.

Step-by-step explanation:

Firstly, you would want to divide 216 by 3. That is 72. Next you would want to divide 72 by 3, because there are 3 best friends. So 72 divided by 3 equals 24. I hope this helps.

The equation in vertex form is y = 2(x+3)² + 1. The vertex is (-3,1), the axis of symmetry is x = -3, and the direction of opening is upwards.

The vertex form of the equation is y = a(x-h)^2 + k, where (h, k) is the vertex. The axis of symmetry is x = h, and the direction of opening is determined by the value of a.

Using this formula, let us write each equation in vertex form and then identify the vertex, axis of symmetry, and direction of opening.

1. y = x² + 8x + 18

To write this equation in vertex form, we need to complete the square. y = x² + 8x + 18 is equivalent to y = (x+4)² - 2. Therefore, the equation in vertex form is y = (x+4)² - 2.

The vertex is (-4,-2), the axis of symmetry is x = -4, and the direction of opening is upwards.2

. y = -x² - 12x - 36To write this equation in vertex form, we need to complete the square. y = -x² - 12x - 36 is equivalent to y = -(x+6)² - 12. Therefore, the equation in vertex form is y = -(x+6)² - 12.

The vertex is (-6,-12), the axis of symmetry is x = -6, and the direction of opening is downwards.3. y = 2x² + 12x + 13To write this equation in vertex form, we need to complete the square. y = 2x² + 12x + 13 is equivalent to y = 2(x+3)² + 1.

To learn more about : vertex form

https://brainly.com/question/31546205

#SPJ8

If the graph doesn't go through the origin (0,0), the relationship is not a proportional one.

To learn more about proportional graph refers to:

brainly.com/question/11514965

#SPJ1

Answer:

the answer is 46.

Step-by-step explanation:

see answer.

According to the information we can infer that the approximate area of the cross-section is 35.5 square meters. Additionally, the approximate volume of water flowing through the cross-section in 10 seconds is 142 cubic meters.

To calculate the approximate area of the cross-section using Simpson's rule, we divide the width of the river (12 meters) into intervals and consider the depth measurements at each interval. Given the depth measurements:

We use Simpson's rule to estimate the area by applying the formula:

Using the given depth measurements, we substitute them into the formula and calculate:

According to the information, the approximate area of the cross-section is 35.5 square meters.

To calculate the approximate volume of water flowing through the cross-section in 10 seconds, we multiply the area of the cross-section by the velocity of the river.

Given the velocity of the river is 0.4 meters per second, and the time is 10 seconds:

According to the information, the approximate volume of water flowing through the cross-section in 10 seconds is 142 cubic meters.

Learn more about Simpson's rule in: https://brainly.com/question/32151972

#SPJ1

Answer:4x-15

Step-by-step explanation:

Answer:

4x-15 <---

Step-by-step explanation)

1) Distribute the X to both the x and the -3

2) You'll end up with, 5x-15-x=...

3) And, now look at the like terms. The like terms in this case are 5x and the -x.

4) 5x-x =4x

5) And, now put them together, and you'll get 4x-15!

HOPE IT HELPS! <3

Answer:

0.45oz or honey

Step-by-step explanation:

5.40/12

10.5 is the mean of 20 .

What are the mean, median, and example?

A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

 x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + ................. + 20/20

  x = 210/20

  x = 10.5

Learn more about mean in mode

brainly.com/question/6813742

#SPJ4

The complete question is -

How do you find the mean of 20 natural numbers?

Answer:

yoooooooooooooooooooooooooooooooooooooooo

wait its not loading

Step-by-step explanation:

Answer:

  x = -0.5, -3.5

Step-by-step explanation:

You want the solution to 4x² +16x +7 = 0 using the quadratic formula.

Comparing the given equation to the standard form quadratic, you can identify the coefficients as ...

Substituting these values into the quadratic formula, you find the solutions to be ...

  \(x=\dfrac{-16\pm\sqrt{16^2-4(4)(7)}}{2(4)}=\dfrac{-16\pm\sqrt{144}}{8}\\\\x=\dfrac{-16\pm12}{8}=\dfrac{-4\pm3}{2}\\\\x=\left\{-\dfrac{7}{2},\ -\dfrac{1}{2}\right\}\)

The possible values of x are -3.5 and -0.5.

Answer:

It's D I think.... Line up B and C with M,N

Answer:

C

Step-by-step explanation:

Let's first convert both Brooke's time and Lamont's time into the same unit so that we can more easily compare them. To make it simpler, we'll convert both times into minutes.

Brooke: 1 hr 45 min

We know that there are 60 minutes in 1 hour, so we essentially have:

60 min and 45 min  ⇒  60 + 45 = 105 min

Lamont: 115 min

This is already in minutes, so we don't have to do anything to it.

We now have 105 minutes for Brooke and 115 minutes for Lamont. Let's compare:

- Since we know Brooke took 105 minutes, we can eliminate A and B.

- Clearly, 105 < 115, which means Brooke took less time that Lamont to finish the race

- If Brooke took less time, that means she's faster.

Thus, the answer is C.

~ an aesthetics lover

Answer:

Time taken by Brooke = 1h 45min

= 60min + 45min

= 105min

Time taken by Lamont = 115min

Brooke finished in 105min, so she was faster.

Option 3 is correct.

In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

Learn more about equations at the following link:

https://brainly.com/question/22688504

#SPJ1

Answer:

6*3= 18

Jeff packed 18 pairs of socks

Step-by-step explanation:

Jeff has 6 packs of new socks. Each pack contains 3 pairs of socks. How many pairs of new socks does Jeff have?

3

6

15

18