evaluate the expression when z= -5
100 divided (-z2)

The value of y that optimizes the function is y = 3/2. The Lagrange Multiplier in this case is -105/8.

To optimize the function \(f(x, y) = -4x^2 + 4xy - 2y^2 + 6x + 8y\) subject to the constraint xy ≤ 15, we can use the method of Lagrange multipliers.

The Lagrangian function is defined as:

L(x, y, λ) = f(x, y) - λ(g(x, y) - 15)

where g(x, y) = xy is the constraint equation.

To find the optimal value of y, we need to solve the following system of equations:

∂L/∂x = -8x + 4y + 6 - λy = 0 (1)

∂L/∂y = 4x - 4y + 8 - λx = 0 (2)

g(x, y) - 15 = xy - 15 = 0 (3)

From equation (1), we can rearrange it as:

-8x + 4y - λy = -6 (4)

From equation (2), we can rearrange it as:

4x - 4y - λx = -8 (5)

To solve this system of equations, we can eliminate λ by multiplying equation (4) by x and equation (5) by y, and then subtracting the resulting equations:

\(-8x^2 + 4xy - λxy = -6x (6)\\4xy - 4y^2 - λxy = -8y (7)\)

Subtracting equation (7) from equation (6), we get:

\(-8x^2 + 4xy - 4y^2 = -6x + 8y\)

Simplifying this equation gives:

\(-8x^2 - 4y^2 + 4xy = -6x + 8y\)

Rearranging terms, we have:

\(-8x^2 + 4xy + 6x - 4y^2 - 8y = 0\)

Factoring, we get:

(2x - y)(-4x - 2y + 6) = 0

Setting each factor equal to zero gives:

2x - y = 0 (8)

-4x - 2y + 6 = 0 (9)

From equation (8), we can solve for y:

y = 2x (10)

Substituting equation (10) into equation (9), we get:

-4x - 4x + 6 = 0

Simplifying, we have:

-8x + 6 = 0

Solving for x, we find:

x = 3/4

Substituting this value of x into equation (10), we can find y:

y = 2 * (3/4) = 3/2

Therefore, the value of y that optimizes the function is y = 3/2.

To find the Lagrange Multiplier, we substitute the optimal values of x and y into the constraint equation (3):

xy - 15 = (3/4) * (3/2) - 15 = 9/8 - 15 = -105/8

Hence, the Lagrange Multiplier is -105/8.

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Answer:

10

Step-by-step explanation:

0.35/x=0.035

x=0.35/0.035

 =10

\( \frac{0.35}{x} = 0.035\)

\(0.035x = 0.35\)

\(x = \frac{0.35}{0.035} \)

\(x = 10\)

\(PLEASE \: \\ MARK \: \\ ME \: \\ AS \\ BRAINLIEST ♥️\)

Shawn saved approximately \(15.85\)‰ of their original bill with the coupon.

The amount remained with Shawn by subtracting the final bill from the original bill -

Saved amount \(= 31.58 - 26.58\)

                      \(= 5.00\)

To convert the amount saved in percentage, divide the amount saved by the original bill and multiply by 100:

Percentage Saved \(=\) (Amount Saved / Original Bill) × \(100\)

Percentage Saved \(=\) (\(5\) ÷ \(31.58\) ) × \(100\)

                             \(=\) \(15.85\) ‰

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Answer:

x=5

Step-by-step explanation:

trust me its right

Answer: AB = 15 because sides AB and AD are congruent

Step-by-step explanation:

Least to Greatest

-14, -8, -7, -2, 4, 17

The integral test states that if a series is a sum of terms that are positive and decreasing, and if the terms of the series can be expressed as the values of a continuous and decreasing function, then the series converges if and only if the corresponding improper integral converges.

Let's apply the integral test to the given series. We need to find a continuous, positive, and decreasing function f(x) such that the series is the sum of the values of f(x) for x ranging from 2 to infinity.

For the first series, we have:

∑n=2∞n(lnn)p

Let f(x) = x(lnx)p. Then f(x) is continuous, positive, and decreasing for x ≥ 2. Moreover, we have:

f'(x) = (lnx)p + px(lnx)p-1

f''(x) = (lnx)p-1 + p(lnx)p-2 + p(lnx)p-1

Since f''(x) is positive for x ≥ 2 and p > 0, f(x) is concave up and the trapezoidal approximation underestimates the integral. Therefore, we have:

∫2∞f(x)dx = ∫2∞x(lnx)pdx

Using integration by substitution, let u = lnx, then du = 1/x dx. Therefore:

∫2∞x(lnx)pdx = ∫ln2∞u^pe^udu

Since the exponential function grows faster than any power of u, the integral converges if and only if p < -1.

For the second series, we have:

∑n=2∞1/n(ln⁡n)²

Let f(x) = 1/(x(lnx)²). Then f(x) is continuous, positive, and decreasing for x ≥ 2. Moreover, we have:

f'(x) = -(lnx-2)/(x(lnx)³)

f''(x) = (lnx-2)²/(x²(lnx)⁴) - 3(lnx-2)/(x²(lnx)⁴)

Since f''(x) is negative for x ≥ 2, f(x) is concave down and the trapezoidal approximation overestimates the integral. Therefore, we have:

∫2∞f(x)dx ≤ ∑n=2∞f(n) ≤ f(2) + ∫2∞f(x)dx

where the inequality follows from the fact that the series is the sum of the values of f(x) for x ranging from 2 to infinity.

Using the comparison test, we have:

∫2∞f(x)dx = ∫ln2∞(1/u²)du = 1/ln2

Therefore, the series converges if and only if p > 1.

In summary, the series ∑n=2∞n(lnn)p converges if and only if p < -1, and the series ∑n=2∞1/n(ln⁡n)² converges if and only if p > 1. For values of p such that -1 ≤ p ≤ 1, the series diverges.
To find the values of p for which the series converges or diverges using the integral test, we will first write the series and then perform the integral test.

The given series is:

∑(n=2 to infinity) [1/n(ln(n))^p]

Now, let's consider the function f(x) = 1/x(ln(x))^p for x ≥ 2. The function is continuous, positive, and decreasing for x ≥ 2 when p > 0.

We will now perform the integral test:

∫(2 to infinity) [1/x(ln(x))^p] dx

To evaluate this integral, we will use the substitution method:

Let u = ln(x), so du = (1/x) dx.

When x = 2, u = ln(2).
When x approaches infinity, u approaches infinity.

Now the integral becomes:

∫(ln(2) to infinity) [1/u^p] du

This is now an integral of the form ∫(a to infinity) [1/u^p] du, which converges when p > 1 and diverges when p ≤ 1.

So, for the given series:

- It converges when p > 1.
- It diverges when p ≤ 1.

In conclusion, using the integral test, the series ∑(n=2 to infinity) [1/n(ln(n))^p] converges for values of p > 1 and diverges for values of p ≤ 1.

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Answer:

2n+8

Step-by-step explanation:

First: Multiply

        2 times n = 16

        2 times 8 = 16

Finally: Combined

        2n+8

\(\huge\text{Answer:}\)

\(\huge\mathrm{2n+16}\checkmark\)

\(\huge\text{Solution:}\)

What does the Distributive Property state?

It states that

\(\huge\mathrm{a(b+c)=ab+ac}\)

How to Solve the Given Math problem:

\(\bigstar\) Multiply 2 by n and 8:

\(\huge\mathrm{2*n=2n;~8*2=16}\)

\(\bigstar\) Add the products:

\(\huge\mathrm{2n+16}\)

Hope you find it helpful.

Feel free to ask if you have any doubts.

\(\huge\bold{-MistySparkles^**^*}\)

Answer:

\(\boxed{\frac{5}{8} x^8 + c}\)

Step-by-step explanation:

\(\int\limits {5x^7} \ dx\)

\(= \frac{5}{8} x^8 + c\)

the answers is 5/8 x⁸ + c

Answer:

25,36,49,64,81,100

................................

Answer:

Your answer is 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Step-by-step explanation:

1 - 4  

+ 3

4 - 9

+ 5

9 - 16

+ 7

+9, +11, +13, +15, +17, +19...

The correct answer is (c): HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, and TTTT.

(a) The generalized multiplication principle states that if there are 'n' independent events, and event 1 can occur in 'n1' ways, event 2 can occur in 'n2' ways, event 3 can occur in 'n3' ways, and so on, then the total number of outcomes is given by the product n1 * n2 * n3 * ...

In this case, each coin toss has two possible outcomes: heads (H) or tails (T). Since there are four coin tosses, the total number of outcomes can be calculated as 2 * 2 * 2 * 2 = 2^4 = 16.

Therefore, there are 16 possible outcomes for this activity.

(b) The possible sequences of heads (H) and tails (T) for four coin tosses are:

a. HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, and TTTT.

(c) The possible sequences listed in option c include an additional sequence: TTTT, which was not included in option b.

(d) The possible sequences listed in option d include fewer sequences than the total number of outcomes. It only includes sequences with four heads and three tails, but it does not include sequences with fewer heads or more tails.

Therefore, the correct answer is (c): HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, and TTTT.

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Answer: 51 degrees

Step-by-step explanation:

Angle sum of a triangle: 180 degrees

78 + 51 = 129

180 - 129 = 51

The value of f(-40) and c(-40) in the linear functions given are -14.4 and 40 respectively.

A linear function is a type of mathematical function whose graph is a straight line. The general form of a linear function is:

f(x) = mx + b

where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept, the point where the line crosses the y-axis.

In this problem, the linear function given

c(f) = 5/9(f - 32) ...eq(i)

f(c) = 9 / 5(c + 32) ...eq(ii)

a.

for f = -40

Using equation (ii)

f(-40) = 9 / 5 (-40 + 32)

f(-40) = -72 / 5

f(-40) = -14.4

b.

for f(-40)

Using equation (i)

c(-40) = 5/9(-40 - 32)

c(-40) = -40

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Toby cycles 12 miles each day.

To find out how far Toby cycles each day, we need to add up the distance he covers during his morning and afternoon trips. Here are the steps we need to follow:

Step 1: Determine Toby's cycling distance from his house to his schoolDistance from Toby's house to his school = 4 miles west. Toby bicycles this distance every day. Therefore, his one-way cycling distance from home to school is 4 miles.

Step 2: Determine Toby's cycling distance from his school to Erica's house.Distance from Toby's school to Erica's house = 3 miles south. Toby cycles this distance every day after school. Therefore, his one-way cycling distance from school to Erica's house is 3 miles.

Step 3: Determine Toby's cycling distance from Erica's house to his house.Distance from Erica's house to Toby's house = we don't know. But we know that Toby takes a bike path that goes straight from Erica's house to his own house. Therefore, we can assume that the distance from Erica's house to Toby's house is the hypotenuse of a right-angled triangle with legs of 3 miles (south) and 4 miles (west).

We can use the Pythagorean Theorem to find the hypotenuse: c2 = a2 + b2c2 = 32 + 42c2 = 9 + 16c2 = 25c = √25c = 5 milesTherefore, Toby cycles 5 miles every day on his bike path from Erica's house to his own house.Step 4: Add up Toby's one-way cycling distances to find out how far he cycles each day.Toby's one-way cycling distance from home to school = 4 milesToby's one-way cycling distance from school to Erica's house = 3 milesToby's one-way cycling distance from Erica's house to his house = 5 milesTotal cycling distance = 4 + 3 + 5Total cycling distance = 12 miles.

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Answer:

X>5273

Step-by-step explanation:

I did the math cuz I needed the answer and got it right so hope I could help.

The measure of angle m is 55 degrees.

Angles on a straight line are pairs of angles that are formed when a straight line intersects two other lines.

The pairs of angles on a straight line are supplementary, which means that their measures add up to 180 degrees.

From the diagram, angle 125° and angle m° are a pair of angle of a striaght line.

Since the measures of the angles on a strainght add up to 180 degrees.

Angle 125° + angle m° = 180°

Solve for m

125° + m° = 180°

Subtract 125 from both sides

125 - 125  + m = 180 - 125

m = 180 - 125

m = 55 degree.

Therefore, angle m measures 55 degree.

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The exact area of each hexagonal shape is 181.5sqrt(3) cm^2. Option B

To determine the exact area of each hexagonal shape formed by the equilateral triangles, we need to calculate the area of one equilateral triangle and then multiply it by the number of triangles that make up the hexagon.

The formula to calculate the area of an equilateral triangle is:

Area = (sqrt(3) / 4) * side^2

Given that the side of each tile measures 11 cm, we can substitute this value into the formula to find the area of one equilateral triangle:

Area = (sqrt(3) / 4) * (11 cm)^2

= (sqrt(3) / 4) * 121 cm^2

= 121sqrt(3) / 4 cm^2

Now, since the hexagon is formed by six equilateral triangles, we can multiply the area of one triangle by 6 to find the total area of the hexagon:

Hexagon Area = 6 * (121sqrt(3) / 4 cm^2)

= 726sqrt(3) / 4 cm^2

= 181.5sqrt(3) cm^2

Therefore, the exact area of each hexagonal shape is 181.5sqrt(3) cm^2.

The correct answer is B: 181.5√3 cm^2.

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Nora could run 7.5 minutes per mile to qualify for the state cross-country championships. The correct answer is option c.

To qualify for the state cross-country championships, Nora needs to run 4 miles in 30 minutes or less. So, her average rate should be:

average rate = total time / total distance

If she runs at the slowest rate possible to still qualify, then her average rate would be:

average rate = 30 / 4 = 7.5 minutes per mile

Therefore, the correct option is c) 7.5.

If she runs slower than this average rate, then her total time would exceed 30 minutes and she would not qualify.

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12.59

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answer:

B:80%

Step-by-step explanation:

15% +5%=20%

100%-20%=80%

Answer:

hi again

Step-by-step explanation:

2(5y-3)= 2×5y - 2×3=10y-6

Answer:

10y -6

Step-by-step explanation:

2(5y-3)

Distribute the 2 to each term in the parentheses

2*5y - 2*3

10y -6

Answer:

85 beats per minute

Step-by-step explanation:

khan academy

The data can be tallied into a frequency distribution using a class interval of 100 and a starting point of 0.

To create a frequency distribution, we group the data into intervals or classes and count the number of data points falling within each interval. The class interval represents the range of values covered by each class, and the starting point determines the first interval.

Here is an example of how the data can be tallied into a frequency distribution using a class interval of 100 and a starting point of 0:

```

Class Interval    Frequency

0 - 99            12

100 - 199         18

200 - 299         24

300 - 399         15

400 - 499         10

500 - 599         8

600 - 699         5

700 - 799         3

800 - 899         2

900 - 999         1

```

In this frequency distribution, the data is divided into classes based on the class interval of 100. The first class, from 0 to 99, has a frequency of 12, indicating that there are 12 data points falling within that range. The process is repeated for each subsequent class interval, resulting in a frequency distribution table.

By organizing the data into a frequency distribution, we gain insights into the distribution and patterns within the dataset. It provides a summarized view of the data, allowing us to identify the most common or frequent values and analyze the overall distribution.

In summary, the data has been tallied into a frequency distribution using a class interval of 100 and a starting point of 0. The frequency distribution table presents the number of data points falling within each class interval, enabling a better understanding of the distribution of the data.

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The start = 1 is the number of rabbit pairings after one month. Each female rabbit births three pairs of rabbits starting in the third month. We can count rabbit pairs at month's end by analysing the trend. After a year, we can count all rabbits, male and female.

a. The initial condition So = 1 represents the number of rabbit pairs alive at the end of the first month. This means that initially, there is one pair of rabbits in the field.

b. To compute the number of rabbit pairs at the end of each month, we follow the given rules. After the first month, the pair of rabbits is still too young to reproduce, so S1 remains 1. In the second month, they still cannot reproduce, so S2 remains 1 as well. However, at the end of the third month, the female rabbit can give birth, resulting in three new pairs of rabbits. Therefore, S3 becomes 1 (initial pair) + 3 (new pairs) = 4. In the fourth month, each of the four female rabbits can give birth, resulting in 3 * 4 = 12 new pairs. So, S4 becomes 4 (existing pairs) + 12 (new pairs) = 16. Following this pattern, we can calculate S5, S6, and so on.

c. We can observe a recurrence relation in the sequence: Sn = Sn-1 + 3 * Sn-3, where n > 3. This relation states that the number of pairs at the end of the nth month is equal to the number of pairs at the end of the previous month (Sn-1) plus three times the number of pairs three months ago (Sn-3).

d. To find the total number of rabbits at the end of the year, we sum up the number of rabbit pairs for each month from the 1st to the 12th month. At the end of the 12th month, we can calculate the total number of rabbits by multiplying the number of pairs by 2 (to account for both male and female rabbits in each pair).

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\( \to\dfrac{4}{48 \times 100} \)

\( \\ \)

\( \to\dfrac{1}{12\times 100} \)

\( \\ \)

\( \to0.00083\)

\( \\ \\ \)

or

\( \\ \\ \)

\( \to \dfrac{4}{48} \times 100\)

\( \\ \\ \)

\( \to \dfrac{1}{12} \times 100\)

\( \\ \\ \)

\( \to 8.33\)

Answer:

The number is 8

Step-by-step explanation:

The warning approach is an example of Detection of error type prevention.

Error is a conscious or unconscious departure from a standard of conduct. A bug is a mistake in computer data. A software bug is an error, flaw, failure, or fault that results in an unwanted behavior from a computer program or system or leads it to deliver an inaccurate or unexpected outcome. Errors caused by bugs may have repercussions. The majority of defects are caused by faults and blunders in a program's source code, in its design, or in the parts and operating systems that these programs rely on.

After pressing submit or a PAR or KC quiz, D2Lprovides a warning if you have not saved your answers to one or more questions before grading your assignment. Since you are still permitted submit a quiz with unanswered questions, using a warning approach is an example of Detection type of error prevention

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The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.

In this case, the ratio of the corresponding sides of the two triangles are:

AB/DE = 3/18 = 1/6

BC/EF = 7/42 = 1/6

Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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