If m∠8=62°, find m∠1.

Consider the first blank is the green box.

Given:

The equations are

\(3x+2y=9\)

\(-x-2y=4\)

To find:

The value belongs in the green box

Solution:

We have,

\(3x+2y=9\)        ...(i)

\(-x-2y=4\)        ...(ii)

Adding (i) and (ii), we get

\(3x+2y-x-2y=9+4\)

\((3x-x)+(2y-2y)=13\)

\(2x+0=13\)

So, the value for the first black is 2x. It means the value belongs in the green box is 2x.

The values of three blanks are 2x, 0 and 13 respectively.

Therefore, the correct option is B.

Answer:

2x + 0 = 13

Step-by-step explanation:

To add the equations, we add the corresponding terms on both sides of the equal sign.

The given equations:

3x + 2y = 9

-x - 2y = 4

Adding the equations term by term:

(3x + (-x)) + (2y + (-2y)) = 9 + 4

Simplifying the equation:

2x + 0 = 13

The term "0" in the equation indicates that the terms (2y and -2y) cancel each other out when added.

The maximum value of the function is 10368 and the minimum value is 0.

The given function is f(x, y) = x² +2y², and the constraint is 12-216y = 15648.

Therefore, the maximum and minimum values of the function are to be found.

Now, to find the maximum and minimum values of the given function, we use the method of Lagrange Multipliers.

We need to maximize and minimize the function f(x, y) subject to the constraint 12-216y = 15648.

So, we need to find the critical points of the function F(x, y, λ) = f(x, y) + λ(12-216y - 15648).

F(x, y, λ) = x² +2y² + λ(12-216y - 15648)

Differentiating F(x, y, λ) w.r.t x, y, and λ and equating to 0, we get the following equations:

2x + 0y + λ(0) = 0 ...(1)

0x + 4y + λ(-216) = 0 ...(2)

12-216y - 15648 = 0 ...(3)

From equations (1) and (2), we get:

λ = 0

And, 4y - 216λ = 0 or λ = 4y/216

Now, equating the two values of λ, we get:

0 = 4y/216or y = 0

Also, from equation (3), we get:12 - 216y = 15648or y = -72

The critical points of the function are (0, 0) and (0, -72).

Now, let's find the values of the function at these points.

f(0, 0) = 0²+ 2(0)² = 0

f(0, -72) = 0² + 2(-72)² = 10368

Thus, the correct answer is:

Maximum = 10368

Minimum = 0.

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x2 = -2.0000. In this way, we get x2, the second approximation to the root of the equation using Newton's method with an initial approximation x1 = −2.

Newton's method is one of the numerical methods used to estimate the root of a function.

The following are the steps for using Newton's method:

Let the equation f (x) = 0 be given with an initial guess x1, and let f′(x) be the derivative of f(x).

Determine the next estimate, x2, by using the formula x2 = x1 - f (x1) / f'(x1).

Therefore, the given equation is x³ + x + 6 = 0.

Let us use Newton's method to solve the given equation. We have x1 = -2, which is the initial approximation.

Therefore, f(x) = x³ + x + 6, and f'(x) = 3x² + 1.

To find x2, the second approximation to the root of the equation, we need to substitute the values of f(x), f'(x), and x1 into the formula x2 = x1 - f (x1) / f'(x1).

Substituting the given values in the above equation we get, x2 = x1 - f (x1) / f'(x1) = -2 - (-2³ - 2 + 6) / (3(-2²) + 1) = -2 - (-8 - 2 + 6) / (3(4) + 1) = -2 - (-4) / 13 = -2 + 4 / 13 = -26 / 13

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answer: basketball c;

A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.

a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`

Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`

b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)

`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)

`Simplifying:`S_n = 2*(2^n - 1)

`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.

Thus, the sum is getting closer and closer to infinity.

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Answer:

29

Step-by-step explanation:

2(2)+(3(3)+(4²))

4+(9+16)

4+25

29

pls if this was h helpful pls tag brainiest

Answer:

900

Step-by-step explanation:

10 times 9 is 90 so just add the missing 0

Answer:

25.52791653032955454422437424679625318128649677442393276098...

Step-by-step explanation:

You can just paste this into wolframalpha.

Answer: 970.72312

Step-by-step explanation:

Straightforward operation.

Answer:

-(-45) and -|45|

Step-by-step explanation:

Opposite of a number can also me termed the conjugate of such number. For example, the conjugate (opposite) of a is -a.

Also any value in the modulus sign can either be a negative or positive value. For example |a| can be +a or -a.

According to the question, we are to find the numbers that are equivalent to opposite of -45 i.e which of them are conjugate of -45.

To do this, we are to select the values in the options that will return +45.

Let's look at each option.

For -(-45):

Since the product of two negative sign will give a positive(+), then -(-45) = +45 and hence the value is opposite of -45

For -45:

-45 is a negative value and can never be positive since 45 is not inside a modulus sign. Hence, -45 is not equal to opposite of -45.

For −|−45|, |-45| can only return a positive value since -45 is already in a modulus sign. What the modulus sign will do is convert it to positive value i.e |-45| = 45. Hence -|-45| ≈ -(45) which is not also equivalent to the opposite of-45.

For -|45|:

The value inside modules will return both +45 and -45, hence it can be written as -|45| = -(-45) = +45. This shows that -|45| is also equivalent to the opposite of -45.

Answer:

-(-45) and -|45|

Step-by-step explanation:

For:

Use distributive property:

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

Let:

x = Unknown number

When the number x is increasesd by 35 the result is 38, so:

Explanation:

We know that:

The fraction of the black beans is the number of black beans divided by the total number of beans.

Solution:

Fraction of black beans: Black beans/Total beans

Hence, the fraction of black beans is 2/3.

Juwan is mailing a package that weighs 10lb

for every 1 lb you have 16 ounces inside the package

if 1 lb ------- 16 ounces

10lb ------- x ounces

reason why we have x ounces is because we dont know how many ounces 10 lb we give us

cross multiplication

1 * x = 10 x 16

x = 10 x 16

x = 160 ounces

10lb we give us a total of 160 ounces

therefore, there are 160 ounces in the 10 lb package juwan is mailing

The answer is 160 ounces

Using simple mathematical operations we know that Kelli will make $360 extra by working for Mr. McHenry and she will cover her budget shortfall by doing so.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.

Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).

So, we know that:

Kelli will be short by $100 in 3 months. That will be,

100 * 3 = $300

She will earn $30 per week through Mr. McHenry:
We know that 1 month has 4 weeks.

Then, 3 months will have:

3 * 4 = 12 weeks

Then, the extra money she will make is:

12 * 30  = $360

And: YES

Therefore, using simple mathematical operations we know that Kelli will make $360 extra by working for Mr. McHenry and she will cover her budget shortfall by doing so.

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Answer:

\(Percentage = 20\%\)

Step-by-step explanation:

Given

\(Heights: 65\ 63\ 66\ 62\ 59\ 69\ 69\ 60\ 70\ 68\)

\(Total = 10\)

Required

Determine the percentage of those shorter than 61

To do this, we need to get the number of those that fall in this category:

\(Shorter\ than\ 61:\ 59\ 60\)

\(Number = 2\)

The percentage is then calculated as thus:

\(Percentage = \frac{Number}{Total} * 100\%\)

\(Percentage = \frac{2}{10} * 100\%\)

\(Percentage = \frac{200\%}{10}\)

\(Percentage = 20\%\)

Answer:

Step-by-step explanation:

\(2 . 4x =\\2 \times 4x\\\mathrm{Multiply\:the\:numbers:}\:2\times \:4=8\\\\= 8x\)

Step-by-step explanation:

B ANSWER OOOOOKKKKKKKKK

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

52.

Step-by-step explanation:

So 143 members represent 100% of the population of the problem. A ratio of 4:7 similarly represent 100%. First, you need to get the value of 4:7 in a representation of 100%. You can do that by adding the two (4+7=11) and then dividing it by each value of it. So 7 divided by 11 is .6363, or 63.63% of the whole. Then 4 divided by 11 is .3636, or 36.36% of the whole. After getting this, seeing that the ratio for union members to non union members is 4 union members to 7 nonunion members, and there are 143 employees in total, just get the value of 36.36% of 143; in this case, it's 51.99 - rounded off to 52 employees.

Answer:

52 members

Step-by-step explanation:

Proportional setup.

(4/11)=(x/143)

Answer:

La cantidad producida para maximizar las ganancias es de 915 unidades

Step-by-step explanation:

Pregunta: Calcule cuánto producirá para maximizar las ganancias.

La función de costo dada se presenta de la siguiente manera;

CT = Q³ - 45 · Q² + 600 · Q + 1200

La función de suministro es Qo = 5 · P - 300

La función de demanda es Qd = 2860 - 8 · P

A precio de equilibrio, tenemos;

Qo = Qd

Por lo tanto;

5 · P - 300 = 2860 - 8 · P

13 · P = 2.860 + 300 = 3.160

P = 3160/13

Por lo tanto;

Q = 2860 - 8 × (3160/13) = 11900/13 ≈ 915,38

La cantidad producida que maximiza las ganancias es de aproximadamente 915 unidades.

El costo total CT = 915³ - 45 × 915² + 600 × 915 + 1200 = 728,935,950

Answer:

Slope = 4, y-intercept = (0,0)

Step-by-step explanation:

This problem is written in slope-intercept form. Meaning it is in the form y=mx+b. "M" is the slope, and "B" is the y-intercept. With that information, we easily see that 4 is the slope of the graph (it will go up 4 points for everyone one point it goes right). It seems that there is no y-intercept though, that is because we are expected to know that y=4x is the same as y=4x+0. Meaning, the problem can also be written this way and the y-intercept must be 0.

Answer:

3.5x

Step-by-step explanation:

Put into numbers, [4*x+(3x)]*1/2. You cant completely solve for x in this, as we would need an answer with no variable. But, 4*x=4x, and 4x+3x=7x because we would need to combine like terms. But you still need to cut it in half. Half of 7x is 3.5x, so there ya go!

Answer:

\(45c - 60 = 75 \\ 45c = 75 + 60 \\ 45c = 135 \\ \\ c = \frac{135}{45} \\ \\ c = 3\)

I hope I helped you^_^

If each person is allowed to fill only one job, there are 604,800 ways to fill the 7 sales territories with the 10 equally qualified persons.

If each person is allowed to fill only one job, we can treat this as a permutation problem. We have 10 equally qualified persons applying for 7 jobs, and we need to determine the number of ways the jobs can be filled.

In this scenario, the order in which the jobs are filled matters because each person is assigned to a specific territory. We can use the concept of permutations to calculate the number of ways the jobs can be filled.

The first job can be filled by any of the 10 persons. Once the first job is filled, there are 9 remaining persons to choose from for the second job. Similarly, for each subsequent job, the number of available persons decreases by 1.

Using the principle of permutations, the total number of ways to fill the jobs is given by:

10 * 9 * 8 * 7 * 6 * 5 * 4 = 604,800

Therefore, if each person is allowed to fill only one job, there are 604,800 ways to fill the 7 sales territories with the 10 equally qualified persons.

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Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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If the scores were from a sample, the sample variance would be calculated using the formula:

s² = Σ(x -  x bar)² / (n - 1)

Where s² is the sample variance, x is each individual score, x bar is the mean of the scores, and n is the number of scores in the sample.

Given that the population variance σ2  is 24 and the population size n is 5, we can plug these values into the formula to find the sample variance:

s² = (5)(24) / (5 - 1)
s² = 120 / 4
s² = 30

Therefore, the sample variance would be 30.

The sample variance would be obtained by multiplying the population variance by the ratio of the sample size to the sample size minus one. This is known as the "correction factor" and is used to account for the fact that a sample is a smaller subset of the population and therefore has less variability.

The formula for sample variance is:

s^2 = (n/(n-1)) * σ^2

Where s^2 is the sample variance, n is the sample size, and σ^2 is the population variance.

Plugging in the values given in the question:

s^2 = (5/(5-1)) * 24

s^2 = (5/4) * 24

s^2 = 30

Therefore, the sample variance would be 30.

In conclusion, a population of n = 5 scores with a variance of σ^2 = 24 would have a sample variance of 30 if the scores were from a sample.

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Answer:

The center three.

Step-by-step explanation:

Rectangular prisms have three measurements of length, width, and height.

You paid $16.05 with taxes for a meal.

The definition of the sales tax is given below.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

1) If you buy a meal from a restaurant that cost $15.00, and the tax is 7%,

then the amount of the tax is,

= 15 x 7 / 100

= $1.05

2) The sales tax:

The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a traditional sales tax is imposed, collected by the shop, and forwarded to the government.

Therefore, the taxed amount is $1.05.

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Answer: 14 percent

Step-by-step explanation:

Not really needed.

To ensure that a triangle is acute, the largest whole-number side length in inches would be 1.

In an acute triangle, each angle measures less than 90 degrees. To determine the largest whole-number side length that ensures an acute triangle, we consider the smallest possible non-zero lengths for the other two sides. By setting these two side lengths as 1, we can construct a triangle where all three angles are acute.

When one side length is 1, the other two sides must have lengths greater than 1 for the triangle to be valid. However, if any side length is equal to or less than 1, it would lead to an obtuse or degenerate triangle. Thus, the largest whole-number side length that guarantees an acute triangle is 1 inch.

In summary, to ensure an acute triangle, the largest whole-number side length in inches would be 1. This guarantees that all three angles of the triangle measure less than 90 degrees, creating an acute triangle.

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