2x+5y=-62x+5y=−6 Determine the intercepts of the line

Given that a square pyramid has a surface area of 10 cm², and a dilation of the pyramid has a surface area of 90 cm², we are to find the scale factor of the dilation.

Step 1: Recall the formula for the surface area of a square pyramid, which is given by: S.A. = l² + 2 × l × sHere, l is the slant height of the pyramid, and s is the length of the base.

Step 2: Let the scale factor of the dilation be k. Therefore, the new slant height of the pyramid after dilation is kl, and the new length of the base is ks.

Step 3: Recall that the surface area of a pyramid is proportional to the square of the slant height, and also proportional to the product of the slant height and the length of the base.

Therefore, we can say:S.A. ∝ (slant height)² × (base length)S.A. = k²l² + 2k²lsAnd since we know that the initial surface area is 10 cm² and the new surface area is 90 cm², we can form the equation:10 = l² + 2ls90 = k²l² + 2k²ls

Step 4: Solve for k by dividing the second equation by the first:90/10 = k²l² + 2k²ls / (l² + 2ls)9 = k²l² + 2k²ls / (l(l + 2s))9 = k² + 2ks / (l + 2s)9(l + 2s) = k²l + 2ks k² = (9l + 18s) / l² + 2sl²k² = 9(l / l² + 2s / l) + 18(s / l² + 2s / l)k² = 9 / l + 18 / s k = √(9 / l + 18 / s)

Therefore, the scale factor of the dilation is: k = √(9 / l + 18 / s)

To know more about square pyramid visit:-

https://brainly.com/question/31621133

#SPJ11

Answer:

34

Step-by-step explanation:

Answer:A

Step-by-step explanation:

Answer:

x=-5

Step-by-step explanation:

-2x=3+7

or,-2x=10

or,x=-10/2

x=-5

Answer:

x = -5

Step-by-step explanation:

I hope this helps!

When a postal worker counts the number of complaint letters received by the united states postal service in a given day, the type of data collected is quantitative.

Quantitative data is data that can be measured and expressed in numbers. In this case, the number of complaint letters received by the United States Postal Service in a given day can be measured and expressed as a number.

Qualitative data, on the other hand, is data that cannot be measured or expressed in numbers. For example, the contents of the complaint letters would be qualitative data.

Learn more about data on

https://brainly.com/question/26711803

#SPJ1

Answer:

Step-by-step explanation:

If it grows by 9% each year, you can simply do the current population times 109%. Because its an additional 9%.

230,000*109% = 250,700

After the first year, there is a population of 250,700 people.

250,700*109% = 273,263

After the second year, there is a population of 273,263 people.

273,263*109% = 297,856.67

After the third year, there is a population of 297,856.67 people.

297,856.67*109% = 324,663.77

After the fourth year, there is a population of 324,663.77 people.

324,663.77*109% = 353,883.509

After the fifth year, there is a population of 353,883.509 people.

353,883.509*109% = 385,733.025

After the sixth year, there is a population of 385,733.025 people

Round it up to 385,733 people.

Answer:

50,000 + 100x = 75,000

Step-by-step explanation:

He sold 250 Computers last year.

Answer:

50,000 + 100x = 75,000

$100 commission

$50,000 = sells

$75,000 = total income

- hope this helps!:)

The long-run cost function is C(q) = 2w(sqrt[rw(q^3)]). The profit-maximizing output can be found by minimizing this cost function with respect to q.

Part a: Deriving the long-run cost function C(q):

To derive the long-run cost function, we need to find the minimum cost of producing a given output level q using the given production function.

Given the production function q = F(L, K) = (KL)^(1/3), we can rewrite it as K = (q^3)/L.

Now, let's express the cost function C(q) in terms of q. We have the cost function as C(q) = wL + rK, where w is the wage rate and r is the rental rate.

Substituting the expression for K in terms of q, we get C(q) = wL + r[(q^3)/L].

To minimize the cost function, we can take the derivative of C(q) with respect to L and set it equal to zero:

dC(q)/dL = w - r[(q^3)/(L^2)] = 0.

Simplifying the equation, we have w = r[(q^3)/(L^2)].

Solving for L, we get L^2 = r(q^3)/w.

Taking the square root, we have L = sqrt[(r(q^3))/w].

Substituting this value of L back into the cost function equation, we get:

C(q) = w(sqrt[(r(q^3))/w]) + r[(q^3)/sqrt[(r(q^3))/w]].

Simplifying further, we have:

C(q) = 2w(sqrt[rw(q^3)]).

So, the long-run cost function C(q) is given by C(q) = 2w(sqrt[rw(q^3)]).

Part b: Solving the long-run profit maximization problem directly:

To solve the profit maximization problem directly, we need to maximize the expression:

max K, L [F(L, K) - wL - rK].

Taking the derivative of the expression with respect to L and K, and setting them equal to zero, we can solve for the optimal values of L and K.

The first-order conditions are:

dF(L, K)/dL - w = 0, and

dF(L, K)/dK - r = 0.

Differentiating the production function F(L, K) = (KL)^(1/3) with respect to L and K, we get:

(1/3)(KL)^(-2/3)K - w = 0, and

(1/3)(KL)^(-2/3)L - r = 0.

Simplifying the equations, we have:

K^(-2/3)L^(1/3) - (3/2)w = 0, and

K^(1/3)L^(-2/3) - (3/2)r = 0.

Solving these two equations simultaneously will give us the optimal values of L and K.

Part c: Using the derived long-run cost function:

In Part a, we derived the long-run cost function as C(q) = 2w(sqrt[rw(q^3)]).

To find the profit-maximizing output, we can minimize the long-run cost function C(q) with respect to q.

Taking the derivative of C(q) with respect to q and setting it equal to zero, we can solve for the optimal value of q.

dC(q)/dq = w(sqrt[rw(q^3)]) + (3/2)w(q^2)/(sqrt[rw(q^3)]) = 0.

Simplifying the equation, we have:

(sqrt[rw(q^3)])^2 + (3/2)(q^2) =

0.

Solving this equation will give us the profit-maximizing output q.

Learn more about long-run cost function here :-

https://brainly.com/question/30882146

#SPJ11

Answer:

13.015625

Step-by-step explanation:

Answer:

13 remainder 1.

I have attached the work to your question.

Please see the attachment below.

I hope this helps!

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

True. The multiplicity of a root r of the characteristic equation of matrix A is indeed called the algebraic multiplicity of r as an eigenvalue of A.

The characteristic equation of a square matrix A is obtained by subtracting λI (where λ is an eigenvalue and I is the identity matrix) from A and taking its determinant. The roots of this equation are the eigenvalues of matrix A.

The algebraic multiplicity of an eigenvalue r refers to the number of times r appears as a root of the characteristic equation. In other words, it represents the multiplicity of r as a solution of the equation.

The algebraic multiplicity provides information about the behavior of the eigenvalue r within the matrix A. If the algebraic multiplicity of r is greater than 1, it means that r is a repeated eigenvalue and there exist multiple linearly independent eigenvectors associated with it. On the other hand, if the algebraic multiplicity is 1, r is a simple eigenvalue, indicating that there is only one linearly independent eigenvector corresponding to r.

Learn more about square matrix here:

https://brainly.com/question/27927569

#SPJ11

To prove that the given categorical syllogism invalid using the counterexample method, we first need to check whether the syllogism follows the standard form of categorical syllogisms. The standard form of categorical syllogism is:

Premise 1: All A are B. (Major Premise)

Premise 2: All C are A. (Minor Premise)

Conclusion: All C are B.

Let's represent the given syllogism in the standard form:

Premise 1: No undocumented individuals are people who are paid decent wages. (Major Premise)

Premise 2: Some undocumented individuals are not farm workers. (Minor Premise)

Conclusion: Some farm workers are not people who are paid decent wages.

Now, we will use the counterexample method to disprove the given syllogism. We will use real-world examples that will make the premises true but will make the conclusion false. Suppose Premise 1 is "No birds can swim." and Premise 2 is "Some penguins are not birds". Then, the Conclusion will be "Some penguins cannot swim." which is true. Here, we see that the premises are true, and the conclusion is also true.

Let's take another example. Suppose Premise 1 is "No reptiles can fly." and Premise 2 is "Some birds are reptiles." Then, the Conclusion will be "Some birds cannot fly." which is false. Here, we see that the premises are true, but the conclusion is false.

Hence, the syllogism is invalid. Using the same method, we can disprove the given syllogism. Some farm workers are not people who are paid decent wages, because no undocumented individuals are people who are paid decent wages, and some undocumented individuals are not farm workers.

Learn more about categorical syllogisms from the given link

https://brainly.com/question/8590978

#SPJ11

Answer: $14.85

Step-by-step explanation:

Ww can solve the question using direct proportion with the formula y = kx

where y = annual salary

x = monthly policy cost.

k = constant of proportionality

Since y = kx

38500 = 11.55k

k = 38500 / 11.55

k = $3333.33

When Randy has an annual salary of $49,500, the amount Randy expect to pay for his policy will be:

y = kx

49500 = 3333.33x

x = 49500 / 3333.33

x = 14.85

The amount that Randy expect to pay for his policy will be $14.85

when you want to solve an elimination question

3x -2y = 11. ( equation 1)

-3x - y = 6. ( equation 2)

To proceed in the solution, we have to make one of the variable' s coefficient equal on both equation.

I want to make the coefficient of variable X equal on both equation and to do this , the coefficient of X in equation 1 will be used to multiply the whole of equation 2 .while the coefficient of X in equation 2 will be used to multiply the whole of equation 1.

(-3) 3X - 2y = 11 ( equation 1)

(3) -3X - y = 6 ( equation 2)

-9X +6y = -33 ( equation 1)

- 9x - 3y = 18 ( equation 2)

( now , we have to eliminate X and inorder to do that , we substrate equation 1 from 2)

-9X -(-9X) ,+6y -(-3y) ,-33-18

-9X +9x , +6y +3y , -51

9 y = -51

y = -51/9

y = -5⅔

Substitute y = -5⅔ in equation 1

3x -2(-5⅔) = 11

3X - 2 ( -17/3) = 11

3X + 34/3 =11

divide through by the LCM which is 3

3( 3x) + 3 ( 34 /3 ) = 3*11

9x +34 = 33

9x = 33-34

9x = -1

X= -1/9

therefore, y = -5⅔ , X = -1/9

please mark me brainlest

Answer:

10 plz mark brainliest

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

first  2/3=.6

1/6=.16

1.6/.16=10

Complete Question:

The enrollment at East Valley High School over a six-year period is displayed in the scatterplot. Student Enrollment at East Valley High School (1st picture)

Which is the equation of the line of best-fit for this scatterplot? (2nd picture)

Answer:

D) y = (81/2)x - (160,069/2)

Step-by-step Explanation:

From the scatter plot in the graph attached below, we are given the ordered pairs of the coordinates (2009, 1330), (2013, 1492), we can derive the equation of the line of best-fit for the scatter plot using the slope-intercept formula.

Thus, the slope-intercept formula is y = mx + b, where m is the slope of the line; and b is the y-intercept.

We need to find m, and then b to input into the formula to get our equation of the line.

==> Finding m using the two sets of coordinate given on the graph [ (2009, 1330) and (2013, 1492) ]:

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

m = (1492 - 1330)/(2013 - 2009)

= 162/4

m = 81/2

Next is to find b, which is the y-intercept

Recall, y = mx + b

Using one of the coordinates given (2009, 1330), we can find b by inputting 1330 for y, 2009 for x, and 81/2 for m in the slope-intercept formula:

Thus, we would have ==>

1330 = (81/2 * 2009) + b

1330 = (162,729/2) + b

1330 - 162,729/2 = b

(2,660 - 162,729)/2 = b

- 160,069/2 = b

Having known the values of m, and b, let's input their values to get the equation of the line.

Thus, using the slope-intercept formula y = mx + b, the equation of the line of best-fit for the scatter plot would be

==> y = (81/2)x +(-160,069/2)

y = (81/2)x - (160,069/2)

Answer:

d

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Plug each equation in:

34-5 = 29

2^3 +18 = 26

Answer:

 -17 and 2

Step-by-step explanation:

Factors of -34 are

-1, 1,-2,2, -17, 17,-34,34

   -17+2=15

so   (-17 ,2)

Answer:

$42

Step-by-step explanation:

The yearly membership is $450.

The monthly membership is $41. This means that in a year, the membership fee will be:

41 * 12 = $492

We have to subtract the yearly fee from this.

That means that if you choose the yearly membership over the monthly membership, you'll save:

492 - 459 = $42

Answer:

The correct answer is $42.

It should be noted that the median remains the same because removing an extreme value from a data set will not have much effect on the median.

Statistical data established on the minimum, first quartile, median, third quartile, and maximum exist shown graphically in a box plot.

The box plot represents the number of kids in 30 distinct households in accordance with the families, and the value of 12 is subtracted for inaccuracy.

Therefore, if there exist two kids in the median for both plots when 12 stood eliminated from the data set, it remained unchanged.

In conclusion, the median stays exact because removing an extreme value from a data set will not have much effect on the median.

To learn more about distribution refer to:

https://brainly.com/question/24756209

#SPJ9

Comparison or relational operations, such as <, >, =, allow for comparing numbers. They determine if a number is less than, greater than, equal to, or not equal to another number, enabling decision-making and comparisons within arithmetic and programming operations.

When comparing numbers, you can use various relational operators to determine the relationship between them. Here are the commonly used comparison operators:

Less than (<): This operator compares two numbers and returns true if the first number is smaller than the second number. For example, 5 < 10 is true.

Greater than (>): This operator compares two numbers and returns true if the first number is larger than the second number. For example, 10 > 5 is true.

Less than or equal to (<=): This operator compares two numbers and returns true if the first number is smaller than or equal to the second number. For example, 5 <= 5 is true.

Greater than or equal to (>=): This operator compares two numbers and returns true if the first number is larger than or equal to the second number. For example, 10 >= 10 is true.

Equal to (==): This operator compares two numbers and returns true if they are equal. For example, 5 == 5 is true.

Not equal to (!=): This operator compares two numbers and returns true if they are not equal. For example, 5 != 10 is true.

These comparison operators allow you to compare numbers and make decisions based on their relationships within arithmetic or programming operations.

To know more about comparison operators:

https://brainly.com/question/29840768

#SPJ4

The value of the definite integral ∫(-1)¹ x¹⁰⁰ dx is 2/101.

To evaluate the integral S(-1)¹ x¹⁰⁰ dx, we can use the power rule of integration, which states that:

∫ \(x^n dx = (x^(n+1)) / (n+1) + C\), where C is the constant of integration.

Applying this formula, we get:

∫ x¹⁰⁰ dx = (x\(^(100+1)\)) / (100+1) + C

\(= (x^101) / 101 + C\)

To evaluate the definite integral from -1 to 1, we can substitute the limits of integration into the antiderivative and then subtract the result evaluated at the lower limit from the result evaluated at the upper limit:

∫(-1)¹ x¹⁰⁰ dx =\([(1^101)/101\) - \(((-1)^101)/101]\)

= (1/101) - (-1/101)

= 2/101

Therefore, the value of the definite integral ∫(-1)¹ x¹⁰⁰ dx is 2/101.

Learn more about integration

https://brainly.com/question/14502499

#SPJ4

Investment X earns the greater amount of interest over a period of 2 years.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let's consider that Ian invests in X, then:

Principle amount, P = $6,000
Time, T = 2 Years

Rate of Interest, R = 4.5% at simple Interest = 0.045

The interest earned is:

Interest = PRT = $6,000 × 0.045 × 2 = $540

Now, consider that Ian invests in Y, then:

Principle amount, P = $6,000
Time, n = 2 Years

Rate of Interest, R = 4% at Compound Interest = 0.04

The interest earned is:

Interest = P(1+R)ⁿ - P

            = $6,000(1+0.04)² - $6,000

            = $489.6

Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.

Learn more about Simple Interest here:

https://brainly.com/question/2793278

#SPJ1

Using the combination, 1716 are 7 digit phone numbers in which the digits are non-increasing and every digit is less than or equal to the previous one.

In the given question,

We have to find how many 7 digit phone numbers are there in which the digits are non-increasing and that is, every digit is less than or equal to the previous one.

We have to write 7 digit phone number.

Let the 7 digit are

A, B, C, D, E, F, G

Every digit is less than or equal to the previous one.

A ≥ B ≥ C ≥ D ≥ E ≥ F ≥ G

The sum of these number is 7.

So |A| + |B| + |C| + |D| + |E| + |F| + |G| = 10

We always have precisely one non-increasing digit for any given set of seven digits. Therefore, the solution to our problem is to make it simpler to calculate the total number of combinations where 7 digits must be chosen from a set of 7 digits where each digit is repeatable.

So the solution should be

= \(^{7+7-1}C_{7}\)

= \(^{13}C_{7}\)

We know that \(^nC_{r}=\frac{n!}{r!(n-r)!}\)

= \(\frac{13!}{7!(13-7)!}\)

= \(\frac{13!}{7!6!}\)

Simplifying

= \(\frac{13\times12\times11\times10\times9\times8\times7!}{7!\times6\times5\times4\times3\times2\times1}\)

Simplifying

= 13×11×2×3×2

= 1716

Hence, 1716 are 7 digit phone numbers in which the digits are non-increasing and every digit is less than or equal to the previous one.

To learn more about combination link is here

https://brainly.com/question/14685054

#SPJ4

a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

To learn more about probability click here: brainly.com/question/31828911

#SPJ11

The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

For more such information on Algebra and Geometry:
https://brainly.com/question/24696219

#SPJ8

Answer: - $83.88

Step-by-step explanation:

$66.11 - $99.01 + $1.20 - $35.92 - $68.67+ $52.41 = $83.88

The radian measures of the given angles are:
- 210°: 7π/6 radians
- 70°: 7π/18 radians
- 230°: 23π/18 radians
- 230°: 23π/18 radians
- 230: 23π/18 radians

To convert an angle from degrees to radians, you can use the following formula:

radian measure = (degree measure × π) / 180

Let's apply this formula to each of the given angles:

1. 210°:
radian measure = (210 × π) / 180 = 7π/6 radians

2. 70°:
radian measure = (70 × π) / 180 = 7π/18 radians

3. 230°:
radian measure = (230 × π) / 180 = 23π/18 radians

Please note that the last two angles you provided are the same as the previous angle (230°). So, their radian measures are also the same: 23π/18 radians.

In summary, the radian measures of the given angles are:
- 210°: 7π/6 radians
- 70°: 7π/18 radians
- 230°: 23π/18 radians
- 230°: 23π/18 radians
- 230: 23π/18 radians

Learn more about radians here:

https://brainly.com/question/27025090

#SPJ11