are skew line coplanar

Answer:

maybe i...............

Answer:

hope it help you

Step-by-step explanation:

\(5x + 3x - 2x \\ 8x - 2x \\ 6x\)

Answer:

6x

Step-by-step explanation:

Take x as the common factor and calculate.

Answer:

A x<7/12 hope this helps

There are 10 children.

Answer:

641799

Step-by-step explanation:

274561

+367238

641799

Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1

Given △FGH ~ △LMN,  all the statements that are true are options A, B , C and E

Since the two triangles are similar, their corresponding angles are going to be congruent and the sides would be proportional as well. This makes A correct

Given that FH ~ LN then the second option is correct

Option C is correct due to the definition of singularity

Option E is correct because ∠H ≅ m∠N

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Answer:

124.6

Explanation:

Let the number be x.

Thus, we have that: 13% of x =16.2

Next, solve for x by cross-multiplying.

Divide both sides by 13.

Thus, 16.2 is 13% of 124.6 (rounded to the nearest tenth).

based on the principle of mathematical induction, we conclude that \(2^{n}\) > \(n^{2}\) for all n greater than 4.

By using mathematical induction, we can prove that \(2^{n}\) > \(n^{2}\) for all n greater than 4.

Base case (n = 5):

When n = 5, we have \(2^{5}\) = 32 and \(5^{2}\) = 25. Since 32 is indeed greater than 25, the inequality holds for n = 5.

Inductive step:

Assuming the inequality holds for some positive integer k: \(2^{k}\) > \(k^{2}\), we need to show that it also holds for k + 1: \(2^{(k+1) }\) > \((k+1)^{2}\)

Starting with the left-hand side:

\(2^{(k+1) }\) = 2 × \(2^{k}\)

Using the inductive assumption, we can rewrite it as:

\(2^{(k+1) }\) > 2 ×\(k^{2}\)

Now let's consider the right-hand side:

\((k+1)^{2}\) = \(k^{2}\) + 2k + 1

We want to show that 2 × \(k^{2}\) > \(k^{2}\) + 2k + 1.

Simplifying the inequality, we have:

\(k^{2}\) - 2k - 1 > 0

By analyzing the quadratic function f(k) = \(k^{2}\) - 2k - 1, we find that it is positive for all k greater than 4.

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Answer:

The median is 8.

Step-by-step explanation:

Answer:

Slope m (Gradient) = 3

y-intercept: (0, -5)

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = 3x - 5

Step 2: Break function

Slope m = 3

y-intercept b = -5

Answer:

SLOPE: 3

Y INTERCEPT: -5

The number with the X is always the slope, and the number without the X is the y intercept, it depends if you are adding or subtracting.

Answer:

Part A

Scale factor

= 1 : 175

Part B

52.5 mm

Part C

99.4%

Step-by-step explanation:

Justin is working with a microscope that magnifies objects to 175 times their actual size.

Part A

Enter a number in each box to determine the scale factor for the microscope.

= 1 : 175

Part B

The diameter of an amoeba cell is 0.30 millimeter. How big will the cell appear to Justin under the microscope?

Scale factor =

1 : 175

Diameter of the Amoeba cell = 0.3mm

1mm = 175 mm

0.3mm = x

Cross Multiply

x = 0.3 × 175

x = 52.5 mm

Part C

What is the percent increase of the area of the amoeba cell under the microscope?

Increase = 52.5 mm - 0.3mm

= 52.2 mm

Percent increase

= 52.2/52.5 × 100

= 99.4%

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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the answer is, the number of packages of corn purchased

Answer:

C. The number of packages of corn purchased.

Step-by-step explanation:

We have been given that a store sells four 1 1/8-pound ears of corn in a package for $3.59. The expression represents the cost of the corn for a number of packages.

Since the cost of each package of corn is $3.59 and represents the cost of 'p' packages of the corn. So 'p' represents the number of packages of corn purchased.

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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Answer:

Y = 1/4x+2

Step-by-step explanation:

So to find the slope of the line you can use rise/run to do this you can pick two points and count how may squares is going up and how many is going to the left.

For this problem the two points can be (0,2) and (4,1) and if we count how many squares it goes up by we can see its 1 and if we count from (0,2) to (4,1) horizontally the space is 4

To find y-int it is just where the line crosses the y axis

The value of the given exponent is \(\frac{5}{2}\)

Given:

The exponent = \((\frac{4}{25})^{\frac{-1}{2}}\)

To find:

The value of a given exponent

Solution:

\((\frac{4}{25})^{\frac{-1}{2}} = ?\)

Using the identity of an exponent : \((\frac{m}{n})^{x} = \frac{m^{x}}{n^{x}}\)

\((\frac{4}{25})^{\frac{-1}{2}} = \frac{(4)^{(\frac{-1}{2})}}{(25)^{(\frac{-1}{2})}}\\\)

Using the identity of an exponent : \(a^{-x} = \frac{1}{a^x}\)

\(=\frac{(25)^{(\frac{1}{2})}}{(4)^{(\frac{1}{2})}}\\=\frac{(25)^{(\frac{1}{2})}}{(4)^{(\frac{1}{2})}}\\=\frac{((5)^2)^{(\frac{1}{2})}}{((2)^2)^{(\frac{1}{2})}}\\\)

Using the identity of an exponent: \((a^{n})^m=a^{m\times n}\)

\(=\frac{5^{(2\times \frac{1}{2})}}{2^{(2\times \frac{1}{2})}}\\=\frac{5^1}{2^1}\\=\frac{5}{2}\)

The value of the given exponent is \(\frac{5}{2}\).

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The nearest whole number after rounding is, 14

Rounding a number to the nearest tenth means finding the nearest multiple of 0.1.

To do this, you need to look at the digit in the hundredths place (the second digit after the decimal point) of the number you want to round.

If that digit is 5 or greater, you round the number up by adding 0.1 to the nearest whole number.

If that digit is 4 or less, you round the number down by leaving the nearest whole number unchanged.

For example, rounding 3.456 to the nearest tenth gives 3.5, while rounding 3.444 to the nearest tenth gives 3.4.

Given that,

The decimal number  13.5,

after using rules of rounding,

it can be rounded as 14

Hence, the nearest whole number is 14

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under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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Linear programming problems are mathematical optimization problems where a linear objective function is subject to linear constraints. These problems can be solved using a variety of methods, including the simplex method and interior point methods.

A nondegenerate basic feasible solution is a solution to a linear programming problem where all the constraints are satisfied and the number of non-zero variables is equal to the number of constraints. This means that the solution is not at the corner of the feasible region and there is no redundant constraint.

Complementary slackness conditions are a set of conditions that must be satisfied by any optimal solution to a linear programming problem. These conditions state that the product of the slack variables (the difference between the left-hand side and right-hand side of a constraint) and the corresponding dual variable must be equal to zero.

Suppose we have a nondegenerate basic feasible solution to the primal. Then, the complementary slackness conditions will lead to a system of equations for the dual vector. Since the solution is nondegenerate, this system of equations will have a unique solution. This is because there are no redundant constraints, so the number of equations will be equal to the number of variables. Additionally, the complementary slackness conditions ensure that the system is not underdetermined or overdetermined.

Therefore, if we have a nondegenerate basic feasible solution to the primal, the complementary slackness conditions will lead to a system of equations for the dual vector that has a unique solution. This is an important result in linear programming, as it helps us to understand the relationship between primal and dual problems and the existence and uniqueness of solutions.

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Answer:

3+13i

Step-by-step explanation:

(10+10i)+(-7+3i)

Combine the real parts

10+-7 = 3

And the imaginary parts

10i +3i = 13i

Combine them to make the complex number

3+13i

Based on the provided information and measures of variability, we can conclude that Bus 18 is the most consistent in terms of travel times to school.

We must examine the offered measures of variability, including the interquartile range (IQR) and the range, in order to compare the consistency of trip times for Bus 18 and Bus 47.

The distance between the maximum and minimum values is the range, while the IQR measures the spread of the middle 50% of the data. A smaller IQR and range typically imply data that is more consistent.

According to the information provided, Bus 18 has a lower IQR of 16 than Bus 47, which has a higher IQR of 24. This shows that because the middle 50% of the data is less dispersed, Bus 18's travel times are more consistent.

We can also see that Bus 18 has a narrower range of 16 than Bus 47, which has a range of 24. The conclusion that Bus 18's travel times are more reliable is further supported by the fact that the data is less variable.

Therefore, we can conclude that Bus 18 is the most constant in terms of travel times to school based on the information supplied and measures of variability.

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True, the standard deviation is a resistant measure of spread.

The standard deviation is calculated as the square root of the variance of the data set. Variance is calculated as the average of the squared differences between each data point and the mean of the data set. The standard deviation is the square root of this average.

In mathematical terms, the standard deviation can be calculated using the following formula:

σ = √(1/n ∑(x - μ)²)

Where σ is the standard deviation, n is the number of data points in the data set, x is the value of the i-th data point, and μ is the mean of the data set.

The standard deviation is an important measure because it gives an idea of how much the individual values in a data set differ from the mean.

In summary, the standard deviation is a resistant measure of spread because it gives a robust measure of the spread of the data in a set and is not easily influenced by outliers or extreme values.

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Answer:

804.2 km³

Step-by-step explanation:

Volume of a cylinder: πr²h

r = radius, h = height

\(\pi r^2h\\\pi(8)^2(4)\\\pi(64)(4)\\\pi(256)\\804.2\)

All values of the given table are calculated below.

In mathematics, a vertex (plural vertices) is a point where two or more lines, curves, or edges meet.

General equation is y = ax² + bx + c

The function is;

f(x) = 3x²     here, a=3, b=0, c=0

Vertex = (-b/2a, f(x)) = (0, 0)

Axes of symmetry = -b/2a = 0

x-intercept ⇒  x = 0

y-intercept ⇒  y=0

Similarly, function g(x) = x² +2x +1   here, a=1, b=2, c=1

Vertex = (-b/2a, f(x)) = (-1, 0)

Axes of symmetry = -b/2a = -1

x-intercept ⇒ x = -1

y-intercept ⇒ y=0

Function, h(x) = -6x² - 4x - 5   here, a= -6, b= -4, c= -5

Vertex = (-b/2a, f(x)) = (-1/3, -13/3)

Axes of symmetry = -b/2a = -1/3

x-intercept ⇒ x = Does not exist.

y-intercept ⇒ y=-5

Function, p(x) = 3x² + 6   here, a= 3, b= 0, c= 6

Vertex = (-b/2a, f(x)) = (0, 6)

Axes of symmetry = -b/2a = 0

x-intercept ⇒ x = Does not exist.

y-intercept ⇒ y= 6

Function, q(x) = x² - 9   here, a= 1, b= 0, c= -9

Vertex = (-b/2a, f(x)) = (0, -9)

Axes of symmetry = -b/2a = 0

x-intercept ⇒ x = ±3

y-intercept ⇒ y= -9

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The vertex of the given functions is,

Vertex = (0, 0)

Vertex = (-1, 0)

Vertex = (-1/3, -13/3)

Vertex = (0, 6)

Vertex = (0, -9)

In mathematics, a vertex (plural vertices) is a point where two or more lines, curves, or edges meet.

General equation is y = ax² + bx + c

The function is;

f(x) = 3x²    

here, a=3, b=0, c=0

Vertex = (-b/2a, f(x))

           = (0, 0)

Axes of symmetry = -b/2a = 0

x-intercept ⇒  x = 0

y-intercept ⇒  y=0

Similarly, function g(x) = x² +2x +1  

here, a=1, b=2, c=1

Vertex = (-b/2a, f(x))

           = (-1, 0)

Axes of symmetry = -b/2a

                              = -1

x-intercept ⇒ x = -1

y-intercept ⇒ y=0

Function, h(x) = -6x² - 4x - 5  

here, a= -6, b= -4, c= -5

Vertex = (-b/2a, f(x))

           = (-1/3, -13/3)

Axes of symmetry = -b/2a

                              = -1/3

x-intercept ⇒ x = Does not exist.

y-intercept ⇒ y=-5

Function, p(x) = 3x² + 6  

here, a= 3, b= 0, c= 6

Vertex = (-b/2a, f(x))

           = (0, 6)

Axes of symmetry = -b/2a

                              = 0

x-intercept ⇒ x = Does not exist.

y-intercept ⇒ y= 6

Function, q(x) = x² - 9  

here, a= 1, b= 0, c= -9

Vertex = (-b/2a, f(x))

           = (0, -9)

Axes of symmetry = -b/2a

                              = 0

x-intercept ⇒ x = ±3

y-intercept ⇒ y= -9

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Answer:

a) 24 cm

Step-by-step explanation:

Tangents form a 90° angle with a radius.

using the Pythagorean theorem:

D² =  25² - 7²

D² =  625 - 49 = 576

D =  24

Answer:

5, 80

Step-by-step explanation:

because 5b / 280 = c2 - b2

Answer:  y= 12x +22

Step-by-step explanation:

Find the slope and y intercept