given the figure below with the provided measurements, what is PQ?

From equation f (x)=7x-9,   f (x+h)= 7h and we can simplify it as 7.

For part (a), we can start by substituting x+h for x in the equation for f(x):

f(x+h) = 7(x+h) - 9

f(x+h) = 7x + 7h - 9

We can then simplify the expression to:

f(x+h) = 7x + 7h - 9

Now, to find f(x+h) - f(x), we can subtract f(x) from both sides of the equation:

f(x+h) - f(x) = 7x + 7h - 9 - (7x - 9)

f(x+h) - f(x) = 7h

Therefore, for part (a) we can conclude that f(x+h) - f(x) = 7h.

Now, we can simplify the difference quotient using f(x+h) and f(x):

f(x+h) - f(x) = [7(x+h) - 9] - [7x - 9]

= 7h

f(x+h) - f(x) / h = 7h / h = 7

We have already simplified the difference quotient  to 7.

Learn more about function at https://brainly.com/question/29186491

#SPJ11

The mean waiting time for these customers is 18.33 minutes.

The mean waiting time can be calculated by multiplying each waiting time by its frequency, summing up these products, and then dividing by the total number of customers.

In mathematical terms, the mean waiting time is:

Mean = (x1 * f1 + x2 * f2 + ... + xn * fn) / (f1 + f2 + ... + fn)

Where x1, x2, ..., xn are the waiting times, and f1, f2, ..., fn are the corresponding frequencies.

Using the data from the table, we can plug in the values and calculate the mean waiting time:

Mean = (5 * 2 + 10 * 4 + 15 * 6 + 20 * 8 + 25 * 10) / (2 + 4 + 6 + 8 + 10)

Mean = (10 + 40 + 90 + 160 + 250) / 30

Mean = 550 / 30

Mean = 18.33 minutes

Therefore, the mean waiting time for these customers is 18.33 minutes.

Learn about Mean

brainly.com/question/521501

#SPJ11

The equation for the description for given number is x + 16 = 124

"A number x increases by 16" means that we start with a certain number, which we don't know yet, and then add 16 to it. So, we can represent this as:

x + 16

The next part of the description tells us that the result of this addition is 124. So, we can set up an equation by equating this expression to 124, like this:

x + 16 = 124

This is the equation that represents the given description. To find the value of x, we can solve for it by subtracting 16 from both sides of the equation:

x = 124 - 16

x = 108

So, the value of x that satisfies the given description is 108.

To learn more about equation follow the link: brainly.com/question/29657988

#SPJ4

The value οf the annuity after 120 depοsits is $1,059,780.64.

Cοmpοund interest is interest that is earned nοt οnly οn the principal amοunt but alsο οn any interest earned οn that principal amοunt οver time.

Tο determine the value οf the annuity, we can use the fοrmula fοr the future value οf an annuity:

[tex]A = P \times \dfrac{(1 + r/n)^{(nt)} - 1)}{(r/n)}[/tex]

where A is the future value οf the annuity, P is the mοnthly depοsit amοunt, r is the annual interest rate, n is the number οf times the interest is cοmpοunded per year, and t is the tοtal number οf depοsits.

In this case, P = $100, n = 2 (since interest is cοmpοunded semi-annually), t = 120, and r is the interest rate per year, sο we need tο find r. Tο dο this, we can use the fοrmula:

[tex]A = P\times (1 + r/n)^{(nt)[/tex]

where A is the future value of the annuity after t depοsits.

Substituting the given vaIues, we have:

[tex]\$100 \times (1 + r/2)^{(2\cdot120)[/tex] = A

SimpIifying, we get:

[tex](1 + r/2)^{240} = A/100[/tex]

Taking the natural lοgarithm of both sides, we get:

[tex]ln(1 + r/2)^{240} = ln(A/100)[/tex]

240*ln(1 + r/2) = ln(A/100)

ln(1 + r/2) = ln(A/100)/240

Solving for r, we get:

[tex]$r = 2 \times \frac{e^{(ln(A/100)}}{240) - 1}[/tex]

Substituting the given vaIues, we get:

r = 0.4902 or 49.02%

Now we can plug in all the values into the original fοrmula for the future value οf the annuity:

[tex]A = $100\times \dfrac{(1 + 0.4902/2)^{(2\cdot 120) - 1)}}{0.4902/2}[/tex]

SimpIifying, we get:

A = $1,059,780.64

Therefοre, the value οf the annuity after 120 depοsits is $1,059,780.64.

To learn mοre about compound interest, visit:

https://brainly.com/question/28020457

#SPJ1

The future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.

To find the future value of this loan, we can use the formula FV = PV(1 + r)^t, where FV is the future value, PV is the present value, r is the interest rate, and t is the time period in years.

In this case, we have PV = $17,592, r = 6.6%, and t = 8 months or 0.667 years (8/12).

Plugging these values into the formula, we get:
FV = $17,592(1 + 0.066)^0.667
FV = $17,592(1.066)^0.667
FV = $18,358.16

Therefore, the future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.

For more information about interest, visit:

https://brainly.com/question/25793394

#SPJ11

They are not the same as the upper and lower limits used in other statistical calculations.

A accumulation of numerical data that has been methodically gathered, arranged, and examined is referred to as statistical data. Numerous phenomena, including economic patterns, demographic traits, health outcomes, and more, are described and measured using this data. Numerous techniques, such as surveys, experiments, observations, and administrative documents, can be used to gather statistical data. After being gathered, the data can be examined statistically to reveal patterns, connections, and trends that can be used to guide policy development and decision-making.

given

This is a histogram showing the frequency distribution of the weights of 30 students. Each bar represents a weight range, and the height of the bar represents the frequency of students in that weight range.

To find the upper and lower boundaries for each weight range, we can use the following formula:

Lower bound = midpoint of the previous range + 0.5

Upper bound = midpoint of the current range - 0.5

For example, the lower bound of the first range (60-64) is:

Lower bound = midpoint of previous range + 0.5

= 57

Upper bound = midpoint of current range - 0.5

= 61.5

We can apply the same formula to find the upper and lower bounds for the other ranges in the histogram. The results are:

60-64: lower bound = 57, upper bound = 61.5

65-69: lower bound = 62, upper bound = 66.5

70-74: lower bound = 67, upper bound = 71.5

75-79: lower bound = 72, upper bound = 76.5

80-84: lower bound = 77, upper bound = 81.5

85-89: lower bound = 82, upper bound = 86.5

90-94: lower bound = 87, upper bound = 91.5

95-99: lower bound = 92, upper bound = 96.5

They are not the same as the upper and lower limits used in other statistical calculations.

To know more about statistical data visit:

https://brainly.com/question/14893265

#SPJ1

Therefore , the solution of the given problem of function comes out to be the limit may not exist, if the function is not continuous at x = 0.

The mathematical discipline encompasses arithmetic, symbols, and their divisions, as well as histology, construction, and both real and imagined geographic places. A function describes the connections between various elements, which all have an associated outcome. A function is composed of an array of different parts that, when combined, result in particular outcomes for each input.

Here,

We must be aware of the precise function or expression under consideration in order to respond to this query.

The action as x moves towards zero from the negative direction can change depending on the function.

If a function is continuous at x = 0, then in general, if the function has a limit as x gets smaller from the downward direction, however this limit will be the same as the limit as x reaches zero from the positive direction.

The limit as x approaches zero from the downward direction may vary from the limit as x approaches zero from the better way, or the limit may not exist, if the function is not continuous at x = 0.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The evaluation of the functions for data in the table and the graphs of the data, created using MS Excel, indicates that we get;

a. Equation 3 appears to be exponential

b. The reason is that as the value of x increases, the output values of the equation increases exponentially

c. The population of a bacteria is most likely modeled by Equation 3, which is an exponential function, because as the number of bacterium increases, the number of offspring they can produce in the next period increases, resulting in an exponential growth

d. Equation 4, which can be modeled using a linear equation, with a positive slope most likely models a tub collecting water from a leak faucet.

A function can be used to model an observation by specifying the relationship between the input and output values of the observation.

a. The function in the table that appears to be exponential is Equation 3

b. An exponential function is a function that has an equation of the following forms;

f(x) = [tex]a\cdot b^{c\cdot x}[/tex]

f(x) = [tex]p\cdot e^{k\cdot x}[/tex]

The values in the table for Equation 3 indicates that the as the value of x increases, the values of f(x) increases several times more, which is an exponential increase, such that an equation that can model the data, obtained using MS Excel is; f(x) = 0.1982 × e^(0.3092·x)

Plugging in the values of x, we get;

The value of f(x) at x = 9 is; f(9) = 0.1982 × e^(0.3092 × 9) ≈ 3.2

The value of f(x) at x = 10 is; f(10) = 0.1982 × e^(0.3092 × 10) ≈ 4.36

The value of f(x) at x = 17 is; f(17) = 0.1982 × e^(0.3092 × 17) ≈ 38.0

Therefore, the function for Equation 3 appears to be exponential

Please find attached the graph for the Equation 3 data values, created with MS Excel

c. The growth of a population is best modelled by an exponential function, therefore, the function that most likely models a bacteria growth in a lab culture is Equation 3.

d. The tub collecting water from a leaking faucet collects water at the steady rate at which the faucets leaks, which can be modelled by a linear equation with a positive slope, because the amount of water in the tub increases steadily.

The graph and trendline obtained from values of the data for Equation 4, indicates that the line of best fit is a line with the equation;

The square of the regression coefficient is; R² = 0.9993

The slope of the line of best fit of Equation 4 is positive, and therefore increasing at a steady rate and can therefore model collecting water from a leaky faucet using a tub

Learn more on trendlines here: https://brainly.com/question/3509046

#SPJ1

It will take 4 years for an investment to double if it is continuously compounded at 18% per year.

The time it takes for an investment to double if it is continuously compounded at 18% per year can be calculated using the formula:
T = ln(2)/r

Where T is the time in years, ln(2) is the natural logarithm of 2, and r is the annual interest rate.

Substituting the given values into the formula, we get:
T = ln(2)/0.18
T ≈ 3.85 years

Therefore, to the nearest year, it will take approximately 4 years for the investment to double if it is continuously compounded at 18% per year.

A neperian logarithm or also known as a natural logarithm, refers to that logarithm that has e as its base, which is worth: 2.718281828.

For more information about neperian logarithm, visit:

https://brainly.com/question/305900

#SPJ11

To solve the inequality -3 > (x)/(4) - 1, we need to isolate the variable x on one side of the inequality. We can do this by following these steps:

Step 1: Add 1 to both sides of the inequality to eliminate the constant term on the right side.
-3 + 1 > (x)/(4) - 1 + 1
-2 > (x)/(4)

Step 2: Multiply both sides of the inequality by 4 to eliminate the fraction on the right side.
-2 * 4 > (x)/(4) * 4
-8 > x

Step 3: Rewrite the inequality with the variable on the left side.
x < -8

Therefore, the solution to the inequality is x < -8.

Note: When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed. However, in this case, we multiplied by a positive number (4), so the inequality symbol remains the same.

To know more about Inequality equation:

https://brainly.com/question/21311270

#SPJ11

The octagon has rotated 45° when the vertex at T is moved to V. This is because the angle of rotation for a regular octagon is 45° when the vertex at T is moved to V.

An octagon is a two-dimensional shape with eight sides and eight angles. It is a polygon which means it is a closed, two-dimensional shape with straight sides. Octagons are used in architecture and design and are commonly seen in stop signs and floor tiles. The angles of an octagon are all equal and each side is the same length.

The regular octagon has eight equal sides and angles. The angles of an octagon are all of the same size, which is 135°. If the octagon is rotated clockwise about its center, then the vertex at T is moved to V. This means that the octagon will have rotated 45° in order to move T to V.

To calculate the angle of rotation, we can use the formula: angle of rotation = (360°/number of sides). Therefore, the angle of rotation for this octagon will be (360°/8) = 45°.

To confirm this, we can use a protractor to measure the angle between the two lines. The angle between the two lines is 45°. This confirms that the octagon has rotated by 45° as the vertex at T has been moved to V.

Therefore, the octagon has rotated 45° when the vertex at T is moved to V. This is because the angle of rotation for a regular octagon is 45° when the vertex at T is moved to V. This can be confirmed by using a protractor to measure the angle between the two lines.

For more questions related to polygon

https://brainly.com/question/26583264

#SPJ1

The function (fg)(x) is the product of the function f(x) and g(x) which is (fg)(x) = 24x² - 16x.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout calculation and are essential for the development of significant links.

The two functions are given below.

f(x) = 8x

g(x)= 3x - 2

The function (fg)(x) is calculated as,

(fg)(x) = f(x) · g(x)

(fg)(x) = (8x) × (3x - 2)

(fg)(x) = 24x² - 16x

The function (fg)(x) is the product of the function f(x) and g(x) which is (fg)(x) = 24x² - 16x.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

The coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

From the given graph, triangle ABC have A(1, 3), B(7, 1) and (1, 1).

Triangle ABC is enlarged with a scale factor of -2 and the origin of the Centre to give triangle A'B'C'.

Now, A(1, 3) → -2(1, 3)→A'(-2, -6)

B(7, 1) → -2(7, 1) → B'(-14, -2)

C(1, 1) → -2(1, 1) → C'(-2, -2)

Therefore, the coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

To learn more about the dilation visit:

https://brainly.com/question/13176891.

#SPJ1

Using a trigonometric relation we will see that the height is  8.62m

On the diagram we can see a right triangle, where we know one of the angles and the adjacent cathetus and we want to find the opposite cathetus.

Then we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing the values that we know we will get:

tan(72°) = n/2.8m

2.8m*tan(72°) =n = 8.62m

That is the height.

Learn more about right triangles at:

https://brainly.com/question/2217700

#SPJ1

The perpendicular line connecting points F and G results in the formation of a triangle with a 14 square unit surface area.

In mathematics, a coordinate is a set of numbers or symbols that describes an object's position or location in a geometric space. The most popular coordinate system is the Geographic coordinate system, which creates a grid on a surface or in three dimensions using a series of perpendicular lines. Each location on the plane or in space is then uniquely identified by an ordered pair or set of three numbers, respectively, that represent a point's distance from the origin along each of the coordinate system's axes.

Given that points F and G share the same x-coordinate, the line connecting them is perpendicular. A degenerate triangle with negative area will be formed by any point H that shares the same x-coordinate as F and G.

D = √((2-2)2 + (6-(-1),2) = √(49), which =  7.

distance(FH)/7  = 2/7.

distance(GH)/7  = 4/7

Distance(FH) / Distance(GH)  = 1 / 2.

The distance between any two points H(x, y) and F(2,6) or G(2,-1) can be calculated using the distance formula as follows:

distance(FH) is  =  √((x-2) + (y-6)).

Distance (GH) is  =  √((x-2) + (y+1)).

By changing the aforementioned values, we obtain:

√((x-2)**2**y+1**2)/7) = 4/7

(x-2)² + (y+1)² = 16

(x-2)² + (y-6) (y-6)² = 1/4 ((x-2)² + (y+1)²)

By condensing and extending, we obtain:

3(x-2)² + 13(y-6)² = 196

5(x-2)² + 25(y+1)² = 784

7(x-2)² + (y-6)² = 1

A triangle with a 14 square unit surface area is created when the perpendicular line joining F and G.

To know more about coordinates  visit:

brainly.com/question/27749090

#SPJ1

Without evaluating the expression, the sum of given expression is 80 is this why its even number.

Using letters or alphabets to represent numbers without giving their exact values is the idea behind algebraic expressions. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables.

In an algebraic expression, both constants and variables can be used. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.

An algebraic expression in mathematics is one that contains variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions are built upon terms.

Calculate the power: 81

Calculate the sum or difference: 81 - 1

Answer is 80

Thus, here we know that 80 is an even number.

to know more about expression visit:

brainly.com/question/14083225

#SPJ1

Scheme procedure to generate a list of all subsets of a set:

(define (subsets set)

 (if (null? set)

     '(())

     (let ((rest (subsets (cdr set))))

       (append rest (map (lambda (x) (cons (car set) x)) rest))))))

The subsets procedure takes a set as input and checks if the set is empty. If the set is empty, it returns a list with an empty set as its only element. Otherwise, it calls the subsets procedure recursively on the rest of the set (without the first element) and stores the result in a variable called rest.

It then appends the rest list to the result of mapping a lambda function over the rest list. The lambda function takes an element x from the rest list and conses the first element of the original set to it to create a new subset. This results in a list of all subsets of the original set.

Learn more about Scheme Procedure:

https://brainly.com/question/15221528
#SPJ4

Answer:

The two teachers are 26 meters apart. To calculate this, you can use the Pythagorean Theorem, which states that the distance between two points is equal to the square root of the sum of the squares of the differences between the coordinates of the two points. In this case, the coordinates of the math teacher are (10, 0) and the coordinates of the science teacher are (0, 24), so the distance between them is the square root of [(10-0)^2 + (0-24)^2] = √(100 + 576) = √676 = 26 meters.

We can use the Pythagorean theorem to solve this problem. Let's draw a diagram:

A (Amy)

/|

/ |

/ |10 meters

/ |

/____|

B C (science teacher)

We have a right triangle ABC, where AB = 10 meters and BC = 24 meters. We want to find the length of AC, which is the distance between the two teachers.

Using the Pythagorean theorem:

AC^2 = AB^2 + BC^2

AC^2 = 10^2 + 24^2

AC^2 = 676

AC = sqrt(676)

AC = 26 meters

Therefore, the two teachers are 26 meters apart.

According to the above, the statement that is true about the expression can be inferred: Since the factor of 5/6 is less than 1, the product of 8 * 5/6 will be less than 8. Additionally, the measure of the giant mouse would be 0.76 meters.

To find the correct statement about the fractions we must analyze each of the statements and check it according to the multiplication information. According to the above, we can establish that the factor of 5/6 is less than one because the division of these two numbers results in a number less than 1.

So each number that we multiply by this fraction will give a result less than the same number. In this case if we multiply 8 by this fraction it would give us 6.66

On the other hand, if we want to know the height of the giant mouse, we must establish what the size of the Chihuahua is. So we develop the fraction 2 1/3 = 2.33

To find the height of the giant mouse we must divide the height of the chihuahua by 3.

Learn more about height in: https://brainly.com/question/10726356

#SPJ1

Answer:

1. [tex]75[/tex]

2. [tex]4x^{8}[/tex]

3. [tex]128[/tex]

Step-by-step explanation:

[tex]\frac{3*5^9}{5^7}=\frac{3*5^2*5^7}{5^7}=3*5^2=75[/tex]

[tex]\sqrt{16x^{16}}=4\sqrt{x^{16}} =4x^8[/tex]

[tex]\frac{(-5)(2^8)}{-6+1}/2=\frac{(-5)(2^8)}{(-5)(2)}=\frac{2^8}{2}=2^7=128[/tex]

A) The probability of at least one red ball being obtained is 1 - the probability of no red balls being obtained.

The probability of no red balls being obtained is (7/17)*(6/16)*(5/15)*(4/14)*(3/13) = 0.0096. Therefore, the probability of at least one red ball being obtained is 1 - 0.0096 = 0.9904.

B) The probability of two red balls and three black balls being obtained is (10/17)*(9/16)*(7/15)*(6/14)*(5/13) = 0.0909. The probability of one red ball and four black balls being obtained is (10/17)*(7/16)*(6/15)*(5/14)*(4/13) = 0.0216.
C) The probability of getting k red balls and (5-k) black balls is (10 choose k)*(7 choose (5-k))/(17 choose 5). This can be calculated for each value of k from 0 to 5 and summed to find the total probability.

For example, when k=0, the probability is (10 choose 0)*(7 choose 5)/(17 choose 5) = 0.0096. When k=1, the probability is (10 choose 1)*(7 choose 4)/(17 choose 5) = 0.0909. The total probability is the sum of these individual probabilities.

You can read more about probability at https://brainly.com/question/13604758

#SPJ11

a) The number of rabbits that escaped from the ship is 24.

b) P(6) = 1 + 24 (0.85)^6 = 91.7, and P(24) = 1 + 24 (0.85)^24 = 436.8.

c) The graph of P(t) for 0 ≤ t ≤ 80 is an exponential curve that increases steadily over time.

d) The graph of P(t) is increasing.

e) The graph shows that the population of rabbits has increased exponentially since they escaped from the ship.

f) Yes, the graph does suggest the growth in population that would be expected among rabbits on an island. This is due to the steadily increasing nature of the graph.

g) The graph suggests that it will take approximately 65 months for the rabbit population to reach 500. This can be seen on the graph, as the y-axis value reaches 500 around the 65th month.

a)This can be calculated by taking the initial population, 1, and multiplying it by the given rate of growth, 0.85, and raising that to the 1000th power.

b) The meaning of these numbers in the context of the problem is that P(6) represents the total rabbit population after 6 months, and P(24) represents the total rabbit population after 24 months.

c)It is labeled with the variable t on the x-axis and the word "Population" on the y-axis, with each axis scaled appropriately.

f) Yes, the graph does suggest the growth in population that would be expected among rabbits on an island. This is due to the steadily increasing nature of the graph.

g)The graph suggests that it will take  65 months for the rabbit population to reach 500. This can be seen on the graph, as the y-axis value reaches 500 around the 65th month.

To know more about exponential curve click on below link:

https://brainly.com/question/1596693#

#SPJ11

a) 6% of 34 is 2.04
b) 17 is 50% of 34

c) 18 is 30% of 60

d) 7% of 49 is 3.43.

a. To find 6% of 34, you can multiply 34 by 0.06 (which is the decimal equivalent of 6%): 34 * 0.06 = 2.04. So 6% of 34 is 2.04.

b. To find what percent 17 is of 34, you can divide 17 by 34 and then multiply by 100 to convert the decimal to a percentage: (17/34) * 100 = 50%. So 17 is 50% of 34.

c. To find what number 18 is 30% of, you can divide 18 by 0.30 (which is the decimal equivalent of 30%): 18 / 0.30 = 60. So 18 is 30% of 60.

d. To find 7% of 49, you can multiply 49 by 0.07 (which is the decimal equivalent of 7%): 49 * 0.07 = 3.43. So 7% of 49 is 3.43.

8. Unfortunately, I cannot see the number line that you are referring to, so I cannot provide an answer for this part of the question.

Learn about Equation

brainly.com/question/29657992

#SPJ11

Answer:

To solve for x, we need to isolate it on one side of the equation by performing inverse operations.

11x - 10 + 80 = 180

First, we combine the constant terms on the left side of the equation:

11x + 70 = 180

Next, we isolate the variable term by subtracting 70 from both sides:

11x = 110

Finally, we solve for x by dividing both sides by 11:

x = 10

Therefore, the solution to the equation 11x - 10 + 80 = 180 is x = 10.

Answer:

To divide £300 in the ratio of 10:20, we need to first add the two parts of the ratio to find the total number of parts:

10 + 20 = 30

This means that the ratio can be expressed as 10/30 and 20/30.

Next, we can use these ratios to find the amount of money for each part of the ratio:

10/30 x £300 = £100

20/30 x £300 = £200

Therefore, the amount of money for the parts of the ratio 10:20 would be £100 and £200 respectively.

The values of x, y, z, and w are 6, -13, -1, and 4, respectively. So, the answer is 6, -13, -1, 4.

To find a basis for the orthogonal complement of the subspace of R4 spanned by the given vectors, we need to find the null space of the matrix formed by the given vectors. The matrix is:
```
1 -1 7 5
2 -1 1 6
1 0 -6 1
```
We can use the reduced row echelon form to find the null space of this matrix. The reduced row echelon form of this matrix is:
```
1 0 -6 1
0 1 13 -4
0 0 0 0
```
The null space of this matrix is the set of all vectors (x, y, z, w) such that:
```
x - 6z + w = 0
y + 13z - 4w = 0
```
We can write the null space in parametric form as:
```
x = 6z - w
y = -13z + 4w
z = z
w = w
```
We can write the null space in the form {(x, y, 1, 0), (z, w, 0, 1)} by setting z = 1 and w = 0 in the first vector, and setting z = 0 and w = 1 in the second vector. This gives us:
```
x = 6(1) - 0 = 6
y = -13(1) + 4(0) = -13
z = 6(0) - 1 = -1
w = -13(0) + 4(1) = 4
```
Therefore, the basis for the orthogonal complement of the subspace of R4 spanned by the given vectors is {(6, -13, 1, 0), (-1, 4, 0, 1)}. The values of x, y, z, and w are 6, -13, -1, and 4, respectively. So, the answer is 6, -13, -1, 4.

Learn more about vectors

brainly.com/question/28180105

#SPJ11

Answer:

y = (4/3)x + 2/3

The y-intercept is the value of y when x is equal to zero. So we can substitute x = 0 into the equation and solve for y:

y = (4/3)(0) + 2/3 = 2/3
The y-intercept of the line y = (4/3)x + 2/3 is 2/3.

Step-by-step explanation:

Answer:

The y-intercept is (2/3)

Step-by-step explanation:

I will assume that the equation is missing the "x," and will rewrite is as:

 y = (4/3)x + (2/3)

This is in standard form of y = mx + b, where m is the slope and b is the y-intercept.

The slope is (4/3) and the y-intercept is (2/3)

The correct option is (c) $768x^{\frac{1}{3}}$

The given expression is as follows; \[ \left(\frac{3 \sqrt[3]{x y} y^{-3}}{\sqrt[3]{y} x^{-\frac{4}{3}}}\right)^{-1} \]Firstly, simplify the numerator and the denominator of the expression.\[\frac{3\sqrt[3]{xy}y^{-3}}{\sqrt[3]{y}x^{-\frac{4}{3}}}=\frac{3}{\sqrt[3]{x}x^{-\frac{4}{3}}\sqrt[3]{y}y^{-3}}\]Next, simplify the denominator of the expression.\[\frac{3}{\sqrt[3]{x}x^{-\frac{4}{3}}\sqrt[3]{y}y^{-3}}=3x^{\frac{1}{3}}y^{\frac{10}{3}}\]Now, let us substitute $y=16$ into the expression of $3x^{\frac{1}{3}}y^{\frac{10}{3}}$.\[3x^{\frac{1}{3}}y^{\frac{10}{3}}=3x^{\frac{1}{3}}(16)^{\frac{10}{3}}=48x^{\frac{1}{3}}(2)^{\frac{10}{3}}=768x^{\frac{1}{3}}\]As we obtained the value of the expression by substituting $y=16$, therefore the correct option is (c) $768x^{\frac{1}{3}}$.

Learn more about expression

brainly.com/question/14083225

#SPJ11

Answer: 119.32 centimeters

Step-by-step explanation:

Circumference = diameter x π

C = 38 (3.14)

C = 119.32

The circumference is 119.32 centimeters

Hope this helps!

a. The polyhedron that can be constructed using the net made of squares is a cube.

b. The polyhedron that can be constructed using the net made of squares is also a cube.

c. The polyhedron that can be constructed using the net made of a regular hexagon and isosceles triangles is a hexagonal pyramid.

For more questions like polyhedron visit the link below:

https://brainly.com/question/9317617

#SPJ11