Write the value with positive exponent (1/2)-4

pls answer fast pls ​

The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.

To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].

We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.

To know more about vector equation, refer here:

https://brainly.com/question/30561769#

#SPJ11

Answer:

6/3=2

30/10=3

Step-by-step explanation:

For simple division like this, you can look and see how many times 3 can go into 6, and 10 into 30.

B) direction ratio of any two diagonals in vector form is 60°.

C) cos²α+cos²β+cos²γ+cos²δ= \(\frac{4}{3}\)

​In Euclidean geometry, a perspective is a parent created by rays, often referred to as the angle's perimeters, sharing a single endpoint known as the perspective's vertex. Angles created by rays are located in the plane that contains the rays. Angles can also be created by intersecting two planes. They are referred to as dihedral angles. Curves that cross may also define an angle, which is the angle formed by rays that are perpendicular to the individual curves at the point of junction.

The degree of an angle or rotation is also expressed in terms of perspective. This metric represents the relationship between a circular arc's length and radius.

To learn more about angle visit here:

brainly.com/question/7116550

#SPJ4

Answer:

$319.2

Step-by-step explanation:

If you multiply 399 and 0.2 (because it's 0.2 out of 1) then you get 79.8. So you subtract 79.8 from 299 and get 319.2 dollars. I hope this helps! Please mark brainliest! <3

Answer:

$319.20

Step-by-step explanation:

The area enclosed by the curve r=2sin(θ) 3sin(9θ) over the interval [0,2π/9] is (243π/64) - (3√3/16).

To find the area enclosed by the curve r=2sin(θ) 3sin(9θ), we first need to determine the limits of integration for θ.

Since the curve is periodic with period 2π/9 (due to the 9 in the second term), we only need to consider the portion of the curve in the interval [0, 2π/9].

Next, we need to convert the polar equation to rectangular coordinates, which can be done using the formulas x = r cos(θ) and y = r sin(θ).

Plugging in the given equation, we get:

x = 2sin(θ) cos(θ) + 3sin(9θ) cos(θ)
y = 2sin(θ) sin(θ) + 3sin(9θ) sin(θ)

Now we can find the area enclosed by the curve by integrating over the given interval:

A = ∫[0,2π/9] (1/2) [x(θ) y'(θ) - y(θ) x'(θ)] dθ

Using the formulas for x and y, we can find the derivatives x'(θ) and y'(θ):

x'(θ) = 2cos(θ) cos(θ) - 2sin(θ) sin(θ) + 27cos(9θ) cos(θ) - 27sin(9θ) sin(θ)
y'(θ) = 2cos(θ) sin(θ) + 2sin(θ) cos(θ) + 27cos(9θ) sin(θ) + 27sin(9θ) cos(θ)

Substituting these expressions into the formula for A and evaluating the integral, we get:

A = (243π/64) - (3√3/16)

Therefore, the area enclosed by the curve r=2sin(θ) 3sin(9θ) over the interval [0,2π/9] is (243π/64) - (3√3/16).

Learn more about area enclosed by polar curves

brainly.com/question/15573662

#SPJ11

The sampling technique is called "simple random sampling."

In the field of statistics, the process of sampling is used to select a subset of individuals or units from a larger population to study and analyze.

The goal of sampling is to gather data that can be used to make accurate and reliable inferences about the characteristics of the entire population.

One of the most common and straightforward methods of sampling is simple random sampling.

In this technique, each member of the population has an equal chance of being selected to be a part of the sample.

The process of selecting individuals for the sample is usually done through a randomization process, which ensures that each member of the population has an equal probability of being chosen.

Simple random sampling is considered to be an unbiased method of sampling because it ensures that all members of the population have an equal chance of being selected.

This helps to minimize the potential for sampling bias, which is a type of error that can occur when the sample selected is not representative of the entire population.

To implement simple random sampling, researchers can use various methods, including a random number generator or drawing names from a hat.

The sample size required for simple random sampling will depend on the size of the population and the level of precision required for the study.

Overall, simple random sampling is a powerful tool for gathering data that can be used to make accurate and reliable inferences about the characteristics of a larger population.

For similar question on sampling.

https://brainly.com/question/27829028

#SPJ11

Answer:

23

Step-by-step explanation:

If the homeowner also had to pay late fees in the amount of $35 four different times, the total cost of the dryer is $809.48. So, correct option is A.

To calculate the total cost of the dryer, we need to add the initial cost of the dryer, the monthly payments, the credit card fees, and the late fees.

The total cost of the dryer can be calculated as follows:

Cost of dryer = $698.27

Total credit card charges = 12 x $1.25 = $15

Total late fees = 4 x $35 = $140

Total cost of the dryer = Cost of dryer + Total credit card charges + Total late fees

= $698.27 + $15 + $140

= $809.27

Therefore, the total cost of the dryer is $809.48, which is the closest option to the calculated answer.

So, correct option is A.

To learn more about cost click on,

https://brainly.com/question/31471609

#SPJ1

Answer:

its D

Step-by-step explanation:

its not A or C because the angle ABC is equal to DAB. that leaves us with B or D. and B is incorrect about the value of a. so the answer is D

Answer:

2.8 units

Step-by-step explanation:

\(d = \sqrt{ {(3 - 1)}^{2} + {(6 - 8)}^{2} } \\ \\ d = \sqrt{ {(2)}^{2} + {( - 2)}^{2} } \\ \\ d = \sqrt{4 + 4} \\ \\ d = \sqrt{8} \\ \\ d = 2.82842712 \\ \\ d \approx \: 2.8 \: units\)

Answer: y=2x+1

Step-by-step explanation:

First, find the slope. 9+3/4+2=2, so m=2 (m stands for the slope in the slope-intercept form of y=mx+b)

So we have y=2x+b

Substitute one of the points into the equation to find b (the y-intercept)

I'll do (4,9) because it's easier

9=4x2+b

9=8+b

b=1

So your final answer is y=2x+1

Answer: y= 2x + 1

Step-by-step explanation:

Slope–Intercept Form is y= mx+b

To find the slope, we take the rise/run

We see that y increased by 12 and x increased by 6, so our slope is

12/6 = 2

Our y-intercept is located at ( 0, 1)

So our answer is y=2x + 1

Answer:

Step-by-step explanation:

Rewrite the function as an equation.

y

=

3

x

−

4

Use the slope-intercept form to find the slope and y-intercept.

Tap for fewer steps...

The slope-intercept form is

y

=

m

x

+

b

, where

m

is the slope and

b

is the y-intercept.

y

=

m

x

+

b

Find the values of

m

and

b

using the form

y

=

m

x

+

b

.

m

=

3

b

=

−

4

The slope of the line is the value of

m

, and the y-intercept is the value of

b

.

Slope:

3

y-intercept:

(

0

,

−

4

)

The standard formula for finding the equation of a line is expressed as

y = mx +b

m is the slope of the line

b is the y-intercept of the line

The slope of a line is the measure of its steepness.

Given the equation y = 2x + 4, the slope of the line is 2 and the y-intercept is 4. The y-intercept shows that the line will cut the y-axis at y = 4

The required graph of the equation is as shown in the attachment.

Learn more here: https://brainly.com/question/17003809

The expansion of the function f = y'x + x'z with respect to x yields (x + y')(x + z'), and the expansion with respect to y gives (x' + y)(x + z').

(a) To expand the function f = y'x + x'z with respect to x, we use the distributive property and apply De Morgan's law to simplify the expression:

f = y'x + x'z

  = x'y + x'z

  = (x'y)'(x'z)'    [Using De Morgan's law]

  = (x + y')(x + z')   [Using De Morgan's law again]

(b) Designing the function using a 2-to-1 multiplexer for the case of expanding f with respect to x involves using the inputs x, y, and z as the select lines of the multiplexer. The inputs x + y' and x + z' will be connected to the data inputs of the multiplexer, and the output of the multiplexer will be the expanded function f.

(c) Similarly, for expanding f with respect to y, the expansion is:

f = y'x + x'z

  = xy' + x'z

  = (xy')'(x'z)'    [Using De Morgan's law]

  = (x' + y)(x + z')   [Using De Morgan's law again]

For this case, the inputs x', y, and z will serve as the select lines of the 2-to-1 multiplexer. The inputs x' + y and x + z' will be connected to the data inputs, and the output of the multiplexer will represent the expanded function f.

In both cases, the 2-to-1 multiplexer is used to implement the logic function by selecting the appropriate data inputs based on the select lines, which are derived from the expansion of the function with respect to the corresponding variable.

In conclusion, the expansion of the function f = y'x + x'z with respect to x yields (x + y')(x + z'), and the expansion with respect to y gives (x' + y)(x + z'). By utilizing 2-to-1 multiplexers, the expanded functions can be designed by connecting the appropriate data inputs to the multiplexer based on the select lines derived from the expansions. This allows for the implementation of the logic functions using multiplexers, providing a compact and efficient circuit design.

Learn more about expansion here:

brainly.com/question/33072567

#SPJ11

Answer:

Step-by-step explanation:

Point A has coordinates:

Rule of 270° rotation:

Coordinates of A':

Answer:

\(7x+21\)

Step-by-step explanation:

Let the number be \(x\).

\(x+3\)

\(7(x+3)\)

Expand the brackets.

\(7x+21\)

Answer: 14a²b³c⁴ = 2 x 7 x a x a x b x b x b x c x c x c

28ab²c².​ = 2 x 2 x 7 x a x b x b x c x c

Step-by-step explanation: is this what your looking for?

Answer: 50% i think (probs wrong)

Step-by-step explanation:

if half the balls are even then presumably another will be

Answer:

ans is 50%

Step-by-step explanation:

i also think so it can also be wrong serch on wgwowowgwlwe

The evaluation of the proportional relationship and the graph of the proportional relationships are presented as follows;

Set 1

(1) Please find attached the graph showing the change in the polar bear's distance over time, created with MS Excel

The polar bear swims 1.5 meters in 1 second

(2) The slope of the line is 1.5

Set 2

(1) y = 2·x

(2) y = 5·x + 2.5

Please find attached the graph of the equations in question (3) (y = -2·x), and question (4), (y = (1/2)·x - 3, created with MS Excel

A proportional relationship is one in which there is an equivalent ratio between the output variable and the input variable.

Set 1

(1) The distance the polar bear swims in 8 seconds = 12 meters

The relationship between the change in the distance swam by the polar bear with time is a proportional relationship of the form, x = v·t

Where;

x = The distance the bear swam

t = The time duration

The constant of proportionality, v = x/t is the speed, which is the distance the polar bear swims in 1 second

Where x = 12 meters and t = 8 seconds, we get;

v = (12 m)/(8 s) = 1.5 m/s

Please find attached the completed graph that shows the change in the polar bears distance with time, created with MS Excel

(2) The equation that can be used for finding the slope, m, of a line with known points (x₁, y₁) and (x₂, y₂) is presented as follows;

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Whereby the points on the line are; (10, 55), and (15, 62.5), we get;

(x₁, y₁) = (10, 55)

(x₂, y₂) = (15, 62.5)

m = (62.5 - 55)/(15 - 10) = 1.5

Set 2;

(1) The points on the line are; (1, 2), (0, 0)

The slope of the line is; 2/1 = 2

The coordinates of the y-intercept of the line is (0, 0)

(2) The points on the line are; (0, 2.5), (1.5, 10)

The slope of the line is therefore; m = (10 - 2.5)/(1.5 - 0) = 5

The coordinate of the y-intercept is; (0, 2.5)

(3) The possible equation in the question is; y = -2·x

The equation with a y-intercept of (0, 0), indicates a proportional relationship, therefore, the points on the graph can be obtained using the following table;

x \({}\)    y

0 \({}\)   0

1 \({}\)   -2

2 \({}\)  -4

3 \({}\)  -6

4 \({}\)  -8

(4) The equation is; y = (1/2)·x - 3

The points on the graph of the equation are found as follows;

x \({}\)       y

0 \({}\)      (1/2)×0 - 3 = -3

1 \({}\)       (1/2)×1 - 3 = -2.5

2 \({}\)      (1/2)×2 - 3 = -2

3 \({}\)      (1/2)×3 - 3 = -1.5

Learn more about graphing linear equations here: https://brainly.com/question/14197974

#SPJ1

Answer:

32,40 in

Step-by-step explanation:

please

give brainliest

Answer:

The length of the hypotenuse side is (9 + 2·√7) cm

Step-by-step explanation:

The given parameters of the triangle are;

The type f triangle = Right triangle

The length of the sides 2 cm and 7 cm shorter than the hypotenuse

Let 'h' represent the length of the hypotenuse side of the triangle, in centimeters we have;

The length of one side of the right triangle = (h - 2) cm

The length of the other side of the right triangle = (h - 7) cm

By Pythagoras's theorem, we have;

h² = (h - 2)² + (h - 7)²

Using search function on the internet, we have;

h² = (h - 2)² + (h - 7)² = 2·h² - 18·h + 53

∴ h² = 2·h² - 18·h + 53

∴ 2·h² - 18·h + 53 = h²

h² - 18·h + 53 = 0

53 is a prime number, therefore, by the quadratic formula, we have;

h = (18 ± √((-18)² - 4×1×53))/(2 × 1)

h = 9 + 2·√7 cm ≈ 14.29 cm or h = 9 - 2·√7 ≈ 3.71

However, given that one of the side is 7 cm shorter than the hypotenuse, for all the sides to remain positive, we have h = 9 + 2·√7 cm ≈ 14.29 cm , because for h ≈ 3.71 cm, we have;

The length of the other side = (h - 7) cm ≈ (3.71 - 7) cm ≈ -3.29 cm which is not possible for a real triangle

Therefore, the length of the hypotenuse side, h = 9 + 2·√7 cm ≈ 14.29 cm.

The value of x is 18 and the value is not extraneous solution as it satisfy the given equation.

What is extraneous solutions ?

The concept of 'extraneous solutions' refers to values that we obtain when solving equations that aren't really solutions.

Solving radical equations

Given the following radical equation expressed as:

3√x-2 + 1 = 13

Subtract 1 from both sides to have:

3√x-2 + 1 -1 = 1 - 13-1

3√x-2  = 12

Divide both sides by 3

3√x-2/3  = 12/3

√x-2 = 4

Square both sides

(√x-2)² = 4²

x - 2 = 4²

x = 16 + 2

x = 18

Now checking if this solution is extraneous or not by substituting back in given equation :

= 3√x-2 + 1

= 3√18-2 + 1

= 3 x 4 +1

= 13

Hence, the value of x is 18 and the value is not extraneous solution as it satisfy the given equation.

Learn more on extraneous solution here:

brainly.com/question/2959656

#SPJ1

The probability of obtaining the same number of heads is 3/8 or 0.375 when each of two persons tosses three fair coins.

The probability that two persons will obtain the same number of heads depends on the number of possible combinations of heads and tails that can be obtained by each person.

Since each coin flip results in either a heads or tails, there are 2 possible outcomes for each flip. Therefore, for three coin flips,

there are 2^3 or 8 possible combinations of heads and tails.

Out of these 8 combinations, there are 3 in which both persons have the same number of heads (i.e., 0 heads, 1 head, or 3 heads).

So, the probability of obtaining the same number of heads is 3/8 or 0.375.

Learn more about probability  :

https://brainly.com/question/30034780

#SPJ4

a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

To know more about median refer here:

https://brainly.com/question/11237736#

#SPJ11

Answer:

So what we're going to do is now take the so drdx of negative 3x plus 1 is equal drdx of x squared

Step-by-step explanation:

The answer is (a) Only I and III are correct.

Now, We can find the first and second partial derivatives of f(x,y):

f(x, y) = x³ y + 3x² y + y² + 1

\(f_{x}\) = 3x² y + 6xy

\(f_{y}\) =x³ + 2xy

\(f_{xx}\) = 6xy + 6x²

\(f_{yy}\) = = 2x

\(f_{xy}\)  = 3x² + 2y

Now we can evaluate each of the statements using the Second Partials Test:

I. f(x, y) has a saddle point at (-3,0)

To check if this statement is true, we need to evaluate the second partial derivatives at (-3,0):

\(f_{xx}\) (-3,0) = 0

\(f_{yy}\) (-3,0) = -6

\(f_{xy}\)(-3,0) = -9

The discriminant D = 0 - (-9)² = 81 is positive and \(f_{xx}\) < 0, which means that we have a saddle point.

Therefore, statement I is true.

II. f(x,y) has a relative maximum at (0,0)

To check if this statement is true, we need to evaluate the second partial derivatives at (0,0):

\(f_{xx}\)(0,0) = 0

\(f_{yy}\)(0,0) = 0

\(f_{xy}\)(0,0) = 0

The discriminant D 0 - 0 = 0 is zero and \(f_{xx}\) = 0, which means that we cannot determine the nature of the critical point using the Second Partials Test alone.

Therefore, statement II is uncertain.

III. f(x,y) has a relative minimum at (-2,-2) To check if this statement is true, we need to evaluate the second partial derivatives at (-2,-2):

\(f_{xx}\)(-2,-2) = -24

\(f_{yy}\)(-2,-2) = -4

\(f_{xy}\)(-2,-2) = -8

The discriminant D = (-24)(-4) - (-8)² = -448 is negative and \(f_{xx}\)  < 0, which means that we have a relative maximum.

Therefore, statement III is false.

From our analysis, we can conclude that only statement I is correct.

Therefore, the answer is (a) Only I and III are correct.

Learn more about discriminant visit:

https://brainly.com/question/24730520

#SPJ4

Answer:

x=11

Step-by-step explanation:

51-x-5*19= -5x

51-5*19= -4x

4x=5*19-51

4x=95-51

4x=44

x=11

Step-by-step explanation:

let x year ago son age was 5 time his father age.

age of son before x year = 19-x

age of father before x year = 51-x

NOW

according to the question

5(19-x) =51-x

95-5x =51-x

95-51 = -X-5x

44 = 4x

x=11

so your ans is 11years ago

The function for the quadratic model that gives the average revenue in dollars where x is the price in dollars of a large one-topping pizza, with data from 9.25 ≤ x ≤ 14.25 is -105.6x² + 254.28x - 12.16.

Quadratic model

In regression, quadratic model means  mathematical model represented by a quadratic equation such as Y = aX² + bX + c, or by a system of quadratic equations.

Given,

A pizza parlor has been experimenting with lowering the price of their large one-topping pizza to promote sales. the average revenues from the sale of large one-topping pizzas on a Friday night (5 p.m. to midnight) at various prices are given below.

Here we need to find the quadratic model function with data from 9.25 ≤ x ≤ 14.25.

While we plot the given table of values in the graph then we get the graph like the following.

Through the graph we have identified that the value of

mean of x 11.75

mean of y 1,165.35

correlation coefficient r 0.9924547615

A -105.6

B 254.28

C -12.16

So, through these values the quadratic model of the function is written as,

=> -105.6x² + 254.28x - 12.16.

To know more about Quadratic model here.

https://brainly.com/question/13496810

#SPJ4

Answer:

B. The second graph

Step-by-step explanation:

Hope this helps! Let me know if you need an explanation! Have a nice day :)

Answer:

Second option

Step-by-step explanation:

Answer:

X = 36/17

y = -8/17

Step-by-step explanation:

Since they both equal y, you could use them equal to each other.

(5/2)x-4=(-1/3)x+2

Then solve for x by combining like terms. X should be 36/17. Plug in x to find y in one of the equations. I will use the top one. (5/3)(36/17)-4=y. That should simplify down to (60/17)-4=y. Y would finally equal -(8/17).

Answer:

What the other guy said. I think he is correct.

Step-by-step explanation: