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

Please solve

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Student A's strategy of reading a consistent number of pages each day will enable them to finish the book in 20 days.

On the other hand, Student B's strategy of gradually increasing the number of pages read each day will result in a longer duration to complete the book.

Student A plans to read a consistent 25 pages each day, while Student B plans to start with 2 pages and increase the number of pages read by 50% each day after the first day.

Let's analyze the outcome of these two strategies.

For Student A:

Since the book has 500 pages and Student A reads 25 pages per day, the total number of days required to finish the book can be calculated as:

Total days = 500 pages / 25 pages per day = 20 days

Therefore, Student A will finish reading the book in 20 days by consistently reading 25 pages each day.

For Student B:

On the first day, Student B reads 2 pages.

From the second day onward, the number of pages read increases by 50% each day.

Let's see the pattern:

Day 2: 2 pages

+ 50% (2 pages) = 3 pages

Day 3: 3 pages + 50% (3 pages) = 4.5 pages

Day 4: 4.5 pages + 50% (4.5 pages) = 6.75 pages

We can observe that the number of pages read increases each day but with diminishing increments due to the 50% increase.

As a result, Student B will take longer to read the book compared to Student A.

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The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2

How to solve a function?

If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:

g(x) = a(4) raise to the power x-k/2

where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:

f(x) = g(x)/2

Substituting the expression for g(x) into this equation and simplifying, we get:

4raise to the power x - 6 = a(4)raise to the power x-k/2

To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:

f(0) = 4 - 6 = -5

f(1) = 4- 6 = -2

Using the equation g(x)/2 = f(x), we can write:

g(0)/2 = -5

g(1)/2 = -2

Substituting the expression for g(x) into these equations, we get:

a(4) raise to the power -k/2 = -10

a(4) raise to the power 1-k/2 = -4

Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":

(4)raise to the power -k/2 / (4)  raise to the power 1-k/2 = -10 / -4

Simplifying this equation, we get:

4.raise to the power(1-k/2) = 5

Taking the logarithm of both sides (with base 4), we get:

1-k/2 = log4(5)

Solving for "k", we get:

k = 2 - 2 log4(5)

Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":

a = -10 / (4)   raise to the power  -k/2

Substituting the numerical value of "k", we get:

k = 2 - 2 log4(5) ≈ 0.872

a = -10 / (4) raise ti the power  -k/2 ≈ 2.323

Therefore, the equation for the transformed function g(x) is:

g(x) = 2.323 (4)raise to the power x-0.872/2

or equivalently:

g(x) = 1.1615 (4) raise to the power -x0.872

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Answer:

g(x) = 1/2 (4)^x - 3

Step-by-step explanation:

A vertical compression by a factor of 1/2

means that the entire function f is multiplied by 1/2:

1/2 f (x) = 1/2 (4^x - 6)

= 1/2 (4)^x - 3

Answer:

4 1/10 when u have a inproper fraction like that every 10 is one whole number

The ratio of the shaded area to the unshaded area in the figure is 1 : 5.5 which can be calculated by adding the areas of the two squares and triangle EDH.

Area is the amount of two-dimensional space taken up by a shape or object. It is measured in square units, such as square centimeters, square meters, or square miles.

The ratio of the shaded area to the unshaded area in the figure can be calculated by adding the areas of the two squares and triangle EDH, and then subtracting the shaded area.

First, calculate the total area of the figure:

Area of the two squares = (BC)²

= (CD)²

= (4)²

= 16

Area of triangle EDH = ½ x BC x DH

= ½ x 4 x 5

= 10

Total area = 16 + 10

= 26

Next, calculate the shaded area:

Shaded area of square CDEF = 25% x 16

= 4

Total shaded area = 4

Finally, calculate the ratio of the shaded area to the unshaded area in the figure:

Unshaded area = 26 - 4

= 22

Ratio of the shaded area to the unshaded area = 4 : 22

= 1 : 5.5

Therefore, the ratio of the shaded area to the unshaded area in the figure is 1 : 5.5.

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Question:

A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.

In the figure, the proportion of shaded to unshaded region is 1:5.5.

The area of the shaded region is the difference between the area of the entire polygon as well as the area of the polygon's unshaded part. In polygons, the area of the shaded portion can occur in two ways. The shaded area can be found in the centre of a polygon or on its sides.

As previously stated, the area of the shaded region is determined by subtracting the area of a complete polygon from the area of the unshaded region.

outer shape region – area of the interior unshaded shape = The shaded area

To begin, compute the entire area of the figure:

Area of the two squares \(=(BC)^2\)

\(=(CD)^2\\\\=(4)^2\\\\=16\)

Area of the EDH triangular \(=\frac{1}{2} \times BC\times DH\)

Substitute values in the above equation

\(=\frac{1}{2} \times 4\times 5\\\\=10\)

Total area = 16 + 10

                 = 26

The shaded region is then calculated as follows:

CDEF square shaded region = 25% x 16

                                                = 4

Total shaded area = 4

Finally, compute the shaded-to-unshaded area ratio in the figure:

Unshaded area = 26 - 4

= 22

Shaded to unshaded region ratio = 4 : 22

= 1 : 5.5

As a result, the shaded area to unshaded area ratio in the image is 1: 5.5.

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The complete question is,

A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.

Answer:

I'd say B bcs it's the only thing that would fit with the shift on x axis and y axis

Answer:

-5ab + 5a - 3

Step-by-step explanation:

its good to know if a number is positive or negative because something as simple as forgetting the signs such as - + could drastically change your answer

Accordingly, x0 = 0, x1 = 3, x2 = 0, and x3 = 3 are the first three iterations of f ( x) = -2x + 3 when x0 = 0.

A loop is described as a section of code that runs repeatedly. The procedure in which a code fragment is run just once is referred to as iteration. One iteration is the single time a loop is run. A loop may run through numerous iterations.

x1 = f(x0) = f(0) = -2 * 0 + 3 = 3

x2 = f(x1) = f(3) = -2 * 3 + 3 = 0

x3 = f(x2) = f(0) = -2 * 0 + 3 = 3

So the first 3 iterates of the function f(x) = -2x + 3 when x0 = 0 are:

x0 = 0, x1 = 3, x2 = 0, x3 = 3

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The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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Answer:

n = 5

Step-by-step explanation:

I think you know the rest

Answer:

The seats in the lower section are x= 1720 , in the upper section are 3x= 5160 and y=24,200 - 4x= 24,200 - 6880= 17320 tickets in the field.

Step-by-step explanation:

Let x represent the number of seats in the lower section then the number of seats in the upper section is 3x and y the number of seats in the field.

The equation can be written as

80x + 60 (3x) + 40 y= $1,140,000-----1

And x+ 3x+ y= 24,200------2

4x+ y= 24,200

or y= 24,200-4x----3

Solving Eq 1

80x + 180x + 40 y= $1,140,000

260x+ 40 y=$1,140,000-----4

Putting Eq 3 in Eq 4

260x+ 40 y=$1,140,000

260x+ 40(24,200-4x-)=$1,140,000

260x + 968,000- 160x= $1,140,000

100x= $1,140,000-968,000

100x= 172,000

x= 1720

The seats in the lower section are x= 1720 , in the upper section are 3x= 5160 and y=24,200 - 4x= 24,200 - 6880= 17320 tickets in the field.

Putting the values of x and y in Eq 1 we get the same revenue.

80x + 60 (3x) + 40 y= $1,140,000

80(1720) + 60 (5160) + 40( 17320)= $1,140,000

137600 + 309600 + 692800= $1,140,000

137600 + 1002400= $1,140,000

The total number of seats in the upper section is 5160, in the lower section is 1720 and the total number of seats in the field is 17320.

Given :

The following steps can be used in order to determine the total number of seats in each section:

Step 1 - In the lower section let the total number of seats be 'x'. So according to the given data, in the upper field, the total number of seats is '3x'. Now, let the total number of seats in the field be 'y'.

Step 2 - The linear equation that represents total revenue from the tickets.

\(\rm 80x + 60(3x)+40y = 1140000\)

260x + 40y = 1140000    --- (1)

Step 3 - The linear equation that represents the total number of tickets is:

x + 3x + y = 24200

y = 24200 - 4x     --- (2)

Step 4 - Substitute the value of y in equation (1).

260x + 40(24200 - 4x) = 1140000

x = 1720 tickets

Step 5 - Substitute the value of 'x' in equation (2).

y = 24200 - 4(1720)

y = 17320 tickets

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Answer:

s = 9

Step-by-step explanation:

calculate the slope m through the 2 points using the slope formula and equate to - 5

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (s, - 7 )

m = \(\frac{-7-3}{s-7}\) = \(\frac{-10}{s-7}\)

equate m to slope of - 5

\(\frac{-10}{s-7}\) = - 5 ← multiply both sides by s - 7

- 10 = - 5(s - 7) ← divide both sides by - 5

2 = s - 7 ( add 7 to both sides )

9 = s

Answer:

A) 0.99413

B) 0.00022

Step-by-step explanation:

A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:

Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes

Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:

μ = n*μ_s ample = 42 × 5 = 210 minutes

While the standard deviation for the population would be:

σ = √nσ_sample = √(42 × 6) = 15.8745 minutes

To find the z-score, we will use the formula;

z = (x - μ)/σ

Thus;

z = (250 - 210)/15.8745

z = 2.52

From the z-distribution table attached, we have;

P(Z < 2.52) ≈ 0.99413

B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.

Thus, total time is now 250 + 10 = 260 minutes

Similar to the z-formula in A above, we have;

z = (260 - 210)/15.8745

z = 3.15

P(Z > 3.15) = 0.00022

Answer: 511cm*2

Step-by-step explanation:

To find the area of a figure with sides of 38cm, 16cm, 20cm, and 18cm, we can use Heron's formula to calculate the area of the two triangles formed by drawing a diagonal. The area of each triangle can be found by using the formula A=1/2 x b x h, where b is the base and h is the height. The formulas for semiperimeter and area using Heron's formula are given in [1]. Using these formulas, we can find the area of each triangle and then add them together to find the area of the quadrilateral. Adding 13 to the final answer will give us the total area, as explained in [2]. The final answer is 511cm^2.

Answer:

x>0.5

Step-by-step explanation:

move the -5 over to the 4 but make the negative a positive, then divide everything by 2 ant there you go x>0.5

The solution is , price of jeans = RD$ 1140 and, price of  handbag =

RD$ 2110.

Here, we have,

given that,

Margarita went to the store and bought a bag and some jeans for a total of RD$3,250.

Knowing that the handbag exceeds the jeans by RD$970,

now, we have to find that, how many do she pay for each article.

let, price of jeans = RD$ x

so, price of  handbag = RD$ (x +970)

ATQ, we get,

RD$ x + RD$ (x +970) = RD$3,250

or, RD$ 2x + 970 = RD$3,250

or, RD$ 2x = RD$ 2280

or, x = RD$ 1140

Hence, price of jeans = RD$ 1140 and, price of  handbag = RD$ 2110.

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

Can you please explain this question so I can actually answer it

the correct option is D:

" The inverse relation must pass the vertical line test."

Remember that a relation is only a function if each value in the domain is only mapped into a single value in the range.

All functions need to pass what is called the "vertical line test" this means that if you draw a vertical line on the graph of the function, the vertical line can intersect the graph at most one time. If the vertical line intercepts the graph two or more times, then it is not a function.

From this we conclude that the correct option is D:

" The inverse relation must pass the vertical line test."

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If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

Answer: f(x) has an axis of symmetry at x = 4 and h(x) has an axis of symmetry at x = -2

Step-by-step explanation:

You can easily find the axis of symmetry by investigating around which line the functions are symmetrical about

for instance, in h(x), the graph is symmetrical on either side of x = -2, meaning that the line x = -2 cuts the parabola in 'half'

in f(x), this is a little harder to think about, but if you know how the graph will be shifted on the x-axis you can figure it out! In this case (x-4)^2 means that the graph will be shifted on the x-axis 4 units to the right (or from the origin to +4 on the X axis)

as such the line x = 4 will cut the function f(x) in 'half'

[  3   9   13 ] is the Matrix showing all types of property available in key west .

A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or an attribute of such an entity in mathematics.

given in the table that how many types of property are there in the table

its a simple matrix which u can directly see

its a  3 x 1 matrix ...

[3  9  13] this matrix shows the required value

hope this helps...

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Answer:  [3 9 13]

Step-by-step explanation:

Answer:

y = 0x + 1

When x=0, y = 1

Step-by-step explanation:

Answer:

Adults: 134

Senior: 241

Step-by-step explanation:

Known

Number of adult tickets sold: x

Revenue from adult tickets: $11x

Number of senior tickets sold: y

Revenue from senior tickets: $8y

From the problem, we found the equation \(y = 2x - 27\) and 3,402 = 11x + 8y

Combining the two equation:

\(3,402 = 11x + 8(2x-27)\\3,402 = 11x + 16x - 216\\3,402 + 216 = 27x\\27x = 3,618\)

Divided both side by 27

\(x = 134\)

Since

\(y = 2x - 27\)

Inserting the value of x,

\(y = 2(134) -27\\y = 268 - 27\\y = 241\)

So, there are 134 adult tickets sold and 241 senior tickets sold.

Answer:

6 inches tall and has a diameter of 2 inchces

Step-by-step explanation: