Please solve and graph the following inequalities. show all steps thank you. ​

The original plot has an area of 209 x 309 = 64581 square meters.

If x is added to both the length and width, the new area becomes 2 times the original area, which is 2 x 64581 = 129162 square meters.

To solve for x, we can use the formula for the area of a rectangle, which is length x width. If we add x meters to the length and width, the new area can be expressed as (209 + x)(309 + x). We can then set this expression equal to 129162 and solve for x.

(209 + x)(309 + x) = 129162

64,881 + 518x + x^2 = 129,162

x^2 + 518x - 64,281 = 0

Using the quadratic formula, we get:

x = (-518 ± sqrt(518^2 - 4(1)(-64281))) / 2(1)

x = (-518 ± sqrt(33404500)) / 2

x = (-518 ± 5772.13) / 2

The negative value is not meaningful in this context, so we take the positive value:

x = (5772.13 - 518) / 2

x = 2627.065 meters

Therefore, adding 2627.065 meters to both the length and width of the original plot will double its area.

The problem involves finding the value of x, which represents the additional length and width added to the original plot of land to double its size. We know the original area of the plot, which is 209 by 309 meters, and we are given that the area doubles when x meters are added to both the length and width.

To solve for x, we need to use the formula for the area of a rectangle, which is length x width. We can set up an equation using this formula and the given information to solve for x. This equation involves a quadratic expression, so we use the quadratic formula to find the two possible values of x.

We discard the negative value of x, as it is not meaningful in this context, and take the positive value as the answer. This value tells us that adding 2627.065 meters to both the length and width of the original plot will double its area.

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Answer:

898/8×41=4602.5

Step-by-step explanation:

I HOPE THIS WILL HELP YOU KEEP WORK HARD FOR STUDIES

The total cost is £220 and he has £220, So he does have enough money.

Find the number of bites that we can fit along the length and width.

120/30=4

120/30=12/3=4

600/30=20

600/30=60/3=20

Multiply the bite for the length and width to find the total bites needed.

Total= Length*width

=20*4

=80

80 tiles are needed. Each tile cost £2. 50. We can find the cost by multiplying these together.

Cost=tiles*cost per tile

=80*£2. 50=£200

=80*2=160

=80*0.5=40

⇒160+40=200

He has enough money because the whole cost is £220 and he has £220 in his account.

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Answer:

Assume we want to find the solution to this system of equations.

The solution is (2,-2)

Step-by-step explanation:

We can find the solution either mathematically or by graphing.  I'll do both.

Math:

Rearrange:

-2x-6y=8

-6y=8 +2x

y = -(1/3)x -(4/3)

---

Now use this expression of y in the second equation:

-6x-6y=0

-6x-6(-(1/3)x -(4/3)) =0

-6x + 2x +8 =0

-4x = - 8

x = 2

---

Use x = 2 in the first equation to find y:

y = -(1/3)x -(4/3)

y = -(1/3)*(2) -(4/3)

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

y = -(6/3) or -2

The solution is (2,-2)

===============

Graphing:

See attached graph.

Answer:

Step-by-step explanation:

-2x - 6y = 8

6x + 6y = 0

4x = 8

x = 2

-4 - 6y = 8

-6y = 12

y = -2

(2, -2)

The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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The value of the t-test statistic for testing whether the effect of passing yards on salary is equal to 0 is 8.041. Therefore, the correct answer is (d) 8.041.

In order to solve this problem, we need to use the t-test formula: t = (b1 - 0) / SE(b1)

where b1 is the slope coefficient (0.051), and

SE(b1) is the standard error of the slope coefficient.

The standard error can be found using the formula: SE(b1) = sb1 / √(n-2)

where sb1 is the standard error of the estimate for the slope coefficient, and

n is the sample size.

The standard error of the estimate can be found using the formula: sb1 = √(SSR / ((n-2) * Sxx))

where SSR is the sum of squared residuals, and

Sxx is the sum of squared deviations of X from its mean.

We can use the R² value to find SSR: SSR = (1 - R²) * SST

where SST is the total sum of squares.

SST can be found using the formula:SST = sum(y - ybar)²

Now we have all the necessary information to find the t-test statistic:t = (0.051 - 0) / (0.014 / √(32-2))t = 8.041

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The graphs to use are box plots, histogram and dot plots

From the question, the most important factors are:

Using the box plots, histogram and dot plots, one would see the shape and the spread.

While the stem and leaf plot would show specific data values

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Answer:

Frequency: 20

A.F: 650

Mean: 30

Step-by-step explanation:

Frequency and A.F were just sums of the values mentioned for each

The mean:

Definition: the average of a data.

Formula: sum of numbers divided by the number of numbers

Answer: (28 x 2 + 29 x 4+ 30 x 8 + 31 x 4+ 32 x 2) divided by 20 = 30

Hope this helps

Answer:

3. m<GHF= 90 degrees

4. m<DGH= 45 degrees

5. HF=5

6. DE=50

Step-by-step explanation:

3. The measure of angle DGF and EFG are 45 degrees each and 45+45 is 90 degrees. When you subtract 90 from 180, you get 90.

4. A square is also a rectangle and a rectangle has four right angles and it is a rhombus and the diagonals bisect the angles. This means that angle DGH is half of angle DGF and 90/2=45.

5. The diagonals of a square are congruent so it is also 5.

6. You use the Pythagorean Theorem and 5^2 + 5^2=50

The diagonals of square DEFG intersect at H. The measure of the following option; 3. m∠GHF= 90 degrees. 4. m∠DGH= 45 degrees 5. HF=5 6. DE=50

That rectangle whose all sides are equal is called a square.

A square is always a rectangle, parallelogram, a rhombus, and a quadrilateral but its reverse statement may or may not be true.

(ie it is not always necessary that a rectangle is a square or a parallelogram is a square or a rhombus is a square).

The diagonals of square DEFG intersect at H.

Given that EH = 5, we need to find the measure of the following option;

3. The measure of ∠DGF and ∠EFG are 45 degrees each .

The sum of the angle of the bisector of diagonal 45 + 45 = 90 degrees.

When you subtract 90 from 180, you get 90.

4. A square is also a rectangle and a rectangle has four right angles and it is a rhombus and the diagonals bisect the angles.

This means that ∠DGH is half of ∠DGF

90/2 = 45.

5. The diagonals of a square are congruent so HF is 5.

6. By Pythagorean Theorem

\(DF^2 = 5^2 + 5^2\\\\DF = \sqrt{50}\)

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To find L{f(t)}, we first need to know the definition of the Laplace transform.  Laplace Transform Definition: The Laplace transform of a function f(t) is defined as  L{f(t)} = ∫[0,∞) e^(-st) f(t) dt, where s is a complex variable.

The Laplace transform is a mathematical tool used to transform a function of time into a function of complex frequency, s. This tool is often used in engineering and physics to solve differential equations and analyze systems.
To find L{f(t)}, we need to use the Laplace transform definition and substitute f(t) into the integral.

Assuming that the function f(t) is known, we can use the Laplace transform definition to find L{f(t)}.
L{f(t)} = ∫[0,∞) e^(-st) f(t) dt
Let's assume that f(t) = sin(t).
L{sin(t)} = ∫[0,∞) e^(-st) sin(t) dt
We can use integration by parts to solve this integral.
Let u = sin(t) and dv = e^(-st) dt.
Then, du/dt = cos(t) and v = (-1/s) e^(-st).
Using integration by parts, we get:
L{sin(t)} = [-1/s * e^(-st) * sin(t)]∞[0] - ∫[0,∞) [-1/s * e^(-st) * cos(t)] dt
Simplifying this expression, we get:
L{sin(t)} = [-1/s * e^(-s∞) * sin(∞)] - [-1/s * e^(0) * sin(0)] - (1/s) ∫[0,∞) e^(-st) cos(t) dt
Since sin(∞) and sin(0) are both zero, we can simplify further to get:
L{sin(t)} = (1/s) ∫[0,∞) e^(-st) cos(t) dt
We can use integration by parts again to solve this integral.
Let u = cos(t) and dv = e^(-st) dt.
Then, du/dt = -sin(t) and v = (-1/s) e^(-st).
Using integration by parts, we get:
L{sin(t)} = (1/s) [(-1/s * e^(-st) * cos(t)]∞[0] - (1/s) ∫[0,∞) [-1/s * e^(-st) * (-sin(t))] dt
Simplifying this expression, we get:
L{sin(t)} = (1/s^2) [cos(0) - cos(∞)] - (1/s^2) L{-cos(t)}
Since cos(0) = 1 and cos(∞) = undefined, we can simplify further to get:
L{sin(t)} = 1/(s^2 + 1)
Therefore, the Laplace transform of f(t) = sin(t) is L{f(t)} = 1/(s^2 + 1).

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Answer:

T = 3.5m

T is trash in pounds

m is members of family

Step-by-step explanation:

Answer:

the width is 46 and the length is 99

Step-by-step explanation:

perimeter = 290 yards

length =2w+7

width =w

perimeter = 2w + 2l =290

2w+ 2(2w+7) =290

2w+4w+14= 290

6w = 276

w= 46

The degree of the Maclaurin polynomial necessary for the error in the estimate of f(0.31) to be less than 0.001 is 4.

To determine the degree of the Maclaurin polynomial necessary for the error in the estimate of f(0.31) to be less than 0.001, we can use Taylor's theorem and the concept of Taylor series.

Taylor's theorem states that if a function f(x) has derivatives of all orders at x = a, then the function can be approximated by a polynomial (Taylor polynomial) centered at a.

In this case, we want to estimate f(0.31) using a Maclaurin polynomial. Since the Maclaurin series is a special case of the Taylor series centered at a = 0, we can use the Taylor polynomial centered at a = 0 to approximate f(0.31).

The error in the estimate of f(0.31) using a Taylor polynomial is given by the remainder term, which is related to the next term in the Taylor series. To ensure that the error is less than 0.001, we need to find the degree of the Maclaurin polynomial such that the absolute value of the next term is less than 0.001.

The given function f(x) = 2ln(x + 1) can be represented by its Maclaurin series expansion as:

f(x) = 2(x - x^2/2 + x^3/3 - x^4/4 + ...)

To find the degree of the Maclaurin polynomial necessary, we need to determine the term with the highest power of x that satisfies |x^(n+1)/(n+1)!| < 0.001.

By evaluating the terms, we find that the term with the highest power of x is x^4/4, which is the fifth term in the series (n = 4). Thus, to ensure the error is less than 0.001, we need a Maclaurin polynomial of degree 4 or higher.

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The equation of the line perpendicular to our supplied line is represented by the equation y = 3/2x - 11.

A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

On the y-axis, this value c is referred to as the intercept.

So, we have the points (8, 1).

The given equation is y = 2/3x + 5.

We are aware that a perpendicular line's slope is the negative reciprocal of the provided line's slope.

As a result, the slope of the line perpendicular to line y = 2/3x + 5 will be equal to the reciprocal of -2/3.

Negative reciprocal of -2/3 = -(-3/2)

Negative reciprocal of -2/3 =3/2

When we enter the coordinates of the location (8, 1) and m = 3/2 into the slope-intercept form of the equation, we get:

1 = 3/2 * 8 + b

1 = 3 * 4 + b

1 = 12 + b

1 - 12 = 12 - 12 + b

- 11 = b

Therefore, the equation of the line perpendicular to our supplied line is represented by the equation y = 3/2x - 11.

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Total for 1500 tickets= $48,250.

Cost adults= $45 x

Cost children= $10. or (x-35)

Number of adult tickets sold= 950

Number of children tickets sold= 550.

We are given the following information

Line AC and EG are perpendicular.

Angle FBC is the complement of the angle ABD.

Angle FBC = (x + 4)°

Angle ABD = (5x - 10)°

We are asked to find the angle EBF.

Recall that when two angles are complementary then they add up to 90°

So we can write

Let us substitute the given values and solve for x.

So the angle FBC is

Since we know that lines AC and EG are perpendicular so the angle FBC and angle EBF must add up to 90°

Therefore, the angle EBF is 70°.

The values of x for each equation is given below:

To find the value(s) of x, you will need to solve each equation for x.

1. -1/2 - 4x/5 = 1/2 - 2x

Add 1/2 to both sides:

-1/2 - 4x/5 + 1/2 = 1/2 - 2x + 1/2

Combine like terms on the left side:

0 - 4x/5 = 1 - 2x

Multiply both sides by 5:

0 - 4x = 5 - 10x

Add 4x and 10x to both sides:

4x + 10x = 5

Combine like terms:

14x = 5

Divide both sides by 14:

x = 5/14

2. 2x - 3x/2 = -x + 1/3

Multiply both sides by 2:

4x - 3x = -2x + 2/3

Combine like terms:

x = 2/3

3. 5/3 - x/5 = -1

Add x/5 to both sides:

5/3 - x/5 + x/5 = -1 + x/5

Combine like terms on the left side:

5/3 = -1 + x/5

Add 1 to both sides:

5/3 + 1 = -1 + x/5 + 1

Combine like terms:

6/3 = x/5

Multiply both sides by 5:

30/3 = x

Divide both sides by 3:

10 = x

4. -2x - 4 = -1/5 + 3x/4

Add 2x to both sides:

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

Add 1/5 to both sides:

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

Combine like terms:

-39/5 = 5x/4

Multiply both sides by 4/5:

-39/5 * 4/5 = 5x/4 * 4/5

Combine like terms:

-39/5 = 5x/4

Multiply both sides by 4:

-39 = 20x/4

Divide both sides by 20:

-39/20 = x

5. -6x + 1 = x - 1

Add 6x to both sides:

-6x + 6x + 1 = x - 1 + 6x

Combine like terms:

0 = 7x

Divide both sides by 7:

0/7 = 7x/7

Combine like terms:

0 = x

The values of x are: 5/14, 2/3, 10, -39/20, and 0.

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No, acute angle can not be equal to 90. if an angle equal to 90 then it is a right angle.

Acute angle

An angle smaller than the right angle is called an acute angle. In other words, the angle which is less than 90 degrees forms an acute angle.

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is equal to 90 degrees). For example, ∠30o, ∠45o, ∠60o, ∠75o, ∠33o, ∠55o, ∠85o, etc. are all acute angles.

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The factored form of 3y - 18 using the G.C.F. is 3 * (y - 6).

What is the factor?

Factor is a mathematical expression or a number that divides another expression or number evenly. The factor of an expression is a number that divides the expression evenly, leaving no remainder.

The expression 3y - 18 can be factored using the greatest common factor (G.C.F.) of 3.

The G.C.F. of 3 and 3y is 3.

So, 3y - 18 can be factored as:

3 * (y - 6)

Hence, The factored form of 3y - 18 using the G.C.F. is 3 * (y - 6).

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Rounded to four decimal places, the p-value is 0.0844.

To determine the p-value for this hypothesis test, we need to follow these steps:

Step 1: State the null and alternative hypotheses.

Null hypothesis: The percentage of readers who own a laptop is 26%.

Alternative hypothesis: The percentage of readers who own a laptop is different from 26%.

Step 2: Determine the test statistic.

We can use a z-test for proportions since we have a large enough sample size and we know the population proportion. The formula for the test statistic is:

z = (p - p) / √(p(1-p) / n)

where p is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

Using the given values, we have:

z = (0.17 - 0.26) / √(0.26(1-0.26) / 100)

z = -1.72

Step 3: Determine the p-value.

Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution that corresponds to a z-score of -1.72. Using a table or a calculator, we find that the area in the left tail is 0.0422 and the area in the right tail is also 0.0422.

Therefore, the p-value is the sum of the areas in both tails:

p-value = 0.0422 + 0.0422

p-value = 0.0844

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Answer: 3 054 in^2

Step-by-step explanation:

Sphere volume formula = 4/3 pi r^3

So... 4/3 pi 9^3

= 3 053.63 in^2

Answer:

B

Step-by-step explanation:

Not much to say but that i the definition.  You sing the midpoint of each side, make a perpendicular line and see where the three perpendicular bisectors intersect.  

A is the incenter, C sounds like the Orthocenter and D sounds like the centroid.

Aside from being able to tell from the parts of the words, you just kinda have to memorize these.  

Step-by-step explanation:

the base is x in.

the area is 14 in².

the area is calculated by :

base × height / 2

so, we have here

14 = x × height / 2

28 = x × height.

height = 28/x in.

Answer:

1. angle addition post

2. 2x=56

The corresponding angles of the lines solved and the value of x = 28°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Given data ,

Let the measure of ∠ELG = 124°

The measure of ∠ELD = 2x

∠ELG and ∠ELD are a linear pairs of angles

So , the measure of ∠ELG  + ∠ELD = 180°

On simplifying , we get

2x + 124° = 180°

Subtracting 124° on both sides , we get

2x = 56°

Divide by 2 on both sides , we get

x = 28°

Therefore , the value of x is 28°

Hence , the angle is x = 28°

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Answer:

38

Step-by-step explanation:

Hope this helps!!

The expression is given as,

The given expression is simplified as follows:

Thus the result of the given expression is,

Given statement solution is :- If I were to assume the flipping process is entirely random and the coin is unbiased, the chances of correctly guessing the outcome of each flip would be 1 out of 2, or a 50% probability.

If I were to assume the flipping process is entirely random and the coin is unbiased, the chances of correctly guessing the outcome of each flip would be 1 out of 2, or a 50% probability. However, the psychic claims to have the ability to sense the outcome of each flip, which would suggest that he believes he can accurately predict the results.

To put the psychic to the test, you can proceed with flipping the coin six times and ask the psychic to guess the outcome of each flip. After the coin has been flipped, compare the psychic's guesses with the actual outcomes to evaluate the accuracy of their predictions.

Keep in mind that even if the psychic does make correct predictions, it does not necessarily prove their psychic abilities. Random chance can occasionally lead to a streak of correct guesses, even if there is no true psychic ability involved. To draw any meaningful conclusions, a larger sample size or repeated testing would be required.

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