Polygon DEFG has coordinates D(2, 5), E(3, 1), F(4, 6), and G(6, 6). If the polygon is translated 3 units to the left, what are the coordinates of F'?

( , )

The width of the rectangle is [tex]4x^8y^6[/tex]inches.

Option A is correct.

What is the area of the rectangle?

A rectangle is a four-sided polygon with two pairs of parallel sides, and all four angles are right angles (90 degrees). The area of a rectangle is the amount of two-dimensional space that it occupies and is given by the product of its length and width. In other words, the area A of a rectangle with length l and width w is given by the formula:

A = l x w

To find the width of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we are given the area and the length of the rectangle, so we can rearrange the formula to solve for the width:

width = Area / length

Substituting the given values, we have:

width = [tex]\frac{(32x^{12}y^{9})}{(8x^4y^3)}[/tex]

Simplifying the expression, we get:

width = [tex]4x^{8}y^{6}[/tex]

Therefore, the width of the rectangle is[tex]4x^8y^6[/tex]inches.

Option A is correct.

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Answer:

Angle P= Angle W=2(2x-6)

=4x-12

Answer:

  1625

Step-by-step explanation:

You want the sum of the first 25 terms of the series 5 +10 +15 +....

The first term is 5, the common difference is 5, so the general term is ...

  an = a1 +d(n -1)

  an = 5 +5(n -1)

The last term of the sum is ...

  a25 = 5 +5(25 -1) = 125

The sum of the series is the average of the first and last terms, multiplied by the number of terms:

  S25 = (a1 +a25)/2 · 25 = (5 +125)/2 · 25 = 65·25 = 1625

The sum of 25 terms of the series is 1625.

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For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

What exactly is a linear inequality?

In mathematics, inequality denotes a mathematical statement with no equal sides. An inequality happens in mathematics when a connection results in a non-equal comparison of two expressions or two numbers. Any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.

The characters "< and >" denote severe inequalities, whereas ‘≤’ and ‘≥’  denote slack inequalities. A linear inequality looks to be a linear equation, however the formula is different.

Now,

As stated in Commutative property the order in addition does not matter and in addition property the value added on both sides does not affect the result.

In step 3 we can write this as 5x-x-5<11x+x-21

which will not change result and

in step 7, 21 is added both sides which will not change result.

Hence,

           For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

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The volume of the cylinder is  

Using the volume of cone given by the formula

= π r² h/3

In the problem the volume is given by  222 and volume of cylinder is equal to

= π r² h

comparing the two volumes and taking proportions

volume of cone / volume of cylinder

π r² h/3 / π r² h = 222 / volume of cylinder

π r² h / 3 π r² h = 222 / volume of cylinder

1 / 3  = 222 / volume of cylinder

volume of cylinder = 3 * 222

volume of cylinder =  666

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Answer:

To find the coefficient of variation (CV) of a sample, we divide the standard deviation by the mean and multiply by 100 to get the percentage.

1. For the systolic sample:

•Find the mean:

mean = (116 + 130 + 157 + 94 + 155 + 122 + 115 + 138 + 124 + 122) / 10 = 130

•Find the standard deviation:

sum = (116 - 130)^2 + (130 - 130)^2 + (157 - 130)^2 + (94 - 130)^2 + (155 - 130)^2 + (122 - 130)^2 + (115 - 130)^2 + (138 - 130)^2 + (124 - 130)^2 + (122 - 130)^2

sum = 165.4

std = sqrt(sum/9) = 7.3

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (7.3 / 130) × 100 = 5.62%

2. For the diastolic sample:

•Find the mean:

mean = (82 + 78 + 74 + 51 + 89 + 88 + 56 + 63 + 72 + 83) / 10 = 72.5

•Find the standard deviation:

sum = (82 - 72.5)^2 + (78 - 72.5)^2 + (74 - 72.5)^2 + (51 - 72.5)^2 + (89 - 72.5)^2 + (88 - 72.5)^2 + (56 - 72.5)^2 + (63 - 72.5)^2 + (72 - 72.5)^2 + (83 - 72.5)^2

sum = 624.75

std = sqrt(sum/9) = 12.24

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (12.24 / 72.5) × 100 = 16.82%

So the CV for systolic is 5.62% and the CV for diastolic is 16.82%. We can see that the diastolic measurement has higher variation than the systolic measurement.

The total distance that Cami walked from home to school, then home, and then library, is 7. 46 miles

The distance walked by Cami, can be found to be :

= Distance from home to school + distance from school to home + distance from home to library

The distance in kilometers is:

= 5 + 5 + 2

= 12 kilometers

In miles, this is:

= 12 / 1. 60934 km per mile

= 7. 46 miles

In conclusion, the distance walked by Cami in miles, was 7. 46 miles.

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WXYZ must be a square, all the sides must have a length of 5.

The vertices of the quadrilateral are:

W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3)

Distance can be calculated using the formula derived from Pythagoras theorem. In coordinate geometry, the distance formula is:

[tex]\sqrt{[(x_2 -x_1)^2 + (y_2 - y_1)^2]}[/tex]

We have to prove that WXYZ is a square.

Using the distance formula :

[tex]WX = \sqrt{(-1-3)^2+(1-4)^2}\\ \\WX = \sqrt{16 + 9}\\ \\WX = \sqrt{25}\\ \\WX = 5[/tex]

Since WXYZ must be a square, all the sides must have a length of 5.

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The given question is incomplete, complete question is:

Select the correct answer from each drop-down menu.

Given: W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3) are the vertices of quadrilateral WXYZ.

Prove: WXYZ is a square.

Using the distance formula, I found that

…

A. all four sides have a length of 5

B. all four sides have different lengths

C. only 2 sides have the same length

D. all four sides have a length of 10

The points M(0, -1), and T(4, 6), on the diagonal [tex]\overline{MT}[/tex] of the rhombus MATH, indicates that the equation of the line containing the diagonal [tex]\overline{AH}[/tex], in slope and intercept form is; [tex]y = 3\frac{9}{14} - 4\cdot \frac{x}{7}[/tex]

A rhombus is a quadrilateral that has four congruent sides.

The specified shape of the quadrilateral MATH = A rhombus

The coordinates of the endpoints of the diagonal [tex]\overline{MT}[/tex] of the rhombus are;

The equation of the line that contains the diagonal [tex]\overline{AH}[/tex] of the rhombus can be found as follows;

The diagonals of a rhombus are perpendicular, therefore, the slope of the diagonal, [tex]\overline{AH}[/tex]is -1 divided by the slope of the diagonal [tex]\overline{MT}[/tex]

The slope of [tex]\overline{MT}[/tex] = (6 - (-1))/(4 - 0) = 7/4

The slope of [tex]\overline{AH}[/tex] = -1/(7/4) = -4/7

The diagonals of a rhombus bisect each other, therefore, the diagonals [tex]\overline{MT}[/tex] and [tex]\overline{AH}[/tex] intersect at the midpoint of point [tex]\overline{MT}[/tex]

Therefore, the midpoint of [tex]\overline{MT}[/tex] is a point on the diagonal line that contains the diagonal [tex]\overline{AH}[/tex]

The midpoint of [tex]\overline{MT}[/tex] = ((0 + 4)/2, (-1 + 6)/2) = (2, 2.5)

The equation of the line containing the diagonal [tex]\overline{AH}[/tex] is therefore;

y - 2.5 = (-4/7)·(x - 2)

y = -4·x/7 + 8/7 + 2.5 = -4·x/7 + 51/14

y = -4·x/7 + 51/14 = -4·x/7 + 3 9/14

y = [tex]3\frac{9}{14}[/tex] - 4·x/7

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Answer:

To make x the subject of the formula, we can isolate x by subtracting 1 from both sides of the equation:

x + 1 = 4y

x + 1 - 1 = 4y - 1

x = 4y - 1

So x is equal to 4y minus 1.

Answer:

[tex]x = 4y - 1[/tex]

Step-by-step explanation:

Currently x is on the left side of the equal sign and is being added to 1. x has to be isolated and be by itself on one side of the equal sign in order to be made the subject of the formula. Therefore the 1 needs to be moved to the other side of the equal sign:

             [tex]x = 4y - 1[/tex]

x^2 - 2x + 1 is the required quadratic equation using the completing the square

Given the quadratic expression below

x^2 - 2x

We need to determine the constant that will make the expression a perfect square.

The constant will be the half of the square of coefficient of 'x'

Coefficient of 'x' = -2

Half of the coefficient of 'x' = -2/2 = -1

Square of the coefficient = (-2/2)^2

Square of the coefficient = 1

Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1

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Answer:

The equation that matches the number of zombies after 2 hours would be:

23 × 4^2 = 23 × 16 = 368

So after 2 hours, there would be 368 aggressive zombies.

Answer:

To solve this problem, we can use the formula for exponential growth:

V(t) = V0 * (1 + r)^t

where:

V(t) is the value of the equipment at time t

V0 is the initial value of the equipment ($15,000)

r is the annual growth rate (15.9% or 0.159)

t is the time in years

We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:

V(t) < 7500

Substituting the formula for V(t), we get:

V0 * (1 + r)^t < 7500

Substituting the given values, we get:

15000 * (1 + 0.159)^t < 7500

Simplifying and solving for t,

we get:(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

So the company's new equipment will be worth less than $7500 after about 2.64 years.

Step-by-step explanation:

The Pythagorean inequality is given below.

Statement of Pythagoras theorem:

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

                                        [tex]AC^{2}=AB^{2} +BC^{2}[/tex]

Let ABC be a triangle with the longest side opposite B

We can also write as follows:

If [tex]AC^{2} > AB^{2} +BC^{2} \\[/tex], then B is an obtuse angle.

If [tex]AC^{2} < AB^{2} +BC^{2} \\[/tex], then B is an acute angle.

If [tex]AC^{2}=AB^{2} +BC^{2}[/tex], then B is a right angle.

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Answer:

69

Step-by-step explanation:

if it bisects that mean both angles are equal which tells us we can just divide the whole angle by 2

angle BOA is 138

so when you divide 138 by 2 you get 69

hope it helped

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Answer:

96 stamps

Step-by-step explanation:

We know

Connor collected 80 stamps last year. This year he increased his collection by 20%.

80 stamps = 100%

100% + 20% = 120%

So, this year he collected 120% of the number of stamps from last year.

120% = 1.2

How many stamps are in his collection?

We take

80 times 1.2 = 96 stamps

So, there are 96 stamps in his collection.

Answer:

The slope between the two points would be 5.

Answer: The slope would be 5

Step-by-step explanation:

The point estimate of the population mean is 6

From the question, we have the following parameters that can be used in our computation:

Measurements: 5, 10, 2, 7, and 6.

Sample size = 5

The point estimate of the population mean is the sample size of the mean

Using the above as a guide, we have the following:

Sample mean  = Sum/Count

substitute the known values in the above equation, so, we have the following representation

Sample mean  = (5 + 10 + 2 + 7 + 6)/5

Evaluate

Sample mean = 6

Hence, the estimate is 6

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Answer:

Step-by-step explanation:

All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people

The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.

To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.

We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.

Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.

To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:

z = (p' - p) / √(p x (1-p)/n)

where n is the sample size.

Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).

Using p = 0.12 and n = 210, we have:

z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08

The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.

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The first order derivative of the given function is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

The given function is [tex]f(x)=\sqrt{x+\sqrt{x+\sqrt{x} } }[/tex].

The derivative using the chain and power rules is

f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex]

Therefore, the first order derivative is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].

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Answer:

12th term = -61

Step-by-step explanation:

Given sequence,

→ 5, -1, -7, ...

Now we have to,

→ Find the 12th term of the sequence.

The common difference is,

→ d = a2 - a1

→ d = -1 - 5

→ [ d = -6 ]

Formula we use,

→ an = a1 + (n - 1)d

Then value of 12th term will be,

→ an = a1 + (n - 1)d

→ a12 = 5 + (12 - 1) × (-6)

→ a12 = 5 + 11 × (-6)

→ a12 = 5 - 66

→ [ a12 = -61 ]

Therefore, the 12th term is -61.

By using the substitution method, the value of x is equal to -1.94 and the value of y is 2.71.

In order to solve the given system of linear equations, we would apply the substitution method. From the information provided in the question above, we have the following system of linear equations:

y = 5x - 7      .......equation 1.

3y - 2x = -12          .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

-3(5x - 7) - 2x = -12

-15x + 21 - 2x = -12

-17x = -12 - 21

17x = -33

x = -33/17 or -1.94

For the value of y, we have:

y = 5(-33/17) - 7

y = -165/17 - 7

y = 2.71

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The probability that in a given week in September, it will rain on at most two days is 0.12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The probability that it rains on any given day in September = 0.3.

P ( rains ) = 0.3

And,

The probability that it will not rain on any given day in September.

P (no rain) = 1 - 0.3

P(no rain) = 0.7

Now,

The probability is that in a given week in September, it will rain on at most two days.

= P (x ≤ 2)

= P(no rain) + P(rain) + P(rain)

= 0.7 + 0.3 + 0.3

= 0.12

Thus,

The probability that in a given week in September, it will rain on at most two days is 0.12.

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8. The center and radius of the circle given the following equation:

(x + 4)^2 + (y - 2) ^ 2 = 5 is

9. The  equation for the circle is

10. The length of arc AB is

Information given in the question

a circle whose equation is (x + 4)^2 + (y - 2) ^ 2 = 5

Equation of a circle is given as:

(x - h)² + (y - k)² = r²

Where

r = radius

h and k are coordinates of the center

x and y is the coordinate of point on the circumference

The equation of the circle is compared with the given equation and this shows that

Using the graph the centers are (-5, -2) and the radius is 3, this will give equation  (x + 5)² + (y + 2)² = 3²

If angle ACB = 60 deg and the radius is 12 cm,  length of arc

= 60 / 360 * 2 * π * 12

= 4π

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If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?

I believe that is what type of story you needed, if wrong let me know.

Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6

Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.

for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.

The answer after multiplying it is 6/24 or 1/4.  

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Answer

[tex] - 95.783[/tex]

Sure! To reduce the fraction 5 to its lowest terms, we need to find the greatest common factor of 5 and divide both the numerator and denominator by it.

The greatest common factor of 5 and 5 is 5, so we divide both the numerator and denominator by 5 to get:

5 / 5 = 1

So, 5 reduced to its lowest terms is 1.

To make it kid-friendly, you could explain it like this: "We can simplify the fraction 5 by dividing the top and bottom by the biggest number that they both share. In this case, 5 is the biggest number that 5 and 5 share, so we divide both 5 and 5 by 5 to get 1."