Find the area of rhombus JKLM given the coordinates of the vertices. Round to the nearest tenth if necessary.

J(-2, -4), K(2, 2), L(6, -4), M(2, -10)

Answer:

fully factored form = 3(x-4)(x+8)

Step-by-step explanation:

first you factor 3 out

3(x^2+4x-32)

then factor it

3(x-4)(x+8)

Answer:

3(x-4)(x+8) This is the answer :)

Step-by-step explanation:

3x^2+12x - 96

3(x^2+4x-32)

3(x^2+4x--32)

3(x^2+8x-4x-32)

3(x^2+8x-4x-32)

3(x(x+8)-4(x+8))

3(x(x+8)-4(x+8))

3(x-4)(x+8)

3(x=4)(x+8)

Answer:

[tex]\frac{x^2}{9}+\frac{y^2}{4}=1[/tex]

Step-by-step explanation:

So an ellipse can be expressed in two different but very similar forms:

Horizontal Major Axis:

   [tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Vertical Major Axis:
   [tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]

In both equations the length of the major axis is "2a" and the length of the minor axis is "2b"

In the equation you provided, the major axis is horizontal, and the minor axis is vertical.

So looking at the horizontal length, you can see that it's 6, and since this ellipse has a horizontal major axis, that means 2a=6, which means a=3

Looking at the vertical length, you can see that it's 4, and since the ellipse has a vertical minor axis, that means 2b=4, which means b=2

The last thing to note is that the center of an ellipse is (h, k) in the equation, and since here the center is (0, 0) it's (x-0)^2 and (y-0)^2 in the denominator which is just x^2 and y^2

So let's plug in the values into the equation:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

(h, k) = (0, 0)

a = 3

b = 2

[tex]\frac{x^2}{3^2}+\frac{y^2}{2^2}=1\\\\\frac{x^2}{9}+\frac{y^2}{4}=1[/tex]

Here we go ~

The given figure is of a horizontal ellipse with :

so, a = 3

hence, b = 2

And as it's shown in the figure, the ellipse has its centre at origin, so we can write it's equation as :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{b {}^{2} } = 1[/tex]

[ now, plug in the values ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {3}^{2} } + \cfrac{ {y}^{2} }{2 {}^{2} } = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {9}^{} } + \cfrac{ {y}^{2} }{4 {}^{} } = 1[/tex]

That's all, ask me if you have any questions ~

The required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.

Given that,
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.

Number of days =  1       2     3      4      5       6            Total = 6
                              1.72  1.8    1.86 1.88  1.74   1.86                  

The average of the values is the ratio of the total sum of values to the number of values.

Since the mean of the heights of the tides,
= sum of heights / number of heights observation
=  (1.7 + 1.8 + 1.86 + 1.88 + 1.74 + 1.86)/6
= 10.86/6
= 1.81 meters

Thus, the required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.

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The speed of the plane will be 875km/h and the speed of the wind will be 125km/h.

It should be noted that the speed is calculated as:

= Distance/Time

Based on the information, the DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr.

Therefore, (v + w) = 3000/3

v + w = 1000 .... I

(v - w) = 3000/4

v - w = 750 .... ii

We'll then add both equations together. Therefore, the speed of the plane will be 875km/h and the speed of the wind will be 125km/h.

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Answer:

9/25 or -1/11

Step-by-step explanation:

2 outcome

1; 7x-5=18x-4

2;-(7x-5)=18-4

The conclusion regarding the publisher's claim regarding the hypothesis is that have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.

The null hypothesis is a statistical theory that suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

Since we reject the null hypothesis , we have sufficient evidence to support the claim. In this case, we have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.

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Complete question:

A newsletter publisher believes that less than 30% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?

The y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4

The y-intercept of a function is the point where the value of x is zero. Given the function below;

4x-9y=36

when the value of x is zero, hence;

4(0) - 9y = 36

Simplify to have:

0 - 9y = 36

-9y = 36

Divide both sides by -9 to have:

-9y/-9 = 36/-9

y = -4

Hence the y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4

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The volume of the solids are 240 cubic yards and 125.6 cubic cm

The complete question is added as an attachment

Solid 1

The shape is a rectangular prism.

The volume of a rectangular prism is

Volume = Length * Width * Height

So, we have

Volume = 8 yd * 5 yd * 6 yd

Evaluate

Volume = 240 cubic yards

Hence, the volume of the solid is 240 cubic yards

Solid 2

The shape is a cylinder.

The volume of a rectangular prism is

Volume = πr²h

So, we have

Volume = 3.14 * 2^2 * 10

Evaluate

Volume = 125.6 cubic cm

Hence, the volume of the solid is 125.6 cubic cm

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Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.

In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:

c = 17/0.83 = $20.48.

In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:

c = 288/18 = $16.

16 < 20.48, hence the souvenir would be less expensive in Egypt.

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The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

The function is given as:

f(x)=−2x3+x2−4x+1 is divided by x+3.

Set the divisor to 0

x + 3 = 0

Solve for x

x = -3

Calculate f(-3)

f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1

Evaluate the expression

f(-3)= 76

Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

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a. The value of cos2θ = -119/169

b. The value of cosθ = -5/13

The question involves trigonometric identities

Trigonometric identities show the relationship between trigonometric ratios.

Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.

Using trigonometric identity

cos2θ = 1 - 2sin²θ

Substituting sinθ = 12/13  into the equation, we have

cos2θ = 1 - 2sin²θ

cos2θ = 1 - 2(12/13)²

cos2θ = 1 - 2(144/169)

cos2θ = 1 - 288/169

cos2θ = (169 - 288)/169

cos2θ = -119/169

So, the value of cos2θ = -119/169

Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.

Using trigonometric identity

cosθ = √(1 - sin²θ)

Substituting sinθ = 12/13  into the equation, we have

cosθ = √(1 - sin²θ)

cosθ = √[1 - (12/13)²]

cosθ = √[1 - (144/169)]

cosθ = ±√(169 - 144)/169

cosθ = ±√25/169

cosθ = ±5/13

θ is the quadrant II, it means that 90° ≤ θ ≤180° it means that cosθ is negative.

So, cosθ = -5/13

So, the value of cosθ = -5/13

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Part 1)  [tex]\displaystyle \frac{1}{n^2}[/tex] or 1/(n^2) goes in the box.

Part 2)  The series converges

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

Work Shown:

[tex]\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\[/tex]

[tex]\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\[/tex]

Because L is finite and positive, i.e. [tex]0 < L < \infty[/tex], this means that the original series given and the series  

[tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/tex]  

either converge together or diverge together due to the Limit Comparison Test.

But the simpler series is known to converge (p-series test).

Therefore, the original series converges as well.

The two series likely don't converge to the same value, but they both converge nonetheless.

Answer:

If the question asked mixed fraction:

7/3 = 2 1/3

4/2 = 2

Step-by-step explanation:

I converted it to mixed fraction because it is already improper fraction.

Answer:

The area of windowpane is answer.

Answer:

The area of the window pane

Step-by-step explanation:

The area of an object is the width x length of said object.

Ex: A  4 x 4 sized square has an area of 16 ( 4 x 4 = 4 by 4)

P.S. The area of Andrea´s windowpane is 648.

Answer:

below

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think you are trying to use synthetic division for

[tex]x^{4} -2x^{3} -2x^{2} +3x-5[/tex] divided by x-3

First  

x -3 = 0 , make it equal to 0 and add 3 to both sides

x = 3

Then we write all the coefficients and continue with

a pattern of multiply by 3 and add to the next coefficient.

See attachment.

If we compare the given values then we can find that the database B is more likely to have smaller standard deviation.

Given that the values in database A are 0 from 100 and has mean of 50 and Database B has entries from 49 to 51 and also has mean of 50.

We are required to find the database whose standard deviation is lower.

Standard deviation measures the variation of values. It is calculated after finding mean. The square of a standard deviation is known as variance.

Database A has values from 0 to 100 and has mean of 50. Because the values are somewhat very larger than 50 and in database B has values from 49 to 51,there are more chances that the standard deviation of database B will have smaller value than from standard deviation of database A.

Hence if we compare the given values then we can find that the database B is more likely to have smaller standard deviation.

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Answer:

  4.346%

Step-by-step explanation:

The points and origination fee are assumed to be capitalized, so the loan payment amount is based on the total of the original loan amount and those fees. The APR is calculated as the rate that would be charged on the original loan value to produce that payment.

The loaned amount is the sum of the original loan value and the added points.

  P = $513,000×(1 +1.4% +0.65%) = $523,516.50

The monthly payment on this amount is given by the amortization formula ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where r=0.04175, the annual interest rate, t=30, the period in years

  A = $523,516.50(0.04175/12)/(1 -(1 +0.04175/12)^-360)) ≈ $2552.45

There is no formula for calculating the APR. It must be developed iteratively or graphically. The attached calculator images show a couple of different ways the value can be found.

The payment of $2552.45 on a loan value of $513,000 represents an APR of 4.346%.

The new curriculum significantly affects the earning potential.

According to the question, Eight kids were chosen at random to take part in a brand-new educational program that emphasizes both academics and mental health education between middle school and high school. The average annual income is $29432. The standard deviation is unknown.

The probability level is given to be 5%.

When the p-value is less than or equal to your significance level, reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data.

A probability level of 0.05 means that the new curriculum significantly affects the earning potential.

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Answer:

assume the formula is true for n is equal to k prove that result is true for n is equal to k + 1 hence result proves since the thorum is true for n is equal to 1 and n k + 1 is unit through a and

The number of $1, $5 and $10 are 49, 44 and 22 respectively.

There are 3 denominations of bills in a wallet: $1, $5, and $10.

There are 5 fewer $5-bills than $1-bills.

let

x = number of $1 bills

Hence,

number of $5 bills = x - 5

There are half as many $10-bills as $5-bills.

number of $10 bills = 1 / 2 (x - 5)

Therefore,

x + x - 5 + 1 / 2 (x - 5) = 115

2x - 5  + 1 / 2 x - 5 / 2 = 115

2x + 1 / 2 x - 5 - 5 / 2 = 115

5 / 2 x  - 7.5 = 115

2.5x  = 115 + 7.5

x = 122.5 / 2.5

x = 49

Number of $1 bills = 49

Number of $5 bills = 49 - 5 = 44

Number of $10 bills = 1 / 2 (49 - 5) = 22

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Answer:

Step-by-step explanation:

(1). A = π r²

A = 4 π

Area of shaded region is [tex]\frac{4\pi *260}{360}[/tex] = [tex]\frac{26}{9} \pi[/tex] or [tex]\frac{26\pi }{9}[/tex]

(2). C = 4 π

In this case, the length of the bigger arc and the area of shaded region happen to be the same.

The length of the arc ADB is  [tex]\frac{26}{9} \pi[/tex] or [tex]\frac{26\pi }{9}[/tex]

The dosage needed for this in an  order for morphine sulfate 1/4 gr IM stat is 1.5 ml.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

One grain =  60mg, hence:

1/4 gr = 1/4 gr * 60 mg per gr = 15 mg

Hence, for 10 mg per ml:

Dosage = 15 mg /  10 mg per ml = 1.5 ml

The dosage needed for this in an  order for morphine sulfate 1/4 gr IM stat is 1.5 ml.

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Using translation concepts, it is found that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The translation y -> y + k represents:

Hence:

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The fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively. option D

9√4.000

= 4.000/9

= 0.444

Approximately,

= 0.4

Fraction

This is a ratio of two numbers, the numerator and the denominator, usually written one above the other and separated by a horizontal bar.

Decimal

This is a number expressed in the decimal system (base 10).

Therefore, the fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively.

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a. By replacing [tex]x[/tex] with [tex]-x^2[/tex] in the power series, we get

[tex]\displaystyle \frac1{1+x^2} = \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n}[/tex]

Integrate both sides to recover [tex]\arctan(x)[/tex] on the left.

[tex]\displaystyle \int \frac{dx}{1+x^2} = \int \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n} \, dx[/tex]

[tex]\displaystyle \arctan(x) = C + \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

By letting [tex]x=0[/tex] on both sides, we find [tex]C=0[/tex], so that

[tex]\displaystyle \arctan(x) = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

Then dividing both sides by [tex]x[/tex] gives

[tex]\displaystyle \boxed{\frac{\arctan(x)}x = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n} \, dx}[/tex]

b. Let [tex]x=\frac1{\sqrt3}[/tex]. Then

[tex]\displaystyle \frac{\arctan\left(\frac1{\sqrt3}\right)}{\frac1{\sqrt3}} = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} \left(\dfrac1\sqrt3\right)^{2n}[/tex]

[tex]\displaystyle \sqrt3 \arctan\left(\frac1{\sqrt3}\right) = \sum_{n=0}^\infty \frac1{2n+1} \left(-\frac13\right)^n[/tex]

Taking the first few terms from the infinite series, we can approximate

[tex]n=0 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1[/tex]

[tex]0\le n\le1 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1+\dfrac13\left(-\dfrac13\right) = \dfrac89[/tex]

which together suggest the value we want is bounded between 8/9 and 9/9 = 1, hence [tex]\boxed{p=8}[/tex].

Since the series is alternating and converges on [tex]-1<x<0\cup0<x<1[/tex],

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^0 a_n \right| < |a_1| = \left|\frac13 \left(-\frac13\right)^1\right| = \frac19[/tex]

and

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^1 a_n \right| < |a_2| = \left|\frac15 \left(-\frac13\right)^2\right| = \frac1{45}[/tex]

which tells us the first approximation is off by at most 1/9 from the actual value of [tex]\frac\pi{2\sqrt3}[/tex], whereas the second approximation is off by at most 1/45 from the actual value. In other words, the second approximation is closer, so [tex]\frac\pi{2\sqrt3}[/tex] is closer to [tex]\frac p9[/tex] :

[tex]\dfrac89 \approx 0.8889[/tex]

[tex]\dfrac{\pi}{2\sqrt3}\approx0.9069[/tex]

[tex]\dfrac99 = 1[/tex]

Answer:

8

Step-by-step explanation:

because all the number is over 1

The two quadrilateral with the listed properties are kite and rhombus respectively.

Thus, the two quadrilateral with the listed properties are kite and rhombus respectively.

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Answer:

your welcome

Step-by-step explanation:

Answer:x2−7x−8=0

Tap to view steps...

Step-by-step explanation:

Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.

Exponential Function can be used for increase rate and also for decay rate.  The difference between the two are the plus and minus signs. To put it in another perspective, If Y = P(M)³

If M is less than one, that means it is decaying or decreasing. And if M is greater than one, that means it is increasing.

Given that Some banks charge a fee on savings accounts that are left inactive for an extended period of time. And the equation

y = 5000(0.98)^x  represents the value, y, of one account that was left inactive for a period of x years.

According to the equation, to know if the balance in this account is increasing or decreasing, we will analyze the value 0.98.

Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.

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