Assume that the two polygons are similiar, with the same orientation.
Write a proportion to determine the lengths of the sides labeled by variables.
(DO NOT SOLVE. You will solve the proportion in the next question.)

Answer:

Step-by-step explanation:

It can be helpful to understand what the square of a binomial looks like:

  (a +b)² = a² +2ab +b²

The middle term on the right is twice the product of the terms in the original binomial on the left.

Here, we want to use this relationship to find "b" when we're given "2ab". We recognize that "b" is half the coefficient of "a" in 2ab.

Choosing a value for b² to turn the sum (a² +2ab) into the trinomial (a² +2ab +b²) is called "completing the square" because that trinomial can now be written as the square (a+b)².

__

The standard form equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

In order to find the center and radius of the circle from the given equation, you're expected to rewrite the equation in this form. You do that by "completing the square" for both x-terms and y-terms.

__

Given

  x² +y² +6x -8y -25 = 0

Regrouping, we have ...

  (x² +6x) +(y² -8y) = 25

Adding the squares of half of 6 and half of -8, we can write this as ...

  (x² +6x +3²) +(y² -8y +(-4)²) = 25 +3² +(-4)²

And writing the trinomials as squares gives us ...

  (x +3)² +(y -4)² = 50 = (5√2)²

Comparing this to the standard form equation above, we see that ...

  (h, k) = (-3, 4)

  r = 5√2

__

The radius is 5√2.

The center is (-3, 4).

__

The attachment shows that the original equation draws a circle with center (-3, 4) and through points that are 5 units horizontally and vertically from the center, such as the point (2, -1). That is, the radius is 5√2.

Answer:

1 story=26, 2 stories=13 3 stories= 8.666666 4 stories= 6.5 5 stories=5.2

Step-by-step explanation:

Hi there! :)

Answer:

[tex]\huge\boxed{x = -4}[/tex]

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

Distribute the coefficient outside of the parenthesis:

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

Simplify:

4x - 12 = 8x + 4

Subtract 4x from both sides:

4x - 4x - 12 = 8x - 4x + 4

-12 = 4x + 4

Subtract 4 from both sides:

-12 -4 = 4x + 4 - 4

-16 = 4x

Divide both sides by 4:

-16/4 = 4x/4

x = -4.

Answer:

x=-4

Step-by-step explanation:

or 4*×-4*3=4*2x+4*1

or 4x-12=8x+4

or 4x-8x=4+12

or -4x=16

or x=16/-4

or =x=-4

The 8 is a, the 3 is b and -45 is c

Plug them into the quadratic formula

Answer:

It means [tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex] also converges.

Step-by-step explanation:

The actual Series is::

[tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex]

The method we are going to use is comparison method:

According to comparison method, we have:

[tex]\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n[/tex]

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

[tex]=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}[/tex]

[tex]\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}[/tex]

Now:

[tex]\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}[/tex]

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

[tex]\sum_{n=1}^{inf}\frac{1}{n^p}[/tex]

if p>1 then series converges. In oue case we have:

[tex]\sum_{n=1}^{inf}b_n=\frac{1}{n^4}[/tex]

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means [tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex] also converges.

Answer:

320

Step-by-step explanation:

There are 320 tens in 3,200.

320 x 10 = 3200

Answer:

320

Step-by-step explanation:

3200/10=320

Answer:

5 apples to 4 bananas

Step-by-step explanation:

Answer:

5:4

Step-by-step explanation:

A ratio divides the number with a colon. And since there are 5 apples to 4 bananas, the ratio of apples to bananas would be 5:4 (or another way to write it is 5 to 4)

Answer:100%

Step-by-step explanation: Think about it for a second S-ea-n w-a-nts t-o e-a-t a-t o-liv-e g-a-rd-e-n their are vowels in every word

Answer:12/27

Step-by-step explanation:there are 12 vowels in the phrase so the probability is 12:27 or 4:9 (you can write these as fractions too, numerators are on the left)

Answer:

[tex]\Large \boxed{\mathrm{\bold{C}}}[/tex]

Step-by-step explanation:

[tex]\sf \displaystyle sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

The side opposite to [tex]\angle C[/tex] is h.

The hypotenuse of the smaller right triangle is a.

[tex]\sf \displaystyle sin(C)=\frac{h}{a}[/tex]

Answer:

sinC = [tex]\frac{h}{a}[/tex]

Step-by-step explanation:

Since the red line is an altitude then the triangles are right, thus

sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{a}[/tex]

This question is incomplete, the complete question is;

A stock price S is governed by dS = aSdt + bSdz

where z is a standardized Wiener process. Find the process that governs G(t) = S^1/2(t)

Answer:

G = S^1/2

Step-by-step explanation:

Solving the Equation

dS = aSdt + bSdz

First we Take S common from Right hand Side

dS = S(a dt + b dz)

Then we also take S Left Hand Side(LHS) from RHS

dS/S = a dt + b dz

So d = a dt + b dz

now we Take d Common from RHS

d = d(a t + b z)

So

d/d = a t + b z

1 = a t + b z

So, t = (1-b z) / a

Now  substitute value of t in equation G(t) = S^1/2(t)

we have

G{(1- b z)/a} = S^1/2 {(1- b z)/a}

(1- b z)/a) from both sides cancels out each other

So we have  G = S^1/2

Answer:

5.1 units

Step-by-step explanation:

A=b x h divide by 2

20.4=4b

b=5.1 units

Answer:

 C.No, because each lime will cost a bit more than 30¢, so 4 limes will cost a bit more than $1.20.Step-by-step explanation:

The unit price of the 8 limes is $0.25 per lime.

The given expression:

The selling price for 8 limes = $2.00

To find:

The unit price of the lime is calculated by dividing the total selling price by the total number of limes purchased.

[tex]unit \ price = \frac{total \ amount \ paid \ for \ 8 \ limes }{8 \ limes } \\\\unit \ price =\frac{\$ \ 2}{8 \ limes } \\\\unit \ price = (\frac{1}{4} ) \frac{\$}{lime} \\\\unit \ price = \$0.25 \ per \ lime[/tex]

Thus, the unit price of the 8 limes is $0.25 per lime.

Learn more here: https://brainly.com/question/12418981

Answer:

35 1/4

Step-by-step explanation:

Answer:

B for edge

Step-by-step explanation:

Answer:

Option (B) will be the correct option.

Step-by-step explanation:

Statement states "five more than the product of seven and a number t is 10."

Split this statement into parts.

1). Product of 7 and a number 't' = 7 × t

2). 5 more than the product of 7 and a number 't' = 7t + 5

3). Five more than the product of 7 and a number t is equal to 10 ⇒ 7t + 5 = 10

Therefore, Option (B) will be the correct option.

Answer:

Step-by-step explanation:

A∩B=[-54,-42]∪[-25,70]

Answer:

See below

Step-by-step explanation:

We can simply use a graphing calculator to carry it out.

See the attached file for more explanation!

Another way is that we can take the values of x as 1,2 and 3 and so on and put it in the equation to get the value of y. We have some coordinates now so we'll plot them in the graph to get the line of y = 2x+5.

Step-by-step explanation:

Hope this helps........

Answer:

8.7+5.22=13.92

Hope it helps you...

Answer:

13.92

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

c² = a² + b²

where

c is the hypotenuse

From the question x is the hypotenuse

So we have

We have the final answer as

Hope this helps you

Answer:

B.) (-202)+(-12)

Step-by-step explanation:

The undersea level is negative then going under again will produce a completely negative answer.

Answer:

0.1354

Step-by-step explanation:

Relevant data provided as per the requirement is shown below:-

Female probability of age between 55 to 69 = 2058

Male probability of age between 55 to 69 = 4571

According to the given situation, the calculation of probability is shown below:-

[tex]= \frac{Female\ from\ 55\ to\ 69 }{Total\ female}[/tex]

where,

Total female is

= 143 + 2333 + 4027 + 5178 + 2058 + 1459

= 15,198

And, the female is 2058

So, the probability is

[tex]= \frac{2058}{15,198}[/tex]

= 0.1354

Therefore for computing the probability of female that lies between 55 to 69 we simply applied the above formula.

Answer:

1

  The  correct option is  C

2

 The  correct option is C

3

The  correct option is A

4

The  correct option is B

Step-by-step explanation:

From the question we are told that

    The  population mean is  [tex]\mu = 100[/tex]

     The  standard deviation is  [tex]\sigma = 15[/tex]

     The  sample size is  [tex]n = 36[/tex]

     The  sample mean is  [tex]\= x = 105.1[/tex]

Generally

    The  null hypothesis is  [tex]H_o: \mu = 100 \ hours[/tex]

     The  alternative hypothesis is  [tex]H_a : \mu \ne 100\ hours[/tex]

Given that the null hypothesis is  true then the  distribution of sample means  [tex]\mu_{\= x }[/tex], from a sample size of 36 is  mathematically represented as

        [tex]\mu_{\= x } = \mu[/tex]

=>     [tex]\mu_{\= x } = 100[/tex]

According to the Central Limit Theorem the test stated in the question is  approximately normally distributed if the sample size is sufficiently large[tex](n > 30 )[/tex] so given that the sample size is  large  n =  36

Then the test is normally distributed and hence the standard deviation is 15

Generally the standard error of mean is mathematically represented as

     [tex]\sigma_{\= x } = \frac{ \sigma }{\sqrt{n} }[/tex]

=>  [tex]\sigma_{\= x } = \frac{15}{\sqrt{36} }[/tex]

=>  [tex]\sigma_{\= x } = 2.5[/tex]

Generally  the approximate probability of observing a sample mean of 105.1 or more is mathematically represented as

        [tex]P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(\frac{\= X - \mu }{\sigma_{\= x }} <\frac{105.1 - 100}{2.5} )[/tex]

=>    [tex]P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(Z<2.04 )[/tex]

From the z-table (reference calculator dot net )

             [tex]P(Z<2.04 ) = 0.97932[/tex]

So

  [tex]P( \= X \ge 105.1 )= 1 - P(\= X < 105.1) = 1- 0.97932[/tex]

 [tex]P( \= X \ge 105.1 ) =0.02[/tex]    

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

Explanation:

Apply the distance formula.

[tex]d = \sqrt{ (x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{ (-1-1)^2+(4-(-1))^2}\\\\d = \sqrt{ (-1-1)^2+(4+1)^2}\\\\d = \sqrt{ (-2)^2+(5)^2}\\\\d = \sqrt{ 4+25}\\\\d = \sqrt{ 29}\\\\d \approx 5.38516\\\\d \approx 5.39\\\\[/tex]

You could also use the pythagorean theorem which is what the distance formula is based off of.

Answer:

26

Step-by-step explanation:

2x + 18

2(4) + 18

8 + 18

26

Answer:

26

Step-by-step explanation:

We just substitute the value of X and find the answer

Answer:

[tex]w=2[/tex]

Step-by-step explanation:

So we have the equation:

[tex]9w-4=14[/tex]

Add 4 to both sides. The left cancels:

[tex](9w-4)+4=(14)+4\\9w=18[/tex]

Divide both sides by 9.The left cancels:

[tex](9w)/9=(18)/9\\w=2[/tex]

So, the value of w is 2.

And we're done :)

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{1.7 \: \%}}}}}[/tex]

Step-by-step explanation:

Given,

Interest ( I ) = $ 17

Principal ( P ) = $ 500

Time ( T ) = 2 years

Rate ( R ) = ?

Finding the simple Interest rate :

[tex] \boxed{ \bold{ \sf{rate = \frac{interest \times 100}{principal \times time}}}} [/tex]

[tex] \dashrightarrow{ \sf{rate = \frac{17 \times 100}{500 \times 2} }}[/tex]

[tex] \dashrightarrow{ \sf{rate = \frac{1700}{1000} }}[/tex]

[tex] \dashrightarrow{ \sf{ rate = 1.7 \: \%}}[/tex]

Hope I helped!

Best regards! :D

Answer:

x=14 z=72

Step-by-step explanation:

(8x-40)+(12x-60)=180

20x-100=180

20x=280

x=14

(12x-60)+z=180

(168-60)+z=180

108+z=180

z=72

Answer:

The confidence interval = (7.8 , 8.0)

Step-by-step explanation:

Confidence Interval formula =

Mean ± z × Standard deviation/√n

Mean = 7.9

Standard deviation = 0.9

n = number of samples = 164

z = z score of an 80% confidence interval = 1.282

Confidence Interval = 7.9 ± 1.282 × 0.9/√164

= 7.9 ± 0.0900966432

Confidence Interval

= 7.9 - 0.0900966432

= 7.8099033568

Approximately to 1 decimal place = 7.8

7.9 + 0.0900966432

= 7.9900966432

Approximately to 1 decimal place = 8.0

Therefore, the confidence interval = (7.8 , 8.0)

Answer:

the answer is d

Step-by-step explanation:

Just multiply and divide

What is probability?

the quality or state of being probable; the extent to which something is likely to happen or be the case

We have,

Surveyed student = 105

Students would prefer to going to a water park= 3/5

According to question

students who expected to prefer the water park

                 = 105 × 3/5

                 = 21×5×3/5

                 = 21×3

                 = 63

Hence, students who expected to prefer the water park is 63

To learn more about probability from here

https://brainly.in/question/20635873

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Answer:

w = -100

Step-by-step explanation:

Step 1: Write out equation

166 = -w + 66

Step 2: Subtract 66 on both sides

100 = -w

Step 3: Divide both sides by -1

w = -100

Answer:

w=-100

Step-by-step explanation:

We are given the equation:

166= -w +66

To solve for x, we must get x by itself on one side of the equation.

66 is being added to -w. The inverse of addition is subtraction. Subtract 66 from both sides of the equation.

166-66= -w+66-66

166-66= -w

100= -w

-1 and w are being multiplied. The invers of multiplication is division. Divide both sides of the equation by -1.

100/-1= -w/-1

100/-1=w

-100=w

Let's check our solution. Plug -100 in for w.

166= -w+66

166= -(-100)+66

166=100+66

166=166

The statement above is true, so we know our solution is correct.

The solution to 166= -w+66 is w= -100