XY and WZ are straight line segments. The angle marked d = 60°. Find the values of a, b and c. Explain the reasons for your answers in the comment box. Please help​

The first eight terms of the sequence are 27, 27, 39, 87, 117.378, 147.755, 178.132 and 208.509.

By (1) we have that [tex]a = 27 - A[/tex], and we simplify the system of equations as follows:

[tex](27-A)+d + A\cdot r = 27[/tex]

[tex]d + (r-1)\cdot A = 0[/tex] (2b)

[tex](27-A) +2\cdot d + A\cdot r^{2} = 39[/tex]

[tex]2\cdot d + (r^{2}-1)\cdot A = 12[/tex] (3b)

[tex](27-A) +3\cdot d + A\cdot r^{3} = 87[/tex]

[tex]3\cdot d + (r^{3}-1)\cdot A = 60[/tex] (4b)

By (2b), we simplify the system of equations once again:

[tex]2\cdot (1-r)\cdot A+(r^{2}-1)\cdot A = 12[/tex]

[tex][2\cdot (1-r)+(r^{2}-1)]\cdot A = 12[/tex] (3c)

[tex]3\cdot (1-r)\cdot A + (r^{3}-1)\cdot A = 60[/tex]

[tex][3\cdot (1-r) + (r^{3}-1)]\cdot A = 60[/tex] (4c)

And by equalising (3c) and (4c) we have an expression in terms of [tex]r[/tex]:

[tex]\frac{12}{[2\cdot (1-r)+(r^{2}-1)]} = \frac{60}{[3\cdot (1-r)+(r^{3}-1)]}[/tex]

[tex]12\cdot [3\cdot (1-r)+(r^{3}-1)] = 60\cdot [2\cdot (1-r) + (r^{2}-1)][/tex]

[tex]36\cdot (1-r) +12\cdot (r^{3}-1) = 120\cdot (1-r)+60\cdot (r^{2}-1)[/tex]

[tex]84\cdot (1-r) +60\cdot (r^{2}-1)-12\cdot (r^{3}-1) = 0[/tex]

[tex]84-84\cdot r +60\cdot r^{2}-60-12\cdot r^{3}-12 = 0[/tex]

[tex]-12\cdot r^{3}+60\cdot r^{2}-84\cdot r +2 = 0[/tex] (5)

The roots of this third order polynomial are: [tex]r_{1} \approx 0.0242[/tex], [tex]r_{2} = 2.488 + i\,0.831[/tex] and [tex]r_{3} \approx 2.488-i\,0.831[/tex]. Since [tex]r[/tex] must be a real number, then [tex]r \approx 0.0242[/tex].

By (4c) we have the value of [tex]A[/tex]:

[tex]A = \frac{60}{3\cdot (1-0.0242)+(0.0242^{3}-1)}[/tex]

[tex]A \approx 31.130[/tex]

By (2b) we find the value of [tex]d[/tex]:

[tex]d = (1-0.0242)\cdot 31.130[/tex]

[tex]d = 30.377[/tex]

And by (1) we find the value of [tex]a[/tex]:

[tex]a = 27-A[/tex]

[tex]a = 27-31.130[/tex]

[tex]a = -4.13[/tex]

The first eight terms are calculated below:

[tex]n_{1} = 27[/tex]

[tex]n_{2} = 27[/tex]

[tex]n_{3} = 39[/tex]

[tex]n_{4} = 87[/tex]

[tex]n_{5} = [-4.13 + 4\cdot (30.377)]+(31.130)\cdot (0.0242)^{4} = 117.378[/tex]

[tex]n_{6} = [-4.13+5\cdot (30.377)+(31.130)\cdot (0.0242)^{5}] = 147.755[/tex]

[tex]n_{7} = [-4.13+6\cdot (30.377)\cdot (31.130)\cdot (0.0242)^{6}] = 178.132[/tex]

[tex]n_{8} = [-4.13+7\cdot (30.377)\cdot (31.130)\cdot (0.0242)^{7}] = 208.509[/tex]

The first eight terms of the sequence are 27, 27, 39, 87, 117.378, 147.755, 178.132 and 208.509. [tex]\blacksquare[/tex]

The statement present typing mistakes and is poorly formatted. Correct form is shown below:

The first four terms of an arithmetic sequence are: [tex]a[/tex], [tex]a + d[/tex], [tex]a + 2\cdot d[/tex], [tex]a + 3d[/tex]. The first four terms of another sequence are: [tex]A[/tex], [tex]A\cdot r[/tex], [tex]A\cdot r^{2}[/tex], [tex]A\cdot r^{3}[/tex]. The eight terms satisfy:

[tex]a + A = 27[/tex] (1)

[tex](a+d)+A\cdot r = 27[/tex] (2)

[tex](a + 2\cdot d) + A\cdot r^{2} = 39[/tex] (3)

[tex](a + 3\cdot d) + A\cdot r^{3} = 87[/tex] (4)

By using the substitution [tex]a = 27-A[/tex], or otherwise, find the all eight terms.

To learn more on sequences, we kindly invite to check this verified question: https://brainly.com/question/21961097

Answer:

4z

Step-by-step explanation:

Simply add z + z + z + z , which is equal to 4 x z

Answer:

(C) 122/153

Step-by-step explanation:

Let x be the required fraction.

(-4/9) + x  =  6/17

Add both sides by 4/9

x  =  (6/17) + (4/9)  

 =  (54 + 68)/153

 =  122/153

Answer:

Step-by-step explanation:

Let's create an equation to solve for the variable x. Then, isolate the x by adding 4/9 to both sides. Lastly, simplify and solve for the x variable.

Looking at all the options, Option C is matching with our result.

Hence, Option C is correct.

Answer:

11.75

Step-by-step explanation:

141/12=11.75 simply math dudette

Answer:

4√10xy/32y is the answer. (I think)

Answer:

[tex] \sqrt{2} \: \: \: \: \: \: \frac{ \pi}{2} \: \: \: \: are \: \: \: \: the \: \: \: \: answers[/tex]

Answer:

I believe the answer is 8

Step-by-step explanation:

5*4=20

4*3=12

20-12=8

Answer:

AB would be 9 and BC would be 7  

Step-by-step explanation:

Answer:

Jake holds 2store credit cards a bank credit card a car loan and a mortgage

Answer:

66,190,000 = 66.19 million

round to 66.2 million

Step-by-step explanation:

Answer:the answer is D

Step-by-step explanation:

it means to that they stay calmly to things

Given what we know, we can say that it is possible for 9 out of 10 students to score above average, but it is not possible for all 10 to score above average.

In order to calculate the average score of the students, we must use addition.

We have to add all of the scores, in this case, 10 scores, and then divide by the number of scores.

One example of 9 out of 10 students scoring above average would be:

[tex]1 + 9 +9+9+9+9+9+9+9+9 = 82[/tex]

[tex]82/10 scores = 8.2[/tex]

This would leave us with an average score of 8.2 and 9 out of 10 students that have scored higher.

Given the way in which we calculate average scores, it is impossible for all 10 students to score above average since even if all 10 students get a perfect score, that would then become the average.

To learn more about average calculations visit:

https://brainly.com/question/18554478?referrer=searchResults

Answer:

21 1/3 ft.

Step-by-step explanation:

5 1/3= original height

4 times the growth

5 1/3 times 4=

Answer: 21 1/3 ft. tall

Answer:

1 is to 2 is the answer. U.got that

Answer:

Anything 5 and above.

Step-by-step explanation:

The sign that is shown is the less than or equal to sign, which means whatever is added to seven, the sum would have to be 12 or above? or it wouldn't work.

Check the picture below.

what if x = 2?

[tex]V=(2)[10-2(2)][12-2(2)]\implies V=2(6)(8)\implies V=96[/tex]

Answer:

11.5

Step-by-step explanation:

basically just take 25% off of 15!! hope this helps!!

Answer:

[tex]{x}^{2} - 14x - 49 = 0[/tex]

[tex] {x}^{2} - (7 + 7)x - 49 = 0[/tex]

[tex] {x}^{2} - 7x - 7x - 49 = 0[/tex]

[tex]x(x - 7) + 7(x - 7) = 0[/tex]

[tex](x - 7)(x + 7) = 0[/tex]

NOW,

x-7=0

or,x=7

And,

x+7=0

or,x= -7

THEREFORE, x= 7, -7

hope it helps you,

make me brainliest plz

Answer:

the value of x= plus minus 7

hope it helps you

Answer:

Step-by-step explanation:

The actual length is 45 1/2 and the estimate is within 4% of error range.

The lower range is:

The higher range is:

So the range is between:

Answer:

E. 1/6

Step-by-step explanation:

There are a total of 6 outcomes on this cube, so the denominator shall be 6. We are looking for the probability of rolling a 6, and on the cube, there's only a single 6. The numerator must be 1.

Therefore, the answer is E. 1/6.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

x = -2

Step-by-step explanation:

you need to use the distribution property first!

4(x + 5) = 12 ------> 4x + 20 = 12

now you need to subtract 20 from both sides so that you can isolate x

4x = -8

finally, divide -8 by four so that x is alone, meaning solve to find x!

x = -2

Hey there!

4(x + 5) = 12

4(x) + 4(5) = 12

4x + 20 = 12

SUBTRACT 20 to BOTH SIDES

4x + 20 - 20 = 12 - 20

CANCEL out: 20 - 20 because it gives you 1

KEEP: 12 - 20 because it help solve for the x-value

NEW EQUATION: 4x = 12 - 20

SIMPLIFY IT!

4x = -8

DIVIDE 4 to BOTH SIDES

4x/4 = -8/4

CANCEL out: 4/4 because it gives you 1

KEEP: -8/4 because it gives the x-value

NEW EQUATION: x = -2

Therefore, your answer is s x = -2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The radius of a circle with the same vertex as a center is 12 units

To get the radius of the circle, we need to determine the diameter of the circle first:

According to SOH CAH TOA:

[tex]sin\theta = \frac{opp}{hyp} \\sin60 = \frac{12\sqrt{3}}{hyp} \\hyp =\frac{12\sqrt{3}}{sin60} \\hyp =\frac{2\times12\sqrt{3}}{\sqrt3}} \\hyp = 24 = diameter[/tex]

Determine the radius of the circle

Radius = dismeter/2

Radius = 24/2

Radius = 12

Hence the radius of a circle with the same vertex as a center is 12 units

Learn more on radius of a circle here: https://brainly.com/question/24375372

Answer:

14,200,000

Step-by-step explanation:

Answer:

There are 1,365 souvenir paperweights that need to be packed in boxes. Each box will hold 14 paperweights. How many boxes will be needed?

boxes will be needed to hold all the souvenir paperweights.

Step-by-step explanation:

Answer:

2x+y=6

Step-by-step explanation:

The standard form of such an equation is Ax + By + C = 0 or Ax + By = C. When you rearrange this equation to get y by itself on the left side, it takes the form y = mx +b. This is called slope-intercept form because m is equal to the slope of the line, and b is the value of y when x = 0, which makes it the y-intercept.

The answer is 2x+y=6. Hope this helps :)

Answer:

The price changed by 20%

Step-by-step explanation:

$1 is 20% of $5,

Therefor, $5+$1 is a 20% increase

Please mark as brainliest ;)

Answer:

Step-by-step explanation:

a = 10/2 = 5

b = [tex]5\sqrt{3}[/tex]

For the Special Triangles

Answer:

y=x + 6

Step-by-step explanation:

yeah-ya........ right?

Answer:17/12

Step-by-step explanation:  2/3 + 3/4 = 2 · 4/3 · 4+ 3 · 3/4 · 3= 8/19+ 9/12 =8+9/12= 17/12

Step-by-step explanation:

Dunno. wish there were more points than this though. bye

if his wasn't algebra, I would've answered answered. hope you have your answer by now though.