7. (6 points) For the following geometric sequence, 3 ,- 1, 1/3,-1/9, …
Find the formula for the nth term

Answer:

b is the answer f(e) gives us b

Answer:

a = b = 1 , c = - 8

Step-by-step explanation:

ax² + bx + c = y

( - 5 )² a - 5b + c = 12

c = - 8

3² a + 3b + c = 4

25a - 5b - 8 = 12 ⇔ 25a - 5b = 20 ⇔ 5a - b = 4 ........ (1)

9a + 3b - 8 = 4 ⇔ 9a + 3b = 12 ⇔ 3a + b = 4 .......... (2)

(1) + (2)

8a = 8 ; a = 1

b = 1

y = x² + x - 8

Answer:

read step-by-step explanation

Step-by-step explanation:

it's a trick question u can't u can get close doing (7+7)×(7+1)-7=105 but it's not 100

Slope is the change in Y over the change in X:

Slope = (25- -25) / (27 - 28)

Slope = 50/-1

Slope = -50

The length of the wingspan of the finished model based on the dimensions of the kit is 0.75 feet

Given:

Kit

Plane = 27 feet

wingspan = 18 feet

Model:

Plane = 13.5 inches

Wingspan = x feet

convert 13.5 inches to feet

1 feet = 12 inches

13.5 inches = 1.125 feet

So,

equate Ratio of plane to wingspan

27 : 18 = 1.125 : x

27/18 = 1.125 / x

cross product

27 × x = 18 × 1.125

27x = 20.25

x = 20.25/27

x = 0.75 feet

Therefore, the length of the wingspan of the finished model based on the dimensions of the kit is 0.75 feet

Learn more about ratio:

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Answer:

5,976 workers

Step-by-step explanation:

498 times 12 = 5976

Answer: 41.5

Step-by-step explanation: you have to do 498 divided by 12 and then you will get your answer.

Answer:

800 shrimp

Step-by-step explanation:

100 plates of shrimp

8 shrimp on each plate

100 × 8 = 800

= 800 shrimp were prepared by the chef

Hope this helps.

Answer:

I think this is right lol

Step-by-step explanation:

f(x)=49+x

plz write your proper question

Answer:

-5, -2, 3, 4

They are in the correct order already :)

Step-by-step explanation:

They greater a negative number is the less it becomes and positive numbers are always greater than negative ones.

Good luck :)

Answer:

17 and a half days OR 18 days

Step-by-step explanation:

7 books : 8 days

20 books: x days

cross multiply

x = (8×20)÷ 7

x = 17.5

therefore

17 and a half days or 18 days

The third ordered pair that satisfies the equation of the circle is (123, 369).

The given parameters;

The third ordered pair of the equation can be determined by using general equation of a circle;

[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]

The radius of the circle is calculated as;

[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]

The value of a can be obtained by randomly choosing numbers less than the radius as values of b.

[tex]b < r\\\\b < 388.96[/tex]

[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]

Thus, the third ordered pair that satisfies the equation of the circle is (123, 369).

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Answer:

y=88

Step-by-step explanation:

-92

Step-by-step explanation:

If a quadratic equation has the following form:

[tex]ax^2 + bx + c =0, \;\;\;a \neq 0[/tex]

then its discriminant D is defined as

[tex]D = b^2 - 4ac[/tex]

In our given quadratic equation, a = 4, b = -2 and c = 6, so its discriminant is

[tex]D = (-2)^2 - 4(4)(6) = -92[/tex]

Note: The value of the discriminant D will determine the characteristics of the roots of the quadratic equation according to the following rules:

[tex]D > 0,\;\;[/tex] there will be 2 real roots

[tex]D = 0,\;\;[/tex] there will be 1 real root

[tex]D < 0,\;\;[/tex] there will be 2 imaginary roots

Hence our given quadratic equation will not have any real roots but only imaginary ones.

Answer:

-36/5

- . 2/5-=+2/5

-36/5+2/5

34/5 or 6 4/5

Answer:

3 6/7

Step-by-step explanation:

Absolute value is the distance a number is away from 0 on a number line; another way of thinking about absolute value is that it is the positive version of every number. So, the absolute value of -1 is 1, and the absolute value of 88 is 88. We can apply this rule to 3 6/7 - how far is it away from 0 on the number line? What is it as a positive number? Well it is 3 6/7 away from 0 on the number line, and it already is positive, so our final answer will be 3 6/7.

Hopefully that's helpful! :)

[tex]|3\frac{6}{7}|=3\frac{6}{7} =\frac{27}{7}[/tex]

ok done. thank to me :>

Answer:

Step-by-step explanation:

4x+2y<3

y<-2x + [tex]\frac{3}{2}[/tex]

Answer:

Unit Price for Brand A: $0.31 per Pencil.

Unit Price for Brand B: $0.35 per Pencil.

Brand A is the better buy.

Step-by-step explanation:

Divide 7.49 by 24 to get 0.312 and round down to 0.31.

Divide 9.97 by 28 to get 0.356 and round down to 0.35 (0.36 is too much making the price $10.08)

Compare 0.31 and 0.35. (0.31 < 0.35)

[tex]\\ \sf{:}\dashrightarrow \dfrac{4}{x}=\dfrac{6}{9}[/tex]

[tex]\\ \sf{:}\dashrightarrow 6x=36[/tex]

[tex]\\ \sf{:}\dashrightarrow x=6[/tex]

#y

[tex]\\ \sf{:}\dashrightarrow \dfrac{y}{12}=\dfrac{12}{18}[/tex]

[tex]\\ \sf{:}\dashrightarrow \dfrac{y}{12}=\dfrac{2}{3}[/tex]

[tex]\\ \sf{:}\dashrightarrow 3y=24[/tex]

[tex]\\ \sf{:}\dashrightarrow y=8[/tex]

Here we go

And

Answer:

To divide a decimal number by a decimal number, multiply the divisor by as many tens as necessary until we get a whole number, and remember to multiply the dividend by the same number of tens. For example, 13.8 ÷ 0.6 becomes 138 ÷ 6 = 23.

Answer:

33y

Step-by-step explanation:

since the equation of perimeter for a rectangle is lengthX2 + widthX2

and the width is given to be 5 1/2y is it? If it is so then the length will be 11y since 2X5 1/2y is 11y

and the perimeter will then be calculated as so;

11yX2 + 5 1/2yX2

so it will be 22y+11y which will give you 33y

Answer:

28x^2+16x-12

Step-by-step explanation:

(4x+4)(7x-3)

28x^2+28x-12x-12

28x^2+16x-12

Check the picture below, tis corrected.

btw the picture is rather long, so the thumbnail here may not show all its size, so you may have to open the image in a new tab or window.

This is the same as typing in 0.5x^7

Other equivalent forms are (1/2)x^7 or (x^7)/2

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

Work Shown:

[tex]\frac{d}{dx}\left[f(x^2)\right] = x^8\\\\f'(x^2)*\frac{d}{dx}(x^2) = x^8\\\\f'(x^2)*2x = x^8\\\\f'(x^2) = \frac{x^8}{2x}\\\\f'(x^2) = \frac{x^7}{2}\\\\f'(x^2) = \frac{1}{2}x^7\\\\f'(x^2) = \boldsymbol{0.5x^7}\\\\[/tex]

I used the chain rule on the second step. The chain rule will apply the derivative to the outer function f(x^2). Then we also apply the derivative to the inner function x^2 to get 2x, which is multiplied with f ' (x^2). From that point, we isolate f ' (x^2).

Side note: When applying the first derivative, it might help to think of f(x^2) as simply f(x) on a temporary basis.

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

Explanation:

To get the point estimate, we average the endpoints of the given confidence interval. Add up the endpoints and divide by 2

(low+high)/2 = (0.262+0.622)/2 = 0.442

The value 0.442 is right in the middle of the confidence interval, so it's a natural point estimate for the population proportion.

--------------

Alternative Method:

Subtract the endpoints to find the confidence interval width

width = high - low = 0.622 - 0.262 = 0.36

Cut this in half to get the margin of error (MoE)

MoE = width/2 = 0.36/2 = 0.18

Then we can either add on the MoE to the low endpoint, or subtract it from the high endpoint, to land on the center

Step-by-step explanation:

remark : it is very unusual for a map to mix two measurement norms. they are normally either fully in the American or fully in the metric system.

but let's do the exercise.

the scale says 1/2 in = 10 km

but our measurement on the map brought us quarter inches.

so,

1/2 in = 2/4 in = 10 km

therefore

1/4 in = 10/2 = 5 km

now,

2 1/4 = 9/4 in

this is 9 times 1/4.

therefore, the distance between the 2 cities is

9 × 5 = 45 km.

Answer: The angled line on graphs!

Step-by-step explanation: :)

Applying the triangle sum theorem, m∠N = 41°

Triangle sum theorem states that the sum of the three interior angles of any triangle equals 180°.

Given the following interior angles of ΔMNO:

m∠M = (6x+1)°

m∠N = (3x-10)°

m∠O = (x+19)°

Find the value of x:

m∠M + m∠N + m∠O = 180°

6x+1 + 3x-10 + x+19 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

x = 17

m∠N = (3x-10)°

m∠N = 3(17) - 10

m∠N = 41°

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