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3 years ago

Find the 72nd term of the arithmetic sequence -27, -11, 5, ...

Mathematics

1 answer:

MAXImum [283]3 years ago

8 0

Step-by-step explanation:

first identify the common difference

The first term which i will define by u⁰=-27

u¹=u⁰+(1)d where d is the common difference and u¹ is the second term

u¹=-27+d

-11=-27+d

d=27-11=16

The 72nd term would be u⁷¹ since we started from u⁰ as our first term:

Use the explicit relation given by:

u(n)=u⁰+(n)d

u(71)=-27+71(d)

u⁷¹=-27+71(16)

u⁷¹=-27+1136

u⁷¹=1109

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Answer:

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Step-by-step explanation:

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3 years ago

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I have some cheese. I used

hram777 [196]

<h3>Answer: 2500 grams</h3>

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

Work Shown:

A = amount of grams of cheese you had originally

B = (2/5)*A = amount of cheese you use up after day 1

C = (3/5)*A = amount of cheese you have left over after day 1

note how B and C add back up to 'A'.

This is because 2/5+3/5 = 5/5 = 1, so,

B+C = (2/5)A+(3/5)A = (2/5+3/5)A = 1*A = A

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

D = (2/5)*C = amount of cheese you use up after day 2

E = (3/5)*C = amount of cheese left over after day 2

the variables D and E add up to C

we are told that there are 900 grams of cheese left after day 2, so E = 900

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

E = (3/5)*C

(3/5)*C = E

(3/5)*C = 900 ... Plug in E = 900

3C = 900*5 .... multiply both sides by 5

3C = 4500

C = 4500/3 .... divide both sides by 3

C = 1500

This means you had 1500 grams of cheese after day 1

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

C = (3/5)*A

(3/5)*A = C

(3/5)*A = 1500 ... plug in C = 1500

3A = 1500*5 ... multiply both sides by 5

3A = 7500

A = 7500/3 .... divide both sides by 3

A = 2500

-----------

<h3>You started off with 2500 grams of cheese.</h3>

After day 1, you use up (2/5)*2500 = 1000 grams of cheese and have 2500-1000 = 1500 grams left over.

After day 2, you use up (2/5)*1500 = 600 grams of cheese and have 1500-600 = 900 grams left over.

The answer is confirmed.

6 0

3 years ago

A line goes through the points (4,16) Ana (7,19). Write a linear function rule in terms of x and y for this line

Eva8 [605]

Linear function rule in terms of x and y for this line is y = x + 12

<em><u>Solution:</u></em>

Given that a line goes through the points (4, 16) and (7, 19)

To find: linear function rule in terms of x and y for this line

A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the slope of the line, and b represents the y-axis intercept

<em><u>The slope intercept form is given as:</u></em>

y = mx + c

Where "m" is the slope of line and "c" is the y - intercept

Let us first find slope of line

<em><u>The slope "m" of a line is given as:</u></em>

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=4 \text { and } x_{2}=7 \text { and } y_{1}=16 \text { and } y_{2}=19$

$m=\frac{19-16}{7-4}=\frac{3}{3}=1$

Thus the slope of line is 1

Substitute m = 1 and (x, y) = (4, 16) in y = mx + c

16 = 1(4) + c

c = 16 - 4 = 12

Substitute c = 12 and m = 1 in slope intercept form

y = 1x + 12

y = x + 12 is the required linear function rule

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Pani-rosa [81]

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