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4 years ago

Find the 72nd term of the arithmetic sequence 11, 7, 3, ...

Mathematics

1 answer:

Katen [24]4 years ago

3 0

Answer:

-273

Step-by-step explanation:

find the common difference:

d = 7 - 11 = - 4

a_1 = 11

a_72 = (72 - 1)* (-4) + a_1

a_72 = (71)* (-4) + 11

a_72 = -273

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The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.

lorasvet [3.4K]

$p = 2w + 2l$ $p = 42$
$a = l * w$ $a = 108$

You want to make either the length or width variable (I chose the width variable to be by itself. It doesn't matter) by itself by:

Divide both sides by 2.
(p) ÷ 2 = (2w + 2l) ÷ 2
$2's$ $cancel$ $out$
$\frac{p}{2} = w + l$

Subtract both sides by either length or width depending on what variable you chose to make by itself (in this case I subtracted the length variable because I wanted the width variable by itself).
$\frac{p}{2} - l = w + l - l$
$l's$ $cancel$ $out$
p/2 - l = w

$a = l * w$

You replace w with the equation above p/2 - l = w
$a = l( \frac{p}{2} - l)$

Multiply out the L.
$a = \frac{p}{2}l - l^{2}$

Plug in all your numbers a = 110 and p = 42
$110 = \frac{42}{2}l - l^{2}$
$110 = 21l - l^{2$

Move everything to the left side so $l^{2}$ would be positive (makes the equation easier when $l^{2}$ is positive).
$l^{2} - 21l + 110 = 0$

Factor.
$(l -10)(l-11) = 0$

Make each parenthesis set equal to 0.
$l-11=0$ $l-10=0$

Add.
$l = 11$ $l = 10$

By doing this you solve for both the width and length so the answer is:
w = 11 L = 10

8 0

3 years ago

Y varies directly with x and y = 12 when x =5 what is the value of y when x = 8

torisob [31]

Y and x are directly proportional, as stated by hypothesis. Let's use the rule of three to find y when x = 8.

x=5 --> y=12
x=8 --> y=?

? = (8*12)/5 = 96/5 = 19.2

So y directly varies with x, and y=12 when x = 5, then y=19.2 when x=8.

Hope this Helps! :D

3 0

3 years ago

What is an equation of the line that passes through the points (3,4) and (-4, -3)?

azamat

Answer:

y=x+1

Step-by-step explanation:

1) Find the slope

m=-3-4/-4-3

m=-7/-7

m=1

2) Use y=mx+c

by using the point (3,4)

4=1(3)+c

4=3+c

c=1

3) The answer

y=x+1

8 0

2 years ago

A line intersects the points

Nimfa-mama [501]

Y= -x+1 because the slope is negative

5 0

2 years ago

Can someone tell me how to solve this and give me the answer please?

kotykmax [81]

9h^2+42h+49 no common factors trial and error try first term and last term all sings are positive since last term and middle terms are possitive factor leading term and coeficient and try those 9=3*3 49=7*7 (3h+7)(3h+7) 9h^2+21h+21h+49 9h^2+42h+49 true (3h+7)(3h+7)=(3x+7)^2 answer is (3h+7)^2 answe ris ths second one

7 0

3 years ago