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# Math and Arithmetic

Keshawn Ziemann

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2y ago
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Cards in this guide (19)
The length of a rectangular floor is 2 feet more than its width The area of the floor is 168 square feet Kim wants to use a rug in the middle of the room and leave a 2 foot border of the floor visib

12 and 14

The perimeter of a rectangle is 18 feet and the area of the rectangle is 20 square feet what is the width of the rectangle

5

The sum of two numbers is 19 and their product is 78 What is the larger number

Let x and y be the two numbers. 1) x + y = 19

2) xy = 78

Solve (1) for y. Subtract x from both sides.

y = 19 - x

Then we can write equation (2) as x(19-x)=78

Simplifying

x(19 + -1x) = 78

(19 * x + -1x * x) = 78

(19x + -1x2) = 78

Solving

19x + -1x2 = 78

Solving for variable 'x'.

Reorder the terms:

-78 + 19x + -1x2 = 78 + -78

Combine like terms: 78 + -78 = 0

-78 + 19x + -1x2 = 0

Factor a trinomial.

(-13 + x)(6 + -1x) = 0

==

Set the factor '(-13 + x)' equal to zero and attempt to solve:

Simplifying

-13 + x = 0

Solving

-13 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '13' to each side of the equation.

-13 + 13 + x = 0 + 13

Combine like terms: -13 + 13 = 0

0 + x = 0 + 13

x = 0 + 13

Combine like terms: 0 + 13 = 13

x = 13

Simplifying

x = 13

==

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

==

x = {13, 6} The answer to your question is that the larger number is 13.

A rectangular garden has a perimeter of 48 cm and an area of 140 sq cm What is the width of this garden

10 cm

The perimeter of a square is 100 feet and the area is 625 square feet What is the length of each side

Perimeter is 100', so each side = 25' and 25 squared = 625. QED

The width of a rectangular poster is half its length The area of the poster is 128 square feet What is the length of the poster

Let the width be x/2 and the length be x:

(x/2)*x = 128

Multiply both sides by 2 and remove the brackets:

x2 = 256

Square root both sides:

x = 16

Therefore: length = 16 feet and width = 8 feet

Check: 16*8 = 128 square feet

The width of a rectangular poster is half it length. the area of the poster is 128 square feet what is the length of the poster

16

The length of a rectangular floor is 5 feet less than twice its width The area of the floor is 150 square feet What is the width of the room

lenght=15, width= 10

The length of a rectangular floor is 5 feet less than twice its width The area of the floor is 150 square feet What is the length of the room

15

A rectangular garden has a perimeter of 48 cm and an area of 140 sq cm What is the length of this garden

14 cm

The product of two positive consecutive numbers is 42 What is the smaller number

The sum of two numbers is 8 and the sum of their squares is 34 what is the larger number

EQ1 x+y=8

EQ2 x2+y2=34

EQ1 x=8-y

EQ1 and EQ2 combined gives (8-y)2+y2=34

simplify

64 -16y +y2+y2=34

simplify

2y2-16y+30=0

solve for -16y

(2y-?)(y-!)=0 EQA

EQ3 -2y!-y?=-16y

simplify

EQ3 2!+? =16

EQ4 ?!=30

EQ3 ?=16-2!

Combined EQ3 and EQ4

gives

(16-2!)!=30

simplify

8!-!2=15

Method of exhaustion

8!-!2 when

!=0 -> 0

!=2 ->12

!=3->15

!=3 into EQ3 gives ?=16-2! gives ?=10

substitute into EQA gives (2y-10)(y-3)=0

solving gives y=5 or 3

solving for EQ1 x+y=8 then x=3 or 5

solving for EQ2 x2+y2=34 gives 9+25 for either combination

so the larger number is 5

The perimeter of a rectangle is 18 feet and the area of the rectangle is 14 square feet what is the length of the rectangle

7 feet

2(7+2) = 18 feet

7*2 = 14 square feet

Ben is planning to fence his rectangular garden The area of the garden is 50 square feet and the length of the garden is twice the width How many feet of fencing will he need

4

30 feet of fencing will be needed

The sum of two numbers is 9 and the sum of their squares is 41 What is the larger number

5

5+4 = 9

52+42 = 41

Ben is planning to fence his rectangular garden the area of the garden is 50 square feet and the lenght of the garden is twice the width what is the width of the fence

Let the length be 2x and the width be x:

length*width = area

2x*x = 50

2x2 = 50

x2 = 25

x = 5 feet

Ben is planning to fence his rectangular garden The area of the garden is 50 square feet and the length of the garden is twice the width What is the width of the fence

A = area, L = length, W = width

A = LW

L = 2W

A = (2W)W = 2W2

2W2 = 50

W = 5 ft

The sum of two numbers is 8 and their product is 15 What is the larger number

5 - the other number is 3

What is the larger number if The product of two positive consecutive numbers is 42

7

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