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3 years ago

Find the length and width of a rectangle whose perimeter is 20 feet and whose area is 21 square feet

Mathematics

1 answer:

ipn [44]3 years ago

6 0

Answer:

Length = 3

Width = 7

Step-by-step explanation:

The perimeter is 20 feet

The area is 21 feet

Let x represent the length

Let y represent the width

20 = 2(x+y)

x+y= 20/2

x+y = 10.........equation 1

x × y= 21......equation 2

From equation 1

x= 10-y

Substitute 10-y for x in equation 2

(10-y)y= 21

10y - y^2 = 21

y^2 -10y + 21= 0

After factorization the result will be

(x-3)(y-7)

x-3= 0

x= 0+3

x= 3

y-7= 0

y= 0+7

y= 7

Hence the length is 3 and the width is 7

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An item is regularly priced at $65. Laura bought it at a discount of 15% off the regular price. How much did Laura pay?

Sonja [21]

Answer:

9.75

Step-by-step explanation:

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3 years ago

2 Here are two equations:

MatroZZZ [7]

a. (3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. No, it is not possible to have more than one (x,y) pair that is solution to both equations

Step-by-step explanation:

a. Decide whether each neither of the equations,

i (3,4)

ii. (4,2.5)

ill. (5,5)

iv. (3,2)

To decide whether each point is solution to equations or not we will put the point in the equations

Equations are:

Equation 1: 6x + 4y = 34

Equation 2: 5x – 2y = 15

i (3,4)

Putting in Equation 1:

$6(3) + 4(4) = 34\\18+16=34\\34=34\\$

Putting in Equation 2:

$5(3) - 2(4) = 15\\15-8 = 15\\7\neq 15$

ii. (4,2.5)

Putting in Equation 1:

$6(4) + 4(2.5) = 34\\24+10=34\\34=34\\$

Putting in Equation 2:

$5(4) - 2(2.5) = 15\\20-5 = 15\\15=15$

ill. (5,5)

$6(5) + 4(5) = 34\\30+20=34\\50\neq 34$

Putting in Equation 2:

$5(5) - 2(5) = 15\\25-10 = 15\\15=15$

iv. (3,2)

$6(3) + 4(2) = 34\\18+8=34\\26\neq 34$

Putting in Equation 2:

$5(3) - 2(2) = 15\\15-4 = 15\\11\neq 15$

Hence,

(3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. Is it possible to have more than one (x, y) pair that is a solution to both

equations?

The simultaneous linear equations' solution is the point on which the lines intersect. Two lines can intersect only on one point. So a linear system cannot have more than one point as a solution

So,

a. (3,4) is only the solution to Equation 1.

(4, 2.5) is the solution to both equations

(5,5) is the solution to Equation 2

(3,2) is not the solution to any equation.

b. No, it is not possible to have more than one (x,y) pair that is solution to both equations

Keywords: Linear equations, Ordered pairs

Learn more about linear equations at:

#LearnwithBrainly

8 0

3 years ago

Ben made a model (shown below) of the square pyramid he plans to build when he grows up.

elena-s [515]

Answer:

$336 m^2$

Step-by-step explanation:

The surface area of a square pyramid is the sum of the area of the squared base + 4 times the area of each triangular face, therefore:

$A=A_b + 4A_t$

where:

$A_b=L^2$ is the area of the base, where

L is the length of the base

$A_t=\frac{1}{2}Lh$ is the area of each triangular face, where

h is the height of the face

Substituting,

$A=L^2+2Lh$

For the model in this problem,

L = 12

h = 8

Therefore, the surface area here is:

$A=12^2 +2(12)(8)=336$

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3 years ago

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tiny-mole [99]

Step-by-step explanation:

A=base length × height

if base is 6cm, and h 4 cm, multiply

6×4=24cm2

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3 years ago

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Lady bird [3.3K]

Answer:

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Step-by-step explanation:

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3 years ago