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2 years ago

The area of a rectangular rug is give. By trinomi r^2-2r-35 what are possible dimensions of the rug

Mathematics

1 answer:

Zolol [24]2 years ago

5 0

Answer:

Step-by-step explanation:

Area of the rug is given by the trinomial,

r² - 2r - 35

Since, area of the rectangular rug = Length × Width

Now we will convert the given trinomial in the factored form,

r² - 2r - 35 = r² - 7r + 5r - 35

= r(r - 7) + 5(r - 7)

= (r + 5)(r - 7)

Therefore, Dimension of the rectangular rug will be (r + 5) × (r - 7)

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On two investments totaling $6,000, Brian lost 7% on one and earned 8% on the other. If his net annual receipts were $420, how m

lianna [129]

Answer:

the amount of money invested at the rate of 7% is $400

the amount of money invested at the rate of 8%. Is $5600

Step-by-step explanation:

Let x represent the amount of money invested at the rate of 7%.

Let y represent the amount of money invested at the rate of 8%.

The total amount of money that Brian invested is $6000. This means that

x + y = 6000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time

Considering the investment at the rate at 7%,

P = x

R = 7%

T = 1

I = (x × 7 × 1)/100 = 0.07x

Considering the investment at the rate of 8%,

P = y

R = 8

T = 1

I = (y × 8 × 1)/100 = 0.08y

If his net annual receipts were $420, it means that

0.08y - 0.07x = 420 - - - - - - - - -1

Substituting x = 6000 - y into equation 1, it becomes

0.08y - 0.07(6000 - y) = 420

0.08y - 420 + 0.07y = 420

0.08y + 0.07y = 420 + 420

0.15y = 840

y = 840/0.15 = 5600

x = 6000 - y = 6000 - 5600

x = 400

8 0

2 years ago

A broker has a four-year contract to manage a rental unit for an investor. He is to receive 50% of the first month's rent and 5%

Alex777 [14]

Answer:

Step-by-step explanation:

600 X .50 = 300.00 1st month

600 X .05 = 30.00 47 months

30 X 47 = 1,410

1,410 + 300 = 1,710 (final answer)

8 0

2 years ago

Read 2 more answers

A gardener has 640 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it doe

kari74 [83]

9514 1404 393

Answer:

160 ft (out from the river)
320 ft (parallel to the river)

Step-by-step explanation:

Let x represent the length of fence parallel to the river. Then the dimension of perpendicular to the river will be half the remaining fence: (640-x)/2. The total area will be ...

A = x(640-x)/2

This is the equation of a parabola that opens downward. It has zeros at x=0 and x=640, so its axis of symmetry is x = (0+640)/2 = 320. That is, the peak of the area curve is found when x=320.

The dimensions of the garden with the largest area are 160 ft wide by 320 ft long, where the long side is the river side.