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vovangra [49]
3 years ago
10

-2x-2y=-8 -4x-8y=-20

Mathematics
1 answer:
Citrus2011 [14]3 years ago
8 0

Answer:

-2x-2y=-8

-4x-8y=-20

From the 1st eqn

Dividing through by 2

you have

-x-y=-4

Multiply through by -(minus)

x+y=4

x=4-y

Substitute into eqn 2

-4x-8y=-20

-4(4-y)-8y=-20

-16 + 4y - 8y = -20

-4y = -20 +16

-4y = -4

y= 1

Substitute into any of the other eqn's to get x

x= 4-y

x= 4-1

x=3

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Alma invests $300 in an account that compounds interest annually. After 2 years, the balance of the account is $329.49. To the n
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Invested amount (P) = $300.

Time in years (t) = 2 years.

Balance after 2 years (A) = $329.49.

Let us assume rate of interest = r % compounds annually.

We know, formula for compound interest

A=P(1+r)^t

Plugging values in formula, we get

329.49=300(1+r)^2

\mathrm{Divide\:both\:sides\:by\:}300

\frac{300\left(1+r\right)^2}{300}=\frac{329.49}{300}

\left(1+r\right)^2=1.0983

Taking square root on both sides, we get

1+r=\sqrt{1.0983}

\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}

1+r-1=\sqrt{1.0983}-1

r=\sqrt{1.0983}-1

r=1.048-1

r=0.048.

Converting it into percentage by multiplying by 100.

r=0.048 × 100

r  = 4.8 %

Therefore, the rate of interest on the account is 4.8% compounds annually.

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3 years ago
Find the 20th term of an A.P whose first term is 102 and common difference -3
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1. David has designed a lawn game that uses a circular center target with alternating gray and
Sholpan [36]

Answer:

Total area of the gray sections of the target is 678 square inches.

Step-by-step explanation:

Given :

Three concentric circles and we have to find the total area of the gray sections.

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⇒ Area of the white circle - Area of the smaller gray circle.

⇒ \pi R^2-\pi r^2

⇒ \pi (R^2-r^2)

⇒ \pi (12^2-6^2)                  <em> ...1 foot = 12 inches and 0.5 foot = 6 inches</em>

⇒ 3.14(144-36)

⇒ 3.14(108)

⇒ 339.12 square inches

The total area of the gray sections is  the area of the bigger gray circle minus the area of the white circle.

Total area of the gray sections:

⇒ \pi R^2 - 339.12

⇒ 3.14(18^2) -339.12    <em> ....where 1.5 foot = 18 inches</em>

⇒ 1017.36-339.12

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The total area of the gray sections of the target, to the nearest square inch is 678.

Option C is the right choice.

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