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3 years ago

8

The length of a rectangle is 2 cm less than twice the width. The area of the rectangle is 112 cm2. Find the length and width of

the rectangle.

1 answer:

ELEN [110]3 years ago

3 0

Let breadth be x

Length=2x-2

We know

$\boxed{\sf Area=Length\times Breadth}$

$\\ \sf\longmapsto 112=x(2x-2)$

$\\ \sf\longmapsto 2x^2-2x-112=0$

$\\ \sf\longmapsto x=-7\:or\:x=8$

Ignore negative value

Now

$\\ \sf\longmapsto Length=2x-2=2(8)-2=16-2=14$

$\\ \sf\longmapsto Breadth=8$

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How many possible lunches can be made if there are 3 choices for entree and 4 choices for drink?

Lunna [17]

Answer:

12 MULTIPLY AALL THE NO.'S

7 0

2 years ago

You have 3 online accounts in three different banks valued at: bank "A" = $250.67, 12% interest, bank "B" $765.13, 7% interest,

gregori [183]

Answer:

$\$882.89$

Step-by-step explanation:

we know that

The simple interest formula is equal to

$I=P(rt)$

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

Bank A

$t=1\ years\\ P=\$250.67\\r=12\%=12/100=0.12$

substitute in the formula above

$I=250.67(0.12*1)=\$30.08$

Bank B

$t=1\ years\\ P=\$765.13\\r=7\%=7/100=0.07$

substitute in the formula above

$I=765.13(0.07*1)=\$53.56$

Bank C

$t=1\ years\\ P=\$28,500.36\\r=9\%=9/100=0.09$

substitute in the formula above

$I=28,500.36(0.09*1)=\$2,565.03$

Find the average interest gained from the three accounts in one year

$[\$30.08+\$53.56+\$2,565.03]/3=\$882.89$

3 0

3 years ago

If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

2 years ago

Rewrite the following fraction as a decimal. 19/25.

sveticcg [70]

0.76 is by a decimal

6 0

3 years ago

International Juice Inc. plans to introduce a new line of fruit juices with three different flavors: cherry, grape and apple. 50

Tanya [424]

Cherry sales as a % of total sales = (0.5 x 1.2)/(0.5 x 1.2 + 0.2 x 1.4 + 0.3 x 1.6) = 0.6 / (0.6 + 0.28 + 0.48) = 0.6 / 1.36 = 0.4412 = 44.12%

Therefore, 44.12% of the total sales will be cherry.

8 0

3 years ago