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lorasvet [3.4K]
3 years ago
10

What are the side lengths of a rectangle if the area = 40 in and the perimeter = 48 in

Mathematics
2 answers:
Serggg [28]3 years ago
4 0
4, 10, 4, 10. 10*4 gives area of 40. 10+10+4+4 gives 48 as shown in question
Leno4ka [110]3 years ago
3 0
a,b-the\ side\ lengths\ of\ a\ rectangle\\ \\a\cdot b=40\ [in^2]\ \ \wedge\ \ \ 2\cdot(a+b)=48\ [in]\\ \\ a+b=24\ \ \ \Rightarrow\ \ \ a=24-b\ \ \ \Rightarrow\ \ \ ab=(24-b)b=24b-b^2\\ \\ab=40\ \ \ \Rightarrow\ \ \ 24b-b^2=40\ \ \ \Rightarrow\ \ \ -b^2+24b-40=0\ /\cdot(-1)\\ \\b^2-24b+40=0\ \ \Rightarrow\ \Delta=(-24)^2-4\cdot40=576-160=416=16\cdot 26\\ \\

\sqrt{\Delta} =4 \sqrt{26} \ \ \ \Rightarrow\ \ \ b_1= \frac{24-4 \sqrt{26} }{2}=12-2 \sqrt{26}\ \Rightarrow\ a_1=12+2 \sqrt{26}  \\ \\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  b_2= \frac{24+4 \sqrt{26} }{2}=12+2 \sqrt{26}\ \Rightarrow\ a_2=12-2 \sqrt{26}
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1. Using powers of 10, which would be the best choice for the first number to subtract in the division problem 956 ÷ 87?​
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Answer:

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Step-by-step explanation:

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3 years ago
Marvin invested 65% of his retirement account in stocks and 35% in gold. Marvin believes that the return to stocks over the next
ser-zykov [4K]

Answer:

1)

the mean rate of return is 17 %

the standard deviation of return is 17.06055

2)

the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325

Step-by-step explanation:

Given the data in the question;

1)

For the portfolio, the mean return and standard deviation are computed as follows;

Mean = Return = 0.65 × 10 + 0.35 × 30

= 6.5 + 10.5

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Therefore, the mean rate of return is 17 %

Standard deviation will be;

σp = √( 0.65² × 15² + 0.35² × 40² )

= √( 0.4225 × 225 + 0.1225 × 1600 )

= √( 95.0625 + 196 )  

= √291.0625

= 17.06055  

Therefore, the standard deviation of return is 17.06055

2)  

probability that Marvin's portfolio will make at least 20% over the next 12 months.

P( X > 20 )

we convert to a standard normal variable;

Z = \frac{20-17}{17.06055} )

Z = 0.17

from z table, p-value is;

p( X < 20 ) = 0.5675

P( X > 20 ) 1 - 0.5675  = 0.4325

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3 years ago
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3 years ago
If a 40,000g cannon ball is 35m above the Earth’s surface, how much potential energy does the cannon ball have?
ELEN [110]

Answer:

Step-by-step explanation:

Remark

You could do this by converting the distance but the much more common way is to use kg and m.

Formula

PE = m * g * h

Givens

m = 40000 grams

m = 40000 grams * 1kg/1000 grams = 40 kg

g = 9.81

h = 35 m

Solution

PE = 40 * 9.81 * 35

PE = 13734 Joules

4 0
3 years ago
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