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Helen [10]
3 years ago
11

Can anyone help me with this ​

Mathematics
1 answer:
Elden [556K]3 years ago
4 0

Answer:

DE = 80.

Step-by-step explanation:

Since the 2 lines are congruent:

5x = 3x + 32

2x = 32

x = 16

So DE = 3(16) + 32

= 48 + 32

= 80.

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You deposit 2000 in account A, which pays 2.25% annual interest compounded monthly. You deposit another 2000 in account b, which
stellarik [79]
To model this situation, we are going to use the compound interest formula: A=P(1+ \frac{r}{n} )^{nt}
where
A is the final amount after t years 
P is the initial deposit 
r is the interest rate in decimal form 
n is the number of times the interest is compounded per year
t is the time in years 

For account A: 
We know for our problem that P=2000 and r= \frac{2.25}{100} =0.0225. Since the interest is compounded monthly, it is compounded 12 times per year; therefore, n=12. Lets replace those values in our formula:
A=2000(1+ \frac{0.0225}{12} )^{12t}

For account B:
P=2000, r= \frac{3}{100} =0.03, n=12. Lest replace those values in our formula:
A=2000(1+ \frac{0.03}{12} )^{12t}

Since we want to find the time, t, <span>when  the sum of the balance in both accounts is at least 5000, we need to add both accounts and set that sum equal to 5000:
</span>2000(1+ \frac{0.0225}{12} )^{12t}+2000(1+ \frac{0.03}{12} )^{12t}=5000

Now that we have our equation, we just need to solve for t:
2000[(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}]=5000
(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}= \frac{5000} {2000}
(1.001875)^{12t}+(1.0025 )^{12t}= \frac{5}&#10;{2}
ln(1.001875)^{12t}+ln(1.0025 )^{12t}=ln( \frac{5} {2})
12tln(1.001875)+12tln(1.0025 )=ln( \frac{5} {2})
t[12ln(1.001875)+12ln(1.0025 )]=ln( \frac{5} {2})
t= \frac{ln( \frac{5}{2} )}{12ln(1.001875)+12ln(1.0025 )}
17.47

We can conclude that after 17.47 years <span>the sum of the balance in both accounts will be at least 5000.</span>
5 0
3 years ago
The formula to find the perimeter of a rectangle is P = 2l + 2w. Solve for w.
8_murik_8 [283]

Answer:

W =<u> P - 2L </u>

         2

Step-by-step explanation:

perimeter P = 2L + 2W

P - 2L = 2W

W =<u> P - 2L </u>

         2

4 0
2 years ago
find the number of running and passing plays using substitution method 110 plays 3 yards per run 7 yards per pass total yards 37
Zinaida [17]

Let x be the number of running plays

Y  be the number of passing plays

Since the total plays is 110

 X + y = 110

And total yard is 378

3x + 7y = 378

Using the first equation

X = 110 – y and substitute to the 2nd equation

3(110 – y) + 7y = 378

And solve for y

Y = 12

Substitute to eqution 1

X = 110 – 12 = 98

7 0
3 years ago
Round 0.42 to the nearst tenth
Archy [21]
0.4 because if it’s five or more, add one more. If it’s four or less, let it rest.
4 0
3 years ago
Daryl took out a single payment loan for $890 that charged a $40 fee. How
umka2103 [35]

Answer:

$930

Step-by-step explanation:

The amount payable at maturity of the loan is simply the sum of the loan amount and the fee charged on the loan.

The loan amount is 890 while the fee charged on the loan is 40. The amount repayable at maturity is thus;

890 + 40 = 930.

Therefore, he has to pay $930 by the time the loan reaches maturity.

7 0
3 years ago
Read 2 more answers
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