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Romashka [77]
2 years ago
7

james invested some money at 13% interest. James also invested $199 more than 3 times that amount at 12%. How much is invested a

t each rate if James receives $1561.50 in interest after one year? (Round to two decimal places if necessary.)
Mathematics
1 answer:
Komok [63]2 years ago
8 0

9514 1404 393

Answer:

  • $3138 at 13%
  • 9613 at 12%

Step-by-step explanation:

Let x represent the amount invested at 13%. Then (3x+199) is the amount invested at 12%. The total interest earned in 1 year is ...

  (13%)(x) +(12%)(3x+199) = 1561.50

  0.49x +23.88 = 1561.50 . . . . simplify

  0.49x = 1537.62 . . . . . . . . . . subtract 23.88

  x = 3138 . . . . . . . . . . . . . . . . divide by 0.49

  3x+199 = 9613

$3138 was invested at 13%; $9613 was invested at 12%.

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Tommy has 6 more than 3 times the amount of money in his bank account than Judy. Judy has $7500 more than a number in her accoun
balu736 [363]

Answer: Judy: n+7500

Tommy: 3(n+7500)+6

Step-by-step explanation:

4 0
3 years ago
Over the interval [0,2pi), what are the solutions to cos(2x) = cos(x)? check all that apply​
kykrilka [37]

\cos(2x)  =  \cos(x)

Solution (1)

2x = x + 2k\pi

2x - x = 2k\pi

x = 2k\pi

for k=0 / for k=1 / for k=-1

x=0 / x=2π / x=-2π

acc / acc / rej

solution (2)

2x =  - x  + 2k\pi

2x + x = 2k\pi

3x = 2k\pi

x =  \frac{2k\pi}{3}

for k=0 / for k=1 / for k=-1

x=0 / x=2π/3 / x=-2π/3

acc / acc / rej

Note that i'm trying values of K which make the answer belong to our interval;

So our solution which i will represent as a set is;

S € {0,2π/3,2π}

6 0
2 years ago
Triangle DEF (not shown) is similar to ABC shown, with angle B congruent to angle E and angle C congruent to angle F. The length
Bezzdna [24]

Answer:

Area of ΔDEF is 45\ cm^2.

Step-by-step explanation:

Given;

ΔABC and  ΔDEF is similar and ∠B ≅ ∠E.

Length of AB = 2\ cm and

Length of DE = 6\ cm

Area of ΔABC = 5\ cm^2

Solution,

Since, ΔABC and  ΔDEF is similar and ∠B ≅ ∠E.

Therefore,

\frac{Area\ of\ triangle\ 1}{Area\ of\ triangle\ 2} =\frac{AB^2}{DE^2}

Where triangle 1 and triangle 2 is  ΔABC and  ΔDEF respectively.

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

\frac{5}{Area\ of\ triangle\ 2} =\frac{2^2}{6^2}\\ \frac{5}{Area\ of\ triangle\ 2}=\frac{4}{36}\\ Area\ of\ triangle\ 2=\frac{5\times36}{4} =5\times9=45\ cm^2

Thus the area of  ΔDEF is 45\ cm^2.

4 0
2 years ago
Read 2 more answers
What kind of number is e? <br><br> a.) integer<br> b.) rational <br> c.) natural <br> d.) irrational
Oliga [24]

Answer:

c.natural

Step-by-step explanation:

The number e , sometimes called the natural number, or Euler's number, is an important mathematical constant approximately equal to 2.71828.

7 0
2 years ago
Read 2 more answers
941 rounded to the nearest 10
Oksana_A [137]

Answer:

900

Step-by-step explanation:

you just see if by the number, if the number is 6 and up your round over and it would become 950 but the number is lower so you make it 900.

3 0
2 years ago
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