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Amiraneli [1.4K]
3 years ago
13

tell whether the system has one solution, infinitely many solutions, or no solution. x = -7y + 24 x + 7y = 32

Mathematics
1 answer:
mylen [45]3 years ago
7 0
This system has no solution.
x = -7y + 24 can be rewritten as x = 24 - 7y
to simplify x + 7y = 32, we have to subtract 7y from both sides
x = 32 - 7y
Now, our system is as follows:
x = 24 - 7y
x = 32 - 7y


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Last one anyone that can help me out?
Usimov [2.4K]

Answer:

Part a. t = 7.29 years.

Part b. t = 27.73 years.

Part c. p = $3894.00

Step-by-step explanation:

The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!

Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!

Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!

4 0
3 years ago
A pile of sand has a weight of 90kg.
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Answer:

9Kg, 18Kg and 63 Kg

Step-by-step explanation:

Sum the parts of the ratio, 1 + 2 + 7 = 10 parts

Divide the weight of sand by 10 to find the value of one part of the ratio

90 Kg ÷ 10 = 9 Kg ← value of 1 part of the ratio, thus

2 parts = 2 × 9 Kg = 18 Kg

7 parts = 7 × 9 Kg = 63 Kg

Thus the weights of each bag are 9 Kg, 18 Kg and 63 Kg

3 0
2 years ago
1/8 in the form of 2^N
KIM [24]

Answer:

1.0905

Step-by-step explanation:

3 0
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Lemur [1.5K]

x=7.5\overline{26}\\10x=75.\overline{26}\\1000x=7526.\overline{26}\\1000x-10x=7526.\overline{26}-75.\overline{26}\\990x=7451\\x=\dfrac{7451}{990}

It can be expressed as a fraction with integer numerator and denominator, so it's a rational number.

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a person had a rectangular-shaped garden with sides of lengths 16 feet and 9 feet. the garden was changed into a square design w
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The are of each side is now 12.5 feet.
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