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Rudik [331]
3 years ago
6

Please help!!! Thank you

Mathematics
1 answer:
denpristay [2]3 years ago
4 0

Answer:

(a) is a real number as the answer is -3

(b) is not a real number as the answer is an imaginary number

Step-by-step explanation:

For (b), when you root a negative number, you will get an imaginary number which is not a real number

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Rationalize the denominator of square root of negative 49 over open parentheses 7 minus 2 i close parentheses minus open parenth
navik [9.2K]

The answer is the option d, which is: d) \frac{-77+21i}{130}

The explanation for this problem is shown below:

1. Smplify the denominator and rewrite the numerator in this form:

\frac{7i}{7-2i-4-9i} \\\frac{7i}{3-11i}

2. Multiply the denominator and the numerator by the conjugated (3+11i) and simplify the expression, as following:

\frac{7i(3+11i)}{(3-11i)(3+11i)} \\ \frac{21i+77i^{2}}{121+9}  \\ \frac{-77+21i}{130}

3. As you can see, you obtain the expression shown in the option mentioned above.

3 0
3 years ago
Amy received a $80 gift card for a coffee store. She used it in buying some coffee that cost $8.24 per pound. After buying the c
SVEN [57.7K]

Answer:

5 pounds

Step-by-step explanation:

Given that:

Amount of gift card = $80

Cost of coffee per pound = $8.24

Amount left in the card = $38.80

To find:

Number of pounds of coffee bought = ?

Solution:

Let the number of pounds of the coffee bought = x pounds

Cost of 1 pound = $8.24

Cost of x pounds = $8.24 \times x

Writing the equation as per question statement:

80 - 8.24x = 38.80\\\Rightarrow 80 - 38.80 = 8.24x\\\Rightarrow  8.24x = 41.2\\\Rightarrow x = \dfrac{41.2}{8.24}\\\Rightarrow \bold{x = 5\ pounds}

Therefore, 5 pounds of coffee was bought.

3 0
3 years ago
The cost to a rent paddle boat at the county park is $8 per hour if x represent the number off hours the boat is rented and for
bazaltina [42]

Answer:

10+8x=y

Step-by-step explanation:

The 10$ is added on because it's a one time exchange and the 8 is multiplied by the x because for every hour you add 8$ to the price and y is the total price at the end depending on x.

4 0
3 years ago
According to the empirical rule, if the data form a bell-shaped normal distribution, __________ of the observations will fall wi
Kaylis [27]

Answer:

95%

Step-by-step explanation:

The empirical rule states that if data follows normal distribution then the percentage of observations falls within one, two and three standard deviation around the mean are

i) 68% falls within one standard deviation

ii) 95% falls within two standard deviation

iii) 99.7% falls within three standard deviation.

Hence 95% of the observations will fall within two standard deviations around the mean if the data follows normal distribution.

5 0
3 years ago
The mean number of books read
taurus [48]

Answer:

I thing Kaleigh read 1.5 more than Austin

Step-by-step explanation:

4 0
3 years ago
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