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Elodia [21]
3 years ago
5

What is the value of the power a if 5^a = 1/25?

Mathematics
1 answer:
attashe74 [19]3 years ago
8 0

When a number is raised to a power it is multiplied by itself so the number gets larger. Because the answer is a fraction, this means the power is a negative value.

Find the number 5 has to be raised to be 125 and then make is negative:

5 x 5 x 5 =125

The answer would be a = -3

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What is the 7th term of the geometric sequence where a1 = -625 and a2 = 125
kykrilka [37]
Since the sequence is geometric, there is some constant r such that the sequence is recursively given by

a_n=ra_{n-1}

By this definition, you can recursively substitute into the right hand side the definition for a_{n-1},a_{n-2},\ldots to find an explicit formula for the nth term.

a_n=ra_{n-1}=r^2a_{n-2}=r^3a_{n-3}=\cdots=r^{n-1}a_1=-625r^{n-1}

You know the second term, which means you can find r:

a_2=-625r^{2-1}\implies125=-625r\implies r=-\dfrac15

So, the 7th term of the sequence is

a_7=-625\left(-\dfrac15\right)^{7-1}=-\dfrac1{25}
8 0
3 years ago
14+16+49+10<br><br>Hint: Add what will get a tens number first!
Leviafan [203]
<span>89 is the correct answer.

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8 0
3 years ago
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To make a shade of lavender paint jon mixes 4 ounces of red tint and 28 ounces of blue tint into one gallon of white paint. if 2
kirill [66]
You can write this as a ratio to find the answer, but you first need to convert the gallon of white paint into ounces, which is 160 ounces. The ratio, red to blue to white, is 4:28:160, which you can simplify by dividing by 4 into 1:7:40. If 80 ounces of red tint are used, you need to multiply each value in the ratio by 80, which gives you 80:560:3200. This shows that you need 560 ounces of blue tint, which can also be written as 3.5 gallons. I hope this helps!
8 0
3 years ago
A triangle has side lengths of 11 cm and 7 cm. Which could be the value of the third side, 19 cm or 17 cm ?
9966 [12]

Answer:

By the triangle side length theorem, the sum of the two shorter sides has to be equal to or larger than the third side. Thus, we can write the following inequation.

a

+

b

≥

c

, where a and b are the shorter sides and c the longest.

11, 9 and 15 satisfies this inequality while 11, 9 and 20 doesn't.

Justification:

The reason for this rule is simple; it's because if the longest side is longer than the sum of the two shorter sides, this means that the shorter sides aren't long enough to connect with the longest side, thus rendering the shape a collection of lines and disqualifying the possibility of having a triangle, which was our objective.

Practice exercises:

Which of the following triangles is possible?

a) 4,6 and 14

b) 5,11 and 16

c) 1,3,6

D). 12,19 and 26

Find the smallest possible value of a to make the following an actual triangle :

a

,

14

,

25

Hopefully this helps:

Step-by-step explanation:

8 0
3 years ago
Simplify the expression to a + bi form:<br> (9 – 2i) + (-2 - 5i)
NARA [144]

Answer:

7-7i

Step-by-step explanation:

4 0
3 years ago
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