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scoray [572]
4 years ago
6

Choose the correct simplification of the expression the quantity a to the 2nd power over b to the 3rd power all raised to the 4t

h power.
a to the 6th power over b to the 7th power
b12
a8b15
the quantity a to the 8th power over b to the 12th power
Mathematics
2 answers:
andrew11 [14]4 years ago
7 0

the answer to this problem is the last one (D)


lord [1]4 years ago
6 0
(a²/b³)^4 

(a²)^4 ⇒ 2 x 4 = 8 = a^8
(b³)^4 ⇒ 3 x 4 = 12 = b^12

(a²/b³)^4 = a^8 / b^12

<span>the quantity a to the 8th power over b to the 12th power</span>
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Find the value of x when 27 - 2x + 1 = 729+ 2x + 3
vagabundo [1.1K]

Answer:

- 2x - 2x = 729 + 3 - 27 - 1 \\

- 4x = 704

x = -704 \div 4 = -176

7 0
3 years ago
A used car dealer has 30 cars and 10 of them are lemons (i.e.~ mechanically faulty used cars), and you don't know which is which
Triss [41]

Answer: Hence, the probability that he will get at least one lemon is 0.70.

Step-by-step explanation:

Since we have given that

Number of cars = 30

Number of lemon cars = 10

Number of other than lemon cars = 30-10 = 20

According to question, he bought 3 cars,

we need to find the probability that you will get at least one lemon.

So, P(X≤1)=1-P(X=0)=1-P(no lemon)

Here, P(no lemon ) is given by

\dfrac{20}{30}\times \dfrac{20}{30}\times \dfrac{20}{30}=(\dfrac{20}{30})^3

so, it becomes,

P(X\geq 1)=1-(\dfrac{20}{30})^3=1-(0.67)^3=0.70

Hence, the probability that he will get at least one lemon is 0.70.

5 0
3 years ago
How to solve the logarithmic equation.
Anna007 [38]
Using logarithmic laws: log(a) + log(b) = log(ab)

log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3

Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.

4^{log_4 (x + 9)(x + 21)} = 4^{3}
(x + 9)(x + 21) = 64
x^{2} + 9x + 21x + 189 = 64

Solving the quadratic we get:
x^{2} + 30x + 125 = 0
(x + 5)(x + 25) = 0

x = -5, -25

BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
7 0
3 years ago
Name the fourth in pane wxv
snow_tiger [21]
Your answer would be U
8 0
3 years ago
The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116.
9966 [12]

Answer:

10 and 42

Step-by-step explanation:

The difficulty with word problems is translating them into math.

Let's do that

---------------------

The sum of a number and two times a smaller number is 62.

let's call the bigger number b, and the smaller number s

b + 2s = 62

Three times the bigger number exceeds the smaller number by 116

3b = s + 116

-----------------------

Now manipulate one of the equations to isolate the variable

3b = s + 116

Subtract 116 from both sides

3b - 116 = s

substitute for s = 3b - 116 in

b + 2s = 62

b + 2(3b - 116) = 62

Distribute

b + 6b - 232 = 62

combine like terms

7b = 294

Divide both sides by 7

b = 42

to find s plug in b = 42 into

b + 2s = 62

42 + 2s = 62

subtract 42 from both side

2s = 20

divide both sides by 2

s = 10

7 0
3 years ago
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