Given: <span>9=(1/27)^(a+3)
[Note: Please review rules of PEMDAS.
The question posted as is means
</span><span>9=[(1/27)^a]+3 which is probably not what you mean. It has been interpreted with (a+3) as the exponent, please check.]
</span><span>
Need to find value of a that satisfies above.
We will first isolate a in order to solve for its value.
</span>9=(1/27)^(a+3)
Switch unknown to the left
(1/27)^(a+3) = 9
Since both 27 and 9 are powers of 3, we can take log to base 3.
take log (base 3) on both sides, applying rule of logarithm of exponents.
(a+3)log_3(1/27)=log_3(9)
(a+3)log_3(3^(-3))=log_3(3^2)
Apply definition of logarithm [log_a(a^k)=k]
(a+3)(-3)=2
(a+3)=-2/3
a=-3 2/3=-11/3
Check: (1/27)^(-11/3+3)=(1/27)^(-2/3)=(3^(-3))^(-2/3)=3^(-3(-2/3))=3^2=9 ok
Answer: a=-11/3 or a=-3.667 (approx.)
Answer:
x<2
Step-by-step explanation:
x-5+3x<2x-1
2x<4
x<2
Answer:
2/0.74
Step-by-step explanation:
To solve the polynomial, factorize it.
2x³-11x²+18x-8=0
After factorizing:
(x-2)(2x^2 - 7x +4) = 0
now, solve each bracket one by one:
x-2 = 0
x = 2
Then
2x^2 - 7x + 4 = 0
use quadratic formula t get 0.74
<h2>a. Answer:</h2>
For this question we'll use the following method:
1. Let's subtract old value from new value
185$-160$ = -25$
The negative value implies that the price has decreased
2. Divide the result by the old value
25$/185$ = 0,1351
3. Convert this value to percentage:
0,1351 x 100 = 13,51%
Finally, by rounding to the nearest tenth:
13,5%
That means 13,5% decrease
<h2 /><h2>b. Answer:</h2>
1. Let's subtract old value from new value
77$-56$ = 21$
The positive value implies that the price has increased
2. Divide the result by the old value
21$/77$ = 0,2727
3. Convert this value to percentage:
0,2727 x 100 = 27,3%
Finally, by rounding to the nearest tenth:
27,3%
That means 27,3% increase
Answer:
Step-by-step explanation:
y = 3x + 14
y = x
.
x = 3x + 14
3x - x = -14
2x = -14
x = -7
.
y = x
y = -7
