Simplify the expression. (Assume that all variables are positive.) 108 15d

Please Hurry! What is the solution to log2_(9x)-log2_3=3?

brilliants [131]

Answer:

$log_{2}(9x) - log_{2}(3) = 3 \\ 3 = log_{2}(8) or log_{2}( {2}^{3} ) \\ log_{2}( \frac{9x}{3} ) = log_{2}(8) \\ \frac{9x}{3} = 8 \\ 9x = 8 \times 3 \\ 9x = 24 \\ x = \frac{24}{9} \\ x = \frac{8}{3} \\ x = 2 \times \frac{2}{3}$

6 0

3 years ago

Read 2 more answers

How do you write 20% as a decimal

77julia77 [94]

Answer:

0.2

Step-by-step explanation:

20/100=0.2

3 0

2 years ago

Read 2 more answers

√₂

snow_lady [41]

Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

Simple Interest Formula

I = Prt

where:

I = interest earned.
P = principal invested.
r = interest rate (in decimal form).
t = time (in years).

Given:

Total P = $7000
P₁ = principal invested at 5%
P₂ = principal invested at 8%
Total interest = $500
r₁ = 5% = 0.05
r₂ = 8% = 0.08
t = 1 year

Create two equations from the given information:

$\textsf{Equation 1}: \quad \sf P_1+P_2=7000$

$\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500$

Rewrite Equation 1 to make P₁ the subject:

$\implies \sf P_1=7000-P_2$

Substitute this into Equation 2 and solve for P₂:

$\implies \sf 0.05(7000-P_2)+0.08P_2=500$

$\implies \sf 350-0.05P_2+0.08P_2=500$

$\implies \sf 0.03P_2=150$

$\implies \sf P_2=\dfrac{150}{0.03}$

$\implies \sf P_2=5000$

Substitute the found value of P₂ into Equation 1 and solve for P₁:

$\implies \sf P_1+5000=7000$

$\implies \sf P_1=7000-5000$

$\implies \sf P_1 = 2000$

$2000 was invested at 5% and $5000 was invested at 8%.

Learn more about simple interest here:

brainly.com/question/27743947

brainly.com/question/28350785

5 0

1 year ago

Find the equation of the line passing through the point (–1, 0) and parallel to the line y = –1∕2x + 3∕7

PilotLPTM [1.2K]

Answer:

y = -1/2x - 1/2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step 1: Define

y = -1/2x + 3/7

Point (-1, 0)

Step 2: Find parallel line

Parallel lines have the same slope as the original but different y-intercepts.

m = -1/2

y = -1/2x + b

0 = -1/2(-1) + b

0 = 1/2 + b

b = -1/2

Step 3: Write parallel line

y = -1/2x - 1/2

7 0

3 years ago

write an equation in y=mx+b for a line that passes through (3,-4) & has a slope of -3. you can write it in point-slope and c

dedylja [7]

Y = -3x + b
Plug in point
-4 = -3(3) + b
-4 = -9 + b, b = 5
Solution: y = -3x + 5

5 0

3 years ago