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3 years ago

How do I solve this. Log 5x = log (2x+9)

1 answer:

3 0

$D:5x\ \textgreater \ 0 \wedge 2x+9\ \textgreater \ 0\\
D:x\ \textgreater \ 0 \wedge 2x\ \textgreater \ -9\\
D:x\ \textgreater \ 0 \wedge x\ \textgreater \ -\dfrac{9}{2}\\
D:x\ \textgreater \ 0\\\\
\log5x=\log(2x+9)\\
5x=2x+9\\
3x=9\\
x=3$

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Use the product rule to simplify sq root 147x^2

klio [65]

Answer:7x√3

Step-by-step explanation:

√147x^2

√49 (3) x^2

√7^2 ⋅ 3x^2

√7^2x^2 ⋅ 3

√(7x)^2 ⋅ 3

7x√3

3 0

3 years ago

Help with math question 24

kykrilka [37]

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3 years ago

Maria took a taxicab from her home to the theater

Artist 52 [7]

Answer:

The answer is the third option, C = 5 + 0.25m

Step-by-step explanation:

We already know that the official price for the taxi is 5 dollars, so we aren't multiplying that value by anything.

However, the text mentions that for each mile, Maria is taxed an extra .25 cents. Therefore, you have to add the base amount, 5, plus the 25cent with the m next to it to symbolize that however many miles she goes, the 25 cents will be multiplied by that value.

4 0

4 years ago

write and solve a real world problem in which you need to find the initial value of the function. Then explain how you solved th

Mama L [17]

you are planting roses

you started at 12 noon

at 3pm, you have 80 roses left

at 6pm, you have 20 roses left

if you planted roses at a constant rate, how many roses did you start with?

so we can find the slope of this linear function as (20roses-80roses)/(6pm-3pm)=60roses/3hrs=-20roses/hr

your quantity goes down by 20 roses per hour (you plant 20 per hour)

r=-20t+?

find ?, the number of roses when t=0

at 3pm yo have 80 roses

80=-20(3)+?

80=-60+?

140=?

you had 140 roses intiailly

if you wanted an exponenntial

the town polpulationn grows at an exponential rate

the town was founded in 2000

in 2010, the town's population was 1000

in 2015, the town's populationw as 2000

find intial polpulation

exponential can be modeled by $y=ab^t$ where y=population, t=time and b and a are constants (a=initial population)

we are given that after 10 years (2010), y=102400

after 15 years, (2015), y=3276800

$102400=ab^{10}$ and $3276800=ab^{15}$

divide the 2nd by the first equation, remembering our exponential properties like $\frac{x^a}{x^b}=x^{a-b}$

$32=b^{5}$

take 5th root of both sides

$b=2$

subsitute back

$102400=ab^{10}$

$102400=a(2)^{10}$

$102400=1024a$

$100=a$

the intial population is 100 people

7 0

3 years ago

. A condo in Orange Beach, Alabama, listed for $1.4 million with 20% down and financing at 5% for 30 years. What is the monthly

vovikov84 [41]

Listed price = $1.4 million
Down payment = 20% of $1.4 million = 0.2 x 1,400,000 = 280,000
Amount left to pay = $1.4 million - 280,000 = $1,120,000
Present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) / r
where: PV = $1,120,000
r = 5% = 0.05
t = 12
n = 30 years.
1,120,000 = P(1 - (1 + 0.05/12)^-(12 x 30)) / 0.05
1,120,000 x 0.05 = P(1 - (1 + 1/240)^-360)
56,000 = P(1 - 0.2238)
P = 56,000 / 0.7761 = 72,148.83
Therefore, the monthly payment is $72,148.83

8 0

4 years ago