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Valentin [98]
3 years ago
6

10. If log10x = 1 + a and log10y = 1 – a, show that xy = 100. How?

Mathematics
1 answer:
gregori [183]3 years ago
7 0

Step-by-step explanation:

log x = 1 + a

a = log x - 1

log y = 1 - a

a = 1 - log y

So

log x - 1 = 1 - log y

log x + log y = 2

log (xy) = 2

xy = 100

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Before the clowns arrived, only 35% of the children wore happy faces. If 117 children did not wear happy faces, how many childre
denis-greek [22]

Answer:

180

Step-by-step explanation:

If 35% did not wear happy faces, then 100% -35% = 65% did wear happy faces.

Then we have ...

... 117 = 65% × (all children)

... 117/0.65 = all children = 180 . . . . . . divide by 65% = 65/100 = 0.65

There were 180 children in all.

4 0
3 years ago
Find the equation of the line passing<br> through the points (3,3) and (4,5).<br> y = [? ]x +[ ?]
muminat

\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{3}}}\implies \cfrac{2}{1}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{2}(x-\stackrel{x_1}{3}) \\\\\\ y-3=2x-6\implies y=2x-3

3 0
3 years ago
Find the total amount of money​ (maturity value) that the borrower will pay back on a loan of ​$1 comma 760 at 13 and one half %
bagirrra123 [75]

Answer:

The borrower will pay back $4,136.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

T = E + P.

In this question:

Loan amount of 1760, so P = 1760

Interest rate of 13 and one half, so 13.5%. This means that I = 0.135.

10 years, so t = 10

Interest on the Loan:

E = P*I*t = 1760*0.135*10 = 2376

Total amount:

T = E + P = 2376 + 1760 = 4136

The borrower will pay back $4,136.

4 0
3 years ago
Is 16/17 and 8/32 proportional
pickupchik [31]
16 has several factors, BUT bear in mind that 17 is a prime number, it has no factors other 1, so 16/17 cannot be simplified,

\bf \cfrac{16}{17}\qquad \cfrac{8}{32}\implies \cfrac{16}{17}\qquad \cfrac{1}{4}\implies \cfrac{16}{17}~\ne~ \cfrac{1}{4}
8 0
3 years ago
A farmer has a rectangular plot of land. There is a bother identical plot of land 100 yards east and 100 yards north. Find the c
Anna [14]

Answer:

Step-by-step explanation:

Area of a rectangular plot = Length × width

With the aid of the diagram attached below.

<u>For plot 1:</u>

The area = ( 60 - 20 ) × ( 80 - 20 )

Area = 40 × 60

Area = 2400 sq yard

<u>For plot 2:</u>

Area = (160 - 120 ) × ( 180 - 120 )

Area = 40 × 60

Area = 2400 sq yard

Therefore, the combined area of the two plots of land = 2400 + 2400

= 4800 square yards

8 0
3 years ago
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