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mixer [17]
4 years ago
8

Question #12 Please help

Mathematics
1 answer:
julia-pushkina [17]4 years ago
7 0
\bf \textit{logarithm of factors}\\\\
log_a(xy)\implies log_a(x)+log_a(y)
\\\\\\
\textit{Logarithm of rationals}\\\\
log_a\left(  \frac{x}{y}\right)\implies log_a(x)-log_a(y)
\\\\\\
\textit{Logarithm of exponentials}\\\\
log_a\left( x^  b \right)\implies   b\cdot  log_a(x)\\\\
-------------------------------\\\\


\bf a)\\\\
log_9\left( \sqrt[3]{y^2+y} \right)\implies log_9\left[ (y^2+y)^{\frac{1}{3}} \right]\implies \cfrac{1}{3}log_9(y^2+y)
\\\\\\
\cfrac{1}{3}log_9[y(y+1)]\implies \cfrac{1}{3}\left[~log_9(y)~+~log_9(y+1) ~ \right]
\\\\\\
\cfrac{1}{3}log_9(y)~~+~~\cfrac{1}{3}log_9(y+1)


\bf b)\\\\
log_4\left( \frac{a^2b}{\sqrt{c}} \right)\implies log_4(a^2b)~-~log_4(\sqrt{c})\implies log_4(a^2b)~-~log_4(c^{\frac{1}{2}})
\\\\\\\
[~log_4(a^2)~+log_4(b)~]~~-~~\cfrac{1}{2}log_4(c)\\\\\\ log_4(a^2)+log_4(b)-\cfrac{1}{2}log_4(c)
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How many three-digit positive integers have three different digits and at least one prime digit?
Blababa [14]

The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.

The only two components in prime numbers are 1 and the number itself.

Any whole number greater than one is a prime number.

It has exactly two factors—1 and the actual number.

There is just one 2-digit even prime number.

Every pair of prime numbers is always a co-prime.

The product of prime numbers can be used to represent any number.

Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960

Learn more about prime numbers here:

brainly.com/question/145452

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6 0
2 years ago
A system of equations is shown:
Harrizon [31]

Answer:

<h2>(1, 4)</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}2x=-y+6&(1)\\-4x+3y=8&(2)\end{array}\right\\\\(1)\\-y+6=2x\qquad\text{subtract 6 from both sides}\\-y=2x-6\qquad\text{change the signs}\\y=6-2x\\\\\text{substitute it to (2):}\\\\(2)\\-4x+3(6-2x)=8\qquad\text{use the distributive property}\\-4x+(3)(6)+(3)(-2x)=8\\-4x+18-6x=8\qquad\text{subtract 18 from both sides}\\-10x=-10\qquad\text{divide both sides by (-10)}\\x=1\\\\\text{put the value of x to (1):}\\\\y=6-2(1)\\y=6-2\\y=4

6 0
3 years ago
Ivanna and her husband are each starting a saving plan. Ivanna will initially set aside $50 and then add $50.85 every week to th
Olenka [21]

Answer:

N=0.019666a-0.983284 or

A = 50.85n + 50

Step-by-step explanation:

Let's solve for n.

a = 50 + 50.85n

Step 1: Flip the equation.

50.85n + 50 = a

Step 2: Add -50 to both sides.

50.85n+50+-50=a+-50

50.85n n = a - 50

Step 3: Divide both sides by 50.85.

50.85n

50.85

=

a-50

50.85

n=0.019666a-0.983284

Let's solve for a.

a = 50 + 50.85n

3 0
3 years ago
This is the floor plan of the house Ben is building.
Travka [436]

Answer:

1 cause when I solve with the college method it is equal to 1

trust me boi

Step-by-step explanation:

4 0
4 years ago
Sandy and sally were able to paint a a at house in 5 hours together: it takes sally 9 hours to finish this job alone. Without he
OLEGan [10]

Answer:

9/44 of an hour, or just over 12 minutes

Step-by-step explanation:

Person 1 + Person 2 divided by Person 1 x Person 2 = Both together

9 + x / 9*x = 5

9+x/9x = 5

Multiply both sides by 9x

9 + x = 45x

Subtract x from both sides

9 = 44x

Divide by 44 to get x.

9/44 of an hour

5 0
3 years ago
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