Sam's rationale for the third step based on logarithm properties would be logb(b^x+y), power rule of exponents. Thus, the correct answer is C.
The first step of Sam's proof is to show that logb(MN) is equal to logb(b^x.b^y), which is a substitution of MN for b^x.b^y. This is based on the product property of logarithms, which states that logb(MN) = logb(M) + logb(N) for any positive numbers M and N and any base b, as long as b doesn't equal 1.
The third step of her proof is to simplify logb(b^x.b^y) further by applying the power rule of exponents, which states that:
b^(x+y) = b^x.b^ySo, by substituting b^(x+y) for b^x.b^y, we get:
logb(b^(x+y)) = logb(b^x+y)So, in short, the justification of the third step is based on the power rule of exponents, and it shows that logb(b^x.b^y) can be simplified further to logb(b^x+y).
The answer choice A, logb(b^xy), power rule of exponents, is incorrect because it implies that the third step is to multiply x and y instead of adding them.
This question should be provided with answer choices, which are:
A. logb(b^xy), power rule of exponents.B. logb(b^x-y), subtraction property of exponents.C. logb(b^x+y), power rule of exponents.D. logb(b^x/y), division property of exponents.The correct answer is C.
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Answer: its c
Step-by-step explanation:
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Mary has a large sum of money to deposit, but since she has heard many stories from her grandmother about the Great Depression, when many banks lost their customers’ deposits, she is worried that the bank might not keep her money safe. Give Mary some recommendations about what she can do to make sure that her money stays protected.
Mary should make sure to choose a bank that is FDIC insured. Furthermore, if she has more than maximum deposit insurance amount to deposit, she should spread her deposits out among several separate banks. These should be totally different banks, not simply different branches of the same bank. The FDIC will insure up to the maximum deposit insurance amount at each bank, even if the bank fails.
Can someone help me, I forgot how to solve this
Answer:
y = mx + b
Step-by-step explanation:
write the following decimals in the form of p\ q= 0 and p,q are con-primes 1) 15.265
Given:
The decimal number is 15.265.
To find:
The decimals in the form of [tex]\dfrac{p}{q}[/tex] and p,q are co-primes.
Solution:
Let the decimal number be [tex]x=15.265[/tex].
It can be rewritten as
[tex]x=15.265\times \dfrac{1000}{1000}[/tex]
[tex]x=\dfrac{15265}{1000}[/tex]
[tex]x=\dfrac{5\times 3053}{5\times 200}[/tex]
Cancel out the common factors.
[tex]x=\dfrac{3053}{200}[/tex]
Here, p=3053 and q=200 and the HCF of (p,q) is 1. So, p and q are co-primes.
Therefore, the requited fraction form is [tex]\dfrac{3053}{200}[/tex].
It's urgent, Please answer, Make Sure you Round it
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
460, 451,442
Find the 37th term.
Answer:
136
Step-by-step explanation:
This is an arithmetic sequence
The formula is an = a1 + f × (n-1)
n= the number we are trying to find = 37
a= the number in any given space on the sequence
a1= 460
f= the common difference between the numbers
f= -9 because you subtract 9 from each to get the number
a37= 460-9(37-1)
a37= 460-9(36)
a37= 460- 324
a37= 136
[tex] \\ [/tex]
The first three terms of a sequence are 460, 451, 442[tex] \\ [/tex]
To Find :[tex] \\ [/tex]
37th term of sequence = ?[tex] \\ [/tex]
Solution :[tex] \\ [/tex]
Clearly these three terms are making an arithmetic sequence, with :
First term, a = 460 Common difference, d = 451 - 460 = - 9[tex] \\ [/tex]
Now, we have to find 37th term of sequence = [tex] \tt a_{37}[/tex]
[tex] \\ [/tex]
Now, we know that :
[tex] \large \underline{\boxed{\bf{a_{n} = a + (n-1)d}}}[/tex]
[tex] \\ [/tex]
[tex] \tt : \implies a_{37} = a + (37-1)d[/tex]
[tex] \tt : \implies a_{37} = a + 36d[/tex]
[tex] \\ [/tex]
Now, by substituting values of a and d :
[tex] \tt : \implies a_{37} = 460 + 36 \times (-9)[/tex]
[tex] \tt : \implies a_{37} = 460 - 324[/tex]
[tex] \tt : \implies a_{37} = 136[/tex]
[tex] \\ [/tex]
Hence, value of 37th term of given sequence is 136.
Help me plz i will give brainlest
Answer:
the answer should be (3,-2)
The translation shown in the graph moves the figure to the right. What kind of translation is shown?
the figure go to the left
Select the equivalent expression.
3-5 = ?
Daniel debe $12.300 a Miguel y paga con un billete de $50.000 ¿cuanto dinero le devuelven ?
Answer:
37,700
Step-by-step explanation:
I believe that you do 50,000 - 12,300. That would get you to your final answer of 37,700. So Miguel has to give 37,700 back to Daniel.
Hope this helped you!
Answer:
Miguel devuelve a Daniel $ 37.70
Step-by-step explanation:
50 - 12.3 = 37.7
The age at which a person can be tried as an adult
Answer:
giyi
Step-by-step explanation:
answer quickly and quietly incorrectly please
Answer:
Your answer is
A & E
Mark my answer as brainlist . I need that urgently . Folow me for more answer.
Step-by-step explanation:
If
f(x) = x^2 + 2x - 4
and
g(x) = 3x + 1
Find
f(g(x)) = ?
Answer;
f (x) = 2x-4g (x) =x^2
Step-by-step explanation:
The solution is 9x² + 12x - 1
The composition function f ( g ( x ) ) is 9x² + 12x - 1
What is Composition of functions?
Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
The value of f ( x ) = x² + 2x - 4
Let the second function be represented g ( x )
The value of g ( x ) = 3x + 1
Now , the composition function f ( g ( x ) ) is calculated by
Substitute the value of x as 3x + 1 , in f ( x ) , we get
f ( g ( x ) ) = f ( 3x + 1 )
f ( 3x + 1 ) = ( 3x + 1 )² + 2 ( 3x + 1 ) - 4
On simplifying the equation , we get
f ( 3x + 1 ) = ( 9x² + 6x + 1 ) + ( 6x + 2 ) - 4
f ( 3x + 1 ) = 9x² + 12x - 1
Therefore , the value of f ( 3x + 1 ) is 9x² + 12x - 1
Hence , the composition function f ( g ( x ) ) is 9x² + 12x - 1
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Find the slope!!!
Quickly please
Answer:
the slope is m= 2
Answer:
2
Step-by-step explanation:
Slope is (y1 - y2) / (x1 - x2) for any 2 respective x's and y's.
For any of the points here, you get 2.
Mrs. Brownstone brought 56 liters of juice for the fifth grade party. How many milliliters of juice did she bring?
Answer:
56000 milliliters
1 liter = 1000 milliliters
56(1000)=56000
Step-by-step explanation:
Find the degree of the following polynomial:
7xy223 + 8y5 – 3x4 + 4
Answer:
224
Step-by-step explanation:
polynomial degree:224
leading term:7x^223
leading coefficient:7
URGENT!!!!!!
Use scientific notation to estimate the number of inches in 1,225 miles. Include all calculations in your final answer.1 inch ≈ 1.578 × 10 -5 miles.
Answer: The number of inches in 1225 miles is [tex]7.763\times 10^7[/tex]
Step-by-step explanation:
Scientific notation is defined as the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.
Example: 3000 is written as [tex]3.0\times 10^3[/tex]
Given : [tex]1.578\times 10^{-5}[/tex] miles = 1 inch
Thus 1 mile = [tex]\frac{1}{1.578\times 10^{-5}}=0.634\times 10^5[/tex] inches
1225 miles = [tex]\frac{0.634\times 10^5}{1}\times 1225=776.3\times 10^{5}=7.763\times 10^7[/tex] inches
Solve 11=h-14 please
Answer:
25
Step-by-step explanation:
25-14=11
Answer:
25
Step-by-step explanation:
11=25-14
Since 11+14 is 25 then h in 11=h-14 must be 25
PLZ HELP ME PLZ I NEED IT
Answer:
Step-by-step explanation:
The intersection occurs at the point (3,-3) so those are the coordinates.
what is domain and range because I got it wrong is not the right one
Answer:
You most likely got it wrong because you didn't plot all the points that are actually in the table, the domain and range are both right.
Which expression is equivalent to 1/4(12x + 16) + 3x + 7
Please help!!!
a. 15/4x + 7
b. 15x + 23
c. 6x + 23
d. 6x + 11
Answer:
the answer is 6x+11
Step-by-step explanation:
1/4(12+16)+3x+7
1/4×4(3x+4)+3x+7
(3x+4)+3x+7
3x+4+3x+7
6x+11
What is the measurement of angle D
HELP PLS
9514 1404 393
Answer:
68°
Step-by-step explanation:
Alternate interior angles are congruent, so we have ...
123° = d° +55°
d = 123 -55 = 68
Angle D measures 68°.
_____
For those of you inclined to use this answer for other questions, here are the other angles in this figure.
A = 55° . . . . alternate interior with 55°, so congruent
B = C = 180° -123°
B = C = 57°
HELPPPPPPP pleaseeeee mathhhh
9514 1404 393
Answer:
y = 1/6x
Step-by-step explanation:
The constant of proportionality is the ratio of y to x:
k = y/x
Using the point you have circled, it is ...
k = 2/12 = 1/6
Then the equation y = kx can be written:
y = 1/6x
Help help help help help help help help help
Answer: a: 23.4
Step-by-step explanation:
Answer:
A.23.4
Step-by-step explanation:
first find the volume of the tank 18x12x25=5400 then find how many gallons of water tank can hold 5400/231=23.4
hope this helps have a blessed day :)
X/4=8
Solve that using the opposite operation
Answer:
x = 32
Step-by-step explanation:
4 • (x/4) = 8 • 4
x = 32
Step-by-step explanation:
[tex]\qquad\sf\dashrightarrow x/4=8 [/tex]
[tex]\qquad\sf\dashrightarrow x=4×8 [/tex]
[tex]\qquad\sf\dashrightarrow x=32 [/tex]
A car corporation produced 1980 fewer cars this month than last.
Write a signed number to represent this month's change in production.
Answer:
there was 1300 fewer cars so your answer would be -1300 :-)
Choose the equations that are equivalent. Select all that apply.
A. 52 = 8n +4
B. 42n + 1) = 52
C. 4 = 52 - 8n
D. 4n = 48
Answer:
A. 52 = 8n +4
C. 4 = 52 - 8n
The masses of 4 containers loaded on a ship are 28 tonnes,45 tonnes,16.8tonnesand 48500kg .What is 5he total mass in tones?
Step-by-step explanation:
first of all we have to change kg into ton= 48500kg into ton =53.462ton(48500/907.168)
after that we add all the weight of 4 container = 28+45+16.8+53.462
total will be his total mass of tones he had =143.262
y=7x+8 can somebody help me
a cylindrical tank has a radius of 3 m and a height of 12 m.
What is the volume of the tank?
Answer:
Volume = 339.12 m^3
Step-by-step explanation:
Volume = Pi(r^2)(height)
Volume = 3.14(3^2)(12)
Volume = 339.12 m^3
Damian’s computer repair shop earned $2,500 in income last week. Expenses were $2,750. What was Damian’s profit or loss for the week?
Answer:
2500-2750 = - 250
hence,he lost $250
What is the solution to the equation 1/3 n =6
Answer:
n=18
Step-by-step explanation: