Expand each logarithm.
log m³/n⁴ p⁻²
After expanding logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c a × b = log_c a + log_c b , c is the baselog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]\frac{log_{10} m^3}{n^4 \\ p^-2} \\[/tex]
apply formula log a^x = x log a
[tex]= > \frac{3 log_{10} (m)}{\frac{n^4}{p^2} }\\ \\= > \frac{3 log_{10} (m) p^2}{{n^4} }[/tex]
Thus, after expanding the logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]
To know more about logarithms, visit :
https://brainly.com/question/12049968
#SPJ4
A tortoise moves
at about 0.05
meters per
second. How
many
centimeters per
second does a
tortoise move?
Answer:
0.05 metrs = 5 cetimeters
Step-by-step explanation:
1 meter = 100 centimeters
0.05 meters = 0.05 * 100 = 5 centimeters
(2x² + 3x³ - 3x²-
3x - 4x-3)÷(x-2)
The simplified form of the expression [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex] is [tex]\frac{3x^{3}-x^{2} -7x-3 }{(x-2)}[/tex]
As per the question statement, we are provided with an expression [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex].
We are supposed to simplify the above mentioned expression.
To solve this question, let us simplify the expression, part by part, i.e., first, let us consider the numerator part which is
[2x² + 3x³ - 3x² -3x -4x - 3].
Here, it is clearly visible that the numerator expression consists of terms having same same variable but with different coefficients, such as
[2x², -(3x²)] and [-(3x), -(4x)]. Therefore, we can perform the mentioned operations on the like terms and thus simplify our numerator.
[tex][2x^{2} +(-3x^{2} )]=(2x^{2} -3x^{2} )=-(x^{2})\\[/tex]
And, [tex][(-3x) + (-4x)]=-(3x+4x)=-x(3+4)=-(7x)[/tex].
Hence, [tex](2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=[+3x^{3}+(2x^{2} -3x^{2})-(3x+4x)-3]\\or, (2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=[+3x^{3}+(-x^{2} )-7x-3]\\or, (2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=(+3x^{3}-x^{2}-7x-3)\\[/tex]
And our denominator is (x - 2). Since, [2x² + 3x³ - 3x² -3x -4x - 3] does not equate to Zero for (x = 2), there (x - 2) is not a factor of the numerator, i.e., the numerator cannot be exactly divided by the denominator.
Therefore, the simplest form of our expression [tex]\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}[/tex] is [tex]\frac{3x^{3}-x^{2} -7x-3 }{(x-2)}[/tex].
Expressions: These are mathematical statements, that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.Like Terms: Terms having the same variable.To learn more about expressions, click on the link below.
brainly.com/question/18077352
#SPJ9
Please help I need this in an hour
if p and q are the robots of the equation 3x^2 _ 16x + 2 = 0, find the value of p+q(1+ p).
Step-by-step explanation:
3x² - 16x + 2 = 0
ax² + bx + c = 0
a = 3 , b = -16 , c = 2
= p + q.(1 + p)
= p + q + p.q
= -b/a + c/a
= -(-16)/3 + 2/3
= (16 + 2)/3
= 18/3
= 6
Write each equation in exponential form.
log₆6=1
Answer:
The answer to the given question is 6
Logarithmic scale: A measurement scale in which the position is marked using the logarithm of a value rather than the actual value.
A logarithmic equation includes a logarithm in the variable x.
An exponential equation is one in which the variable is represented by an exponent. A logarithmic equation is one in which the logarithm of a variable-containing expression is used.
For logarithmic equations, log b (x) = y is equivalent to b^y = x such that x > 0, b > 0 and b is not equal to 1.
In the given problem, b = 6, x = 6 and y = 1
b = 6
x = 6
y = 1
Substituting the values of b, x and y into the equation b^y = x;
6^(1) = 6
therefore, the value of the given equation log₆6=1 is 6
Learn more about logarithm here:
https://brainly.com/question/25710806
#SPJ9
Please help me please help me
Answer:
Step-by-step explanation:
90 degree
Please help!
Rebecca has twice as much money as Rachel. If Rebecca gives Rachel $60, then the two of them will have the same amount of money. How much money did Rebecca have originally?
A.
B.
C.
D.
E.
Answer:
Rebecca originally had 240 dollars.
Step-by-step explanation:
Let's set B as Rebecca's money and C as Rachel's.
Rebecca has twice as much money as Rachel
B = 2C
If Rebecca gives Rachel $60, then the two of them will have the same amount of money
B - $60 = C + $60
let's combine the 2 by subtracting the second from the first
B - (B - $60) = 2C - (C + $60)
$60 = C - $60
$120 = C
so Rachel had 120 dollars.
Rebecca had twice as much, so 240 dollars.
If Rebecca gives $60 to Rachel, they have $180 each. Everything checks out.
At a baseball game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team. If 735 people attending the game supported the home team, what was the total number of people attending the game?
Answer:
1300
Step-by-step explanation:
455 divided by 35%
= 455 x 100/35
= 455 x 20/7
= 65 x 20
= 1300
The total number of people attending the game is 2100.
Given that, at a baseball game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the total number of people attending the game be x.
Given, 735 people attending the game supported the home team.
Now, 35% of x=735
⇒ 35/100 × x=735
⇒ 35x=73500
⇒ x=73500/35
⇒ x=2100
Therefore, the total number of people attending the game is 2100.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ2
In a science lab, a number of rock samples are weighed. If the scientist finds one of the rocks to weigh 6 pounds and this is 38.7% of the total weight of all of the rocks, what is the weight of all of the rocks? If necessary, round your answer to the nearest tenth.
10.5 lb
2.3 lb
232.2 lb
15.5 lb
Answer:
15.5
Step-by-step explanation:
We are trying to find out:
38.7% of what number is 6?
38.7% as a decimal is .387
.387x = 6 Divide both sides by .387
x = 15.503875969
Round 15.5
An item is regularly priced at $30. It is now priced at a discount of 70%
off the regular price. What is the price now?
If something is priced at 30$,then 70% off would make it 9.00$!
Do the math: the price of iron ore can be measured per ton. a ton is about the
weight of a cow. if the price of 1 ton of iron ore starts at $104 per ton with a
quantity demanded of 90 tons, then rises to $211 per ton, what is the new quantity
demanded at this price? assume the slope of the demand curve is -3.2 and the
y-intercept is $392. round your answer to the nearest tenth of a ton.
Answer:
Step-by-step explanation:
56.6 tons.
Based on the slope of the demand curve and the new price of iron ore, the new quantity demanded at the new price of $211 is 49.60 tons
What is the new equilibrium quantity demanded?The equation given will allow us to find the new quantity demanded:
y = Mx + c
y = new quantity demanded
m = slope of the demand curve
x = change in price of iron ore
c = y intercept
Solving for the new quantity demanded at the new price gives:
= -3.2 x (211 - 104) + 392
= -342.40 + 392
= 49.60 tons
Find out more on new quantity demanded at https://brainly.com/question/2822773.
#SPJ1
Rachel earns $6000 less than twice as much as Tom. Their two incomes total $48,000. How much does Rachel earn?
Answer:
30,000
Step-by-step explanation:
Add 6,000 to 48,000, which equals 54,000
You then divide 54,000 by three = 18,000
Multiply 18,000 by 2 = 36,000
Subtract 6,000 frome 36,000 = 30,000
*Please mark brainliest
Every Tuesday so far, I noticed that
Casey wears yellow to class. This
Tuesday she will probably wear yellow to
class. Is it inductive or deductive or a detachment or syllogism
Answer:
inductive
Step-by-step explanation:
vbkugu stottlxd5xlhlhclxylyyldydpdyxyo
Write each expression as a single logarithm.
log₃4 + log₃y + log₃8 x
The expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in a single logarithm form.
Given that the expression is log₃4 + log₃y + log₃8 x.
We are told to write the expression as a single logarithm.
Change of base theorem is basically used when we have to find the log values having different bases from 10 as we have tables which tell the log values with base 10. We know that [tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex] and
log mn=log m+log n.
The expression is log₃4 + log₃y + log₃8 x.
log₃4 + log₃y + log₃8x=[tex]log_{3}[/tex] (4*y)+ [tex]log_{3}[/tex] 8x
=[tex]log_{3}[/tex] (4*y*8x)
=[tex]log_{3}[/tex] 32xy
Hence the expression log₃4 + log₃y + log₃8x can be written as [tex]log_{3}32xy[/tex] in a single logarithm form.
Learn more about change of base theorem at https://brainly.com/question/24788069
#SPJ4
30 POINTS! Question is on the attachment below :D
A. 35 in. x 17 in.
B. 36 in. x 18 in.
C. 35 in. x 18 in.
D. 36 in. x 17 in.
Answer:
B
Step-by-step explanation:
35 [tex]\frac{3}{4}[/tex] ≈ 36 ( to the nearest whole number
17 [tex]\frac{5}{6}[/tex] ≈ 18 ( to the nearest whole number )
then 36 in × 18 in
how many gallons are in a liter again i forgot
Answer:
The exact conversion rates between Liters and Gallons is as follows...
1 Liter = 0.264 Gallons
and
1 Gallon = 3.785 Liters
An elephant charged 13.3 meters on 15 seconds. At this rate, how far would the elephant go in one minute? (20 seconds = 1/3 minute)
Answer: 53.2 meters
Step-by-step explanation:
Since 15 seconds is 1/4 of 1 minute, multiply 13.3 by 4 to get 53.2.
Choose Yes or No to tell if the equation is true.
I'll give u brainliest and i'll do anything this is really important
Answer:
true,true,false,false
Step-by-step explanation:
true it's the amount of decimal places
true: same with this true
false: if it was 10^5 then yes but it's not
false: there is one too many 10s
write the number below (81) as a power with a base of 3 and a base of 9
Answer:
base of 3 --> 3^4 (three to the fourth); base of 9 --> 9^2 (nine squared)
Step-by-step explanation:
3 x 3 = 9 x 3 = 27 x 3 = 81 = 3^4
You multiply 3 by itself 4 times.
9 x 9 = 81 = 9^2
You multiply 9 by itself 2 times.
PLEASE ANSWER Quick in a game!
Slope of a line passing through
(1, 5) and (7, 9)?
-1/5
5/2
2/3
1/2
Answer:
Choice 3 (2/3)
Step-by-step explanation:
Slope is equal to the change in y over the change in x.
If we look at the two coordinates, we'll see that to get from (1, 5) to (7, 9), you need to move up 4 and to the right 6.
4/6 = 2/3, which matches the 3rd choice
Hope this helps
help i need help with this maths question
x add 3 = 8
Answer:
i guess X=5 because 3+5=8?
Step-by-step explanation:
write an expression that represents the phrase "one third the difference of 15 and a number"
Answer: 1/3-5(n)
Step-by-step explanation:
Which of the following interpretations for the given expression is correct
(x+y)^n/2
The correct interpretation for the given expression is the sum of x and y raised to the power of half n
How to determine the correct interpretations for the given expression?The expression is given as
(x + y)^n/2
To interpret the expression, we start by evaluating the expression in the bracket and the exponent
So, we have
(x + y): The sum of x and yn/2: n divided by 2Hence, the correct interpretation for the given expression is the sum of x and y raised to the power of half n
Read more about expressions at
https://brainly.com/question/8797023
#SPJ1
order the following rational and irrational numbers from least to greatest
1.25,square root of 2,1 3/8, and 1 3/5
The ordering of the numbers will be 1.25, 1 3/8, ✓2, 1 3/5 and 1.875.
How to illustrate the information?It should be noted that ✓2 = 1.414
It should be noted that 1 3/8 = 1.375
It should be noted that 1 3/5 = 1.6
The other numbers given are 1.25 and 1.875
Therefore, the ordering of the numbers will be 1.25, 1 3/8, ✓2, 1 3/5 and 1.875.
Learn more about numbers on:
brainly.com/question/24644930
#SPJ1
PLEASE HELP!! DUE TODAY!! WILL MARK BRAINLIEST IF MULTIPLE PEOPLE RESPOND RIGHT AND FAST!
Question: The sets of numbers 6, 8, 10 and 5, 12, 13 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples! (5 points)
We know that 6, 8, 10 and 5, 12, 13 are Pythagorean triples.
The formula to see if a set of three numbers is a pythagorean triple is:
[tex]a^{2} +b^{2} =c^{2}[/tex]
For the first one, we can do
6^2 + 8^2 = 10^2 and see if it is true.
36 + 64 = 100, so this works.
The next one, we can do
5^2 + 12^2 = 13^2
25 + 144 = 169
This also works.
So in conclusion, using the formula, we can prove that they are both Pythagorean triples.
I hope this is clear to you, have a great day! :)
a = y² - x²
b = 2xy
c = x² + y²
where x and y are positive integers y > x
→ In Pythagorean triple number set 6,8,10
c² = a² + b²(10)² = (6)² + (8)²100 = 36 + 64100 = 100→ In Pythagorean triple number set 5,12,13
c² = a² + b²13² = 5² + 12²169 = 25 + 144169 = 169
Solve each equation. Round to the nearest ten-thousandth. 5x +3=12
the value of the given equation 5x +3=12 Round to the nearest ten-thousandth = 1.8000
What is rounding off?In a given base, a round number is a number that ends with one or more "0s." So, 590 is more round than 592, but less round than 600. A round number is frequently interpreted in both technical and casual language to stand for a value or values close to the nominal value represented.
According to the given data:given:- 5x +3=12
simplifying:
5x +3=12
5x = 12 - 3
5x = 9
x = 9/5
x = 1.8000
the value of the given equation 5x +3=12 Round to the nearest ten-thousandth = 1.8000
To know more about rounding off visit:
https://brainly.com/question/13391706
#SPJ4
Show that k=(4 + 3j)/(5-j) can be rearranged to j =(5k - 4)/(3 + k)
Answer: f(x)=4
f(x)=√3x−4
f(x)=4x−5
Step-by-step explanation:
What is the simplest form of the quotient √72 x⁵ y³ z⁸ / √3 x y²z² ?
(A) √24 x⁴ y z⁶
(C) 24 x⁴ y z⁶
(B) 2 x² z³ √6y
(D) 12 x² y z⁶
The simplest form of the quotient √72x⁵y³z⁸/√3xy²z² is (B) 2x²z³√6y.
What do we mean by simplest form?When the numerator and denominator have no common factors other than one, the fraction is in its simplest form. When the top and bottom cannot be any smaller while still being whole numbers, the fraction is in its simplest form. To simplify a fraction, divide the top and bottom numbers by the largest number that divides both numbers exactly (they must stay whole numbers).So,
Given: 72x⁵y³z⁸/√3xy²z²Then,
72x⁵y³z⁸/√3xy²z²Simplify the radical by dividing it into a product of known factors and assuming positive real numbers, which gives us:2x²z³√6yTherefore, the simplest form of the quotient √72x⁵y³z⁸/√3xy²z² is (B) 2x²z³√6y.
Know more about the simplest form here:
https://brainly.com/question/21298204
#SPJ4
Mrs. morton has a special reward system for her class. when all her students behave well, she rewards them by putting 333 marbles into a marble jar. when the jar has 100100100 or more marbles, the students have a party. right now, the jar has 242424 marbles. write an inequality to determine the number of additional times, rrr, mrs. morton could reward the class in order for the students to have a party. will the students have a party if mrs. morton rewards them 313131 additional times?
Yes the students have a party is mrs. Morton reward them 313131 additional times.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most of the time, size comparisons between two numbers on the number line are to be made. Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a > b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since a is apparently less than or solely greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
Read more about inequalities here:
https://brainly.com/question/20383699
#SPJ4