Applying the negative exponent rule, the value of 9^-1/2 is calculated as: 1/3.
What is the Negative Exponent Rule?If a number has a negative exponent, i.e. a^-1/2, it can be rewritten and expressed as:
a^-1/2 = 1/a^½
1/a^½ can also be rewritten or expressed as:
1/a^½ = 1/√a
Thus, we would apply the negative exponent rule to find the value of the expression, 9^-1/2 as explained below:
9^-1/2 = 1/9^½
Rewrite 1/9^½ as 1/√a
1/9^½ = 1/√9
Take the square root of 9
1/√9 = 1/3
This implies that, the value of the expression, 9^-1/2 is 1/3.
In conclusion, applying the negative exponent rule, the value of 9^-1/2 is determined as: 1/3.
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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]
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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.
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Select the correct answer. The square of y varies directly as the cube of x. When x = 4, y = 2. Which equation can be used to find other combinations of x and y? A. B. C. D.
The direct variation equation can be used to find other combinations of x and y is y² = 4x³/27
What is direct variation?Direct variation is variation in which one quantity increases as another quantity increases or decreases as anothe rquantity decreases.
How to find equation can be used to find other combinations of x and y?Since we have that the square of y varies directly as the cube of x.
Writing this as a direct variation mathematically, we have
y² ∝ x³
So, the direct variation equation is
⇒ y² = kx³ where k = constant of proportionality
Now, given that when x = 4, y = 2.
Substituting the values of x and y into the equation, we have
y² = kx³
2² = k(3)³
4 = k(27)
k = 4/27
Substituting the value of k into the expression, we have
y² = kx³
y² = 4x³/27
So, the direct variation equation can be used to find other combinations of x and y is y² = 4x³/27
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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.
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Select the correct answer. Consider the formula for the slope between two coordinate points, m, shown below. m = y 2 − y 1 x 2 − x 1 Which of the following equations is equivalent to the slope formula? A. y 2 = m ( x 2 − x 1 ) + y 1 B. x 1 = m ( y 2 − y 1 ) + x 2 C. x 2 = m ( y 2 − y 1 ) + x 1 D. y 1 = m ( x 2 − x 1 ) + y 2
The equation that is equivalent to the slope formula is y₂ = m(x₂ - x₁) + y₁
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The slope between two points A(x₁, y₁) and B(x₂, y₂) is:
Slope (m) = (y₂ - y₁) / (x₂ - x₁)
m = (y₂ - y₁) / (x₂ - x₁)
m(x₂ - x₁) = y₂ - y₁
y₂ = m(x₂ - x₁) + y₁
The equation that is equivalent to the slope formula is y₂ = m(x₂ - x₁) + y₁
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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.
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
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.
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.
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A florist buys a dozen roses for $12.96 and sells them for $48.48. Find the amount of markup on a single rose.
The amount of markup on a single rose is $2.96
What is profit?Profit = Selling Price – Cost Price.
We have,
We can consider the cost price as:
Bought amount = $12.96
We can consider the selling price as:
Selling amount = $48.48
Now,
Markup price can be considered as the profit:
Profit = Sellin price - Cost price
Profit = $48.48 - $12.96
Profit = $35.52
Since in a dozen we have 12 roses the markup price for each rose is:
= $35.52 / 12
= $2.96
Thus the amount of markup on a single rose is $2.96
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this multi answer so please put multi
The pair of numbers that have the greatest common factor of 3 will be:
18 and 15
6 and 9
3 and 9
How to illustrate the information?It should be noted that the factor of a number can be multiplied with another number that get the original number.
Therefore, the of pair of numbers that have the greatest common factor of 3 will be:
18 and 15
6 and 9
3 and 9
It should be noted that they have 3 as a common factor.
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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
After four years of higher education, Marshall just graduated with a Bachelor's degree in Physics from NYU where the annual cost of tuition was $20,000. He paid for college by earning $11,000 annually through the work study program and receiving an annual scholarship. He covered the remainder of the costs by taking out $20,000 in student loans. If he didn't fund his education with savings or grant money, what was the amount of Marshall's annual academic scholarship?
The annual academic scholarship amount is $15000.
This problem can be solved by unitary method and also by addition and subtraction.
Total annual tuition fee of Marshal is $20000.
His annual earning through the scholarship is $11000.
He also took an loan of about $20000 from student loan.
Total fee for the four years Bachelor's degree in Physics is = $20000×4
= $80000
He cleared $20000 by student loan then remaining amount
=(80000-200000)
= $60000
Then the amount he earned through the scholarship program in total to clear the dues = $60000
Annual amount of scholarship is =$15000
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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
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Find the sum: 1/3+1/4
Answer:
7/12
Step-by-step explanation:
i used lowest common denomator
Answer:
answer is 7/12
Step-by-step explanation:
hope this helps
The equation of the line through the point (2, 3) with slope -2 is
The correct answer is 2x - y +7 =0.
Various equations like equation of slope, y-intercept, slope- intercept must be known.
We have a line equation in the provided problem, and we must determine the slope and intercepts in order to create the graph. Assuming that m is the slope and c is the y-intercept, the slope intercept form is known as y=mx+c. We may determine the slope by utilizing the slope intercept formula.
The equation for the line in the problem can be written using the point-slope formula. The linear equation's point-slope form is: (y-y1) = m(x-x1)
( y - (3))=-2(x-2)
y - 3 = 2x + 4
2x - y +7 =0
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Please help me please help me
Answer:
Step-by-step explanation:
90 degree
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
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5 - (x - 2)² for x =- 1
Answer: -4
Step-by-step explanation:
5 - (x - 2)²=
5 - (-1 - 2)²=
5 - (-3)²=
5 - (3)²=
5-9=-4
Answer:45
Step-by-step explanation:
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 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.
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
Expand each logarithm.
log₃[(xy 1/3)+z²]³
After expanding logarithm equation is : [tex]3.log_3(xy^\frac{1}{3} + z^2)[/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]log_3[xy^\frac{1}{3} + z^2]^3[/tex]
apply formulas log a^x = x log a
=> [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]
Thus, after expanding the logarithm equation is : [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]
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(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.
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Let f(x)=3 x²-4 and g(x)=x-2 . Calculate (f ⁰ g⁻¹)(x) for x=-3 .
If the inverse of f exists, it is represented by f⁻¹ and exists only if f is a bijective function.
If x = -3 then (f ⁰ g⁻¹)(x) is 23.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Let the two functions be f(x) = 3x² - 4 and g(x) = x - 2
(g⁻¹)(x) = 1 - 2
(g⁻¹)(x) = -1
substitute (g⁻¹)(x) value in (f ⁰ g⁻¹)(x)
(f ⁰ g⁻¹)(x) = (f ⁰ ) (-1)
then f(x) equation is 3 x² - 4 substitute -1 in x
f(-1) = 3(-1)² - 4
f(-1) = -1
Now when x = -3 the (f ⁰ g⁻¹)(x) value is
f(-3) = 3(-3)² - 4
f(-3) = 23
Therefore, the value of (f ⁰ g⁻¹)(x) for x = -3 is 23.
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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
a random two-digit number(10-99) is drawn.find the probability p(32)
Based on the sample space, the probability of P(32) is 1/90
What is probability?The probability of an event is the chance or the likelihood that the event would occur.
Note that the chance or the likelihood is represented as a numerical value
How to determine the probability?The sample space is given as
Space = two-digit numbers
There are 90 two-digit numbers
So, the sample size is
Size = 90
There is only one two-digit number with the value 32
So, we have
n(32) = 1
The probability of selecting 32 is
P(32) = n(32)/Size
So, we have
P(32) = 1/90
Hence, the probability of P(32) is 1/90
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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$!
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
d(n)=-5(1/2)n-1 what is the third term in the sequence
Answer: d3 = - 17/2
correction: This is an explicit formula
All we have to do is plug n = 3 in the formula to find the 3rd term.
2. d(3)=-5(1/2)3-1
= -5/4
Step-by-step explanation: