10/3 * 3^x -3^(x-1) = 81
Solve for x.
Answers
Answer:
\(x=3\)
Step-by-step explanation:
\(~~~~~~~\dfrac{10}{3} \cdot 3^x - 3^{x-1} = 81\\\\\\\implies 10 \cdot 3^{x-1} - 3^{x-1} = 81~~~~~~~~~~~~~~~~~~~~;\left[\dfrac{a^m}{a^n} =a^{m-n} \right]\\\\\\\implies 9\cdot 3^{x-1} = 81\\\\\\\implies 3^{x-1} = \dfrac{81}{9}\\\\\\\implies 3^{x-1} = 9\\\\\\\implies 3^{x-1} = 3^2\\\\\\\implies x -1 = 2\\\\\\\implies x = 2+1\\\\\\\implies x = 3\)
Answer:
\( \boxed{ \rm \: x = 3}\)
Step-by-step explanation:
Equation given:
10/3 × 3^x -3^(x-1) = 81
Finding the value of x :
\( \implies \rm \: \cfrac{10}{3} \times 3 {}^{x} - \cfrac{3 {}^{x} }{3} = 81\)
(We took 3^x-1 as 3^x/3 because according law x^m-n = x^m/x^n)\( \implies \rm \cfrac{10 \times 3 {}^{x} }{3} - \cfrac{3 {}^{x} }{3} = 81\)
\( \implies \rm \cfrac{10 \times 3 {}^{x} - 3 {}^{x} }{3} = 81\)
Taking 3x common,we get:
\( \implies \rm \cfrac{3 {}^{x}(10 - 1) }{3} = 81\)
\( \implies \rm3 {}^{x} \times \cfrac{ \cancel9}{ \cancel{3} } = 81\)
\( \implies \rm3 {}^{x} \times 3 = 81\)
\( \implies \rm {3}^{x} = \cfrac{ \cancel{81} \: {}^{27} }{ \cancel3} \)
\( \implies \rm3 {}^{x} = 3 {}^{3} \)
Since according to the law of exponents,if the bases are equal then the powers are equal too.
\( \implies \rm{x} = \boxed3\)
Hence,the value of x is 3.
Related Questions
help due in 30 min!!!!!!!!!!!!!!!
Answers
Answer:
They have the same slope
Step-by-step explanation:
slope=4
What are the factors of 36xyz?
Answers
Answer:
1
Step-by-step explanation:
If Fx) = 7x, which of the following is the inverse of (Fx)?
A. F^1(x) = x/7
B. F^1(x) = 7x
C. F^1(x) = x-7
D. F^1(x) = x+7
Answers
Answer:
A. F^1(x) = x/7
Step-by-step explanation:
\(y = 7x \\ x = 7y \\ \frac{x}{7} = \frac{7y}{7} \)
\(y = \frac{x}{7} \)
Therefore the inverse is
\(f {}^{1} = \frac{x}{7} \)
Wiyot is earning money for a longboard by selling lemonade at the soccer fields. Being a precocious and poorly-supervised 12 year old, Wiyot has no transportation and decides to use water from a nearby river.
Business is booming! He sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up. How many TOTAL cups of giardia-laced lemonade will Wiyot have sold by the time his parents get a call from county health officials on day 8?
________
Answers
The cups of giardia-laced lemonade that Wiyot will have sold by the time his parents get a call from county health officials on day 8 is 75 cups.
How to calculate the value?From the information, Wiyot sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up.
This is an arithmetic sequence and will be expressed as:
= a + (n - 1)d
a = first term = 33
d = common difference = 6
n = 8
This will be:
= a + (n - 1)d
= 33 + (8 - 1)6
= 33 + (7 × 6)
= 33 + 42
= 75
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What is the slope intercept form equation that represents the line with a slope of 5 that passes through the point (0,-2)
Answers
Answer:
Step-by-step explanation:
y + 2 = 5(x - 0)
y + 2 = 5x - 0
y = 5x - 2
Answer:
y = 5x - 2
Step-by-step explanation:
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
The y-intercept is where x = 0, or where the graph crosses the y-axis. Given in the problem, we have that the y-intercept is (0, -2), so b = -2.
We also know the slope is 5.
So, our slope-intercept form is:
y = 5x - 2
~ an aesthetics lover
what is the slope of the line passing through po bye A and B?
Answers
Which statement is most likely to show a constant rate of change???
A. The outside temp compared with the time of day.
B. The cost of a new car compared with the number of tires it has.
C. The weight of a child compared with its age in months.
D.The distance traveled by a truck driving at a constant speed compared with time.
Answers
I believe you answer would be D) The distance traveled by a truck driving at a constant speed compared with time.
What is the rental cost? Step by step.
Answers
The rental cost in dollars per square foot is $11,00
What is the rental cost in dollars per square foot?Cost of renting 1.250 square feet = $13, 750 per month
Rental cost per square foot = Total renting cost / total renting area
= $13, 750 per month / 1.250 square feet
= $11,000
Hence, $11,000 is the rental cost in dollars per square foot.
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Select the correct answer. Rewrite the following expression.
Answers
The solution of the expression, \(x^{\frac{9}{7} }\) is \(\sqrt[7]{x^{9} }\).
How to solve an expression?An expression is a combination of numbers, variables, functions such as addition, subtraction, multiplication or division etc.
Therefore, let's rewrite the expression to it's equivalent expression.
An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.
Therefore, using indices rule
\(x^{\frac{9}{7} }\) = \(\sqrt[7]{x^{9} }\)
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do
any one need points
Answers
Trapezoid ABCD is rotated 180 degrees about the origin and then reflected over the x-axis, followed by a reflection over the y-axis. What is the location of point A after the transformations are complete? Trapezoid ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 2, 3. D is at negative 1, 1. (5, −1) (−5, −1) (5, 1) (−5, 1)
Answers
Based on the set of transformations for trapezoid ABCD, the location of point A after the transformations are complete is: D. (−5, 1).
What is a rotation?In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
By applying a rotation of 180° to the given point, the coordinates of its image is given by:
(x, y) → (-x, -y)
Points A = (-5, 1) → Points A' = (-(-5), -(1)) = (5, -1).
Next, we would reflect the given point over the x-axis as follows;
(x, y) → (x, -y)
Points A' = (5, -1) → Points A' = (5, -(-1)) = (5, 1)
Lastly, we would reflect the given point over the y-axis as follows;
(x, y) → (-x, y)
Points A' = (5, 1) → Points A' = (-(5), 1) = (-5, 1)
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How much will you need to invest at 2.5% to have earned $900 in interest in 5 years
Answers
Answer:
we need $7200 to earn $900 in 5 years.
Step-by-step explanation:
Simple Interest formula: \(\frac{PRT}{100}\) .......where p is principal, r is rate of interest, t is time
Using the formula:
\(\frac{p*2.5*5}{100} =900\)
\({p*2.5*5} =900*100\)
\(12.5p =90000\)
\(p = 90000/12.5\)
\(p=7200\)
Answer:
7200 is the principal
needed
There are fifty people standing in the concession line at the movies. Two fifths of them, want to purchase popcorn. One half of this group, will purchase a drink. How many people will buy popcorn and a drink?
A. 100 people
B. 20 people
C. 10 people
D. 5 people
Answers
Answer:
C. 10 people
Step-by-step explanation:
2/5 of 50 = 20
1/2 of 20 = 10
hope this helps, brainliest plz!!
After a storm, Micheal measured 6 7/8 inches of snow. What is this amount as a decimal?
Answers
The monthly mortgage payment on the Anderson's home is $604.29.
Additionally, they pay $1,213.87 in annual real estate taxes and $1,031 per year
in homeowner's insurance.
What is the total amount of their entire monthly payment?
Answers
1031/12 = 85.92
604.29+101.16+85.92= $791.37
2. Given the measures of the sides of a triangle below, which set could form a right triangle?A. 6, 7, 8B. 9, 12, 15C. 12, 15, 20D. 20, 25, 30
Answers
A Right triangle is a triangle that has an angle whose measure is 90 degrees.
The Pythagorean Theorem states that:
\(a^2=b^2+c^2\)Where "a" is the hypotenuse (the longest side of the Right triangle) and "b" and "c" are the legs of the triangle.
Knowing the above, you can check each set:
Set A
\(6,7,8\)Notice that the longest side is 8. Then:
\(\begin{gathered} 8^2=6^2+7^2 \\ 64\ne85 \end{gathered}\)This set couldn't form a Right triangle.
Set B
\(9,12,15\)The longest side is 15. Then:
\(\begin{gathered} 15^2=9^2+12^2 \\ 225=225 \end{gathered}\)This set could form a Right triangle.
Set C
\(12,15,20\)Knowing that the longest side is 20, you get:
\(\begin{gathered} 20^2=12^2+15^2 \\ 400\ne369 \end{gathered}\)This set couldn't form a Right triangle.
Set D
\(20,25,30\)The longest side is 30. Then:
\(\begin{gathered} 30^2=20^2+25^2 \\ 900\ne1025 \end{gathered}\)This set couldn't form a Right triangle.
The answer is: Option B.
Find sin theta if cos theta is 4/5
Answers
Answer:
Step-by-step explanation:
hello :
cos²θ +sin²θ = 1 and cosθ =4/5
(4/5)² + sin²θ = 1 so : sin²θ = 1 - 16/25
sin²θ = 9/25 = (3/5)²
sinθ = 3/5 or sinθ = - 3/5 because : (3/5)²= (- 3/5)²= 9/25
I please help me I need the answers
Answers
Answer:
43 white flowers, and 43 pink flowers in the first bed
86 white flowers, and 129 pink flowers in the second bed
129 white flowers total, and 172 pink flowers total
Step-by-step explanation:
Given =(5,-2, 3) and >= (1, 1, 2) find an ordered triple that represents 3u - 2v.
Answers
The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).
To find an ordered triple representing \(3u - 2v\),
where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),
we can perform the following operations:
\(3u = 3(5, -2, 3)\)
\(3u = (15, -6, 9)\)
\(2v = 2(1, 1, 2)\)
\(2v = (2, 2, 4)\)
Now, subtracting 2v from 3u gives:
\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)
\(3u - 2v = (15-2, -6-2, 9-4)\)
\(3u - 2v = (13, -8, 5)\)
Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).
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Find the slope from the line of best fit y = 5 - 3x.
Answers
Answer:
slope = -3
Step-by-step explanation:
⭐ What is the equation of a line in slope intercept form?
\(y = mx+b\)m is the slope. It is always multiplied with the variable (x)b is the y-intercept. It is always the term without a variableThe given line of best fit is written in slope-intercept form. All we have to do is identify which term is the slope.
\(y = -3x + 5\)
-3 is the coefficient of x. Therefore, -3 is the slope.
Step-by-step explanation:
What is the equation of a line in slope
intercept form?
mr + b
m is the slope. It is always multiplied with
the variable (x)
b is the y-intercept. It is always the term
without a variable
The given line of best fit is written in slope-
intercept form. All we have to do is identify
which term is the slope.
Y
-30+5
-3 is the coefficient of x. Therefore, -3 is
the slope.
solve system of equations
y= 8x + 1
y = 6x + 3
(2,4)
(0,1)
(1,9)
or (4,14)
Answers
Use the properties of exponents to simplify the expression:
Answers
The simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.
How can you simplify → aˣ/aⁿ?We can write the simplified form of the given expression using the exponent rule as -
{aˣ/aⁿ} = {aˣ a⁻ⁿ} = {aˣ ⁻ ⁿ}
Given is the expression as -
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\)
We can simplify the expression as -
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (27)^{\frac{1}{2} \times \frac{2}{3} }\)
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 27^{\frac{1}{3} }\)
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (3)^{3}^{\frac{1}{3} }\)
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 3\)
Therefore, the simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.
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In the Gaussian integral, how does the left side of this equation equal the right side? An answer would be really appreciated, thank you.
Answers
the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.
How do we calculate?
using completing the square method:
Starting with the left side of the equation:
∫\(e^(^-^x^2)\) dx
\(e^(^-^x^2) = (e^(^-x^2/2))^2\)
∫\((e^(^-^x^2/2))^2 dx\)
let u = √(x²/2) = x = √(2u²).
dx = √2u du.
∫ \((e^(^x^2/2))^2 dx\)
= ∫ \((e^(^-2u^2)\)) (√2u du)
The integral of \(e^(-2u^2)\)= √(π/2).
∫ \((e^(-x^2/2))^2\) dx
= ∫ (√2u du) \((e^(-2u^2))\\\)
= √(π/2) ∫ (√2u du)
We substitute back u = √(x²/2), we obtain:
∫ \((e^(-x^2/2))^2\)dx
= √(π/2) (√(x²/2))²
= √(π/2) (x²/2)
= (√π/2) x²
A comparison with the right side of the equation shows that they are are equal.
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Horacio is solving the equation-3/4 + 2/5x = 7/20x -1/2. Which equation represents possible ways to begin solving for x?
Answers
The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2
Which equation represents possible ways to begin solving for x?From the question, we have the following parameters that can be used in our computation:
-3/4 + 2/5x = 7/20x -1/2
The first step is to collect the like terms
So, we have
2/5x - 7/20x = 3/4 - 1/2
This represents an equation of the possible way to begin solving for x
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I got B and C wrong does anyone know the right answer ?
Answers
(B) 1/5
Divide the numerator and denominator by 10(C) 0.2
1/5 = 0.2Answer:
B:1/5
Step by step explanation:
The number that can fully simply 10 /50 is 10 ,10 goes 1 (once) into 10 and 10 goes 5 times into 50 .
C:1/5
a single rose costs 3$ and a bunch of roses costs 12$.How many times as much does the bunch of roses cost than the single rose?
Answers
The bunch of roses costs $12/$3 = 4 times as much as a single rose.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
The bunch of roses costs 4 times as much as a single rose.
To see why, we can divide the cost of the bunch of roses by the number of roses it contains. If a bunch of roses costs $12 and contains, say, 4 roses, then each rose in the bunch costs $3. On the other hand, a single rose costs $3 on its own.
Therefore, the bunch of roses costs $12/$3 = 4 times as much as a single rose.
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Ramon needs 12 oranges to make 3 glasses of juice. How many oranges does he need to make 5 glasses?
Answers
Answer:
20 oranges
Step-by-step explanation:
4 oranges per glass
Answer:
20
Step-by-step explanation:
12 divided by 3 to work out how many oranges per glass which is 4
4 times 5=20
Which shows the correct way to
calculate the percent change if the
original value of your stock was $750
and the new value of your stock is
$1,000?
A. (1,000+ 750)/750 = 230%
B. (750-1,000)/1,000 = -25%
C. (1,000-750)/750 = 33%
Answers
The correct way to calculate the percent change between the original value of $750 and the new value of $1,000 is option C.
C. (1,000 - 750)/750 = 250/750 = 1/3 ≈ 0.3333 = 33.33%
Therefore, the correct answer is option C, which represents a percent change of approximately 33.33%.
Find the volume of the object.
Answers
Answer:
pretty hard
Step-by-step explanation:
What is the equation of the graphed line in standard from?
A. 1/2x+y=6
B. 1/2x-y=-6
C. y=2x+6
D. -2x+y=6
