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Rewrite the given expression in the form 3^u where u is a constant or an algebraic expression.
(5√3)^x
Rewrite the expression in the form 2^u where u is an algebraic expression
(1/2)^x-3
Rewrite the expression in the form 2 Superscript u where u is an algebraic expression
9/3√3
Rewrite the expression in the form 2 Superscript u where u is an algebraic expression
16/3√2^x
Solution: (1) The expression [tex](5\sqrt{3} )^x[/tex] [tex]\text{ is written as }[/tex] [tex]5^x3^{\frac{x}{2}[/tex].
[tex](5\sqrt{3} )^x=5^x(\sqrt{3} )^x\\(5\sqrt{3} )^x=5^x(3^\frac{1}{2} )^x\\(5\sqrt{3} )^x=5^x3^\frac{x}{2}[/tex]
The value of u is [tex]\frac{x}{2}[/tex].
(2) The expression [tex](\frac{1}{2})^x-3[/tex] is written as [tex]2^{-x}-3[/tex].
[tex](\frac{1}{2})^x-3=(2^{-1})^x-3\\(\frac{1}{2})^x-3=2^{-x}-3[/tex]
The value of u is -x.
(3) The expression [tex]\frac{9}{3\sqrt{3} }[/tex] is written as [tex]\sqrt{3} (2^0)[/tex].
[tex]\frac{9}{3\sqrt{3} }=\frac{9}{3\sqrt{3} }(\frac{\sqrt{3}}{\sqrt{3}} )\\\frac{9}{3\sqrt{3} }=\frac{9(\sqrt{3}) }{3(3) }\\\frac{9}{3\sqrt{3} }=\sqrt{3} \\\frac{9}{3\sqrt{3} }=\sqrt{3}(2^0)[/tex]
THe value of u is 0.
(4)The expression [tex]\frac{16}{3(\sqrt{2^{x}} )}[/tex] is written as [tex]\frac{1}{3}(2^{4-\frac{x}{2}})[/tex].
[tex]\frac{16}{3(\sqrt{2^{x}} )}=\frac{2^4}{3(2^x)^{1/2}}\\\frac{16}{3(\sqrt{2^{x}} )}=\frac{1}{3}(2^{4-\frac{x}{2}})[/tex]
The value of u is [tex]4-\frac{x}{2}[/tex].
Final Answer:
1. [tex]\( (5\sqrt{3})^x \) in the form \( 3^u \): \( 3^{x\log_3(5\sqrt{3})} \)[/tex]
2. [tex]\( (1/2)^{x-3} \) in the form \( 2^u \): \( 2^{-(x-3)} \)[/tex]
3. [tex]\( \frac{9}{3\sqrt{3}} \) in the form \( 2^u \): \( 2^{2/3} \)[/tex]
4. [tex]\( \frac{16}{3\sqrt{2^x}} \) in the form \( 2^u \): \( 2^{(2x-4)/3} \)[/tex]
Explanation:
1. [tex]\( (5\sqrt{3})^x \) in the form \( 3^u \): \( 3^{x\log_3(5\sqrt{3})} \)[/tex]
To express [tex]\( (5\sqrt{3})^x \)[/tex] in the form [tex]\( 3^u \)[/tex], we use the logarithmic property [tex]\( a^{\frac{1}{n}} = n\sqrt[n]{a} \)[/tex]. Applying this, we get [tex]\( 5\sqrt{3} = 3^{\frac{\log_3(5\sqrt{3})}{\log_3(3)}} \)[/tex], and raising it to the power ( x ) yields the desired form.
2. [tex]\( (1/2)^{x-3} \) in the form \( 2^u \): \( 2^{-(x-3)} \)[/tex]
To rewrite [tex]\( (1/2)^{x-3} \)[/tex] in the form [tex]\( 2^u \)[/tex], we use the property [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex]. Applying this, we transform the expression to [tex]\( 2^{-(x-3)} \)[/tex], achieving the desired form.
3. [tex]\( \frac{9}{3\sqrt{3}} \) in the form \( 2^u \): \( 2^{2/3} \)[/tex]
By canceling out the common factor of 3 in the numerator and denominator, we simplify [tex]\( \frac{9}{3\sqrt{3}} \)[/tex]to [tex]\( 2^{2/3} \), as \( \sqrt{3} = 3^{1/2} \)[/tex].
4. [tex]\( \frac{16}{3\sqrt{2^x}} \)[/tex] in the form [tex]\( 2^u \): \( 2^{(2x-4)/3} \)[/tex]
Applying the property[tex]\( a^{-b} = \frac{1}{a^b} \)[/tex] to the denominator, we simplify [tex]\( \frac{16}{3\sqrt{2^x}}[/tex] to [tex]\( 2^{(2x-4)/3} \)[/tex], achieving the desired form.
what is the scale factor of 25ft by 75ft and 1:15
fast help plz.Brennon has a computer game that responds with either "go" or "stop" when a button is pressed. The probability that the response is "stop" is not known to game players. Brennon presses the button repeatedly and records the numbers of "stop" responses.
Number of button presses 10 50 100
Number of "stop" responses 2 18 33
Estimate P(go) using the collected data
G. 67%
O. 18%
L. 50%
D. 33%
plz help i had to write this whole thing
Each pair of polygons is similar .Determine the transformation that maps one figure onto the other . Then find the missing side measures number 4 please
the speed of an object in space is shown in the graph
what is the slope of the line ?
Answer:
Step-by-step explanation:
The answer is fifteen
Explanation: 6-3/0.4-0.2=3 over 0.2 which is equivalent to 15
Answer B: 15
Step-by-step explanation:
When 8 is added to the number that is produced by doubling the number x, the result is equal to 8 times the number that is 5 less than x. What is the value of x?
can someone help me i am confused
Answer:
It is 8
Step-by-step explanation:
A bicycle manufacturer is reducing the number of spokes on each bicycle wheel by 4. a wheel on one of the other companies new cross-country bike has 32 spokes. Which equation could be used to determine the number of spokes that a wheel on a cross country bike used to have?
The original number of spokes on the wheel was 36.
The question seeks to determine the original number of spokes on a bicycle wheel, given that the current number is 32 after reducing by 4. To find the original number of spokes, we need to use a simple algebraic equation that adds the removed spokes back to the current number.
Let x represent the original number of spokes. The manufacturer has reduced the number of spokes by 4, so we subtract 4 from the original number to get the current number of spokes. The equation that represents this scenario is:
x - 4 = 32
To find the original number of spokes, we need to solve for x:
x = 32 + 4
x = 36
Therefore, the original number of spokes on the wheel was 36.
light travels at a rate of 1.86 x 10^5 miles per second. if the distance from a star to a planet and its orbit is 32,000,000 miles, find how long it takes to light of the star to reach the planet in seconds.
Checking on answer to this
Solve the following system of equations by linear combination:
3d – e = 7
d + e = 5
The solution is (3, 2).
The solution is (2, –1).
There is no solution.
There are an infinite number of solutions.
beer Bottles are filled so that they contain an average of 475 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 8 ml.
Final answer:
The question is related to the mathematics subject area and addresses the high school grade level. It involves understanding the normal distribution, mean, standard deviation, and the application of these concepts in quality control and filling volumes for beverage containers.
Explanation:
The subject of the question relates to the concept of normal distribution, which is a fundamental concept in statistics, a branch of mathematics. The student is provided with the information that beer bottles are filled so that they contain an average of 475 ml of beer, with the amount of beer being normally distributed and having a standard deviation of 8 ml. This scenario involves understanding concepts like mean, standard deviation, and the properties of a normal distribution.
To visualize similar quantities, consider that an eyedropper holds about 1 milliliter, a juice box holds about 25 centiliters (or 250 milliliters), and a soda bottle holds about 1 liter. The provided beer bottle contains roughly half the amount of a typical soda bottle. Knowledge of standard units such as liters and milliliters is essential in this context.
Furthermore, the question can be connected with practical scenarios such as the filling volumes for beverage containers, where manufacturers need to ensure that the bottles and cans contain the labeled amount of liquid. Quality control relies on statistics to test whether the actual amounts meet the desired standards, factoring in variations from measurement processes or filling mechanisms.
Graph the set of points. Which model is most appropriate for the set? (-2, 10), (-1,1), (0, -2), (1, 1), (2, 10)
Quadratic
Quadratic
Liner
Exponential
Answer:
The model that is most appropriate for the set is:
Quadratic.
Step-by-step explanation:
Clearly after looking at the graph of the function which is made from the given set of points ; we observe that the graph is similar to a graph of the quadratic function whose vertex is at (0,-2) and also the line x=0 is the axis of symmetry of the graph.
Since, the graph is symmetric to this line.
Hence, the model is:
Quadratic.
The shaded area represents a cement walkway around a pool. State the algebraic expression that represents the difference between the outside perimeter of the walkway and the perimeter of the pool.
The difference between the outside perimeter of the walkway and the perimeter of the pool in algebraic expression is (2x + 14).
How to solve perimeter of rectangle?Pool:
Length = 2x - 1
Width = 12
The perimeter of the pool = 2(length + width)
= 2{(2x - 1) + 12}
= 2(2x - 1 + 12)
= 2(2x + 11)
= 4x + 22
Outside perimeter of the walkway:
Length = (2x - 1) + x
= 3x - 1
Width = 12 + 7
= 19
The perimeter of the walkway = 2(length + width)
= 2{(3x - 1) + 19}
= 2(3x - 1 + 19
= 2(3x + 18)
= 6x + 36
Difference between the outside perimeter of the walkway and the perimeter of the pool = The perimeter of the walkway - The perimeter of the pool
= (6x + 36) - (4x + 22)
= 6x + 36 - 4x - 22
= 2x + 14
Hence, (2x + 14) is the expression which represents the difference between the perimeter of the walkway and the perimeter of the pool.
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Owen plots the numbers 4, ???6, ???8, and ???3 on a horizontal number line. Which list shows the numbers in the order in which they would appear from left to right on the number line?
???8, ???6, ???3, 4
???3, ???6, ???8, 4
???3, 4, ???6, ???8
???8, ???6, 4, ???3
Answer:
The answer is a. the real answer
Step-by-step explanation:
Harrison saved $48.97 from his first paycheck and $67.09 from his second paycheck. How much did he save from the paychecks? A. $18.12 B. $115.96 C. $116.06 D. $116.16
Subtract.
(6k+2)−(3k−2)
Enter your answer, in simplified form, in the box.
Please answer!
The graph shows how the cost of gasoline
How do you convert a whole number to a percentage?
Final answer:
To convert a whole number to a percentage, multiply the number by 100 and add the percent symbol. For instance, converting the whole number 3 to a percentage results in 300%.
Explanation:
How to Convert a Whole Number to a Percentage
To convert a whole number to a percentage, you simply multiply the number by 100 and add the percent (%) symbol to the result. This is because a percentage represents a part per hundred. For example, to convert the whole number 3 to a percentage, you multiply it by 100, which equals 300%. Here's the step-by-step process:
Start with the whole number (e.g., 3).
Multiply the whole number by 100 (3 x 100 = 300).
Add the percent symbol to express the result as a percentage (300%).
This method is a straightforward percentage calculation, turning a whole number into its equivalent percentage form.
Factories and solve x^2 +x -12=0
The annual inflation rate is 3.5% per year. If a movie costs $7.50, determine which of the following graphs best models the change in price, with respect to time, of the movie ticket.
Answer:
Step-by-step explanation:
Let's model the cost by the following exponential function: c (t) = (7.50) * (1.035) ^ t Where, c (t): cost of the movie after t years. 7.50: initial cost of the movie in $ 1,035: annual percentage increase due to inflation. t: time in years. for t = 0 We have: c (t) = (7.50) * (1.035) ^ 0 c (t) = (7.50) * (1) c (t) = 7.50 Answer: The graph that best models the function is: GRAPH 2 (from left to right).
Amy walks 5 miles north. Then, she turns east and walks another 6 miles before she stops to rest.
How far is Amy from her starting point when she stops to rest?
Round your answer to the nearest tenth
A carpenter makes custom desks. He currently has 7 desks in his showroom. If he can build 3 desks each week, how many weeks will it take him to have a total of 22 desks?
Which expression represents the product of Z and 7?
A. Z+7
B. Z-7
C. Z•7
D. Z divided by 7
Each of the two congruent sides of an isosceles triangle is 8 inches less than twice the base.the perimeter of the triangle is 74 inches ,what is the length of the base
The length of the base of the isosceles triangle is 18 inches.
Explanation:Let the length of the base be 'b' inches. According to the given information, each of the congruent sides of the isosceles triangle is 8 inches less than twice the base. So, the length of each congruent side is (2b - 8) inches.
The perimeter of the triangle is the sum of all three sides, which is given as 74 inches. So, we can write the equation:
(2b - 8) + (2b - 8) + b = 74
Simplifying the equation, we get:
5b - 16 = 74
5b = 90
b = 18
Therefore, the length of the base is 18 inches.
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The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1). If ΔDEF ∼ ΔABC and DE = 4AB, what is the length of EF? √10
Answer:
The length of EF is [tex]4\sqrt{17}[/tex] units.
Step-by-step explanation:
The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1).
Using distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]BC=\sqrt{(3+1)^2+(1-2)^2}=\sqrt{17}[/tex]
It is given that ΔDEF ∼ ΔABC.
If two triangles are similar then the corresponding sides are proportional.
[tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]
[tex]\frac{AB}{4AB}=\frac{BC}{EF}[/tex] (DE = 4AB)
[tex]\frac{1}{4}=\frac{BC}{EF}[/tex]
[tex]EF=4\times BC[/tex]
[tex]EF=4\times \sqrt{17}[/tex]
[tex]EF=4\sqrt{17}[/tex]
Therefore the length of EF is [tex]4\sqrt{17}[/tex] units.
You don't need to explain, just try to write the answer and then PRESS PIC
3 and 1/3x + 5.3 = -2. What is x?
5. this gate contains a series if congruent quadrilaterals. Are the quadrilaterals also parallelograms? Explain.
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