Answer:
The equivalent functions are;
\(g(x) = 3^{-2 \cdot x }\)
\(g(x) = 9^{-x}\)
\(g(x) = \left (\dfrac{1}{9} \right )^x\)
Step-by-step explanation:
The given function is f(x) = (1/3)^(2·x)
\(f(x) = \dfrac{1}{3} ^{2 \cdot x}\)
The given function can be simplified as follows;
\(f(x) = \dfrac{1}{3} ^{2 \cdot x} = 3^{-1 \cdot2 \cdot x } = 3^{-2 \cdot x } = g(x)\)
∴ \(f(x) = \dfrac{1}{3} ^{2 \cdot x}\) ≡ \(g(x) = 3^{-2 \cdot x }\)
2) The given function can also be simplified as follows;
\(f(x) = \dfrac{1}{3} ^{2 \cdot x} = \left (\dfrac{1}{3} ^2\right )^x = \left (\dfrac{1}{9} \right )^x = (9^{-1}) ^x} = 9^{-1 \times x} = 9^{-x} = g(x)\)
∴ \(f(x) = \dfrac{1}{3} ^{2 \cdot x}\) ≡ \(g(x) = 9^{-x}\)
3) The given function can also be simplified as follows;
\(f(x) = \dfrac{1}{3} ^{2 \cdot x} = \left (\dfrac{1}{3} ^2\right )^x = \left (\dfrac{1}{9} \right )^x = g(x)\)
∴ \(f(x) = \dfrac{1}{3} ^{2 \cdot x}\) ≡ \(g(x) = \left (\dfrac{1}{9} \right )^x\)
Choose all the numbers that are common multiples of 3 and 12
- 21
- 27
- 48
- 63
- 72
- 81
- 84
Answer:
Step-by-step explanation:
-48
-72
-84
basically if its divisible by 12 its divisible by 3
Write an algebraic expression for "8 less than the product of 3 and j"
Answer: 3(j)-8
Step-by-step explanation: well first the product means multiplication, so u multiply 3 and j. and the second part is 8 less than that, so 8 is the last part so u do 3 times j minus 8. i graduated from high school last year so i know what im doin
According to the question,
Let,
The first number be "3".The second number be "j".The third number be "8".Now,
The product of "3" and "j" will be "3j" and the third number i.e., "8" less than the product.
Then the equation will be:
\(3j-8\)Thus the above response is appropriate.
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What is the slope intercept form of -8x+2y=4
Answer:
y=4x+2
Step-by-step explanation:
Answer:
y=4x+4
Step-by-step explanation:
move 8x to the left side than divide 2y by 8x and 4 to give u that answer. hope it helps
Help!! Please :( #54 Please help
Answer:
Range is 61.
Step-by-step explanation:
You plug in the highest and lowest number in for x and then work the problem out. In this case, plugging in 1 gives you -5 and -7 gives you 56. then, take 56+5 to figure out the distance between the two.
prove(sec theta-tan theta)(sec theta+tan theta)=1
Answer:
\(( \sec \theta - \tan \theta)( \sec \theta + \tan \theta)\)
from difference of two squares:
\({ \boxed{ \tt{( {a}^{2} - {b}^{2}) = (a - b)(a + b) }}}\)
\( = { \sec }^{2} \theta - { \tan}^{2} \theta \\ = (1 + { \tan}^{2} \theta) - { \tan}^{2} \theta \\ = 1\)
hence proved
let . explain how to find a set of one or more homogenous equations for which the corresponding solution set is w
The homogeneous equation corresponding to W = Span(2, 1, -3) is 0.
To discover a set of one or more homogeneous equations for which the corresponding answer set is W = Span(2, 1, -three), we will use the idea of linear independence.
The set of vectors v1, v2, ..., vn is linearly unbiased if the only strategy to the equation a1v1 + a2v2 + ... + anvn = 0 (wherein a1, a2, ..., an are scalars) is a1 = a2 = ... = an = 0.
Since W = Span(2, 1, -3), any vector in W may be represented as a linear aggregate of (2, 1, -three). Let's name this vector v.
Now, to find a homogeneous equation corresponding to W, we need to discover a vector u such that u • v = 0, in which • represents the dot product.
Let's bear in mind the vector u = (1, -1, 2). To check if u • v = 0, we compute the dot product:
(1)(2) + (-1)(1) + (2)(-3) = 2 - 1 - 6 = -5.
Since u • v = -five ≠ zero, the vector u = (1, -1, 2) is not orthogonal to v = (2, 1, -3).
To discover a vector that is orthogonal to v, we can take the go product of v with any other vector. Let's pick the vector u = (1, -2, 1).
Calculating the cross product u × v, we get:
(1)(-3) - (-2)(1), (-1)(-3) - (1)(2), (2)(1) - (1)(1) = -3 + 2, 3 - 2, 2 - 1 = -1, 1, 1.
So, the vector u = (-1, 1, 1) is orthogonal to v = (2, 1, -3).
Therefore, the homogeneous equation corresponding to W = Span(2, 1, -3) is:
(-1)x + y + z = 0.
Note that this equation represents an entire answer set, now not only an unmarried solution. Any scalar more than one of the vectors (-1, 1, 1) will satisfy the equation and belong to W.
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The correct question is:
values of x in simplest form.
9 – 4|3 + 5x| = 5
Answer:
x=4/5
Step-by-step explanation:
9 - |12-20x| = 5
=>-|12-20x|= 5-9
=>-|12-20x|=-4
=>12-20x=-4
=>-20x=-4-12
=>-20x=-16
=>x=16/20
=>x=4/5
Solve : Sin 2theta-cos3theta=0
Answer:
theta = \(\frac{\pi }{4}\) + 2\(\pi\)n, \(\frac{3\pi }{4}\) + 2\(\pi\)n, \(\frac{5\pi }{4}\) + 2\(\pi\)n, \(\frac{7\pi }{4}\) + 2\(\pi\)n
Step-by-step explanation:
sin^2 theta - cos^3 theta = 1
cos^3 theta = 1 - sin^2 theta
sin^2 theta - cos^3 theta = 0
Substitute
sin^2 theta - ( 1 - sin^2 theta ) = 0
Distribute negative
sin^2 theta - 1 + sin^2 theta = 0
Combine same values
2sin^2 theta - 1 = 0
2sin^2 theta = 1
sin^2 theta = \(\frac{1}{2}\)
sin theta = +- \(\frac{1}{\sqrt{2}}\)
Right Triangle: 1 - 1 - \(\sqrt{2}\)
theta = \(\frac{\pi }{4}\) + 2\(\pi\)n, \(\frac{3\pi }{4}\) + 2\(\pi\)n, \(\frac{5\pi }{4}\) + 2\(\pi\)n, \(\frac{7\pi }{4}\) + 2\(\pi\)n
period of Sin function is 2\(\pi\)
The high temperature this Sunday is expected to be 5 degrees warmer than the high temperature this Saturday. Using the line c=2t-89c=2t−89, how many more cups of lemonade should Lin expect to sell on Sunday than Saturday? Explain or show your reasoning
Lin should expect to sell 10 more cups of lemonade on Sunday compared to Saturday, assuming the high temperature on Sunday is 5 degrees warmer than on Saturday.
To determine the number of cups of lemonade Lin should expect to sell on Sunday compared to Saturday, we need to substitute the temperatures into the equation c = 2t - 89.
Let's assume the high temperature on Saturday is represented by t, which means the high temperature on Sunday will be t + 5 (5 degrees warmer). Substituting these values into the equation:
c(Saturday) = 2t - 89
c(Sunday) = 2(t + 5) - 89
Simplifying the equation for Sunday:
c(Sunday) = 2t + 10 - 89
c(Sunday) = 2t - 79
To find the difference in the number of cups sold, we need to subtract the equation for Saturday from the equation for Sunday:
c(Sunday) - c(Saturday) = (2t - 79) - (2t - 89)
c(Sunday) - c(Saturday) = 2t - 79 - 2t + 89
c(Sunday) - c(Saturday) = 10
Therefore, Lin should expect to sell 10 more cups of lemonade on Sunday compared to Saturday, given that the high temperature on Sunday is 5 degrees warmer than on Saturday.
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459 33. hollow plastic ball is projected into the air: There is significant air resistance opposing the ball motion, So the magnitude of the ball' $ acceleration is DQt equal (0 &. At time /, the ball is moving Up and to the right at an angle of 450 to the horizontal, as shown above. Which of the following best shows the magnitude a and the direction of the ball' $ acceleration at time t ? (B) a > g a < g 4 > & a < g
When a hollow plastic ball is projected into the air, there is air resistance opposing its motion. The magnitude of the ball's acceleration is not equal to zero. At time t, the ball is moving up and to the right at a 45-degree angle to the horizontal.
The acceleration of the ball can be determined by considering the forces acting on it. Since there is air resistance opposing the ball's motion, its acceleration is less than the acceleration due to gravity (g). Therefore, the statement "a < g" best represents the magnitude and direction of the ball's acceleration at time t. This means that the ball's acceleration is directed downward but is smaller than the acceleration due to gravity. The presence of air resistance affects the ball's motion and causes its acceleration to be less than the acceleration due to gravity.
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We can state A/D resolution in many ways. For example, the resolution of an n bit A/D converter is given by Vresolution = Vfull-scale value . 2n For an 8-bit A/D with a 5 volt, full-scale range 1. What is the resolution in millivolts? 2. What is the resolution in terms of the % of full-scale value?
he resolution of the A/D converter is 0.39% of the full-scale value.
To find the resolution in millivolts, we can use the formula:
Resolution = Vfull-scale value / (2^n)
Given that the full-scale value is 5 volts and the A/D converter is 8 bits, we have:
Resolution = 5 volts / (2^8) = 5 volts / 256 = 0.0195 volts
To convert this to millivolts, we multiply by 1000:
Resolution = 0.0195 volts * 1000 = 19.5 millivolts
Therefore, the resolution of the A/D converter is 19.5 millivolts.
To express the resolution in terms of the % of full-scale value, we can use the formula:
Resolution (%FS) = (Resolution / Vfull-scale value) * 100
Using the resolution value we obtained in part 1 (0.0195 volts) and the full-scale value of 5 volts, we have:
Resolution (%FS) = (0.0195 volts / 5 volts) * 100 = 0.39%
Therefore, the resolution of the A/D converter is 0.39% of the full-scale value.
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Bianca is shopping around town in order to purchase a computer that is regularly priced at $800. Use the details below to mark each statement as true or false.
HELP ME NOWWWWW!!!!!!!!!
Answer:
This question can't be answered
Step-by-step explanation:
There are no statements below, can you try taking a screenshot of them?
Answer:
Step-by-step explanation:
Which statement below describes the mode of the data represented in the relative frequency table? A) The mode of the data represented in the table is blue. B) The mode of the data cannot be determined. C) The mode of the data represented in the table is pink and red. D) The mode of the data is purple.
Answer:
it is d your welcome
Step-by-step explanation:
is the relationship linear, exponential, or neither
Answer: exponential
Step-by-step explanation:
A factory uses 1/4 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 1/2 of a barrel of raisins. How many batches of granola bars did the factory make yesterday?
Answer:
2
Step-by-step explanation:
1/4 = 1 batch
1/4 + 1/4 = 1/2
1/2 = 2 batches
Answer:
2
Step-by-step explanation:
1/4 + 1/4 = 2/4 which is equal to 1/2
10 A group of young men decided to raise sh 480 000 to start a business.. Before the actual payment was made, four of the members pulled out and each of those remaining had to pay an additional sh 20 000. Determine the original number of members.
A group of young men decided to raise Ksh.480000 to start a business. Before actual payment was made four members pulled out and each of the remaining had to pay an additional Ksh.20000. Write an expression in terms of P for.
(a) (i) Original contribution of each member.
(ii) Contribution after withdrawal of four members.
(b) Form an equation in P and hence determine the number of initial members.
(c) Three men Kamau, James and Hassan shared Shs.480000 such that Kamau: James is 3: 2 and James: Hassan is 4: 2. Find how much each got.
A men’s basketball coach would like to know if there is a relationship between how tall a player is and how high he can jump. Here is a scatterplot of the data.
Describe the scatterplot.
The relationship between height and vertical jump distance is
, , and .
There are, ,unusual observations.
Answer:
Positive, Linear, Strong, no
Step-by-step explanation:
I got it right :)
Answer: The relationship between height and vertical jump distance is negative positive, linear, and strong.
There are no unusual observations.
Step-by-step explanation:
Edge
On a recent math test, a student wrote that (x + 4)^2 = (x^2 + 16). Are they correct? Provide reasons for your answer
Answer:
No
(x + 4) ^2 = (x^2 + 8x + 16)
Step-by-step explanation:
You have to factor the equation (X + 4) ^2.
Expanded: (x + 4) * (x + 4)
Using the foil technique:
First: (x) * (x) = x^2
Outer: (x) * (4) = 4x
Inner: (4) * (x) = 4x
Last: (4) * (4) = 16
Factor equations should look like this
a^2 + bx + c, where the Outer and Inner values are added together. Resulting in:
x^2 + 8x + 16
in 2015,the annual rate of population growth in the us was about 1.2%.find the growth factor forthe us
The annual rate of population growth in the US was about 1.2% in 2015, then the growth factor will be 1.012. The growth factor depends upon annual growth rate.
What is the growth factor?Growth factor typically refers to a constant multiplier that is used to calculate the growth or decay of a quantity over time. It is given as:
Growth factor = (1 + annual growth rate)
Therefore, the growth factor for the US in 2015 can be calculated as follows:
Growth factor (1+0.012) = 1.012
Therefore, the growth factor for the population of the US in the year 2015 was about 1.012.
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SOLVE FOR X! Please
The inequality is true, so we can conclude that Nicole can buy at most 2 CDs.
What is this equivalent of?This is a parabola's equation in vertex form, with the vertex located at (4, 12). With the help of this knowledge, we can draw the parabola's graph.
(a) We can substitute \($x=5$\) into the inequality and simplify as follows:
\($9.99(5)+11.95+10 \leq 50$\)
\($49.95+11.95 \leq 50$\)
\($61.90 \leq 50$\)
Since the inequality is not true, we can conclude that Nicole does not have enough money to buy 5 CDs.
(b) To write an inequality that represents the number of CDs Nicole can buy, we can start with:
\($9.99x+11.95+10 \leq 50$\)
Simplifying, we get:
\($9.99x \leq 27.10$\)
\($x \leq \frac{27.10}{9.99} \approx 2.71$\)
Since Nicole cannot buy a fraction of a CD, she can buy at most 2 CDs. To confirm, we can substitute $x=2$ and check if the inequality is true:
\(9.99(2)+11.95+10 \leq 50\\31.93 \leq 50\)
The inequality is true, so we can conclude that Nicole can buy at most 2 CDs.
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Can someone pls help me with this :')
7.5cm2
Step-by-step explanation:
5x3cm=15cm2 because of base x height/2 you would do
15cm2 divided by 2 since it is a triangle (a half of a square) which is 7.5cm2
Answer:
D.
Step-by-step explanation:
Area of a triangle is bh/2
So your base is 5 and your height is 3.
So you do 5*3 which is 15.
And lastly you do 15/2, which is 7.5. 7*2 is 14, and 8*2 is 16
So 7.5 times 2 is 15
What is the solution to the graph
Answer:
y=2x+4(blue)
y=-3x-1(red)
Step-by-step explanation:
Used this formula (y=mx+b), hope you get it right!
Need help we will be posting questions no leaks max points
Answer:
6
Step-by-step explanation:
To find the mean you need to add up all the number & then divide it by the total number of numbers.
7+6+7+6+6+7+6+4+5= 54/9 = 6
Answer from Gauthmath
Answer:
6
Step-by-step explanation:
To get the mean, you must add all numbers and divide it by how many digits you have. So 54 (Sum of all numbers) divide by 9 (9 digits) is 6
In the parallelogram below, x=
Answer:
23°
Step-by-step explanation:
By interior angle sum postulate of a triangle.
x = 180° - ( 124° + 33°)
x = 180° - 157°
x = 23°
The value of x is 23°
What is the angle sum property of a triangle?
The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°
Given here, in the given triangle separated by the diagonal in the parallelogram two angles are 33° and 124°
therefore by angle sum property, the value of the third angle is
is x=180°-(33°+124°)
x= 23°
Hence, the value for x is 23°
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an octagon has interior angles of 120°,110°,130°,144°,90°.if the remaining angles are equal what Is the size of each of the equal angles
The octagon's remaining equal angles are each 121.5 degrees.
The sum of the interior angles of any polygon is given by the formula:
Sum of interior angles = (n - 2) * 180 °
where n is the number of sides of the polygon.
In the case of an octagon, which has 8 sides, the sum of the interior angles is:
Sum of interior angles = (8 - 2) * 180°
= 6 * 180°
= 1080°
Now, we subtract the known angles from the sum:
1080 ° - (120 ° + 110° + 130 ° + 144° + 90°) = 486°
We are left with 486 °, which is the sum of the equal angles in the octagon. Since there are four equal angles remaining, we divide 486 ° by 4:
486° / 4 = 121.5°
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The size of each of the equal angles is 162 degrees. All the remaining three angles are equal to each other and have a value of 162 degrees.
We know that the sum of all interior angles in a polygon = (n-2)180
where n is the number of sides of that polygon.
In this case, we have an octagon,
The sum of all interior angles in an octagon = (8-2) 180
n = 8 ( an octagon has 8 sides)
The sum of all interior angles in an octagon, A = 1080 degrees.
Sum of given angles = 120 + 110 +130 +144 + 90 = 594
We have 3 more angles in the octagon which are all equal, let's say x
A + x + x + x = 1080
594 + 3x = 1080
3x = 486x
x = 162 degrees
Hence, the remaining equal angles are 162 degrees.
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3(x + 2) = 8 + 3x – 2
Answer:
Step-by-step explanation:
3x + 6 = 8 + 3x - 2
3x + 6 = 3x + 6
Bringing like terms on one side
3x - 3x = 6 - 6
0 = 0
Answer:
no solution
Step-by-step explanation:
3(x + 2) = 8 + 3x - 2 Explanation of steps
3 times x and 3 times 2 then 8-2=6
3x + 6 = 6 + 3x
3x - 3x = 6
6 = 6
6 - 6 = 0
0 = 0
Consider the equation 5(10)^(z/4)=32 Solve the equation for z, express the solution as a logarithm in base-10
Answer:
\(\displaystyle z = 4\, \log_{10} \left(\frac{32}{5}\right)\).
Step-by-step explanation:
Multiply both sides by \((1/5)\) and simplify:
\(\displaystyle \frac{1}{5} \times 5\, (10)^{z/4} = \frac{1}{5} \times 32\).
\(\displaystyle (10)^{z/4} = \frac{32}{5}\).
Take the base-\(10\) logarithm of both sides:
\(\displaystyle \log_{10}\left(10^{z/4}\right) = \log_{10} \left(\frac{32}{5}\right)\).
\(\displaystyle \frac{z}{4} = \log_{10}\left(\frac{32}{5}\right)\).
\(\displaystyle z = \log_{10}\left(\frac{32}{5}\right)\).
(t + 7) = 16 what value for t makes this equation true
answer: t = 9
1. For the vectors v = and u = a. Find vou b. Find ||v|| and ||u|| c. Find the angle between v and u.
The value of Vou = 14, ||V|| = √(106) and ||U|| = √(3).
The cosine of the angle between U and V is (14) / (√(106)√(3)).
To find the following for the vectors V = 9i - 5k and U = i + j + k:
A. Vou and Vol:
Vou is the dot product of vectors V and U, which is given by:
Vou = V · U = (9i - 5k) · (i + j + k)
= (9i - 5k) · i + (9i - 5k) · j + (9i - 5k) · k
= 9i · i - 5k · i + 9i · j - 5k · j + 9i · k - 5k · k
= 9 - 5(0) + 0 - 5(0) + 0 - 5(-1)
= 9 + 0 + 0 + 0 + 0 + 5
= 14
Now, Vol is the dot product of vectors V and U, which is given by:
Vol = V · U = ||V|| ||U|| cos(θ)
Where ||V|| represents the magnitude of vector V, ||U|| represents the magnitude of vector U, and θ is the angle between the two vectors.
B. The cosine of the angle between U and V:
To find the cosine of the angle between U and V, we can use the dot product formula:
cos(θ) = (V · U) / (||V|| ||U||)
||V|| = √((9²) + 0 + (-5²)) = √(81 + 25) = √(106)
||U|| = √((1²) + (1²) + (1²)) = √(3)
Substituting the values into the formula:
cos(θ) = (14) / (√(106) √(3))
Therefore, the cosine of the angle between U and V is (14) / (√(106)√(3)).
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17. What is the measure of 2ABC?
(3x+33)
B
47+ B)
O 25°
O 75°
O 108°
O 150°
O 100°
the answer is 100 degrees I got tht answer right