The correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).
To express log₃ 6 as a logarithm of base 2, we can use the change of base formula. The change of base formula states that logb x = (logc x) / (logc b), where c is any positive value other than 1.
Applying the change of base formula to log3 6:
log₃ 6 = (log₂ 6) / (log₂ 3)
Therefore, the correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).
To calculate it properly, we need to find the decimal approximation of this expression:
Using the appropriate logarithmic functions, we have:
(log₂ 3) / (log₂ 6) ≈ 1.58496 / 2.58496 ≈ 0.6124
Thus, log₃ 6 as a logarithm of base 2 is approximately 0.6124.
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Paper cost $49 for 10 reams. How much for 1 ream?
To calculate the cost of 1 ream of paper from the total cost of 10 reams, divide $49 by 10 to get $4.90 per ream.
To find out how much it costs for 1 ream of paper when 10 reams cost $49, we simply divide the total cost by the number of reams. In this case:
Cost per ream = Total cost / Number of reams
Cost per ream = $49 / 10
Cost per ream = $4.90
Therefore, the cost for 1 ream of paper is $4.90.
5. If p || q, which pair of angles must be congruent?
1 and 8
2 and 5
4 and 6
7 and 8
Answer:
1 and 8.
Step-by-step explanation:
Two angles will be congruent if both measure the same. Then, as p is parallel to q we have that the alternate external angles (pair of angles out of the parallel lines, one on the right of the transversal line and the other on the left of the transversal line) has the same measure. In this case, 1 and 8 are alternate external angles.
A snake is slithering toward you at 1.5 m/s. If you start walking when it is 5.0 m away, how fast must you go in order that the snake not overtake you when you have gone 40.0 m?
The polynomial 6x2 + 37x – 60 represents an integer. Which expressions represent integer factors of 6x2 + 37x – 60 for all values of x?
3x – 4 and 2x + 15
3x + 4 and 2x – 15
2(x – 2) and 3(x + 5)
2(x + 2) and 3(x – 5)
Answer:
[tex]\text{The integral factors are }(3x-4)(2x+15)[/tex]
Step-by-step explanation:
Given the quadratic polynomial
[tex]6x^2+37x-60[/tex]
we have to find the integral factors of the above polynomial.
[tex]\text{The polynomial is }6x^2+37x-60[/tex]
By splitting middle-term, the polynomial can be written as
[tex]6x^2+37x-60[/tex]
[tex]6x^2-8x+45x-60[/tex]
Taking 2x common from first two terms and 15 from last two terms.
[tex]2x(3x-4)+15(3x-4)[/tex]
Taking (3x-4) common
[tex](3x-4)(2x+15)[/tex]
which are required factors of given polynomial.
Hence, option 1 is correct.
Line 1
x y
−1 1
0 3
Line 2
x y
1 5
3 3
(a) Write the equation for Line1 in slope-intercept form.
(b) Write the equation for Line 2 in slope-intercept form.
Answer:
im cool
Step-by-step explanation:
Put these numbers in order from least to greatest.
-15-26/40, -15, 18/25, 15.85
A function f satisfies the following conditions: f(5)=20, f'(5)=2, and f"(x)<0, for x>=5. Which of the following are possible values for f(7)? possible choices are 28, 20, 26, 24, 22
Given the function's conditions, the value of f(7) must be less than or equal to 24 due to the concave-down nature indicated by the negative second derivative, making 20, 22, or 24 possible values for f(7).
Explanation:The student asked about determining possible values for a function f(x) given a set of conditions: f(5)=20, f'(5)=2, and f"(x)<0 for x>=5. The negative second derivative indicates that the function is concave down for x>=5, meaning the rate of increase of f(x) is decreasing. Starting at x=5 with a value of 20 and a slope of 2, we can deduce that after moving 2 units to x=7, the value of f(7) cannot be greater than what it would be if f(x) were linear, since f"(x)<0 implies the function's rate of growth is decreasing. Therefore, f(7) must be less than or equal to 20 + 2*(7-5), which is 24.
Since the rate of increase is decreasing and the function cannot increase at a rate faster than the initial slope of 2, the possible values for f(7) among the given choices must be less than or equal to 24. Thus, the possible values for f(7) could be 20, 22, or 24.
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The value of f(7) is 24.
Given the function f with conditions f(5)=20, f'(5)=2, and f''(x)<0 for x ≥ 5, we need to find possible values for f(7) from the choices given: 28, 20, 26, 24, and 22.
Here is a step-by-step solution:
f(5)=20 indicates that at x=5, the value of the function is 20.f'(5)=2 tells us that the slope or the derivative at x=5 is 2, which implies the function is increasing at this point.f''(x)<0 for x ≥ 5 indicates that the function is concave down, meaning its slope is decreasing as x increases.Since the function is concave down, the rate of increase of the function will decrease as x moves from 5 to 7:
f(x) initially increases from 5 to 7 with a slope of 2, so f(7) cannot be lower than f(5): 7 − 5 = 2 * 2 = 4, thus the function increases by at most 4 from 5 to 7.So the maximum possible value considering the concavity is 20 + 4 = 24.Therefore, among the choices 28, 20, 26, 24, and 22, the possible value for f(7) given the conditions is 24.
PLZZZ HELP ME!!
Edward’s recipe for salad uses a ratio of 2 1/4 cups of lettuce to 1/2 lb of tomatoes.
(a) Use a complex fraction to compare the amount of lettuce to the amount of tomatoes.
(b) Determine how many cups of lettuce Edward needs to mix with 1 lb of tomatoes. Show your work.
Answer:
4.5 cups of lettuce for 1 cup of tomatoes
Step-by-step explanation:
If f(x) = x3 – 2x2, which expression is equivalent to f(i)?
–2 + i
–2 – i
2 + i
2 – I
Answer:
It's D
2-i
Step-by-step explanation:
a 6 feet tall boy cast a shadow of 9 feet at the same time of the day if the shadow of a tree measures 21 feet what is the height of the tree
The product of (1/2 3/4i) and(1/2-3/4i) divided by (2-3i)
Factorise this
72-6x
Holly made fruit punch for an office party a few months ago; she used 1 gallon of strawberry juice and 3 gallons of watermelon juice, which cost her a total of $8. For today’s party, she used 3 gallons of strawberry juice and 2 gallons of watermelon juice, spending a total of $10. How much does a gallon of each type of juice cost?
Write a system of equations to describe the situation and solve using elimination. (use x for strawberry juice and y for watermelon juice)
Which answer describes the type of sequence?
200, 40, 8, 1.6, ...
geometric
neither arithmetic nor geometric
arithmetic
Answer:
it is geometric
Step-by-step explanation
We have been given with the series
200,40,8,1.6
Arithmetic sequence is the sequence in which difference between consecutive terms is same that is common difference d
d=a_2-a_1
d=40-200=-160 herea_2=40,a_1=200
d=8-40=-32 herea_2=8,a_1=40
We can see the difference is not same
Hence, the given sequence is not arithmetic sequence.
Geometric sequence is the sequence in which ratio of consecutive terms is same that is common ratio r
r=\frac{a_2}{a_1}
r=\frac{40}{200}=\frac{1}{5} herea_2=40,a_1=200
r=\frac{8}{40}=\frac{1}{5} herea_2=8,a_1=40
r=\frac{1.6}{8}=\frac{1}{5} herea_2=1.6,a_1=8
We can see the ratio is same.
Hence, given sequence is geometric
Therefore, Option 1 is correct given sequence is geometric.
Answer:
The correct answer is A. geometric
Step-by-step explanation:
A graph thAt has a finite or limited number of data points is
The correct answer is:
Discrete graph.
Explanation:
A discrete graph is a graph of disconnected points.
Since they are disconnected, this means the graph only has values at the points drawn, not between.
The opposite of a discrete graph is a continuous graph; it is a graph of connected points. Since the points are connected, the graph has values between all of the points. This is similar to what we learned in geometry about a line; a line has an infinite number of points. This is true of the connections between points in a continuous graph.
Since a discrete graph is the opposite of a continuous graph, this means it does not have an infinite number of points; a discrete graph has a finite number of points.
A^2 + 4^2 = 5^2
A = __
I need to know 0.98 as a percent
Answer:
98% hope this helped
Step-by-step explanation:
what is the sum of the square roots of 16i?
The sum of the square roots of 16i is zero, as the positive and negative square roots cancel each other out when summed up.
Explanation:The sum of the square roots of 16i is found by first determining the square roots of the given complex number. The complex number 16i can be expressed in terms of its polar form, which then allows us to apply De Moivre's Theorem in order to find the square roots.
First, 16i is purely imaginary, with a magnitude of 16 and an argument that is π/2 or -3π/2 radians. By taking the square root of its magnitude and halving the argument, we find the two square roots, which are in fact ±4√i. Therefore, if we consider both the positive and negative square roots, the sum of the square roots of 16i would be 4√i + (-4√i), which simplifies to 0.
The sum of the square roots of 16i is 4 + 4i * cos (π/8) + 4i * sin(π/8).
Explanation:To find the sum of the square roots of 16i, we first need to find the square root of 16i. To do this, we can write 16i in polar form.
16i = 16(cos (π/2) + isin(π/2))
Then, we can find the square root of 16i by taking the square root of the magnitude and halving the argument.
√16i = √16(cos (π/4) + isin(π/4))
√16i = √16 * cos (π/8) + √16 * isin(π/8)
√16i = 4(cos (π/8) + isin(π/8))
Therefore, the sum of the square roots of 16i is 4 + 4i * cos (π/8) + 4i * sin(π/8).
The seventh term of the sequence -2, -6, -10, -14, ... is _____.
-26
-24
-22
-20
please help...
how do you solve (x3 + 6x2 + 3x + 1 ) ÷ (x - 2)
Mary baked 21 cookies on Saturday and twice that many on Sunday for a school fundraiser. 4 cookies fell on the ground and had to be thrown out. If she packaged 3 cookies to a bag, how many cookies were left over?
A) 0
B) 1
C) 2
D) 3
Identify the degree of the polynomial 8x^3y^2 – 10xy + 4x^2y^2 + 3.
Answer:
The degree of the polynomial is 5
Step-by-step explanation:
Solve this problem
13=24+c
what is the angular velocity of a 6-foot pendulum that takes 3 seconds to complete an arc of 14.13 feet?
16,000 rolls of paper were purchased and 12,500 were sold at $1.79, what is the total ending inventory?
Order the numbers from least to greatest.
0.21,1/5 , 0.18, 24%
The arrangement from least to greatest is 0.18 < 0.20< 0.21< 0.24.
What is Ascending Order?Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.
Given:
0.21,1/5 , 0.18, 24%
Now, writing each fraction in decimal form
1/5 = 0.2
24% = 24/100 = 0.24
So, we have the following numbers
0.21, 0.20, 0.18, 0.24
Hence, the arrangement from least to greatest is 0.18 < 0.20< 0.21< 0.24.
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Solve this 7(3x-4)=56
Translate the algebraic expression 3x+5 into a word phrase
At wild thing zoo, you can rent a motorized cart to tour grounds for a $3 initial charge and $7 per hour. at safari zoo, you can rent the same cart for a $7 initial charge and $6 per hour. for how many hours is the total charge the same?
Which equation represents the line that passes through (–6, 7) and (–3, 6)?
Answer:
Equation of line become [tex]y= \frac{- 1 *x}{3}+ 5[/tex].
Step-by-step explanation:
slope of the line
we know that the formula to calculate the slope between two points is equal to
Slope (m) = [tex]\frac{y_{2}- y_{1} }{x_{2}-x_{1}}[/tex].
substitute the values
(m) = [tex]\frac{6 - 7} }{ -3 - (-6)}[/tex].
(m) = [tex]\frac{-1} }{3}[/tex].
With the slope m and the point (-6, 7) find the equation of the line
we know that
the equation of the line in the point-slope form is equal to
[tex](y - y_{1}) = m ( x - x_{1})[/tex].
substitute the values
[tex](y - 7) = \frac{-1}{3} (x - ( -6))[/tex].
[tex](y - 7) = \frac{-1}{3} (x + 6)[/tex].
[tex](y - 7) = \frac{-x}{3} +2 )[/tex].
On adding both sides by 7.
[tex]y= \frac{-x}{3} - 2 + 7 [/tex].
[tex]y= \frac{-x}{3}+ 5[/tex].
Therefore, equation of line become [tex]y= \frac{-1 *x}{3}+ 5[/tex].