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Answer:
g(x) = 1/2
Step-by-step explanation:
The applicable relations are ...
[tex]\log_b(x)=a\ \Longleftrightarrow\ b^a=x\\\\\log_b(x^a)=a\cdot\log_b(x)\\\\\log_b(b)=1[/tex]
__
We want to find logb(x) for x = b^(1/2). Using the first relation, we see ...
g(x) = logb(x)
b^(g(x)) = b^(1/2) . . . . . using g(x) = a
g(x) = 1/2 . . . . . equating exponents
__
Alternatively, using the last two relations, we have x = b^(1/2), so ...
g(b^(1/2)) = logb(b^(1/2)) = (1/2)logb(b) = (1/2)(1)
g(x) = 1/2
_____
Additional comment
I find it useful to remember that a logarithm is an exponent. The first applicable relation shown above is a statement to that effect.
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -3 - 2 cos θ
Answer: symmetric on the x-axis only.
Step-by-step explanation:
How do i reflect triangle ABC if A (2,3), B (1,1), C(4,-3) over the x axis. Also rotating the triangle 90 degrees clockwise about the origin.
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Answer:
see attached. red = reflected; blue = rotated
Step-by-step explanation:
The relevant coordinate transformations are ...
(x, y) ⇒ (x, -y) . . . . . reflection over the x-axis
(x, y) ⇒ (y, -x) . . . . . rotation 90° CW
In the attached figure, the red triangle A'B'C' is reflected. The blue triangle A"B"C" is rotated.
__
Additional comment
Learning to visualize these transformations can take a little practice. It can help to draw the figure on a graph, trace it on another piece of paper or transparency, then move the copy to the new position relative to the old axes.
For reflection across the x-axis, the x-axis of the copy is aligned with the original, but the copy is flipped over so the old +y axis is aligned with the -y axis, and vice versa.
For rotation 90° CW, what was the +y axis becomes aligned with the +x axis, and what was the +x axis becomes aligned with the -y axis. That is, the figure is rotated 90° CW about the origin so anything in the first quadrant is moved to the 4th quadrant.
1 1/3 x 1/14
Help please
Step-by-step explanation:
=11/3×1/14
=3.67×0.07
=0.2568
find an equation for the line passing through (4, 1) and perpendicular to the line 2y+4=6x
Answer:
y = 3x - 11
Step-by-step explanation:
2y+4=6x
2y = 6x - 4
y = 3x - 2
y = 3x + b
1 = 3(4) + b
1 = 12 + b
-11 = b
Consider the set A with n(A) = 20. How many subsets could be formed from this set?
Answer:
There are [tex]2^{20}[/tex] subsets of [tex]A[/tex]
Step-by-step explanation:
Using the formula for the number of subsets of a given (finite) set, the number of subsets of [tex]A[/tex] is
[tex]2^{n(A)}=2^{20}[/tex]
The shaded rectangle, which is the correct expression of its perimeter
Answer:
2x + 2y - 4
Step-by-step explanation:
The opposite sides are congruent so perimeter (P) is
P = 2(x + 2) + 2(y - 4)
= 2x + 4 + 2y - 8
= 2x + 2y - 4
Choose a linear function for the line represented by the point-slope equation y - 5 = 3(x - 2).
f(x) = 3x - 1
Step-by-step explanation:
[tex]y - 5 = 3(x - 2) \\ y - 5 = 3x - 6 \\ y = 3x - 6 + 5 \\ y = 3x - 1[/tex]
What is the inverse of f(x) = 2x2 –4?
Answer:
The inverse of the function is
[tex]{ \underline{f {}^{ - 1}(x) = \sqrt{ \frac{x + 4}{2} } }}[/tex]
Step-by-step explanation:
let the inverse of f(x) be m:
[tex]m = {2x}^{2} - 4 [/tex]
take 4 to the left hand side ( changes sign to positive ):
[tex]m + 4 = {2x}^{2} \\ \frac{m + 4}{2} = {x}^{2} [/tex]
take a square root on all sides:
[tex] \sqrt{ \frac{m + 4}{2} } = \sqrt{ {x}^{2} } \\ \\ x = \sqrt{ \frac{m + 4}{2} } [/tex]
substitute x in place of m:
[tex] {f}^{ - 1} (x) = \sqrt{ \frac{x + 4}{2} } [/tex]
solve 4x+y=24 and y=-4x+24 using substitution
Answer:
no solutions
Step-by-step explanation:
[tex]4x + y = 24 - - - (a) \\ y = - 4x + 24 - - - (b)[/tex]
substitute for y in (a) with (b):
[tex]4x + ( - 4x + 24) = 24 \\ 0x = 0[/tex]
Answer:
infinite solutions
Step-by-step explanation:
substitute y in the first equation
4x+(-4x+24)=24
4x and -4x cancel out
24/24=1
or solve for x, you should also get 1
the temperature was -6 degree ferahit. it rose so that the temperature was 0 degree ferahit . what represents the change in temperature
Answer:-6+6=0
Step-by-step explanation: basically just put the sentence into an equation.
d=degrees farenheit
-6d+6d =0d
Answer:
if ur wondering on how to solve it u should solve it by an equation.
Step-by-step explanation:
just make sure to explain us answer and the answer is 6+6=0
Is square root of 11+10 a rational or irrational number
Answer:
Irrational Number is the answer
Answer:
[tex] \sqrt{11 + 10} = \sqrt{22} = 4.69041576 [/tex]
THIS IS IRRATIONAL
Step-by-step explanation:
The correct answer is irrational and the reason for that is the decimals for sqrt of 22 are non-recurring, are non-terminating and lastly it cannot be expressed in a form of a fraction.
I hope this makes sense
:)
5=2+3x i need help plzzzzzzzzzzzzzzzzzzzz
Answer:
x = 1
Step-by-step explanation:
5 = 2 + 3x
=> 5 - 2 = 3x
=> 3 = 3x
=> 3/3 = x
=> 1 = x
Answer:
x=1
Step-by-step explanation:
5=2+3x
5=3x+2
-2 -2
3=3x
/3 /3
x=1
hope this helps
brainliest pls?
Trying to find the equation for the pattern 5, 11, 18, 26, 35, 45
Answer:
Step-by-step explanation:
[tex]u_{n+1}=u_n+n+5\\\Longrightarrow\ u_{n+2}=u_{n+1}+(n+1)+5\\u_{n+2}-u_{n+1}=u_{n+1}+n+1+5-u_n-n-5\\u_{n+2}=2u_{n+1}-u_n+1\\u_{n+3}=2u_{n+2}-u_{n+1}+1\\\\u_{n+3}-u_{n+2}=2u_{n+2}-u_{n+1}+1 -2u_{n+1}+u_n-1\\\\u_{n+3}-3u_{n+2}+3u_{n+1}-u_n=0\\\\\\Equation\ caract\' eristique:\\r^3-3r^2+3r-1=0\\(r-1)^3=0\\\\\boxed{u_n=a+b*n+c*t^2}\\\\u_1=5\\u_2=11\\u_3=18\\u_4=a+4*b+16*c=26\\u_5=a+5*b+25*c=35\\u_6=a+6*b+36*c=45\\\\[/tex]
a=0
b=9/2
c=1/2
Proof:
n=1 ==> u_1=1/2*(9+1)=5
n=2 ==> u_2=2/2*(9+2)=11
n=3 ==> u_3=3/2*(9+3)=18
n=4 ==> u_=4/2*(9+4)=26
n=5 ==> 5/2*(9+5)=35
n=6 ==> 6/2*(9+6)=45
...
Answer: i have found one that calculates differences when given a sigma with a sigma rule, you could adjust the formula for patterns, if you create a sigma equation and then apply the formulas and then make up a pattern that falls within it, knowing the connection is they go up in the same numbers or knowing it and for some patterns being able to solve it. when given such a sigma problem such as n=1 sigma 3 is the end point 7n-1 is the rule, we would use the value of n until the end point 3, but consider 7n-1 equal to 6+13+20 which equals 39 since 7*1-1=6 and 7*2-1=13, 7*3-1=20 and 6+13+20 is 39. remeber it is equal to that since we plug the value of n from the starting point to the end point of any sigma. a1=7*n-1=6,a2=7*2-1=13, 7*3-1=21 is what you should manipulate for another sigma problem that calculates the diffrence of a sequence as well as its total. the one equation that calculates the total of your patterns is:∑_(n=0)^20▒〖7n-0=140〗
the ones i know to find that represent the patterns in terms of what it would be in the nth term is 58ns it represents what the pattern would be in the nth terms but it is not equal to the pattern.
finding the nth term by looking for an expression to use for the nth term is the same as finding an expression representing the nth term. the nth term is is the numerical difference in the given series with the letter n on the right of that and the number from the beginning of a series in some cases. one more thing for a negative number at the beginning of a pattern you get the missing number i.e the numerical difference on the left and then and the function of the first number. for example: there is a pattern going from -1 to 19 so the pattern would be -1, 3, 7,11, 15,19. the numerical difference is 4, n is the letter that would come after and -1 , -1 is a function in the area of nth term since the whole expression would be 4n subtracted by 1 and subtraction is a function, a function is a operation in mathes.
Step-by-step explanation:
11-5=6
18-11=7
26-35
45-35=10
6+7+35+10=13+45=58 (the differences added up)
5+11+18, 26+35+45=140
Help me with this question
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Answer:
see attached
Step-by-step explanation:
The statement of proportionality tells you ...
m = kr³
The values in the fourth column can tell the value of k:
k = m/r³ = 6.75/1.5³ = 2
Then we have ...
m = 2r³
Solving for r gives ...
m/2 = r³
r = ∛(m/2)
These two relations were used to fill in the spaces in the table. (It is convenient to let a spreadsheet do the calculations.)
7/12- 1/2[tex]7/12-1/2[/tex]
Answer:
1/12
Step-by-step explanation:
7/12 - 1/2
~Find common denominators
7/12 - 6/12
~Subtract
1/12
Best of Luck!
what is credit invoice
The sum of three consecutive integers is 147. Find the integers.
The integers are
(Use a comma to separate answers.)
(Answer quickly)
Answer:
48, 49, 50
Step-by-step explanation:
x + x+1 + x+2 = 147
3x + 3 = 147
3x = 147 - 3
x = 144/3
x = 48
state the domain: A= {(-3,2), (5,4), (7,-3)}
The required domain is [tex]\{-3,5,7\}[/tex].
Given:
A set of ordered pairs is:
[tex]A=\{(-3,2),(5,4),(7,-3)\}[/tex]
To find:
The domain of the given set of ordered pairs.
Solution:
Domain is the set of input values.
In the set of ordered pairs [tex](x,y)[/tex], then the set of all the [tex]x[/tex]-values is domain and the set of all the [tex]y[/tex]-values is range.
We have,
[tex]A=\{(-3,2),(5,4),(7,-3)\}[/tex]
In the above set of ordered pairs, the x-values are [tex]-3,5,7[/tex].
[tex]Domain=\{-3,5,7\}[/tex]
Therefore, the domain of the given set of ordered pairs is [tex]\{-3,5,7\}[/tex].
Learn more:
https://brainly.com/question/3269807
What are the coordinates of the midpoint
of the segment joining the points
A(-3,-1) and B(4,2)?
Midpoint = (***
x1 + x2 Y1 +92
2 2.
O (2,-4)
(-1.0.5)
O (1.-2)
(0.5, -1)
Answer:
(0.5, -1)
Step-by-step explanation:
You need to make 48 servings of roast beef gravy. Each serving takes .75 cups of brown stock. How many quarts of brown stock do you have to make
Answer:16 q
Step-by-step explanation:
Can anyone help?
Plis
Answer:
B. 50%
Step-by-step explanation:
7/20 = 35%
35% + 15% = 50%
100% - 50% = 50%
white → 15%
red → 7/20 · 100% = 35/100 · 100% = 35%
blue → 100% - 35% - 15% = 50%
Answer: B)
Will give brainliest
Use the distributive property to simplify
the equation below.
7(x - y + 3) = [? ]x -
[ ]y
+
Answer:
7x - 7y + 21Step-by-step explanation:
7(x - y + 3)
=> 7 × x - 7 × y + 7 × 3
=> 7x - 7y + 21
Answer:
[tex]7(x - y + 3) = 7x - 7y + 21 \\ thank \: you[/tex]
The quantities x and y are proportional.
Answer:
r = 1
Step-by-step explanation:
Given the equation of proportion
y = rx ← r is the constant of proportionality
Divide both sides by x
[tex]\frac{y}{x}[/tex] = r
Choose any ordered pair from the table
Using x = 5.8 and y = 5.8 , then
r = [tex]\frac{5.8}{5.8}[/tex] = 1
Determine the range of the following graph:
12
11
10
9
8
100
1
-12-11-10-9-8-7-6-574-3-2-4
1 2 3 4 5 6 7 8 9 10 11 12
-2
-3
- 4
-5
-6
-8
-9
-10
-11
-12
Need help fast!!! This question is for algebra 2 and for a Quiz.
Thank youu.
Step-by-step explanation:
it is unclear what is meant by f1 and f2. do you mean f' and f'' ?
I don't think so, as you mentioned algebra 2.
so, is it just a way to identify different functions ? like function 1 vs. function 2 ?
if that's the case, then both functions represent lines.
both lines go through the origin.
but as their slopes are of same size but different sign, one is actually the mirrored version of the other one (mirrored around the x-axis).
FYI - the created visible pattern (4 lines emanating from the origin) would also indicate that the visible pattern (but not the functions) is also mirrored around the y-axis.
Simplify addition radical expression
√36+√64
Answer:
14
Step-by-step explanation:
√36+√64
√36=6
√64=8
6+8
14
THANK YOU
find any points of discontinuity for the rational function... y=x-3/x^2-3x-10
Answer:
x = -2 or 5
Step-by-step explanation:
y = (x-3)/((x-5)(x+2))
y is undefined when the denominator is zero.
Anthony has a bank balance of $45. Sara has a bank balance of -$90. Sean has a bank balance of -$208. Marsha has a bank balance of $153. Which is the smallest debt?
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Answer:
Marsha and Anthony
Step-by-step explanation:
Here a negative bank balance represents a debt. The larger the magnitude of the negative number, the more debt it represents. A positive bank balance corresponds to no debt.
Anthony and Marsha -- no debt . . . . smallest debt
Sara -- $90 in debt . . . . smallest non-zero debt
Sean -- $208 in debt
On those with non-zero debt, Sara has the smallest debt. Overall, Anthony and Marsha have the smallest debt: zero debt.
7 + 3x - 12x = 3x+ 1
Solve for x
Answer:
x = 1 /2
Step-by-step explanation:
isolate the variable by dividing each side by factors that dont contain the variable
decimal form will be: x = 0.5
hope that helps>3
There are 35 boys in band and 49 girls in band Ryan says the boys to girls is 5 to 7 is he correct or incorrect show how he is correct or incorrect
Answer:
He is correct.
Step-by-step explanation:
[tex]\frac{35}{49} =\frac{5}{7}[/tex]