We are given:
aᵇ = bᵃ
b = 2a
Finding (a+b):
Finding a:
replacing b by 2a in the first equation, we get:
(a²)ᵃ = (2a)ᵃ
(a²)ᵃ = 2ᵃ * aᵃ
a²ᵃ / aᵃ = 2ᵃ [dividing both sides by aᵃ]
aᵃ = 2ᵃ [because xᵃ / xᵇ = xᵃ⁻ᵇ]
a = 2 [raising both sides to 1/a]
Finding b:
We are given that b = 2a
now that we know what a equals, we will plug that value here
b = 2(2)
b = 4
Finding a+b:
We found that a = 2, b = 4
a + b = 2 + 4 = 6
2x - y when x = 0 and y = -5
Answer:
5
Step-by-step explanation:
2x - y when x = 0 and y = -5
2(0) - (-5) =
= 0 + 5
= 5
Answer:
5
Step-by-step explanation:
2x-y
2(0)-(-5)
0-(-5)
0+5
5
List a function that's it's own inverse
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Explanation:
If g(x) is the inverse of f(x), and vice versa, then we have these two properties:
f(g(x)) = xg(f(x)) = xSince we want to find a function that is its own inverse, we want f(x) and g(x) to be the same function.
Through trial and error, you should find that f(x) = g(x) = x fit the description.
f(x) = x
f( g(x) ) = g(x) ... replace every x with g(x)
f( g(x) ) = x
You should find that g(f(x)) = x as well.
One possible answer is f(x) = x
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Through more trial and error, you should find that f(x) = g(x) = 1/x works as well. In fact, anything of the form f(x) = g(x) = k/x will work.
The proof can be written as follows
f(x) = k/x
f( g(x) ) = k/( g(x) )
f( g(x) ) = k/( k/x )
f( g(x) ) = (k/1) divide (k/x)
f( g(x) ) = (k/1) * (x/k)
f( g(x) ) = x
Through similar steps, you should find that g(f(x)) = x is the case also.
This proves that f(x) = k/x is its own inverse, where k is a real number constant.
Another possible answer is anything of the form f(x) = k/x
If we pick k = 3, then we get f(x) = 3/x which is the answer I wrote above.
You can pick any k value you want.
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There may be other types of functions that have this property, but I'm blanking on what they might be.
A cubical water tank can contain 1000/125 cubic meters of water. Find the length of a
side of the water tank.
2 meters 3 meters
1/2 meters
1/3 meters
Answer:
2 meters.
Step-by-step explanation:
We know that a cube of sidelength L has a volume:
V = L^3
Here, we know that the volume of water that the cube can hold is:
(1000/125) m^3
Then the volume of our cube is exactly that:
V = (1000/125) m^3
Then we have the equation:
L^3 = (1000/125) m^3
Which we can solve for L
L = ∛((1000/125) m^3 ) = (∛1000/∛125) m
Where we used that:
∛(a/b) = ∛a/∛b
Solving the cubic roots, we get:
L = (10/5) m = 2m
The length of the side of the water tank is 2 meters.
Based on the table below, what is the relationship between cups and tablespoons?
Answer:
the answer is A
Step-by-step explanation:
Someone tell me where everyone is going right please !!
Answer:
A 2
B 1
C 4
D 3
Step-by-step explanation:
( ) means not including (also used for infinity)
[ ] means including
The answer choices are in interval form, showing all the possible answer choices between two numbers and if the answer choice includes or excludes a number using the () []
Explanation for A:
x < 7.8 means x won't include 7.8 since the symbol is "less than" and not "less than or equal to".
x can be anything, it just has to be less than 7.8, so the answer is:
2 (-infinity, 7.8)
Explanation for B:
x <= 7.8 means x will include 7.8 since the symbol means "less than or equal to".
x can be anything, it just has to be less than or equal to 7.8, so the answer is:
1 (-infinity, 7.8]
Explanation for C:
x >= 7.8 means x will include 7.8 since the symbol means "greater than or equal to".
x can be anything, it just has to be greater than or equal to 7.8, so the answer is:
4 [7.8, infinity)
Explanation for D:
x > 7.8 means x won't include 7.8 since the symbol means "greater than" and not "greater than or equal to".
x can be anything, it just has to be greater than 7.8, so the answer is:
3 (7.8, infinity)
Hope it helps (●'◡'●)
Answer:
A:2 B:1 C:4 D:3
Step-by-step explanation:
WILL MARK BRAINLIEST
Create diagrams to represent the possible cases for common tangents between two circles. Please give justification for each diagram.
1. No common tangents
2. One common tangent
3. Two common tangents
4. Three common tangents
5. Four common tangents
Refer to the diagram below for examples of what I mean.
find the shortest distance between the lines 3x+4y+10=0 and 3x+4y+20=0
Answer:
the lines are parallel they are 10 units apart
Step-by-step explanation:
The shortest distance between these two parallel lines is 2.5
Given equations:
3x + 4y + 10 = 0 ----- (1)
3x + 4y + 20 = 0 ---- (20)
To find:
the shortest distance between the two lines
The slope and y-intercept of the first equation is calculated as;
3x + 4y + 10 = 0
4y = -3x - 10
[tex]y = \frac{-3x}{4} - \frac{10}{4} \\\\y = \frac{-3x}{4} - \frac{5}{2}[/tex]
The slope = -³/₄ and the y-intercept = - ⁵/₂ = - 2.5
The slope and y-intercept of the second equation is calculated as;
3x + 4y + 20 = 0
4y = -3x - 20
[tex]y = \frac{-3x}{4} - \frac{20}{4} \\\\y = \frac{-3x}{4} - 5[/tex]
The slope = -³/₄ and the y-intercept = - 5
The two equations have the same slope = -³/₄
This shows that they are parallel with different y-intercepts
The shortest distance between the two lines is at their y-intercepts
The shortest distance between these two lines is calculated as;
[tex]distance = \sqrt{(-5 - (-2.5) )^2} \\\\distance = \sqrt{(-5+ 2.5)^2} \\\\distance = \sqrt{(-2.5)^2 } \\\\distance = \sqrt{6.25} \\\\distance = 2.5[/tex]
Thus, the shortest distance between these two parallel lines is 2.5
learn more here: https://brainly.com/question/11566480
What is the area of a cross section that is parallel to face BFGC?
Answer: 216cm2
Step-by-step explanation: 36x6
Solve the inequality. 2 + |t + 6| < 12
Answer:
[tex]2 + (t + 6) < 12[/tex]
[tex]2 + t + 6 < 12[/tex]
[tex]t + 8 < 12[/tex]
[tex]t < 12 - 8[/tex]
[tex]t < 8[/tex]
Find the midpoint of the line segment with the given endpoints.
(-4,-2) (3, 3)
Answer : - 4 + 3 = - 1
- 2 + 3 = 1
By half gives - 1/2 and 1/2
So midpoint (-1/2, 1/2)
Kathy travels in a taxi which charges $ 5.75 flat rate in addition to $ 2.50 per mile. Kathy has only $25 in her wallet. How many miles can Kathy travel without exceeding her limit?
HELPP
Answer: 7.7 miles
Step-by-step explanation:
2.5x + 5.75 = 25 (x = each mile traveled)
2.5x = 25 - 5.75
2.5x = 19.25
x = 7.7 miles
Help and explain pls and ty
[tex]\displaystyle\bf (3-5\sqrt{5} )-(5\sqrt{3} -3)=3+3-5\sqrt{5} -5\sqrt{3} =\boxed{6-5\sqrt{5} -5\sqrt{3} } \\\\\\\\\sqrt{5} (\sqrt{5} -2x)=\boxed{-2x\sqrt{5} +5}[/tex]
What percent did the price drop
Answer:
10%
Step-by-step explanation:
You have the correct answer. Nice job!
Help and explain !!!!
i believe it's y-intercept!
to be honest i was never taught why it was the y-intercept, i was just told that it was. hope this helps!
Question 1: Use the image and your knowledge of the isosceles triangle to find the value of x
Answer:
35 degrees
Step-by-step explanation:
since both sides are equal, so are the angles involved.
Type the correct answer in each box. Use numerals instead of words
Answer:
a) 1.73
b)1.32
Step-by-step explanation:
y = f(x) = 3^x
f(1/2) = 3^1/2 = √(3) = 1.73
f(1/4) = 3^1/4 = 1/4√3 = 1.32
The tables below show the values of y corresponding to different values of x: Table A x 3 3 2 y 1 0 0 Table B x 3 5 5 y −2 2 −2 Which statement is true for the tables? (1 point) Both Table A and Table B represent functions. Both Table A and Table B do not represent functions. Table A does not represent a function, but Table B represents a function. Table A represents a function, but Table B does not represent a function.
Answer:
is it possable you can show the graph
Step-by-step explanation:
Answer:
2nd option ,that is, Both tables do not represent a function.
Step-by-step explanation:
For a table to represent a function it's input value must correspond to exactly one output value.
As in Table A the input value of 3 corresponds to 2 different outputs, where
as in table B the input value of 5 corresponds to 2 different outputs.
x is taken as the input and y is taken as output for both the tables.Therefore, Both tables dobnot represent a function.
Two data sets are represented by the graphs below.
A.)Smaller range
B.) Lager median
C.)Larger mean
D.)Smaller standard deviation
What is the equation of the line graphed below?
Answer:
y=2/5x
Step-by-step explanation:
Rise over run: you rise by 2, run by 5. Or you can use the slope formula: m=y2-y1/x2-x1
2-0/5-0=2/5=m
What is the phenomenon that many types of data analysis become significantly harder as the dimensionality of the data increases
Answer:
the curse of dimensionality
Step-by-step explanation:
the cause of dimensionality has to do with the different phenomena that comes up whenever data is to be analyzed or organized in high dimensional spaces which do not happen in low dimensional spaces. This curse can be explained simply as having error increase just as there are increases in the number of features. when the features we have is more than the observations, it could cause the model to be overfitted.
What percentage of 1hour is 6munites 20seconds
Answer:
10
Step-by-step explanation:
10 percentage for this question answer
Which function is graphed below?
algebra 2
Answer:
x=0..............................
What is the value of x to the nearest tenth?
A) 9.2
B) 7.2
C) 4.8
D) 12.0
Answer:
B. 7.2
Step-by-step explanation:
radius=24÷2= 12
other line =19.2÷2=9.6 because line from centre bisects chord and is perpendicular to it
Therefore: X²=√ 12²-9.6² ( theorem of Pythagoras)
X=7.2
Hey guys please try this is kinda urgent. what is the value of x in the geometric progression. 16/9 , x, 1, y.
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Explanation:
Let r be the common ratio. Also, we'll make r nonzero, i.e. [tex]r \ne 0[/tex]
Multiplying this common ratio by any term gets us the next term of the geometric sequence.
16/9 is the first term, so that makes (16/9)*r the second term
Since (16/9)r is the second term, the third term is (16/9)r*r = (16/9)r^2
Set this equal to 1 and solve for r.
(16/9)r^2 = 1
r^2 = 1*(9/16)
r^2 = 9/16
r = sqrt(9/16) or r = -sqrt(9/16)
r = 3/4 or r = -3/4
Now that we know what r is, we can determine the second term
If r = 3/4, then,
(16/9)*r = (16/9)*(3/4) = 4/3
Or if r = -3/4, then,
(16/9)*r = (16/9)*(-3/4) = -4/3
So the second term is either 4/3 or -4/3 depending on which r value you go for.
what shape is this cause I'm having a bit of trouble?
Answer:
isn't that a square or is it called sum eles-
Step-by-step explanation:
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
Solution given:
Relationship between perpendicular and hypotenuse is given by sin angle
Sin 30°=opposite/hypotenuse
½=[tex]\frac{x}{9}[/tex]
x=[tex]\frac{9}{2}[/tex]
The value of x is [tex]\frac{9}{2}[/tex]
Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.
10 + 2.5 x less-than-or-equal-to 40
Which best describes the number of bags of balloons she can buy?
Answer:
She can buy from 0 to 20 bags, but no more.
Answer:
b <3
Step-by-step explanation:
Estimate the value of \frac{\sqrt{2\pi }}{\sqrt{5}}
Answer:
the exact answer is 1.98
if we rationalize denominator we get root 0f 10 times pi divided by 5
root of 10 is about 3.1 ([tex]\pi[/tex]) so we have [tex]\frac{\pi ^{2} }{5}[/tex] ≈ 9.6/5 = 1.92
Step-by-step explanation:
[tex]\frac{\sqrt{2\pi }}{\sqrt{5}} * \frac{\sqrt{5 }}{\sqrt{5}}[/tex] = [tex]\frac{\sqrt{10} \pi }{5}[/tex]
what is the volume of the square pyramid? answer i need this done for my geometry credit thank you
Answer: 171.5
Step-by-step explanation:
1/2 x 7 x 7 x7 = 171.5 cm3
Answer:
[tex]volume=1/3(area ~of ~base) \times( height)[/tex]
[tex]v=1/3(7\times7)\times7[/tex]
[tex]v=343/3[/tex]
[tex]v=114[/tex]
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hope it helps...
have a great day!!
PLS HELP ASAP, I give 15 pts!
Suppose an isosceles triangle ABC has A=pi/4 and b=c=3. What is the length of a^2?
A. 3^2(2 - sqr2)
B. 3^2( sqr2 - 2)
C. 3^2(2 + sqr2)
D. 3^2 sqr2
Answer:
I believe it would be A 3^2(2-sqr2)
