Answer:
[tex]\displaystyle y = x^{-\frac{2}{3}}[/tex]
Step-by-step explanation:
Logarithms
Some properties of logarithms will be useful to solve this problem:
1. [tex]\log(pq)=\log p+\log q[/tex]
2. [tex]\displaystyle \log_pq=\frac{1}{\log_qp}[/tex]
3. [tex]\displaystyle \log p^q=q\log p[/tex]
We are given the equation:
[tex]\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }[/tex]
Applying the second property:
[tex]\displaystyle \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}[/tex]
Substituting:
[tex]\displaystyle \log_{2}(x) = 3\log_{2}(xy)[/tex]
Applying the first property:
[tex]\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))[/tex]
Operating:
[tex]\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)[/tex]
Rearranging:
[tex]\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)[/tex]
Simplifying:
[tex]\displaystyle -2\log_{2}(x) =3\log_{2}(y)[/tex]
Dividing by 3:
[tex]\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}[/tex]
Applying the third property:
[tex]\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)[/tex]
Applying inverse logs:
[tex]\boxed{y = x^{-\frac{2}{3}}}[/tex]
Solve for x.
And solve for Z
From Tales theorem: [tex]\dfrac{8x-2}{2x+1}=\dfrac{3z+z+22}{3z}[/tex]
Solving for x:[tex]\dfrac{8x-2}{2x+1}=\dfrac{4z+22}{3z}\\\\(8x-2)(3z)=(2x+1)(4z+22)\qquad\qquad\{divide\ both\ sides\ by\ 2\}\\\\(4x-1)(3z)=(2x+1)(2z+11)\\\\12xz-3z=2x(2z+11)+1(2z+11)\\\\12xz-2x(2z+11)=3z+2z+11\\\\x(12z-4z-22)=5z+11\\\\x(8z-22)=5z+11\qquad\qquad\{divide\ both\ sides\ by\ (8z-22)\}\\\\x=\dfrac{5z+11}{8z-22}[/tex]
Solving for z:[tex]\dfrac{8x-2}{2x+1}=\dfrac{4z+22}{3z}\\\\(8x-2)(3z)=(2x+1)(4z+22)\qquad\qquad\{divide\ both\ sides\ by\ 2\}\\\\(4x-1)(3z)=(2x+1)(2z+11)\\\\(12x-3)(z)=(2x+1)(2z)+(2x+1)(1)\\\\(12x-3)(z)-(4x+2)(z)=(2x+1)\\\\\ [(12x-3)-(4x+2)](z)=(2x+1)\\\\(12x-3-4x-2)(z)=(2x+1)\\\\(8x-5)(z)=(2x+1)\qquad\qquad\{divide\ both\ sides\ by\ (8x-5)\}\\\\z=\dfrac{2x+1}{8x-5}[/tex]
What is a simplified eCarlotta thinks that 3y + 5y3 is the same as 8y4. Which statement shows that it is NOT the same?Xpression for (x + y) – (x – y)?
Questions:
(a) What is a simplified expression for (x + y) – (x – y)?
(b) Carlotta thinks that [tex]3y + 5y^3[/tex] is the same as [tex]8y^4[/tex]. Which statement shows that it is NOT the same?
Answer:
[tex](x + y) - (x - y) =2y[/tex]
[tex]3y + 5y^3 \ne 8y^4[/tex]
Step-by-step explanation:
Solving (a):
Given
[tex](x + y) - (x - y)[/tex]
Required
Simplify
[tex](x + y) - (x - y)[/tex]
Open brackets
[tex](x + y) - (x - y) = x + y - x + y[/tex]
Collect Like Terms
[tex](x + y) - (x - y) = x - x+ y + y[/tex]
[tex](x + y) - (x - y) = y + y[/tex]
[tex](x + y) - (x - y) =2y[/tex]
Solving (b):
Given
[tex]3y + 5y^3[/tex] and [tex]8y^4[/tex]
Required
Which expression shows they are not the same
The expression that shows this is:
[tex]3y + 5y^3 \ne 8y^4[/tex]
Take for instance; y=2
Substitute 2 for y in [tex]3y + 5y^3 \ne 8y^4[/tex]
[tex]3*2 + 5*2^3 \ne 8*2^4[/tex]
Evaluate all exponents
[tex]9 + 5*8 \ne 8*16[/tex]
[tex]9 + 40 \ne 128[/tex]
[tex]49 \ne 128[/tex]
The above expression supports [tex]3y + 5y^3 \ne 8y^4[/tex]
Find the slope (m) of the line
that passes through the pair of
points
(4.5, 5.7) and (14.5, 18.9)
help! Giving out extra points and brainlist
Solving a Real-World Problem
Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
O x + y = 29, 5x + 2y = 100
O x + y = 100, 5x + 2y = 29
0 5x + y = 29, 2y + x = 100
O 2x + y = 100, 5y + x = 29
Answer: From the conditions given, the total number of the problems should be 29. This means that the sum of x and y should be 29. With this and the point-system, the best system of equation that is useful for this problem is,
x + y = 29
5x + 2y = 100
Your first answer choice is the correct answer.
Fact: I suggest looking up the question before asking it because sometimes others have asked the questions and it will be answered. Just letting you know to help you save points.
Answer:
x + y = 29, 5x + 2y = 100
Step-by-step explanation:
just did it
➥ The base of a parallelogram is thrice its height. If the area is 897 sq.cm. Find the base and height of the parallelogram.
Answer:
The height of parallelogram is 51.87 cm
Step-by-step explanation:
Let The height of a parallelogram = a cm
Then
The base of a parallelogram = 3a cm
So by the given condition
3a×a = 897
3a^2 = 897
a^2 = 897/3
a^2 = 299
a = 17.29
So the height of parallelogram = 3×17.29= 51.87 cm
I NEED HELP PLSS
Functions of composition~
Find −369+(−7) need help
Answer:
-376
Step-by-step explanation:
I hope that this helps you out..
Answer:
-376
Step-by-step explanation:
find the magnitudes of 9.109 X 10^-31
9514 1404 393
Answer:
9.109×10^-31
Step-by-step explanation:
The magnitude of a positive number is the number itself.
9.109×10^-31
2 triangles are shown. They have one congruent side. The first triangles has angle measures of 98 degrees and 35 degrees. The second triangle has angle measures of 35 degrees and 47 degrees. Are the triangles congruent? If so, how do you know?
Answer: Yes.
Step-by-step explanation:
Two triangles are said to be congruent when the sides of the triangles are all of same length and also when their angles are equal as well.
In this case, the first triangles has angle measures of 98 degrees and 35 degrees. This means that the 3rd angle in the triangle will be:
= 180° - (98° + 35°)
= 180° - 133°
= 47°
Since the second triangle has angle measures of 35 degrees and 47 degrees. The 3rd angle will be:
= 180° - (35° + 47°)
= 180° - 82°
= 98°
The triangle is congruent as they all have same angles
Answer:
yes because of ASA or AAS
Step-by-step explanation
got it right
Question 6 of 10
Two triangles that have the same side lengths will always be congruent.
A. True
B. False
Answer:
True.
Step-by-step explanation:
We have to tell about the statement true or false
Two triangles that have the same side length will always be congruent
The SSS congruency rule states that if all three sides of one triangle are equal to corresponding three sides of another triangle, then the triangles are congruent.
∴ we say that when the sides are the same then the triangles are congruent.
Hence, the statement is true.
Because the definition of a congruent triangle is a triangle with every side of same length.
A rectangular prism measures 7 & 1/2 cm by 12 cm by 15 & 1/2 cm. Calculate the number of cubes with edge length 1/2 cm that fit in this prism.
Answer: 8 cubes
Step-by-step explanation:
Volume of a rectangular prism is length × height × width
Length=7 1/2
Width= 15 1/2
Height=12
Volume of the prism is therefore:
7 1/2×12×15 1/2= 1395cm3
No of cubes with edge length 1/2 to fit into the prism will be:
Volume of cube is L*W*H
1/2*1/2*1/2= 1/8cm3
Therefore the no of cubes to fit into the Prism will be:
1395/(1/8)= 11160 cubes.
If one was stuck,the number of 1/2 edge length
cube to fit into 1cm will be:
1/(1/8)= 8 cubes
Find the roots for y = (2x-3)(x+5) (The x values)
Answer:
x = [tex]\frac{3}{2} , -5[/tex]
Step-by-step explanation:
We know that we have to find the roots of the equation - which is another way of saying the x-intercepts, or the points that are on the x-axis that the graph passes through. All points on the x-axis have a y-value of 0. So, in order to find the roots for this equation, we need to find which values of x make the y equal 0.
The equation has already been factored out. So, we just need to find which values of x for each of the expressions in the parentheses will make the result 0. To do this, set the expressions in the parentheses to 0 and isolate x.
1) First, let's look at (2x-3). Write the equation 2x-3 = 0. Then, isolate x:
[tex]2x-3 = 0\\2x = 3\\x = \frac{3}{2}[/tex]
Therefore, [tex]\frac{3}{2}[/tex] is one of the roots.
2) Next, let's look at (x+5). Write the equation x+5 = 0. Then, isolate x:
[tex]x+5 = 0\\x = -5[/tex]
Therefore, -5 is a root as well.
The roots of the equation would be [tex]\frac{3}{2}[/tex] and -5.
Divide £128 in the ratio 1:3
Answer:
£32 : £96
Step-by-step explanation:
add the parts of the ratio, 1 + 3 = 4 parts
Divide the amount by 4 to find the value of one part of the ratio
£128 ÷ 4 = £32 ← value of 1 part of the ratio, then
3 parts = 3 × £32 = £96
£128 in the ratio 1 : 3 is £32 : £96
The amount, £128 when divided in the ratio 1:3 is; £32: £96.
RatiosWe are required to divide in the ratio 1:3;
Therefore, we must divide the total by (1+3); so that we have;
128/4= 32.Therefore, each unit is £32 and 3× £32 = £96.
The amount, £128 when divided in the ratio 1:3 is therefore; £32: £96.
Read more on Ratios;
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Help & explain answer pls
Solving linear equation study island
Answer:
Step-by-step explanation:
(x-9)/5))(5) = 2(5)
answer is B
I WILL MARK BRAINLIEST
World Without Engines: Explain what todays world without engines would be like? How would it change your life? The world? The way we do things? Please write in paragraph format and include introduction, body, and conclusion.
A world without engines is certainly an appealing idea. Although engines are a vital transportation source that allow us to move around and travel much faster and efficiently, passenger vehicles are a major pollution contributor. they produce large amounts of carbon monoxide, nitrogen oxides, and other forms of pollution. Removing all engines would definitely have downsides, but the significant amount of help it would provide towards lowering pollution rates would be extremely impactful towards our environment and earth. Engines are important parts of human life, and getting things done faster is much more efficient, without engines humans would have to do many things by hand and it would slow production of many things that are necessities. There are also many situations regarding human lives that require the fastest transportation possible, and without engines many things wouldn't get done fast enough. In conclusion, a world without engines would have many benefits towards the environment, however, we've grown to be too dependent on these machines and without them production of many things would start to slow and many trips around the world would be near impossible or extremely delayed.
sorry about it being one big block, wasnt sure how u wanted it to be spaced. hope this helps atleast a little, gl
Help pls
The first few partial sums of a series consisting of only
positive terms are shown.
Answer:
The partial sums are increasing in value.
The series converges to the same value as what the partial sums approach.
The partial sums appear to approach 0.33.
The series might converge to One-third.
Step-by-step explanation:
Answer:
The partial sums are increasing in value.
The series converges to the same value as what the partial sums approach.
The partial sums appear to approach 0.33.
The series might converge to One-third.
Step-by-step explanation:
Please answer for brainliest and 10 points !!
Answer:
4 1/2 or -1 1/2
Step-by-step explanation:
1 1/3-3= -1 1/2
1 1/2+3=4 1/2
Can someone pls help me with this! I need help!!!
A ramp of 13 feet in length is constructed in front of a house that is at a height of 5 feet from the ground. What is the horizontal distance between the front door and the point where the ramp touches the ground?
The horizontal distance between the front door and the point where the ramp touches the ground will be equal to 12 feet.
What is the Pythagoras' Theorem?According to the Pythagoras theorem, if a triangle has a straight angle (90 degrees), the hypotenuse's square is equal to the total of its other two sides' squares.
As per the given information in the question,
Length of the ramp, h = 13 feet
Height of ramp from the ground, p = 5 feet
Let the horizontal distance is b.
Then, use the equation of Pythagoras' Theorem,
h² = p² + b²
13² = 5² + b²
b² = 169 - 25
b = √144
b = 12 feet.
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Given that f ( x ) = x 2 − 6 x + 8 f(x)=x 2 −6x+8 and g ( x ) = x − 2 g(x)=x−2, find f ( x ) + g ( x ) f(x)+g(x) and express the result in standard form.
Answer:
Step-by-step explanation:
Your problem → f(x) = x^2 - 6x + 8,g(x) = x - 2,find f(x) + g(x)
f(x)=x^2-6x+8
g(x)=x-2
f(x)+g(x)=?
Now f(x)+g(x)
=(x^2-6x+8)+(x-2)
=x^2-6x+8+x-2
= x^2 - 6x + x + 8 -2
=x^2 -5x + 6
I can't change it to standard form but i hope this helps:)
Need help please will give brainliest
Answer:
x = 60
Step-by-step explanation:
The formula for this kind of question is
Area of sector = x / 360 * pi * r^2 = 24*pi
x/360 * pi * 12^2 = 24 pi
x/360 * pi * 144 = 24 pi the pi s cancel out
x / 360 = 24/144 Multiply both sides by 360
x = 24 * 360/144
x = 60
What is 12.6254748322 rounded to nearest tenth
Answer:
12.6
Step-by-step explanation:
Answer:
13.0
Step-by-step explanation:
The price of a flight was increased by 3% to £650. What was the price before the increase?
Give your answer to the nearest penny.
Please help me! Brainliest to the correct answer along with 25 points, no point thieves please! If I don't get this right I might fail my class! The question is in the picture!
Answer:
Option D
Step-by-step explanation:
5 * 58
= 5 ( 50 + 8 ) ~This is because 50 + 8 is the same as 58, essentially rewriting the problem
5 * 50 + 5 * 8 ~This is distributing the 5, so every term in this the parenthesis is multiplied by 5
250 + 40 ~This is simplifying the problem
290 ~This is the final answer
Answer:
my mind cant take that Kacchan, you know that....
Step-by-step explanation:
sorry I couldn't help Kacchan!!!
Love: Deku <3
Find each function value f(3) if f(x) = 2x + 2
Answer: The function value is 8.
Step-by-step explanation: Substitute 3 for x.
f(3) = 2(3) +2f(3) = 6 +2f(3) = 8Answer:
Step-by-step explanation:
okay soooo first you must multiply 3 by 2 because 3 is the element of the function (x)
your answer should be 6
now add 2 to your answer (6) and you should get 8
Charlotte measures the distance from the center of a circular garden to its edge and finds it is 43 meters. How long is the path which goes around the outside of the garden?
Answer: 270.29 meters
Step-by-step explanation:
This is a circle which means that the distance that Charlotte measured from the center of a circular garden to its edge is the radius.
The length of the path which goes around the garden would therefore be the circumference.
Circumference = π * diameter
Diameter = radius * 2
= 43 * 2
= 86 meters
Circumference = 22/7 * 86
= 270.29 meters
What is the area of the parallelogram?
36 m 2
18 m 2
24 m 2
72 m 2
Answer:
36m^2
Step-by-step explanation:
A=bh
=6m*6m
=36m^2
Aubrey has a new art box in the shape of a rectangular prism. The box is 12\text{ cm}12 cm12, start text, space, c, m, end text by 20\text{ cm}20 cm20, start text, space, c, m, end text by 5\text{ cm}5 cm5, start text, space, c, m, end text. The only thing in the art box is a new pink eraser with the dimensions shown below. What is the volume of the art box not taken up by the eraser?
Answer:
1196cm^3
Step-by-step explanation:
The height of the box with the smaller base is 4 times larger than that of the box with the larger base.
What is the volume of a rectangular prism?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The volume of a rectangular prism=Length X Width X Height
The volume of a box is the product of the base area and the height of the box,
Volume = base area × height
For the smaller base box,
base = 5 cm by 5 cm,
Therefore, the base area of the smaller base box
= 5 cm × 5 cm
= 25 cm².
Let the height of the smaller base box be h
The volume of the small box = 25 cm² × h
For the larger base box,
The base of 10 cm by 10 cm
Therefore, the base area of the larger base box
= 10 cm × 10 cm
= 100 cm².
Let the height of the large base box be H.
The volume of the larger base box = 100 cm² × H
Since both boxes have the same volume so,
100 cm² × H = 25 cm² × h
h / H = 4
h = 4H
Hence, The height of the box with the smaller base is 4 times larger than that of the box with the larger base.
Learn more about a rectangular prism;
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what was the price of 1 mug before the sale
tip
I need the hold thing to know the question like or the picture