If the given equation is
[tex]27^{\frac13} = 9^{14} + 3^{x + 1}[/tex]
first simplify the left side using the fact that 27 = 3³:
[tex]27^{\frac13} = (3^3)^{\frac13} = 3^{\frac33} = 3^1 = 3[/tex]
and on the right side, 9 = 3²:
[tex]9^{14} = (3^2)^{14} = 3^{2\times14} = 3^{28}[/tex]
So we have
[tex]3 = 3^{28} + 3^{x + 1}[/tex]
Next,
[tex]3^{x+1} = 3^x \times 3^1 = 3 \times 3^x[/tex]
so that
[tex]3 = 3^{28} + 3 \cdot 3^x[/tex]
and dividing both side by 3 gives
[tex]1 = 3^{27} + 3^x[/tex]
Isolate 3ˣ :
[tex]3^x = 1 - 3^{27}[/tex]
Solve for x by taking the base-3 logarithm of both sides:
[tex]\log_3(3^x) = \log_3(1-3^{27})[/tex]
[tex]x \log_3(3) = \log_3(1-3^{27})[/tex]
[tex]\boxed{x = \log_3(1-3^{27})}[/tex]
perform the operation and simplify
Answer:
[tex] \frac{x + 4}{3x(x + 1)} \\ [/tex]
Step-by-step explanation:
[tex] \frac{ {x}^{2} + 10x + 24 }{3 {x}^{2} + 3x} \div (x + 6) \\ \frac{ {x}^{2} + 4x + 6x + 24}{ 3x(x + 1)} \times \frac{1}{(x + 6)} \\ \frac{x( x+ 4) + 6(x + 4)}{3x(x + 1)} \times \frac{1}{(x + 6)} \\ \frac{(x + 4)(x + 6)}{3x(x + 1)} \times \frac{1}{(x + 6)} \\ \frac{(x + 4)}{3x(x + 1)} \\ [/tex]
Answer: the finished equation is (x+4)/3x*(x+1), so fill in one in the green square
Step-by-step explanation: it worked for me, the explanation is very long, but I would recommend using tiger algebra for a very detailed step by-step explanation, hope I could be a help
What is -105/-77 simplified?
Answer:
[tex]\frac{-15}{-11}[/tex]
Step-by-step explanation:
To simplify more known as reduced we have to find the fraction as and equivalent fraction
DefinitionEquivalent Fraction - are the fractions that have different numerators and denominators but are equal to the same value.
Look for the GCFTo find the we must list out the of and
[tex]77:1, 7, 11 ,77\\\\1, 3, 5, 7, 15, 21, 35 , 105[/tex]
Our [tex]GCF[/tex] is [tex]7[/tex]
Our fraction[tex]\frac{-105}{-77}[/tex]ReduceDefinition of reduce - reduction refers to the rewriting of an expression into a simpler form
Divide the numerator and denominator by [tex]7[/tex]
Our fraction is [tex]\frac{-15}{-11}[/tex]Simplify.
510√
2√
2√2
10√2
5√
Answer:if you know how to do this your smart and in two years if someone can Answer ill give you a mil in cash swear
Step-by-step explanation:
Answer:
√10/2
Step-by-step explanation:
I took le test
which two expressions are equivalent to 7(t + 5)?
A). 7 • 5 • t
B). 7 • 5 + t
C). 7 • 5 + 7 • t
D). (5 + t) • 7
E). 5(t + 7)
Answer:
7.5+7.t
and
(5+t).7
are equivalent to 7(t+5)
Option D and E are equivalent to 7(t + 5) That is :
(5 + t) • 7 and 5(t + 7)
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
The given equation is :
7(t + 5)
7(t+5) multiply 7 with inside the parenthesis
7(t+5) = 7t + 7x5
this result is equivalent to option D and E which will give the same result.
Therefore, Option D and E are equivalent to 7(t + 5).
Read more about expressions at :
https://brainly.com/question/12030750
#SPJ2
The initial population of a town is 3800, and it grows with a doubling time of 10 years. What will the population be in 8 years?
Please show step by step!
Answer:
The population was 3040 people in 8 years.
Step-by-step explanation:
find unit rate;
3800/10 = 380
380 x 8 = 3040
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 14 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to two decimal places.)
Answer:
Step-by-step explanation:
V = 4πR³/3 + πR²h
h = (V - 4πR³/3) / πR²
A = 4πR² + 2πRh
A = 4πR² + 2πR((V - 4πR³/3) / πR²)
A = 4πR² + 2((V - 4πR³/3) / R)
A = 4πR² + 2V/ R - (8πR³/3) / R
A = 4πR² + 2(14)/ R - 8πR²/3
A = (4π - 8π/3)R² + 28/R
A = (4π/3)R² + 28/R
dA/dR = (8π/3)R - 28/R²
0 = (8π/3)R - 28/R²
28/R² = (8π/3)R
R³ = 28(3 / 8π)
R = 1.49513...
R = 1.50 cm
which makes the cylinder height 0.00 cm. The figure is a sphere.
1. What is the ratio of 10 notebooks to 5 ballpens in simplest form?
Answer:
2:1 or 2
Step-by-step explanation:
*** (Ratios can be written as " a : b", or can be written as a fraction " a / b".
>> therefore 10/5 can be simplified to 2/1 )***
For every 10 notebooks, there are 5 ballpens.
Therefore, for every 2 notebooks there is 1 ballpen (The simplification).
EXTRA:
**Also remember that the ratio of notebooks to ballpens cannot be reversed into ballpen to notebook ratio, because this would change the meaning.
2/1 is not the same as 1/2 **
If an item that originally cost $20 is increased to $27, what is the percentage of increase in the item?
A 11 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth.
Check the picture below.
What's fish + nine?
I NEED HELP!?
Answer:
nine fish............
Answer: 9 Fish
Step-by-step explanation:
Find the value of [tex]$6+\frac{1}{2+\frac{1}{6+\frac{1}{2+\frac{1}{6+\cdots}}}}$.[/tex] Your answer will be of the form [tex]$a+b\sqrt{c}$[/tex] where no factor of $c$ (other than $1$) is a square. Find $a+b+c$.
Let
[tex]x = 6 + \dfrac1{2 + \dfrac1{6 + \dfrac1{2 + \cdots}}}[/tex]
Then
[tex]x = 6 + \dfrac1{2 + \dfrac1x}[/tex]
and solving for x gives
[tex]x = 6 + \dfrac x{2x + 1}[/tex]
[tex]x = \dfrac{13x + 6}{2x + 1}[/tex]
[tex]x(2x+1) = 13x + 6[/tex]
[tex]2x^2 + x = 13x + 6[/tex]
[tex]2x^2 - 12x - 6 = 0[/tex]
[tex]x^2 - 6x - 3 = 0[/tex]
By the quadratic formula,
[tex]x = 3 \pm 2\sqrt{3}[/tex]
but x must be a positive number, so only the positive square root solution is valid.
[tex]x = 3 + 2\sqrt{3}[/tex]
We identify a = c = 3 and b = 2, so a + b + c = 8.
Use point-slope form to write the equation of a line that has a slope of 2/3 and passes through (-3, -1). Write your final equation in slope-intercept form
y=2/3x -3
the picture is the explanation
Solve the equation: q –10 = -10
Answer:
q=0
Step-by-step explanation:
-----------------------------
q - 10 = - 10
q = 0
<3
Mikey's family is taking a road trip. Their car can travel no more than 260 miles without needing to refill the gas tank. They have traveled 112 miles since they last filled the gas tank.
Mikey knows that the inequality representing this situation is 112+x≤260.
Select from the drop-down menu to correctly interpret the solution of this inequality.
Mikey's family can drive
at most 148
more miles before they need to refill the gas tank.
Answers choices are:
More than 372
More than 372
at most 148
at least 148
The solution to the inequality is that Mikey's family can drive at most 148
Inequality shows the non equal comparison of numbers or expressions.
Given that Mikey situation can be represented by the inequality:
112 + x ≤ 260
Solving the inequality:
112 + x ≤ 260
Subtract 112 from both sides of the equation:
112 + x - 112 ≤ 260 - 112
x ≤ 148
Hence from the inequality, we can see that Mikey's family can drive
at most 148
Find out more at: https://brainly.com/question/25285332
no link no bot right please
9514 1404 393
Answer:
10.49
Step-by-step explanation:
Since we know 110 = 10² +10, we can make a first approximation to the root as ...
√10 ≈ 10 +10/21 . . . . . where 21 = 1 + 2×integer portion of root
This is a little outside the desired approximation accuracy, so we need to refine the estimate. There are a couple of simple ways to do this.
One of the best is to use the Babylonian method: average this value with the value obtained by dividing 110 by it.
((220/21) + (110/(220/21)))/2 = 110/21 +21/4 = 881/84 ≈ 10.49
An approximation of √110 accurate to hundredths is 10.49.
__
The other simple way to refine the root estimate is to carry the continued fraction approximation to one more level.
For n = s² +r, the first approximation is ...
√n = s +r/(2s+1)
An iterated approximation is ...
s + r/(s +(s +r/(2s+1)))
The adds 's' to the approximate root to make the new fraction denominator.
For this root, the refined approximation is ...
√110 ≈ 10 + 10/(10 +(10 +10/21)) = 10 +10/(430/21) = 10 +21/43 ≈ 10.49
_____
Additional comment
Any square root can be represented as a repeating continued fraction.
[tex]\displaystyle\sqrt{n}=\sqrt{s^2+r}\approx s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}[/tex]
If "f" represents the fractional part of the root, it can be refined by the iteration ...
[tex]f'=\dfrac{r}{2s+f}[/tex]
__
The above continued fraction iteration adds 1+ good decimal places to the root with each iteration. The Babylonian method described above doubles the number of good decimal places with each iteration. It very quickly converges to a root limited only by the precision available in your calculator.
Describe in words a sequence of transformations that maps ABC to A' B' C
Write an ordered-pair rule for this sequence of transformations.
Answer:
A reflection over the y-axis followed by a translation 4 units down
Step-by-step explanation:
hope this helps!
plsssss helpppppp i’ll give brainliest
Answer:
[tex]-6\leq x\leq 6[/tex]
Step-by-step explanation:
This is answer for the last question.
What is a common denominator for 1 3/4 and 1 4/5
Answer:
20
Step-by-step explanation:
A common denominator is a number that is a multiple of both denominators.
To find it just write the multiplication table of the numbers and find a number that appears in both of them.
In this case, we have 4 and 5:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Since it only asks for a common denominator, it can be 20, 40, 60, 80... Although it's usually smarter to pick the lower number.
[tex]1\dfrac 34 =1+ \dfrac 34 =\dfrac 74 = \dfrac{35}{20}\\\\\\1\dfrac 45 = 1+ \dfrac 45 = \dfrac 95 =\dfrac{36}{20}\\\\\text{The answer is 20}[/tex]
Christina has these two tiles. Draw a new shape she can create with both tiles. Then name the shape and how many sides the new shape has.
Square and triangle
Answer:
quadangle
Step-by-step explanation:
a square made of triangles and If a triangle is called a triangle, why is a square not called a quadangle?
Squares and triangles can be combined to form a pentagon
The new shape is a pentagon.The shape has 5 sides.The two shapes are given as:
SquareTriangleWhere the base of the square equals the side length of the triangle
When these shapes are combined i.e. when the base of the triangle is merged with the side length of the square, then it forms a pentagon.
See attachment for the image of the new shape.
From the attached image, we can see that the shape has 5 sides
Read more about pentagons at:
https://brainly.com/question/9317617
All of the points in the picture are on the same line *help asap*
Answer:
yes all of the points are on the same line
Step-by-step explanation:
WILL AWARD BRAINLIEST AND 5 STAR
2. Marcus is writing the program for a video game. For one part of the game, he uses the rule
(x, y) ➡️ (x + 8, y – 3) to move points on the screen.
(a) What output does the rule give when the input is (-2, 1)? Show your work.
(b) What output does the rule give when the input is (0, -5)? Show your work.
(c) Is the rule a function? Explain why it is or why it is not.
Answer:
I might be getting somthign comfised but here is what I derived from it.
Step-by-step explanation:
Marcus uses a rule of (x+8, y-3). What will be the output if the input is (-2,1) and (0,-5).
If it is going off of the math functions then the outputs would be simple math -
(6, -2) -2+8 and -3+1; (8, -8) 0+8 and -5-3 [if im doing the correct functions].
The X and Y is what gets me when trying to answer if it is a function or not, I would say it is because the x and y values are given and they are their values are substituted, the actual function is adding the 8 to the X and subtracting the 3 from the Y.
Hope this helps some
bill planted 4 pecan trees and 2 apple trees what fraction of that is pecan
Answer:
4 / 6 or 2/3
pecan total tree
Answer:
2/3
Step-by-step explanation:
So, Bill planted -
Pecan trees = 4
Apple trees = 2
Total trees = 6
We want the fraction of Pecan trees. Thus,
4/6
Where 4 is Pecan trees, (What we want)
And 6 is the total.
4/6 in its simplest form is 2/3.
I hope it helps.
I need help on the "the slopes are" part on these 2 plz help
Answer:
Negative reciprocals
A baseball pitcher has made 53 pitches in the first four innings of a baseball game and plans to pitch 3 mote innings. The manager of the team has committed to allowing his pitcher to throw, at most, pitches during the game. Write an inequality to find the average number of pitches the pitcher can throw over the next three innings Solve the inequality from Part 1. What is the maximum number of pitches the pitcher can make in cach of the next 3 innings ? Graph your solution from Part 2 on a number line and explain what your solution means. If the pitcher threw just 6 pitches in the fifth inning, what is the greatest number of pitches the pitcher can throw per inning he wishes to pitch nine innings? Write and solve an inequality to answer this part.
Answer:
at most 17 pitches per inning
Step-by-step explanation:
It is given that a baseball pitcher makes 53 pitches in the first 4 innings of a game and plans to pitch in the next 3 innings.
We need to write and solve an inequality to find the possible average pitches per inning the pitcher made in the next 3 innings if the pitcher is assigned a maximum of 105 pitches.
From part (a) we know 3 p + 53 3p+53 represents the total number of pitches made if the pitcher makes an average of p pitches per inning in the next 3 innings.
If the pitcher can make at most 105 pitches, then:
3 p + 53 ≤ 105 3p+53≤105
To solve the inequality, first subtract 53 on both sides of the inequality to isolate the variable term:
3 p + 53 − 53 ≤ 105 − 53 3 p ≤ 53
3p+53≤105 [tex]p\leq 17\frac{1}{3}[/tex]
at most 17 pitches per inning
(Hope this helps can I pls have brainlist (crown)☺️)
what is the area of the soccer field if x=40m?
base is 2x+20
height is x+20
6,600,000,000 exponential notation
Answer:
6.6 x 10^9
Step-by-step explanation:
In circle O, what is mArc A E?
Answer:
Step-by-step explanation:
By using the theorem of secants intersecting externally, Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs. m∠C =. 36° =. 72° = °. …
By using the theorem of secants intersecting externally, Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs. m∠C =. 36° =. 72° = °. …
4(x-3) < x+3, Where x ∈ W
Please help me
[tex]\large\underline{\sf{Solution-}}[/tex]
Given:
[tex]\rm\longmapsto 4(x-3)<x+3, x\in \mathbb{W}[/tex]
[tex]\rm\longmapsto 4x-12<x+3[/tex]
[tex]\rm\longmapsto 4x-12-x<x+3-x[/tex]
[tex]\rm\longmapsto 3x-12<3[/tex]
[tex]\rm\longmapsto 3x-12+12<3+12[/tex]
[tex]\rm\longmapsto 3x<15[/tex]
[tex]\rm\longmapsto \dfrac{3x}{3}<\dfrac{15}{3}[/tex]
[tex]\rm\longmapsto x<5, x\in\mathbb{W}[/tex]
[tex]\large\underline{\sf{Answer-}}[/tex]
Therefore:
[tex]\rm\longmapsto x=\{0,1,2,3,4\}\ \ \ [/tex]
Plot the point (6, 0) on the coordinate plane.
Answer:
Just go to the 6 on the bottom line, and add a point
Answer:
see below
Step-by-step explanation:
(6,0)
The first coordinate is the x coordinate. Since it is positive we go to the right 6 units. The second coordinate is the y coordinate. We go up zero units
-
Find the equation of the line that
is parallel to y = 2x – 7 and
contains the point (-3,6).
Step-by-step explanation:
The first step is to Know the condition for two lines be parallel is that have the same slope, and this form the slope given is 2, therefore the new function has its slope too
2) with the slope and the two points givens, you can find the equation
Y-Y1 = m( X-X1) , Y-6 = 2[(X-(-3)] ⇒Y-6 = 2X+6 ⇒Y = 2X+12, AND THIS IS THE EQUATION PARALLEL TO THE LINE Y = 2X-7
