Answer:
[tex]\boxed{2^{\frac{802}{27}} \cdot 3^9}[/tex]
Step-by-step explanation:
I will try to give as many details as possible.
First of all, I just would like to say:
[tex]\text{Use } \LaTeX ![/tex]
Texting in Latex is much more clear and depending on the question, just writing down without it may be confusing or ambiguous. Be together with Latex! （＊＾Ｕ＾）人（≧Ｖ≦＊）/
[tex]$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$[/tex]
Note that
[tex]\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }[/tex]
The denominator can't be 0 because it would be undefined.
So, we can solve the expression inside both parentheses.
[tex]\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3[/tex]
Also,
[tex]\boxed{a^{0} = 1, a\neq 0 }[/tex]
[tex]\left(\dfrac{1}{9} \cdot \dfrac{1}{1024} \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]
Note
[tex]\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq 0}[/tex]
[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]
[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]
[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]
[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]
Note
[tex]\boxed{\dfrac{1}{\dfrac{1}{a} } = a}[/tex]
[tex]9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]
[tex]\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)[/tex]
Once
[tex]9216=2^{10}\cdot 3^2 \implies 9216^3=2^{30}\cdot 3^6[/tex]
[tex]\boxed{(a \cdot b)^n=a^n \cdot b^n}[/tex]
And
[tex]$4^{\frac{4}{27}} = 2^{\frac{8}{27} $[/tex]
We have
[tex]\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)[/tex]
Also, once
[tex]\boxed{\dfrac{c^a}{c^b}=c^{a-b}}[/tex]
[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27[/tex]
As
[tex]30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27} =\dfrac{802}{27}[/tex]
[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3[/tex]
[tex]2^{\frac{802}{27}} \cdot 3^9[/tex]
Chapter 1 MathXL: Mid-Chapter Practice and Review
1.1.9
Translate to an algebraic expression.
25 more than t
The translation is
Answer:
25>t
Step-by-step explanation:
25 is more than t
if it is more than that means 25 is greater so "Pacman"would would eat the bigger number
Answer:
lol
riajgeripaeohnpoaetnhaethaehte
Step-by-step explanation:
Harvey has 514 stamps. He places an equal number of stamps in 3 stamp books. How many stamps are in each book? Are there any stamps left over
6
Ms. Banks walks at about 3 feet per second. How many miles per day could she travel.if she walked without
taking a break?
1
0.81 miles per day
16.36 miles per day
49.09 miles per day
2.04 miles per day
Answer:
49.09 miles per day
Step-by-step explanation:
There are 5,280 feet in one mile.
There are 60 seconds in one minute.
3 * 60 = 180 feet per minute
There are 60 minutes in one hour.
180 * 60 = 10,800 feet in one hour.
There are 24 hours in one day.
10,800 * 24 = 259,200 feet per day.
Divide to find how many miles she can walk.
259,200 / 5,280 = 49.09 miles
Best of Luck!
PERCENTAGE of 7.50 OF ₹6
Answer:%80 or 0.8
Step-by-step explanation:
Total = 7.50
Part of 7.50 is 6
The percentage of 6 in 7.50 is 6*100/7.50
0.8* 100
80%
Or you could do it this way:
6/7.5
x10 on both
60/75
by 5 times
12/15
4/5
=0.8
ASAP! I will give you branilest
Elena wants to make a scale drawing of her bedroom. Her bedroom is a rectangle with length 500 cm and width 300 cm. She decides on a scale of 1 to 50.
b. Elena's bedroom door is 80 cm wide. How wide should the door be on the scale drawing? Explain your reasoning.
(*Hint #1* a good explanation uses Words, Numbers, or Pictures to justify your thinking).
Answer:
1.6cm
Step-by-step explanation:
80/50=1.6 cm
Good Luck!
6 divided by 2 over 3
Answer: 1
Step-by-step explanation: 6/2=3 3/3= 1
Answer:
9
Step-by-step explanation:
6 divided by [tex]\frac{2}{3}[/tex] 2 over 3
6/(2/3) = 9
Check- [tex]\frac{2}{3}[/tex]*9 = 6
Let f(x)=4x−1 and g(x)=x2+ 2.
Find (f◦g)(5).
Step-by-step explanation:
[tex]f(g(x) = 4(2x + 2) - 1 \\ 4(2(5) + 2) - 1 \\ 4(12) - 1 \\ 48 - 1 = 47[/tex]
If you had six candy bars and you gave 12 people an equal piece, how much would
each person receive?
Answer:1/2 a candy bar
Step-by-step explanation:6 / 12 = 1/2
The Suarez family paid $23.00 for 4 movie tickets. How much would they have paid for 12 tickets?
Answer:
$69
Step-by-step explanation:
23 + 23+23 = $69
What is the value of a?
Enter your answer in the box. Enter your answer as a simplified fraction.
==========================================
Work Shown:
The scalar (2/5a+6) multiplies with the matrix on the left side to get the matrix on the right side
So this is what your steps could look like
[tex](\frac{2}{5}a+6)\begin{bmatrix}3 \\ -2 \\ 7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\\begin{bmatrix}(\frac{2}{5}a+6)*3 \\ (\frac{2}{5}a+6)*(-2) \\ (\frac{2}{5}a+6)*7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\[/tex]
[tex]\begin{bmatrix}\frac{2}{5}a*3+6*3 \\ \frac{2}{5}a*(-2)+6*(-2) \\ \frac{2}{5}a*7+6*7\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\\begin{bmatrix}\frac{6}{5}a+18 \\ -\frac{4}{5}a-12 \\ \frac{14}{5}a+42\end{bmatrix}=\begin{bmatrix}15 \\ -10 \\ 35\end{bmatrix}\\\\\\[/tex]
The last matrix equation leads to this system of equations
[tex]\begin{cases}\frac{6}{5}a+18=15 \\ -\frac{4}{5}a-12=-10 \\ \frac{14}{5}a+42=35\end{cases}\\\\\\[/tex]
If we pick any of those equations, and solve for 'a', then we'll get our answer.
---------------------
Let's say we pick the first equation
(6/5)a+18 = 15
(6/5)a = 15-18
(6/5)a = -3
a = -3(5/6)
a = -15/6
a = -5/2
--------------------
If we pick on the second equation, then,
(-4/5)a-12 = -10
(-4/5)a = -10+12
(-4/5)a = 2
a = 2(-5/4)
a = -10/4
a = -5/2
--------------------
Or we could solve the third equation for 'a'
(14/5)a+42 = 35
(14/5)a = 35-42
(14/5)a = -7
a = -7*(5/14)
a = -35/14
a = -5/2
-------------------
You only need to solve one equation to find 'a', though it's good practice to solve all three to see all three rows agreeing with one another.
The multiplication of the matrix by a constant will multiply for each term in the matrix value of the "a" given system of the matrix will be -2.5.
What is a matrix?A matrix is a collection of numbers lined up in rows and columns to produce a rectangular array.
In computer graphics, where they have been used to describe picture transformations and other alterations, matrices have vital applications as well in many sectors.
As per the given system of the matrix.
When we multiply anything in a matrix then it will multiply to each and every term of the matrix.
Therefore the (2/5)a + 6 will be multiplied by 3,-2, and 7 each.
So the first term of the left-hand side matrix becomes,[(2/5)a + 6]3
If we compare two matrices then each corresponding term will be the same.
Therefore, the first term of the left-hand matrix = first term of the right-hand matrix
[(2/5)a + 6]3 = 15
6a/5 + 18 = 15
6a/5 = -3
6a = -15
a = -15/6 = -2.5
Hence "The value of the "a" given system of the matrix will be -2.5".
For more about matrices,
brainly.com/question/11367104
#SPJ5
Find each percent increase. Round to the nearest percent
Answer:
1. 15 to 21 = 21 - 15 / 15 = 0.4*100% = 40%
2. 12 teachers to 48 teachers = 48 - 12/48 = 0.75 * 100% = 75%
3. 80 pencil to 120 pencil = 120 - 80 / 80 = 0.5*100% = 50%
4. 40 cans to 70 cans = 70 - 40 / 70 = 0.43 * 100% = 43%
one last question please
Answer:
B
y = -4x
Step-by-step explanation:
PLZ mark brainliest
This is due soon solve asap please.
Answer:
Home to school through mall: 11 miles
Home to school through theater: 13 miles
Step-by-step explanation:
The route from home to school that passes the mall is x + 1 + x + 2 = 2x + 3.
The route from home to school that passes the theater is 2x + 1 + x = 3x + 1.
The route from home to school that passes the mall is 2 miles shorter than the route that passes by the theater.
2x + 3 = 3x + 1 - 2
2x + 3 = 3x - 1
-x = -4
x = 4
Home to school through mall:
2x + 3 = 2(4) + 3 = 11
Home to school through theater:
3x + 1 = 3(4) + 1 = 13
Answer:
Home to school through mall: 11 miles
Home to school through theater: 13 miles
PLS HELP! which graph is the function 3x + 2y = 8 with the given domain {-2,0,2,4}??
Answer:
D
Step-by-step explanation:
Domain of the function 3x + 2y = 8 are the possible set of x-values represented as {-2, 0, 2, 4}.
To know which graph represents the above given function, find the range values of the function by plugging in each value of x into the equation, to find y.
For x = -2,
3(-2) + 2y = 8
-6 + 2y = 8
2y = 8 + 6
2y = 14
y = 14/2
y = 7
(-2, 7)
For x = 0,
3(0) + 2y = 8
0 + 2y = 8
2y = 8
y = 8/2
y = 4
(0, 4)
For x = 2,
3(2) + 2y = 8
6 + 2y = 8
2y = 8 - 6
2y = 2
y = 2/2
y = 1
(2, 1)
For x = 4,
3(4) + 2y = 8
12 + 2y = 8
2y = 8 - 12
2y = -4
y = -4/2
y = -2
(4, -2)
The graph which shows the following set of coordinates pairs calculated above, ((-2, 7), (0, 4), (2, 1), (4, -2)), is the graph of the function 3x + 2y = 8.
Thus, the graph in option D the shows the following calculated coordinate pairs. Therefore, graph D is the answer.
Please help!!!!!!!!!!):$:
1/4+2/3
LCM=12
3+8/12
11/12
HOPE IT HELPS YOU OUT PLEASE MARK IT AS BRAINLIEST AND FOLLOW ME PROMISE YOU TO FOLLOW BACK ON BRAINLY.INMartina swam 4 kilometers against the current in the same amount of time it took her to swim 12 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Martina swim if there were no current
please help 50 points
Answer:
|J| = -40
Step-by-step explanation:
The determinant of a 2×2 matrix is the difference between the product along the down diagonal and the product along the up diagonal:
|J| (-2)(8) -(4)(6) = -16 -24
|J| = -40
Answer:
|J| = -40
Step-by-step explanation:
After 3.5 hours, Peyton had traveled 161 miles. If she travels at a constant speed, how far will she have traveled in 4 hours
Answer:
1.3 more miles i think
Step-by-step e
3.5 hours equal 210 and i divided it by 163 and thats what came up
Answer:
46
Step-by-step explanation:
C:
Its correct dont worry!
By the way I have no idea why I am doing this but have some free emojis :D
✌︎ ✎ ☁︎☾ ABC: ℂℍℕℙℚℝV☘︎☞❀❁❄︎␘ I have way more but it does not fit D:what is the inverse function of y=x^2+4
Answer:
does not exist
Step-by-step explanation:
The inverse relation is found by swapping x and y, then solving for y.
x = y^2 +4
x -4 = y^2
y = ±√(x -4)
This is the inverse relation. Since it is double-valued, it is not a function.
__
The function given does not pass the horizontal line test, so there is no inverse function.
0.1 is 1/10 as much as
Answer:
10%
Step-by-step explanation:
Because 0.1 is equivalent to 1/10 and 10%
The total amount of money that he had deposited into his account at the end of March is what
Answer: 1,200.65+ 985.43+ 1,200.23= 3,386.31
Step-by-step explanation:
Can someone help me please
Answer:
y= -3/4x-1
Step-by-step explanation:
y-(-4)= -3/4(x-4)
y+4= -3/4x+3
y= -3/4x-1
-2 = g -9g what is the answer to this
Answer:G=1/4 or the same as g=0.25
Step-by-step explanation:
Answer:
1/4 is the answer.
Step-by-step explanation:
So first, you subtract the g-9g. You get -2 = -8g, correct?
Next, you divide -2 by -8, you then get -2/-8
This simplifies to 1/4.
Hope this helped. :)
simplify (7x +2) 3 +8x
Stanley is looking to retire and move near the ocean. The Jersey Shore has seen a rise in sea levels the past few years. These high tides have caused floods in 100 places that call themselves Jersey Shore towns, which are on or within reasonable distance of the ocean. Stanley is nervous about possible floods and would like to be prepared for costs associated with them. As Stanley’s friend and an expert in risk management, you collect past information and have constructed the following probability distribution for the number of floods per town per summer at the Jersey Shore. # of floods per town per summer Probability 0 0.10 1 0.15 2 0.26 3 0.30 4 0.15 5 0.04 a. Calculate the expected frequency of floods per town per summer. (2 points) b. Calculated the variance. (2 points)
Answer:
2.37 ; 1.6731
Step-by-step explanation:
Given the data:
X:___0____1____2____3____4____5
P(x):_0.10_0.15_0.26__0.30_0.15__0.04
the expected frequency of floods per town per summer
Σ(flood per Town per summer) * probability
Σ(X)*p(x)
Σ(0*0.10) + (1*0.15) + (2*0.26) + (3*0.30) + (4*0.15) + (5*0.04)
= (0 + 0.15 + 0.52 + 0.90 + 0.60 + 0.2)
= 2.37
Variance (s²) :
Σ[x². P(x)] - u²
Using an online variance calculator to save computation time :
s² = 16731 / 10000
s² = 1.6731
One class is selling tickets for $2.50 each and has already raised $350.
• The other class is selling tickets for $3.00 each and has already raised $225.
Which equation can be used to find t, the number of tickets each class needs to sell so that the total amount raised is the same for both classes?
Answer: 2.5t + 350 = 3t + 225
t = 250 btw
Answer:
b
Step-by-step explanation:
b
jenna is a professional typist. she can type 22,500 words in 5 hours of typing. in one hour, jenna can type blank words. in one minute, she can type blank words
Find the volume of the prism.
6 cm
5 cm
7 cm
5 cm
6 cm
Answer: Possibly, 105 cm³ if it is a triangular prism, or
Possibly 210 cm³ if it is a rectangular prism
Step-by-step explanation: Without knowing exactly what kind of prism it is, it is impossible to give an exact answer.
If the bases are triangles with altitude and and base of 5 and 6, anf the height of the prism is 7, the volume is
(6×5)/2 × 7
30/2 ×7
15 × 7 = 105 cm³ for a triangular prism
If the bases are rectangles with length and and width of 6 and 5, and the height of the prism is 7, the volume is
6×5×7 = 210 cm³ for a rectangular prism
72 red roses, 60 pink roses, and 48 yellow roses. What is the greatest number of bouquets that the florist can make if no roses are left over?
Answer:
12 bouquets
Step-by-step explanation:
Determine what the greatest common factor is in this case...
72/12 = 6 red roses
60/12 = 5 pink roses
48/12 = 4 yellow roses
As you can see the greatest common factor is 12. Therefore the greatest number of bouquets that the florist can make if no roses are left over should be 12 bouquets.
c) Write j(x) -h(x) in standard form.
Answer:
The answer is 0.
Step-by-step explanation:
