The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].
From the principle of indices we get,
Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]
Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]
Multiplication, [tex]a^{mn}=(a^m)^n[/tex]
negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]
Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]
Calculating we get,
[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]
[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae
[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]
[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices
[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula
Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].
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Answer:
b
Step-by-step explanation:
edge 23
The courthouse is the tallest building in the city. If it is 71/2 6 inches tall in the model, how tall is the actual building?
The actual height of the building is 67 1/2 feet
Complete questionThe courthouse is the tallest building in the city. If it is 7 1/2 inches tall in the model, how tall is the actual building?
Scale factor: 1 inch = 9 feet
How to determine the actual height?The given parameters are:
Scale height = 7 1/2 inchesScale factor: 1 inch = 9 feetThis means that:
7 1/2 inches : Actual = 1 inch = 9 feet
So, we have:
Actual =7 1/2 * 9 feet
Evaluate the product
Actual = 67 1/2 feet
Hence, the actual height of the building is 67 1/2 feet
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Does this graph represent a function? Why or why not?
10.
8
6
4
2
-10 8 6 4 2
88
-8
10
2468 10
A. No, because it fails the vertical line test.
O B. No, because it is not a straight line.
OC. Yes, because it passes the horizontal line test.
OD. Yes, because it passes the vertical line test.
Answer:
D
Step-by-step explanation:
The graph in the picture given is obviously a function of f(x) = x^3 which answers whether the graph is a function or not. In addition, the answer the part on why it's a graph, it's because it passes the vertical line test.
Another way to write g(h(x)) is
(gOh)(x)
(hog)(x)
Answer:
A. Another way to write g(h(x)) is (g×h)(x)
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
Pls Help! Will Give Brainliest for the right answer!
a. The survey method is unlikely to result in a representative sample
b. Interview people on all days of the week.
What is a Representative Sample?A representative sample is a sub-section of a larger population and has similar characteristics of the main group population.
a. The population of the study is the entire consumers that shop at the supermarkets who shop all days of the weeks. Therefore, asking only shoppers who shopped on Monday will most likely give you a bias response as most customers may select Wednesday. The sample doesn't represent the entire population.
b. A better survey method is picking samples on all days of the week and ask them.
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Which inequality is equivalent to |x-4| less than 9? –9 > x – 4 < 9 –9 < x – 4 < 9 x – 4 < –9 or x – 4 < 9 x – 4 > –9 or x – 4 < 9
hii guys please answer this question
if two -1 and 2 are two zeroes of the polynomial 2x3- x2 - 5x - 2, find its third zero
Answer:
-1/2
Step-by-step explanation:
Zeros of a polynomial function are its x-intercepts, the values of x that make the polynomial zero. Each zero x=p corresponds to a linear factor (x-p) of the polynomial.
Monic polynomialA monic polynomial is one that has a leading coefficient of 1. For a monic polynomial of degree n, the coefficient of the term of degree n-1 is the opposite of the sum of all of the zeros. The constant term of any odd-degree monic polynomial is the opposite of the product of the zeros.
The given polynomial can be made monic by dividing by its leading coefficient:
(2x^3 -x^2 -5x -2)/2 = x^3 -(1/2)x^2 -(5/2)x -1
Sum of zerosThe given polynomial has degree 3, so we're interested in the coefficient of the x^2 term. That coefficient is -1/2, so the sum of zeros will be ...
sum of zeros = -(-1/2) = 1/2
If z represents the third zero, then we have the sum ...
1/2 = -1 +2 +z
z = -1/2 . . . . . . subtract 1 from both sides
The third zero is -1/2.
Product of zerosThe given polynomial is of odd degree, so the product of the zeros is the opposite of the constant.
(-1)(2)(z) = -(-1)
z = 1/(-2) = -1/2 . . . . . divide by the coefficient of z
The third zero is -1/2.
GraphOf course, a graph will show all of the (real) zeros. The attached graph from a graphing calculator shows the third zero is -1/2.
Select the correct answer from each drop-down menu.
onsider this equation.
-1-5 = I-8
The equation has
and
A valid solution for x is
The equation √(x – 1) – 5 = x – 8 has the solution 2 and 5. But the valid solution for x will be 5.
The complete question is attached below.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
√(x – 1) – 5 = x – 8
Add 5 on both sides, then we have
√(x – 1) = x – 3
Square on both sides, then
x – 1 = (x – 3)²
x – 1 = x² – 6x + 9
x² – 7x + 10 = 0
Then the factor of the equation will be
x² – 7x + 10 = 0
x² – 5x – 2x + 10 = 0
(x – 5)(x – 2) = 0
x = 5, 2
Then the valid solution will be 5.
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Instructions: Simplify the algebraic expression:
[tex]-\frac{1}{2} (32x-10y)[/tex]
I NEED HELP !!! Right now!!!
Answer:
Step-by-step explanation:
Is this pattern a net for the three-dimensional figure?
no
yes
Answer:
no
Step-by-step explanation:
the bet displays 3 hexagonal bases when in the figure there is only 2 bases.
Answer:
No.
Step-by-step explanation:
Examples of three-dimensional figures are: Cuboid, Cube, Cylinder, Sphere, Pyramid, and a Cone.
A middle school took all of its 6th grade students on a field trip to see a play. The
students filled 341 seats, which was 55% of the total number of seats in the theater.
How many total seats were in the theater?
¿Es necesario que los triángulos congruentes tengan el mismo tamaño?
I don't understand your question
Sorry!!! :)
The figure below is a right rectangular prism.
X
W
४
M
N
x
Y
N
O
12
2x
T
Which expression represents the volume of the prism?
01x³
O
O
(+)
0 (x)
Answer:
1/2x^3
Step-by-step explanation:
The formula for the volume of a rectangular prism is v = b x w x h (volume is base times width times height).
Just plug the numbers (or in this case variables) into the formula:
v = x times x times 1/2x
v = 1/2 times x^3
v = 1/2x^3
Volume
LBH1/2x(x)(x)1/2(x)³Option A
Eschool
geometry v19, cindy mcdermott ( 4872/ s) -
question 14 multiple choice worth 1 points)
(04.03 mc)
a segment with endpoints a (3, 4) and c (5, 11) is partitioned by a point b such that ab and bc form a 2:3 ratio. find b.
o (3.8, 6.8)
o (3.9, 4.8)
o (4.2, 5.6)
o (4.3, 5.9)
question 15(multiple choice worth 1 points)
The location of point B that partitions A(3, 4) and C(5, 11) in the ratio 2:3 is (3.8, 6.8).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let b = (x, y) represent the location of the point B, hence:
x = (2 / (2 + 3))(5 - 3) + 3 = 3.8
y = (2 / (2 + 3))(11 - 4) + 4 = 6.8
The location of point B that partitions A(3, 4) and C(5, 11) in the ratio 2:3 is (3.8, 6.8).
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which one is the correct graph
Graph f(x) = -1/2x
Click on the graph until the graph of f(x) = -1/2x appears
Answer:
The third graph
Step-by-step explanation:
The third graph depicts the function f(x) = -1/2x because for every 1 unit decrease along the y-axis, you travel 2 units on the x-axis.
Also, the two points on the third graph can satisfy the equation.
Point 1: (-2,1)
f(-2) = (-1/2)(-2)
f(-2) = 1
Point 2: (0,0)
f(0) = (-1/2)(0)
f(0) = 0
PLS HELP THANK YOU I REALLY NEED IT
Answer:
25
Step-by-step explanation:
x+115=180 (straight angle)
x= 65
y= 180-90-65
=25
Hi pls help
1) -15+4r=-9
2) 5-y/3=-1
3) 42=-5x-8
1) -15+4r=-9
-15+4r=-9
We move all terms to the left:
-15+4r-(-9)=0
We add all the numbers together, and all the variables
4r-6=0
We move all terms containing r to the left, all other terms to the right
4r=6
r=6/4
r=1+1/2
2) 5-y/3=-1
5-y/3=-1
We move all terms to the left:
5-y/3-(-1)=0
We add all the numbers together, and all the variables
-y/3+6=0
We multiply all the terms by the denominator
-y+6*3=0
We add all the numbers together, and all the variables
-1y+18=0
We move all terms containing y to the left, all other terms to the right
-y=-18
y=-18/-1
y=+18
3) 42=-5x-8
42=-5x-8
We move all terms to the left:
42-(-5x-8)=0
We get rid of parentheses
5x+8+42=0
We add all the numbers together, and all the variables
5x+50=0
We move all terms containing x to the left, all other terms to the right
5x=-50
x=-50/5
x=-10
Here are the first five terms of a number sequence .
10 16 22 28 34
The nth term of a sequence T is given by n squared-3
There are numbers that are terms in both the sequence S and the sequence T.
Find one of these numbers.
Answer:
t=4+6n
Step-by-step explanation:
a = 10
d=6
in general
tn = a + (n-1)*d
tn = 10 + (n-1)*6
tn = 10 + 6n - 6
tn = 4 + 6n
So if n = 5 then
t5= 4+6*5
t5= 4 + 30
t5 = 34 which agrees with your givens.
What order do I put the numbers in
We have following associations:
m ∠ADC + m ∠CDB = 180° → Definition of linear pair∠ADC is supplementary to ∠CDB → Definition of supplementary angles 2 · m ∠BDC = 180° → Substitution property of equalitym ∠BDC = 90° → Division property of equalityHow to complete the proof of a geometric theorem
In this question we need to fill the blanks of a given proof by understanding and taking advantage of the most important axioms and theorems of Euclidean geometry and real algebra. In this case, a linear pair is the combination of two angles whose sum equals 180°, and those angles are always supplementary.
Thus, we have following associations:
m ∠ADC + m ∠CDB = 180° → Definition of linear pair∠ADC is supplementary to ∠CDB → Definition of supplementary angles 2 · m ∠BDC = 180° → Substitution property of equalitym ∠BDC = 90° → Division property of equalityTo learn more on Euclidean theorem: https://brainly.com/question/13104788
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The function y=3^x is called an_______ function because the exponent is a _______. Now, let’s look at how to graph the exponential function y=3^x
The function is called an exponential function became the exponent is a variable.
The function is called an exponential function became the exponent is a variable.
What is an exponential function?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
So, here given a fill in the blank statement, we need to find the words to be filled in the blanks,
So, the whole statement is =
The function is called an exponential function became the exponent is a variable.
The function y = 3ˣ is an exponential function because it is having a power which is a variable.
The graph of the same is attached to the solution.
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PLS HELP IM BEGGING ITS DUE IN 10 MINUTES WHOEVER ANSWERS FIRST AND CORRECTLY I WILL GIVE BRAINIEST!!!
Write a similarity statement comparing the two triangles:
The triangle ABE and triangle DEC are similar by AAA option third is correct.
What is the similarity law for triangles?It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
We have given two triangles in the picture.
As we can see in the triangle ABE
Angle ABE = 90 degree or right angle
Similarly, in a triangle DEC
Angle DEC = 90 degree or right angle
Angle ABE = Angle DEC
Angle EAB = Angle CDE
If the corresponding two angles are the same as two triangles then the third the angle will be the same.
Angle AEB = Angle DCE
The triangle ABE and triangle DEC are similar to AAA
Thus, the triangle ABE and triangle DEC are similar by AAA option third is correct.
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Which two points on the number line represent numbers that can be combined to make zero?
B and D
A and B
C and D
A and C
An angle is bisected, forming two new
angles. If the original angle had a measure
of 48 degrees, what is the measure of each
new angle?
First let's define bisected
To bisect an angle means to split an angle exactly in half. Both sides of a bisected angle are equal to each other
The original angle (48 degrees) is bisected so we must divide 48 by 2 to find a degree of each angle
48 ÷ 2 = 24
The measure of each new angle is 24 degrees
What is 12x³-9x² - 4x + 3 in factored form?
²-[
po
kx-
-
Answer:
(3x^2 - 1) * (4x - 3)
Step-by-step explanation:
Answer:
[tex]( {3x}^{2} - 1)(4x - 3) \\ [/tex]
2 3/5t + 5 1/4t + 4t
Answer:
11 17/20t
Step-by-step explanation:
add the whole numbers first then add the numbers in fraction then there you get your answer.
Jack goes to a restaurant in a state with a 7.25% sales tax. He buys a
meal and tips 20% before tax. Select the meal cost that would allow his
total bill, including tip and tax, to have a total cost equal to $15.
The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the meal cost, hence:
Total cost = x + 0.2x + 0.0725x
15 = 1.2725x
x = 11.79
The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.
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only a genius can solve it !!
[tex] \frac{ \cos(A) }{1 - \sin(A) } + \frac{ \sin(A) }{1 - \cos(A) } + 1 = \frac{ \sin(A) \cos(A) }{(1 - \sin(A)(1 - \cos(A)} [/tex]
[tex]\text{L.H.S}\\\\=\dfrac{\cos A}{1-\sin A} + \dfrac{\sin A}{1-\cos A} +1\\\\\\=\dfrac{\cos A(1-\cos A) + \sin A(1-\sin A) + (1-\sin A)(1 - \cos A)}{(1-\sin A)(1 -\cos A)}\\\\\\=\dfrac{\cos A - \cos^2 A + \sin A - \sin^2 A + 1 - \cos A - \sin A + \sin A \cos A}{(1 -\sin A)(1 - \cos A)}\\\\\\=\dfrac{-(\sin^2 A + \cos^2A) +1 + \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\dfrac{-1 + 1 + \sin A \cos A }{(1 - \sin A)((1 - \cos A)}\\\\\\=\dfrac{0+ \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\[/tex]
[tex]=\dfrac{\sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Evaluate:
20
Σ 4(8/9)^n-1 = [?]
1
Round to the nearest hundredth.
Answer:
32.59 (nearest hundredth)
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
Given:
[tex]\displaystyle \sum^{20}_{n=1} 4 \left(\dfrac{8}{9}\right)^{n-1}[/tex]
Therefore:
a = 4r = 8/9Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:
[tex]\implies S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]
[tex]\implies S_{20}=32.58609013...[/tex]
[tex]\implies S_{20}=32.59\:\: \sf (nearest\:hundredth)[/tex]
General form of geometric progression
ar^n-1On comparing to the summation
a=4r=8/9Apply Sum formula
[tex]\boxed{\sf S_n=\dfrac{a(1-r^n)}{1-r}}[/tex]
[tex]\\ \implies \sf S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]
[tex]\\ \implies\sf S_{20}=32.586[/tex]
[tex]\\ \sf\mplies S_{20}=32.59[/tex]
Please help, I have been trying for a while :(
question on photo
Answer:
[tex]\frac{x-22}{(x+2)(x-4)}[/tex]
Step-by-step explanation:
multiply the numerator/denominator of the first fraction by (x - 4)
multiply the numerator/denominator of the second fraction by (x + 2)
this ensures that the fractions have a common denominator
[tex]\frac{4}{x+2}[/tex] - [tex]\frac{3}{x-4}[/tex]
= [tex]\frac{4(x-4)}{(x+2)(x-4)}[/tex] - [tex]\frac{3(x+2)}{(x+2)(x-4)}[/tex] ← subtract numerators leaving the common denominator
= [tex]\frac{4x-16-3x-6}{(x+2)(x-4)}[/tex]
=[tex]\frac{x-22}{(x+2)(x-4)}[/tex]
Given the image below, find the maximum value for z.
-3.5 < z < ___
I am so confused on how it's even possible to solve this
Answer:
-2.5 < x < 71
Step-by-step explanation:
I don't see a 'z' here, so I'll use x from the picture.
You would line up your values as such:
0 < 2x+5 < 71
You have a zero at the beginning because even without having an x value, your outcome would still be 5.
Subtract 5 from all sides.
-5 < 2x < 66
You now divide by two on both sides.
-2.5 < x < 33.
Which is your final answer.
You cannot go over 33, since 71 is your largest angle, and having something like say, 34, would give you 73.
-2.5 is your lowest value since if you went lower, you would have a negative angle, which isn't possible.
