Given:
Consider the given expression is:
[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]
By using the quotient property of exponents, we get
[tex]=x^{4-2}y^{-4-(-2)}z^{-2-4}[/tex] [tex]\left[\because \dfrac{a^m}{a^n}=a^{m-n}\right][/tex]
[tex]=x^{2}y^{-4+2}z^{-6}[/tex]
[tex]=x^{2}y^{-2}z^{-6}[/tex]
By using negative exponent property, we get
[tex]=\dfrac{x^{2}}{y^{2}z^{6}}[/tex] [tex]\left[\because a^{-n}=\dfrac{1}{a^n}\right][/tex]
The simplified form of the given expression is [tex]\dfrac{x^{2}}{y^{2}z^{6}}[/tex].
Therefore, the correct option is B.
Write the equation of a line that passes
through point (-5,3) and is perpendicular to
y=3/5x +2.
Answer:
[tex]y=-\frac{5}{3}x-\frac{16}{3}[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, 4/3 and -3/4, etc.)1) Determine the slope (m)
[tex]y=\frac{3}{5} x +2[/tex]
From the given equation, we can see that [tex]\frac{3}{5}[/tex] is the slope of the line since it's in the place of m. Because perpendicular lines always have slopes that are negative reciprocals, the line we're currently solving for would have a slope of [tex]-\frac{5}{3}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-\frac{5}{3}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{5}{3}x+b[/tex]
Plug in the given point (-5,3)
[tex]3=-\frac{5}{3}(-5)+b\\3=\frac{25}{3}+b[/tex]
Subtract [tex]\frac{25}{3}[/tex] from both sides to isolate b
[tex]3-\frac{25}{3}=\frac{25}{3}+b-\frac{25}{3}\\-\frac{16}{3} = b[/tex]
Therefore, the y-intercept is [tex]-\frac{16}{3}[/tex]. Plug this back into [tex]y=-\frac{5}{3}x+b[/tex]
[tex]y=-\frac{5}{3}x+(-\frac{16}{3})\\y=-\frac{5}{3}x-\frac{16}{3}[/tex]
I hope this helps!
NEED HELP PLZ!!!!!!George and John travel 392 miles in 7 hours. If they travel at the same rate, how long will it take them to travel 728 miles?
a) Find their rate: _____ mph
b) It took them ____ hours to travel 728 miles
Answer:
Step-by-step explanation:
a. Find the unit rate, or how many miles they traveled in one hour, by dividing:
[tex]\frac{392}{7}=56 mph[/tex]
b. Now that we know how fast they were going, we can use it in either a proportion or in the d = rt equation. For the proportion set up, put miles on the top and hours on the bottom and solve for the unknown:
[tex]\frac{mi.}{hr}:\frac{56}{1}=\frac{728}{x}[/tex] and cross multiply to solve for x:
56x = 728 so
13 hours.
Now use the d = rt equation:
728 = 56t so
t = 13 hours
Which of the following best describes area?
A. Distance
B. Cover
C. Fill
D. Time
Answer:
I dont know
Step-by-step explanation:
oop
Answer:
I think it would not be fill since i think that would be referring to volume so it would most likley be B.cover
Answer- Cover
Step-by-step explanation:
none really
which of the following is equal to |-8+4|?
Answer:
-8+4=-4
sign of bigger number, and -×+=-
129,454,475,954 Which digit is in the hundred-thousands place?
Answer
129,454,475,954
Step-by-step explanation:
it is the four in bold
Answer:
4 is in the hundred-thousands place.
Explanation:
129,454,475,954
(the one that I bolded and underlined out)
What is the surface area of a cone with a 6 in. diameter and a length (slant height) of 8 in?
A. 11in^2
B. 75in^2
C. 104in^2
D. 179in^2
Answer:
The formula of a surface area of a cone:
SA=pi rl+\pi r^2SA=pirl+πr
2
r - radius
l - slant height
We have the diameter d = 6 in and a slant height l = 8 in.
d=2r\to r=6in:2=3ind=2r→r=6in:2=3in
Substitute:
SA=\pi(3)(8)+\pi(3^2)=24\pi+9\pi=\boxed{33\pi\ in^2}SA=π(3)(8)+π(3
2
)=24π+9π=
33π in
2
Answer:
Hello there,
So the answer is C,
The real result is approximately 103,53 and by rounding up the result to the nearest inch, we find C!
PLEASE MAKE SURE TO GIVE ME BRAINLIEST THX <3
Find the area of the triangle
Answer:
Hello! answer: 84 sq mm
Step-by-step explanation:
To find triangle area we would do
base × height × 1/2 or
base × height ÷ 2 So...
14 × 12 = 168 168 ÷ 2 = 84 therefore the area is 84 sq mm HOPE THAT HELPS!
help me plsss :( math
The two diagonal lines cross at the center point so each section of the lines are identical:
3x + 3 = 4x -4
Add 4 to both sides:
3x + 7 = 4x
Subtract 3x from both sides:
X = 7
The answer is x = 7
Answer:
x = 7
Step-by-step explanation:
KU = UM
as the center of a rectangle bisects the diagonal
3x + 3 = 4x - 4
7 = x
x = 7
Expand the function.
f(x) = (3x - 1)3
Answer:
[tex](a-b)^3 = a^3 - b^3 - 3a^2b + 3ab^2\\\\a = 3x, \ b = 1\\\\(3x-1)^3 = (3x)^3 - (1)^3 - 3(3x)^2(1) + 3(3x)(1)^2\\\\[/tex]
[tex]= 27x^3 - 1-3(9x^2)+ 9x\\\\=27x^3 -27x^2 +9x -1[/tex]
The expanded form of the function f(x) = (3x - 1)³ is 27x³ - 9x² + 9x - 1.
We have,
To expand the function f(x) = (3x - 1)³, we can use the binomial expansion formula, which states:
(a + b)³ = a³ + 3a²b + 3ab² + b³
In this case,
a = 3x and b = -1.
Substituting these values into the formula, we get:
[tex](3x - 1)^3 = (3x)^3 + 3(3x)^2(-1) + 3(3x)(-1)^2 + (-1)^3[/tex]
Simplifying further:
(3x - 1)³ = 27x³ - 9x³ + 9x - 1
Therefore,
The expanded form of the function f(x) = (3x - 1)³ is 27x³ - 9x² + 9x - 1.
Learn more about functions here:
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The function f (x) = 2* and g(x) = f(x) + k. if k = 2, what can be concluded about the graph of
g(x)?
the graph of g(x) is shifted vertically
Select a Value
the graph of g(x) is shifted horizontally
Select a Value
Answer:
g(x) shifted vertically by 2, no horizontal shift
Step-by-step explanation:
Any addition outside the function creates a vertical shift of the same value. Addition within the function moves the graph in the horizontal direction but opposite.
An n-sided polygon has one interior angle of 90°. The other interior angles are all equal.
If the size of one of the equal angles is 150°, calculate the value of n.
1/5 divided by 2 = ___
Answer:
0.1
Step-by-step explanation:
According to my calculator lol
Answer:
1/10
Step-by-step explanation:
1/5 / 2/1
1*1/5*2
=1/10
A parallelogram has a base of 9 km and a height of 5 km. A triangle has a base of 6 km and a height of 3 km. How many times greater is the area of the triangle?
Answer:
Parallelogram has greater area.
Step-by-step explanation:
Given:
Base of parallelogram = 9 km
Height of parallelogram = 5 km
Base of triangle = 6 km
Height of triangle = 3 km
Find:
Greater area
Computation:
Area of parallelogram = Base x Height
Area of parallelogram = 9 x 5
Area of parallelogram = 45 km²
Area of triangle = (1/2)(b)(h)
Area of triangle = (1/2)(6)(3)
Area of triangle = (1/2)(18)
Area of triangle = 9 km²
Parallelogram has greater area.
Which number is the closest approximation of 39?
Answer:
Because 39 is significantly closer to 36 than it is 49, the approximation of the square root of 39 to the nearest whole number would be 6
Step-by-step explanation:
Work out the circumference of a circle with radius 6.5cm
Answer:
circumference=13π cm (see below if you need π approximated)
Step-by-step explanation:
Hi there!
The formula for the circumference of a circle is given as 2πr, where r is the radius and π is pi
we are given that the radius of the circle is 6.5 cm
substitute what we know into the equation:
circumference=2πr
circumference=2π*6.5
circumference=13π cm
some places will accept the answer as 13π, but others ask to have π substituted, usually as 3.14 or 22/7
if you need π substituted as 3.14, the answer will be 40.82 cm
if you need π substituted as 22/7, the answer will be about 40.86 cm
Hope this helps! :)
Pls, help with this question
Answer:
[tex]m\text{ arc BC} =32\\m\angle 2=16\\m\angle3=74\\m\angle4=74\\m\angle5=16[/tex]
Step-by-step explanation:
Arc BC is the intercepted arc for the central angle COB, so its measure is the same as the central angle.
Angle 2 is an inscribed angle, so its measure is half the measure of the intercepted arc BC.
Angles 3 and 4 are congruent inside an isosceles triangle (OB = OC, both radii), and the sum of all angles in triangle COB is 180 degrees, so
180 - 32 = 148 (sum of angles 3 and 4)
Each of angles 3 and 4 measure half that remaining 148 degrees.
Angle 5 is one of two congruent angles in an isosceles triangle AOC (OA = OC) so its measure is that of angle 2.
S = {x | x is a multiple of 4 and 9 ≤ x < 37}
Which set is equivalent to S?
A) {8, 12, 16, 20, ...}
B) {8, 12, 16, ..., 36}
C) {9, 12, 16, ..., 37}
D) {12, 16, 20, 24, ...}
E) {12, 16, 20, ..., 36}
PLEASE HELP RNNNN
Answer: the answer is either e or d but I guessed d
Step-by-step explanation:
The equivalent set to set S will be {12, 16, 20, ..., 36} thus, option (E) is correct.
What is a set?A set is a collection of distinct values where each variable's meaning must be the same.
For instance, the set of natural numbers 1, 2, 3, 4, 5, and 6 is made up of variables that each represent a different natural number.
As per the given,
x is the multiple of 4,
4,8,12..
But is it restricted in the domain as, 9 ≤ x < 37
Thus, {12, 16, 20, ..., 36} will be correct.
Hence "The equivalent set to set S will be {12, 16, 20, ..., 36}".
To learn more about the sets,
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Question: Find the area of the orange shaded region in terms of pi.
Answer:
84π sq. units
Step-by-step explanation:
radius of little orange circles = 2
There is a total of 3 little orange circles (1 + 1 + 1/2 + 1/2).
Total area of 3 little orange circles = 3*π*2^2 = 12π
radius of 4 medium white circles = 3
Total of area of 4 medium white circles = 4*π*3^2 = 36π
radius of middle white circle = 6
Area of middle white circle = π*6^2 = 36π
Radius of the big circle = 12
Area of the big circle = π*12^2 = 144π
Area of orange = area of big circle - area of middle white circle - area of 4 medium white circles + area of 3 little orange circles = 144π - 36π - 36π + 12π = 84π
Two angles are supplementary. One angle is twenty less than four times the other angle. Find the measure of the larger angle.
180°
140°
130°
40°
NO LINKS
If two angles are supplementary, then they add up to 180.
Angle 1 = twenty less than four times the other angle
Angle 2 = the other angle
Angle 2 = 1x
Angle 1 = 4x - 20
Next, we can add up angles 1 and 2 and set the sum equal to 180.
x + 4x - 20 = 180
5x - 20 = 180
5x = 200
x = 40
Now that we know x, we can find the values of our angles.
Angle 1 = 4(40) - 20 = 160 - 20 = 140 degrees
Angle 2 = 40 degrees
Hope this helps!! :)
What is the equation of direct variation given that y is 16 when x is -2
A x= -8y
B y = 8x
C y= -8x
D y= -1/8 x
/\
| It means one eighth as a fraction
Answer:
C.
explanation:
I just know.
Answer:
c
Step-by-step explanation:
y=-8x
Find (-14
-14
14
7
-7
Answer:
21
Step-by-step explanation:
A running track has two semi-circular ends with radius 29m and two straights of length 91.3m as shown. Calculate the total area of the track rounded to 1 DP.
Answer:
13617.2 m^2
Step-by-step explanation:
5281.5
mr.lewis shared 3/4 of a loaf of bread equally aming her children what fraction of the whole loaf would 4 of her children recieve in total
Answer:
3/16 or in decimal 0.1875
Step-by-step explanation:
I need help asap plz.
23% of what number is 46?
Answer: 200
Step-by-step explanation:
first, you set up your proportion. (23% at the top right, 100 at the bottom right, 46 at the top left, and x and the bottom left.) next, you multiply x * 23% = 23x then 46*100 = 4600. 4600 divided by 23 = 200. therefore, x = 200. please let me know if you have further questions!
Good luck !
the sum of three consecutive natural number is 30 find the numbers
Answer:
9 + 10 + 11
Step-by-step explanation:
guess and check
Answer:
9,10,and 11
Step-by-step explanation:
what are the domain and range of the function represented by the set of the ordered pairs?
4 people can stay in a hotel for 5 days for $ 240. Find the bill for 5 people staying in
the hotel for a week
Answer:
$420
Step-by-step explanation:
Divide to isolate the cost
240 / 4 = 60 - amount per person (for 4 people)
60 / 5 = 12 - amount per person per day (5 days)
Multiply using that cost and new values.
12 x 5 = 60
60 x 7 = 420
The simple interest on 400 invested for 4 month was 12.what is the yearly rate of interest
Answer:
9%
Step-by-step explanation:
If you get 12 for 4 months, then you get 36 for the year/12 months
Annual interest is $12 x 3 Months =36
36/400=9%.
A basketball has a diameter of 9.40in find the volume of the basketball
Answer:
Volume = 434.89
Step-by-step explanation:
Answer.
Answer:
Half of 9.4 is 4.7
4.7^3(radius cubed) = 103.823
103.823 x 3.14(pi) = 326.00422
326.00422 x 4/3 = 434.672293333 rounded = 434.67
Step-by-step explanation:
Volume Of Sphere Formula:
4/3 x pi(3.14 or 22/7 OR ANY NUMBER depending on what they tell you to use for pi) x radius(half of your diameter or given radius)^3(cubed, to the power of 3)
4/3 x pi x radius cubed