Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{3 {x}^{2} y {}^{ - 1}}{27x {}^{ - 3} {y}^{8} } [/tex]
Now, let's get the common terms out :
[tex]\qquad \sf \dashrightarrow \: \dfrac{3 {x}^{2} y {}^{ - 1}}{3 {x}^{2} {y}^{ - 1}(9 {x}^{ - 5} {y}^{9} )} [/tex]
cancel out the common terms in numerator and denominator
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{9 x {}^{ - 5} {y}^{9} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{5} }{9 {}^{ } {y}^{9} } [/tex]
So, the correct choice is C
Related Questions
Write standard form of the equation of the line through the given point with the given slope
through: (4, -4), slope = -1
Answers
Answer:
x+1y=-4
Step-by-step explanation:
use ax+by=c
A line that passes through the points (x, 4) and (6, -1) has a slope of 56. what value of x will yield the given slope?
Answers
The value of x that yields a slope of 56 is 6.09
How to determine the value of x?The given parameters are:
Slope = 56Points: (x,4) and (6,-1)The slope of two points is:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
This gives
[tex]\frac{-1 -4}{6 -x} = 56[/tex]
Evaluate the difference
[tex]\frac{-5}{6 -x} = 56[/tex]
Cross multiply
56(6 - x) = -5
Divide both sides by 56
6 - x = -0.09
Make x the subject
x = 6 + 0.09
Evaluate
x = 6.09
Hence, the value of x that yields a slope of 56 is 6.09
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Find (a) arc length and (b) Area of a sector.
Answers
Answer:
a) 38.40 yd (2 dp)
b) 211.18 yd² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Calculation
Given:
[tex]\theta[/tex] = 200°r = 11 yd[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (11)\left(\dfrac{200^{\circ}}{360^{\circ}}\right)\\ & = 22 \pi \left(\dfrac{5}{9}\right)\\ & = \dfrac{110}{9} \pi \\ & = 38.40\: \sf yd \:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{200^{\circ}}{360^{\circ}}\right) \pi (11)^2\\& = \left(\dfrac{5}{9}\right)\pi \cdot 121\\& = \dfrac{605}{9} \pi\\& = 211.18\: \sf yd^2 \:(2\:dp)\end{aligned}[/tex]
Please note: As you have not specified if π should be approximated, I have not used an approximation for π.
A ball is dropped from a height of 600 feet. The function describing the height of the ball at t seconds after it dropped is [tex]f(t)=-16t^2+600[/tex].
a) Find the average velocity of the object during the first 3 seconds.
b) Verify that at some time during the first 3 seconds the instantaneous velocity equals the average velocity. Find that time.
The average velocity: _ ft/sec
The instantaneous velocity equals to the average velocity at t = _ sec
Answers
The average velocity of the object after during the first three seconds is: 48m/s
The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.
What is instantaneous and average velocities?Instantaneous velocity is the speed of an object at a particular point in time.
Average velocity is the velocity of an object after covering a certain distance for a period of time
Analysis:
Given
initial height = 600 feet
Height with respect to time = f(t) = -16[tex]t^{2}[/tex] + 600
a) Height at t = 0 = 600 feet
Height at t = 3 seconds = f(3) = -16[tex](3)^{2}[/tex] + 600 = 456 feet
Distance travelled = 600 - 456 = 144 feet
Average velocity = distance travelled/time taken = 144/3 = 48 feet/seconds
b) instantaneous velocity at time t = [tex]\frac{df(t)}{dt}[/tex] = [tex]\frac{d(-16t^{2} + 600) }{dt}[/tex] = -32t
when instantaneous velocity equal average velocity
-32t = -48
t = 1.5 seconds
In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.
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Which equation is the inverse of y = x2 – 36? y = plus-or-minus startroot x endroot 6 y = plus-or-minus startroot x 36 endroot y = plus-or-minus startroot x endroot 36 y = plus-or-minus startroot x squared 36 endroot
Answers
The inverse of the given function is expressed as y = ±√x + 38
Inverse of an equationGiven the equation below expressed as:
y = x² - 36
Replace y with x
x = y² - 38
Add 38 to both sides of the equation
x + 38 = y² - 38 + 38
y² = x + 38
Take the square root of both sides
√y² = ±√x + 38
y = ±√x + 38
Hence the inverse of the given function is expressed as y = ±√x + 38
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Answer:
B on edge 2022
Step-by-step explanation:
took the quiz
HELP IM STUCK ON THIS
Answers
Answer: Let's just say that each of the units are 1 inch in sides, and since it's an irregular shape you have to separate each shape. So, the rectangle I separated is 14 inches.
The semicircle is 12.56.
Adding those two answers together comes out to 26.56.
Drag numbers to the table so it shows a proportional relationship between x and y.
PLEASE HELP
Answers
Answer:
See below ~
Step-by-step explanation:
Finding the proportionality constant, k :
y = kxTake the point (0.5, 3)3 = 0.5kk = 6Table :
[tex]\left[\begin{array}{ccc}0.5&3\\1.5&9\\4.5&27\end{array}\right][/tex]
what is -3(4+(-7) + (-2( 5) -17) with examples please
Answers
Answer:
90
Step-by-step explanation:
◄) There were 60 dogs at the dog park last Saturday, and 30 of them were purebreds.
Considering this data, how many of the next 18 dogs to arrive at the park next Saturday
should you expect to be purebreds?
purebreds
Submit
Answers
30!outcof 60 were purebreds 30/60 = 1/2
1/2 of the dogs were purebreds.
18 x 1/2 = 9
Answer: 9 dogs
Answer:9 points
Step-by-step explanation:in the hyperproberbillity of things it’s this answer.
CAN SOMEONE HELP ME PLEASE
Answers
Answer:
13.9
Step-by-step explanation:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Find the difference between coordinates:
(x2 - x1) = (-5 - 0) = -5
(y2 - y1) = (-3 - 10) = -13
Square the results and sum them up:
(-5)^2 + (-13)^2 = 25 + 169 = 194
Now Find the square root and that's your result:
Exact solution: √194
Approximate solution: 13.9284
The length of a
rectangle is 12 cm
more than the width.
The perimeter is 44
cm. What is the
length of the
rectangle?
Answers
Answer:
length= 5+ 12= 17
Step-by-step explanation:
will take width as x
then the length is x+12
perimeter = x+ x+12+x+x+12= 44
=4x= 44-24= 36
x= 20/4
x= 5
Tasha has foam blocks stored in a box that measures 214 ft long by 2 ft wide by 2 ft tall.
Each foam block is a cube with 12ft edge length.
How many blocks can fit into the box?
Answers
which represents possible choices for the third missing side of the triangles given the other two sides?
1st side 30ft
2nd side 21ft
answer choices
a 9ft<51ft
b 9ft
c 30ft
d 0ft
Answers
Based on the triangle inequality theorem, the possible length of the third side of the triangle is: 9 < x < 51
What is the Triangle Inequality Theorem?The triangle inequality theorem states if a and b are two sides of a triangle, the possible length of the third side would be: a + b < x < a - b.
Two given sides of the triangle are 30 ft and 21 ft. The possible length of the third side of the triangle would be:
30 - 21 < x < 30 + 21
9 < x < 51
Possible length of the third side would range between: 9 < x < 51
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There are 90 people going on this feild trip. The budget allows for $542.94 total for tickets to the Buccaneers game. There is a service fee of $45.82. How much does each ticket cost?
Answers
Given zy = 4 and x² + y² = a, which expression is equal to (x + y)²?
Answers
The value of the given expression will be equal to ( x + y )² = a + 8.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
xy = 4 and x² + y² = aThe expression will be calculated as:-
( x + y )² = x² + y² + 2 xy
( x + y )² = a + 2 x ( 4 )
( x + y )² = a + 8
Therefore the value of the given expression will be equal to ( x + y )² = a + 8.
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Which of the following figures uses the SSS theorem to prove that AEFG SAHIJ?
Answers
Answer:
W.
Step-by-step explanation:
SSS, or Side-Side-Side is used to prove two triangles similar
Figure W. is the only one that uses three side marks, all of the others use at least one angle to prove them similar.
Which situation can be represented by the inequality 150 ≤ 15x + 55 ?
a. Thomas has 15 baseball cards in his collection. He will buy 55 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
b. Thomas has 15 baseball cards in his collection. He will buy 55 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at least
150 baseball cards?
c. Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
d. Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at least 150 baseball cards?
Answers
Inequalities help us to compare two unequal expressions. The correct option is C.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The situation that can be represented by the inequality 150 ≤ 15x + 55 is Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?
Hence, the correct option is C.
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does someone know this answer
Answers
[tex]\bold{ANSWER:}[/tex]
Sample 3: 6 boys; 7 girls
[tex]\bold{SOLUTION:}[/tex]
If the perimeter of a pool is 102ft, and the length is 6 more than twice the width, what are the dimensions?
Answers
Length = 36 ft
Width = 15 ft
Step-by-Step Explanation:
Let length of pool be ‘x’ ft
Let width of pool be ‘y’ ft
Perimeter = 2(x + y) = 102 ft
By Given:
2(x + y) = 102
=> 2x + 2y = 102 (Eq. 1)
=> x = 2y + 6 (Eq. 2)
Substitute value of ‘x’ from Eq. 2 in 1 :-
2x + 2y = 102
2(2y + 6) + 2y = 102
4y + 12 + 2y = 102
6y + 12 = 102
6y = 102 - 12 = 90
=> y = 90/6 = 15
Therefore, y = 15
Substitute value of ‘y’ in Eq. 2 :-
x = 2y + 6
x = 2(15) + 6
x = 30 + 6
=> x = 36
Therefore, x = 36
Verification:
2x + 2y = 102
2(36) + 2(15) = 102
72 + 30 = 102
=> 102 = 102
LHS = RHS
Therefore,
Length (x) = 36 ft
Width (y) = 15 ft
In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval
Answers
95% of molds filled by this machine will hold weights in are within 1106 pounds to 1194 pounds
What is an empirical rule?The empirical rule states that for a normal distribution, about 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within one standard deviation from the mean
Given a mean of 1150 pounds and a standard deviation of 22 pounds. Hence:
95% are within two standard deviations of the mean = 1150 ± 2(22) = (1106, 1194)
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Answer:
1106 - 1194
Step-by-step explanation:
Find the equation of a line that passes through point (2,4) and has a gradient of 3
Answers
Answer:
y=3x-2
Step-by-step explanation:
y-y0=m(x-x0)
y-4=3x-6
y=3x-2
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Find the equation of a line that passes through (2,4) and has a gradient of 3.
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
First, let's take a look at our provided information.
| Provided information:-
Point (2,4)Gradient 3What we need to find:-the line's equationHow to find it using our provided information (gradient & point)? write the equation of the line in point-slope form
point-slope form:-[tex]\sf{y-y_1=m(x-x_1)}[/tex]how to solve:-Replace y₁ with 4Replace m with 3 (m is the gradient)Replace x₁ with 2therefore,[tex]\sf{y-4=3(x-2)}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\sf{y-4=3x-6}[/tex][tex]\bigstar[/tex] On further simplification,
[tex]\sf{y=3x-6+4}[/tex]Which results in:-
[tex]\sf{y=3x-2}[/tex]Good luck with your studies.[tex]\rule{300}{1}[/tex]
9 in.
5 in.
4
5 in.
What is the volume of a square pyramid that has a
base length of 5 inches and a height of 9 inches?
cubic inches
Volume of a pyramid: V = Bh Where "B" is the area of the pyramid's base)
Answers
Answer:
75
Step-by-step explanation:
1/3 * 5² * 9 = V
1/3 * 25 * 9
= 75
The diameter of the circle is 5 inches, the circumference is 15.70 inches, and the area is 19.625 square inches.
Use the formula for area and solve for the value of pi for the circle.
Answers
Answer:
it is approximately 19.63.
Step-by-step explanation:
Area= pi r^2
Hi everyone i hope you can help with this exercise
Answers
s = area = 11.76
p = perimeter = 16.8
r=2*11.76/16.8=23.52/16.8=1.4
r=1.4
a= 90 degrees
b=36.87 degrees
c=53.13 degrees
triangle is in a circle
Circumradius: R = 3.5
please help me out!!!
A trapezoid with short base fourteen centimeters, long base thirty-eight centimeters, height sixteen centimeters, and diagonal side lengths twenty centimeters.
320 square centimeters
608 square centimeters
416 square centimeters
560 square centimeters
Answers
Answer:
416 square centimeters
Step-by-step explanation:
Formula for finding area of a trapezoid :
A = 1/2 x (a + b) x h
a and b = parallel sides of the trapezoidh = height of the trapezoidSolving :
A = 1/2 x (38 + 14) x 16A = 8 x 52A = 416 square centimetersAnswer:
416 cm²
Step-by-step explanation:
The figure we are given, is a trapezoid. Let's apply the "area of trapezoid" formula to determine the area of the trapezoid provided.
[tex]\boxed{\text{Area of trapezoid:} \ \dfrac{a_1 + a_2}{2} h}[/tex]
[Where a₁ and a₂ are the measure of the parallel sides and h is the height]
Let's plug the height and the parallel sides into the formula and simplify it:
[tex]\text{Area of trapezoid} = \dfrac{38 + 14}{2} \times 16}[/tex]
[tex]\text{Area of trapezoid} = \dfrac{52}{2} \times 16}[/tex]
[tex]\text{Area of trapezoid} = 26 \times 16}[/tex]
[tex]\boxed{\text{Area of trapezoid} = 416 \ \text{cm}^{2}}[/tex]
Therefore, the area of the trapezoid is 416 cm².
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Can this please be worked out so I can have a better understanding?
Given the equation (picture 1)
and using the formula(picture 2)
find A, B, and C
Please if take your time to break it down for me so I can use it as a guide for the rest of the test!!! Thx <3 :)
Answers
Step-by-step explanation:
no, no, you use the equation to identify a, b and c.
then you use the formula with these values to get the solutions to the equation (the values of x for which the equation delivers 0).
always remember, a quadratic equation always has 2 solutions. sometimes at least one of them are not a real number, sometimes the 2 springs are equal, ...
x² - 4x - 2 = 0
a, b, c are the factors of the terms in x and the constant term.
so,
a = 1
b = -4
c = -2
x = (-b ± sqrt(b² - 4ac))/(2a)
x = (4 ± sqrt((-4)² - 4×1×-2))/(2×1) =
= (4 ± sqrt(16 + 8))/2 = (4 ± sqrt(24))/2 =
= (4 ± sqrt(4×6))/2 = (4 ± 2×sqrt(6)) / 2 =
= 2 ± sqrt(6)
x1 = 2 + sqrt(6)
x2 = 2 - sqrt(6)
Answer:
x = 4.45 and x=-0.45
Step-by-step explanation:
A = 1
B= -4
C = -2
= [tex]\frac{-(-4) \sqrt{ (-4)^{2} -4 (1)(-2) } }{2(1)}[/tex]
= [tex]\frac{4\sqrt{16+8} }{2}[/tex]
= [tex]\frac{4\sqrt{24} }{2}[/tex]
X = 4 + [tex]\sqrt{24}[/tex] / 2
x = 4.45
For x2
x= 4 - [tex]\sqrt{24}[/tex] / 2
x=-0.45
5 cm
3 cm
5 cm
8 cm
2 cm
7 cm
what is the volume of the prism? show your thinking. organize it so it can be followed by others.
Answers
8400
Step-by-step explanation:
use multiplication
I cant reveal any more things that I know
What is the solution to the linear equation? 6k 10. 5 = 3k 12 k = 0. 5 k = 2 k = 7. 3 k = 9.
Answers
The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.
What is Linear Equation?Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.
Here, 6k + 10.5 = 3k + 12
6k - 3k = 12 - 10.5
3k = 1.5
k = 1.5/3
k = 1/2
Thus, The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.
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a drawer contains black socks and white socks. 70% of the socks are black socks.
Answers
Answer:
30% are white socks
Step-by-step explanation:
percent - per 100
100- 70 = 30
=> 30% of the 100 are white socks.
can someone help me with this
Answers
angles in a triangle always equal to 180° so:
1. all the angles are equal to each other
180°÷3=60°
2.
•we know 1 angle, 68°
• straight lines are 180°-> 180°-126°= 54°
180°-68°-54°= 58°