Which expression is equivalent
Answer:
Option B is correct.
[tex]\frac{81m^2n^5}{8}[/tex] is equivalent to [tex]\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}[/tex]
Step-by-step explanation:
Given expression: [tex]\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}[/tex]
Using exponents power:
[tex](ab)^n = a^nb^n[/tex][tex](a^n)^m = a^{nm}[/tex][tex]a^m \cdot a^n = a^{m+n}[/tex]Given: [tex]\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}[/tex]
Apply exponent power :
⇒ [tex]\frac{3^4 (m^{-1})^4(n^2)^4}{2^3(m^{-2})^3 n^3}[/tex]
⇒ [tex]\frac{81 m^{-4}n^8}{8m^{-6}n^3} = \frac{81 m^{-4} \cdot m^6 n^8 \cdot n^{-3}}{8}[/tex]
⇒[tex]\frac{81 m^{-4+6} n^{8-3}}{8} = \frac{81 m^2 n^5}{8} = \frac{81m^2 n^5}{8}[/tex]
Therefore, the expression which is equivalent to [tex]\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}[/tex] is, [tex]\frac{81m^2 n^5}{8}[/tex]
Answer:
Correct choice is B
Step-by-step explanation:
Consider expression
[tex]\dfrac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}.[/tex]
1. Simplify numerator:
[tex](3m^{-1}n^2)^4=3^4\cdot (m^{-1})^4\cdot (n^2)^4=81m^{-4}n^8.[/tex]
2. Simplify denominator:
[tex](2m^{-2}n)^3=2^3\cdot (m^{-2})^3\cdot n^3=8m^{-6}n^3.[/tex]
Then,
[tex]\dfrac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}=\dfrac{81m^{-4}n^8}{8m^{-6}n^3}=\dfrac{81}{8}m^{-4-(-6)}n^{8-3}=\dfrac{81}{8}m^2n^5.[/tex]
Job A pays $32,448 per year. How much would Job A pay per hour based on a 52 weeks working 40 hours per week?
Answer$15.60
Step-by-step explanation:
First you would go 32,448 divided by 52. That would give you how much you make in one week. Then you do 624 divided by 40. This would give you Job A's hourly wage ($15.60). I hope this helps.
How to solve this problem
Answer:i fffffffffffffffffffffoooooooooooooooooooooorrrrrrrrrrrrrrrrrrggggggggggggggggggggggooooooooooooooooooottttttttttttttttttttttttttt
Step-by-step explanation:
Someone help me on this question.
Let's go:
6x + 7 + 12x - 3 = 112
18x + 4 = 112
18x = 112 - 4
18x = 108
x = 6
mADB = 6.6 + 7 = 43°
I hope I helped you.
Answer:
43°
Step-by-step explanation:
Since we know that ∠ADC, which is the sum of ∠ADB and ∠BDC, is 112, we can solve for x:
112 = 6x + 7 + 12x - 3
112 = 18x +4
112 - 4 = 18x → 108 = 18x
108/18 = x → 6 = x.
Now, we can substitute 6 for x in the equation for ∠ADB to get the answer:
6(6) + 7 ⇒ 36 + 7 ⇒ 43°.
Hope this helps! Have a nice day!
What is the vertex of the graph of y = 2(x − 3)2 + 4? (1 point)
A (4, 3)
B (4, −3)
C (3, 4)
D (−3, 4)
The vertex form of the quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
(h, k) - vertex
We have
[tex]y=2(x-3)^2+4[/tex]
h = 3, k = 4
Therefore your answer is:
C. (3, 4)The vertex of the parabola given by the equation [tex]y = 2(x - 3)^2 + 4[/tex] is at the point (3, 4), which corresponds to answer option C.
The question is asking to identify the vertex of the parabola given by the equation y = 2(x − 3)^2 + 4. In this form, the equation is in vertex form of a parabola, which is [tex]y = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola. Comparing the given equation to the vertex form, we can see that h = 3 and k = 4, hence, the vertex of the parabola is at the point (3, 4). Therefore, the correct answer is C (3, 4).
25 Points!!! Help plzz!! Will give Brainliest!!!
Answer:
Option C : ASA
Step-by-step explanation:
Side WS Lies between ∠W and ∠S
Side NT lies between ∠N and ∠T
Hence the theorem which supports the congruency of the two triangles
is ASA
Angle - Side - Angle
The boat moves 138 miles every 3 hours. How far does it move in 10 hours?
Cal es el volumen de un cono que tiene una altura 10 pulgadas y un radio de 6 pulgadas
Answer:
≈ 376.99 pulgadas
Step-by-step explanation:
El volumen de un cono con una altura de 10 pulgadas y un radio de 6 pulgadas es de aproximadamente 376.99 pulgadas en cubos.
La fórmula para el volumen de un cono es π (r ^ 2) (h / 3). Puedes sustituir r con 6 yh con 10 para obtener El volumen de un cono con una altura de 10 pulgadas y un radio de 6 pulgadas es de aproximadamente 376.99 pulgadas en cubos.
La fórmula para el volumen de un cono es π (r ^ 2) (h / 3). Puedes sustituir r con 6 yh con 10 para obtener aproximadamente 376.99
6 - x = -12
what the answer?
Answer:
x=18
Step-by-step explanation:
6 - x = -12
+x +x
6=-12 + x
+12+12
18=x
this is the workk and the answer :}
Answer:
x =18
Step-by-step explanation:
6 - x = -12
Subtract 6 from each side
6-6 - x = -12-6
-x =-18
Multiply by -1
-1*-x = -1 * -18
x = 18
Jerry hears 5 case ever 2 3/8 hours Jerry hears a constant rate how many case does Jerry hear per hour
Answer:
The rate of cases is [tex]\frac{40}{19}[/tex] per hour
Step-by-step explanation:
we are given
Total number of cases =5
total time is
[tex]=2\frac{3}{8}[/tex] hour
we can simplify it
total time is
[tex]=\frac{2\times 8+3}{8}[/tex] hour
[tex]=\frac{19}{8}[/tex] hour
we can use formula
rate of cases = ( total number of cases)/( total time)
now, we can plug values
Rate of cases is
[tex]=\frac{5}{\frac{19}{8} }[/tex]
[tex]=\frac{40}{19}[/tex]
Answer: -Jerry hears [tex]2\frac{2}{19}[/tex] per hour.
Step-by-step explanation:
Since time is given in mixed fraction [tex]2\frac{3}{8}[/tex] , thus first convert it into improper fraction
Time=[tex]\frac{19}{8}[/tex] hours
The total number of cases Jerry hears in =5 cases
⇒The number of cases Jerry hears in 1 hour
[tex]=\frac{5}{\frac{19}{8}}\\\\=\frac{5\times8}{19}\\\\=\frac{40}{19}=2\frac{2}{19}[/tex] cases per hour.
Thus, Jerry hears [tex]2\frac{2}{19}[/tex] cases per hour .
Estimate the square root of 4.92+2.18x7.31
Answer:
4.36
Step-by-step explanation:
The given expression is
[tex]\sqrt{4.98+2.18\times 7.31}[/tex]
We need to estimate the value of given expression.
First approximate each term of the given expression.
First term : [tex]4.92\approx 5[/tex]
Second term : [tex]2.18\approx 2[/tex]
Third term : [tex]7.31\approx 7[/tex]
The value of given expression after approximation is
[tex]\sqrt{5+2\times 7}[/tex]
[tex]\sqrt{5+14}[/tex]
[tex]\sqrt{19}[/tex]
The approximate value of [tex]\sqrt{19}[/tex] is 4.36.
Therefore, the estimated value of given expression is 4.36.
The estimated square root of 4.92 + 2.18 x 7.31 is between 4 and 5.
To estimate the square root of 4.92 + 2.18 x 7.31, we first calculate the value inside the square root:
4.92 + 2.18 x 7.31 = 4.92 + 15.8678 = 20.7878
Next, we estimate the square root of 20.7878:
Since the square root of 16 is 4, and the square root of 25 is 5, we can estimate that the square root of 20.7878 is between 4 and 5.
Therefore, the estimated square root of 4.92 + 2.18 x 7.31 is between 4 and 5.
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rebecca is given two triangles, ABC and DEF. at first glance, she thinks that the triangles are congruent l. how can she use what she knows about rotations and triangle congruence to prove the triangle congruence?
Answer:
She can use rotation and overlap the two triangles, and if they overlap perfectly/identically, that means they are surely congruent.
Rebecca can prove triangle congruence by applying the rotation property. If she can rotate one triangle to align with the other, maintaining the same shape and size, then the triangles are congruent. Additionally, she can compare corresponding angles and sides to confirm congruence.
Rebecca can use rotations to prove triangle congruence by performing a sequence of rotations, translations, and reflections on one triangle to align it with the other. If she can manipulate one triangle to superimpose it exactly onto the other triangle without changing its shape or size, then they are congruent. She can also use the properties of triangle congruence, such as side-angle-side (SAS), angle-side-angle (ASA), side-side-side (SSS), or angle-angle-side (AAS), to verify their congruence. By demonstrating that the corresponding sides and angles of the two triangles are congruent based on these properties, she can conclusively prove their congruence. This approach ensures that both triangles share identical measurements and configurations, providing geometric evidence for their congruence.
you are buying one flower for each member of the swim team to wear at an awards tonight there are 19 members on the team you have decided to buy pink roses and yellow roses the pink roses cost $3 and the yellow roses cost $2 you will spend $50 how many pink roses should you buy?how many yellow roses should you buy?
Answer: There are 12 pink roses and 7 yellow roses.
Step-by-step explanation:
Since we have given that
Total number of members = 19
Let the number of pink roses be x
Let the number of yellow roses be 19-x
Cost of pink roses be $3
Cost of yellow roses be $2
Total amount spend to buy = $50
According to question,
[tex]3x+(19-x)2=\$50\\\\3x+38-2x=\$50\\\\x+38=\50\\\\x=\$50-\$38\\\\x=\$12[/tex]
Hence, Number of pink roses be 12
and number of yellow roses be
[tex]19-12=7[/tex]
Hence, there are 12 pink roses and 7 yellow roses.
To solve the problem, we set up two equations representing the number of team members and the total cost of roses, respectively. By solving these equations, we find that we should buy 8 pink roses and 11 yellow roses.
Explanation:This problem is a type of algebraic word problem. We need to find out the number of pink roses and yellow roses to purchase with the total amounts of $50. Here's how we can solve this: Assuming that 'p' stands for pink roses and 'y' stands for yellow roses. We have two equations based on the problem:
p + y = 19 (This is because there are 19 members on the team.) 3p + 2y = 50 (That's because the pink roses cost $3 and the yellow roses cost $2 and you'll spend a total of $50.)By resolving these system of equations, the solution yields that you should buy 8 pink roses and 11 yellow roses.
Learn more about Algebraic Word ProblemPls help with correct choice
Answer:
(-1, -1)
Step-by-step explanation:
Rotating the point (-1, -1) about the origin at -90° will be a 90 degree clockwise rotation. This will map switch the x- and y-coordinates and negate the x-coordinate:
(x, y)→(y, -x)
(-1, -1) → (-1, 1)
Following this with a 90 degree counter-clockwise rotation will map
(x, y)→(-y, x)
(-1, 1)→(-1, -1)
This is the same point we started with. Thinking about this logically, if we rotate something 90 degrees clockwise and then follow that with a 90 degree counter-clockwise rotation will put the object back in its original position.
Answer:
The correct option is 3.
Step-by-step explanation:
The coordinates of point P are (4,3).
We have to find the value of
[tex]R_{p,90}\circ R_{o,-90}:(-1,-1)[/tex]
The operations area operated from right to left it means first we have to apply
[tex]R_{o,-90}[/tex], then [tex]R_{p,90}[/tex].
[tex]R_{o,-90}[/tex] means rotation 90 degree clockwise about the origin, it is defined as
[tex](x,y)\rightarrrow (y,-x)[/tex]
[tex](-1,-1)=(-1,1)[/tex]
[tex]R_{p,90}[/tex] means rotation 90 degree counter clockwise about the the point P, it is defined as
[tex](x,y)\rightarrrow (-(y-3)+4,(x-4)+3)[/tex]
[tex](x,y)\rightarrrow (-y+7,x-1)[/tex]
[tex](-1,1)\rightarrrow (-1+7,-1-1)[/tex]
[tex](-1,1)\rightarrrow (6,-2)[/tex]
Therefore the coordinates of image are (6,-2). Option 3 is correct.
Anjali is adding a border to her 4 tablecloths. Each tablecloth requires 6 3/4 yards of border. How many yards of border will she use?
Answer:
27 yards
Step-by-step explanation:
multiply 4*6 3/4
Is the equation y=3x in slope-intercept form? Explain.
Answer:
y = 3x is in slope intercept form.
Step-by-step explanation:
The slope intercept form of an equation is y =mx+b where m is the slope and b is the y intercept.
y =3x can be written as
y = 3x+0
where 3 is the slope and has a y intercept of 0
y = 3x is in slope intercept form.
James swam 3 and 1/3 miles. For 2/6 of his swim he did the backstroke. How many miles did he swim the backstroke?
Answer:i believe thats only a third of a mile
Step-by-step explanation:
if you have the both take on the same denominator the 3 miles would be 3/3 and then it would be 6/6 and the 1/3 mile would become 2/6 hope i helped
Answer: yes its 1/3 of a mile
Step-by-step explanation:
What are the intercepts to graph the equation -4x - 3y = 36?
Answer:
The x intercept = -9
The y intercept = -12
Step-by-step explanation:
To find the x intercept, set y = 0 and solve for x
-4x - 3y = 36
-4x -0 = 36
Divide by -4
-4x/-4 = 36/-4
x = -9
The x intercept = -9
To find the y intercept, set x = 0 and solve for y
-4x - 3y = 36
0 -3y = 36
Divide by -3
-3y/-3 = 36/-3
x = -12
The y intercept = -12
Answer:
x = -9
y = -12
Step-by-step explanation: Substitute 0 for x & y to get your points.
-4x - 3y = 36
-4(0) - 3y = 36
0 - 3y = 36
-3y = 36
-3y -3y
y = -12
-4x - 3y = 36
-4x - 3(0) = 36
-4x - 0 = 36
-4x = 36
-4 -4
x = -9
Remember, a negative divided by a positive is a negativeAnything times 0, is the number itself. Like for example, 0 times 46 = the number itself, which is 46.Hope this helps you!!! :)
The table below shows the distance d(t) in feet that an object travels in t seconds: t (seconds) d(t) (feet) 2 64 4 256 6 576 8 1024 What is the average rate of change of d(t) between 2 seconds and 6 seconds, and what does it represent? 128 ft/s; it represents the average speed of the object between 2 seconds and 6 seconds 80 ft/s; it represents the average speed of the object between 2 seconds and 6 seconds 128 ft/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds 80 ft/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds
Answer:
128 ft/s; it represents the average speed of the object between 2 seconds and 6 seconds
Step-by-step explanation:
The average rate of change is another way to say slope.
slope = (y2-y1)/(x2-x1)
= (576-64)/(6-2)
= (512/4)
=128 ft/s
This represents the change in ft per second, or the average speed the object is going during the time period.
Answer:
it's A
Step-by-step explanation:
the formula for the volume of a cylinder is V=π^2h. The cylinder to the right has an exact value of 180π cubic meters.find its height.
Answer it's more singler to the right angle then the left angle ×{3*25+16=}
Step-by-step explanation:
The height of the cylinder is 20 meters.
Given,
The formula for the volume of a cylinder is V=πr²h.
The cylinder to the right has an exact value of 180π cubic meters.
Its radius is given as 3 meters in the figure.
We need to find its height.
What is the volume of a cylinder?
It is given by:
V = π r² h
Find the volume of the cylinder.
V = π r² h
We have,
V = 180π cubic meters
180π cubic meters = πr²h
Find the height of the cylinder.
We have,
180π cubic meters = πr²h
Divide both sides by π
180 cubic meters = r²h
We have,
r = 3 m
180 cubic meters = 3² square meters x h
180 cubic meters = 9 square meters x h
Divide both sides by 9.
20 meter = h
h = 20 meters
Thus the height of the cylinder is 20 meters.
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The perimeter of a rectangle is 276 centimeter. It's length is 5 times its width find it dimension
Answer:
A) 2 * Length + 2 * Width = 276
B) L = 5W then multiplying equation B) by -2 we get
-2L +10W = 0 then we add this to A)
A) 2L + 2W = 276 and get
12W = 276
Width = 23
Length = 115
Step-by-step explanation:
[[IGNORE MY ANSWER]]
which fact would help Estelle prove that the measure of angle KNQ is equal to the measure of MNS
To demonstrate that the measure of angle KNQ is equal to the measure of angle MNS, one should use geometric principles to show congruency or similarity between the angles, which could involve establishing congruent triangles or proportional relationships.
Explanation:To prove that the measure of angle KNQ is equal to the measure of angle MNS, one would need to establish a relationship between the two angles based on geometric principles or congruent triangles. This could involve demonstrating that the angles are corresponding angles of similar triangles, alternate interior angles of a transversal crossing parallel lines, or possibly vertical angles resulting from intersecting lines. Given the information provided, it seems that if one could show that triangles KNQ and MNS are congruent, then by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, it would follow that the angles in question are equal.
Applying trigonometry in proving congruency or similarity might be necessary, especially if an equivalence can be drawn from given proportional relationships or if one can establish that angles are congruent through right triangles and the definition of trigonometric ratios.
If it is 40 degrees Celsius, what is the temperature in Fahrenheit?
A. 40 degrees
B. 104 degrees
C. 54 degrees
D. 102 degrees
Answer:
104 = B
Step-by-step explanation:
A quick way to do this is to use this formula
F = 2*C + 30C = 40F = 2*40 + 30 F = 80 + 30F = 110Since this is an estimate, you are only guided to whether your answer is correct or not. Here's the actual formula
F = (9/5) * 40 + 32F = 360/5 + 32F = 72 + 32F = 104A dripping faucet loses about 2.5×10^−4 liters of water each minute. There are approximately 3×10^5 minutes in a month. About how many liters of water are lost because of the dripping faucet in a month?
Answer:
750 liters are lost.
Step-by-step explanation:
This question can be solved with multiplication.
Its important that when multiplying scientific forms of number together, always remember to add the exponents. -5+4=-1
-25 x -30= 750
750 liters are lost in a month.
Hope this helps!
Answer:
The answer should be 7.5*10 ^1 and that equalls 75
Step-by-step explanation:
a 1 kg ball has 10 joules of kinetic energy and starts to roll up a hill how far up the hill will it be when it stops
Answer:
The ball will roll upto 1 m.
Step-by-step explanation:
A 1 kg ball has 10 joules of kinetic energy and starts to roll up a hill.
As along the hill the ball rises up, it loses its kinetic energy. The kinetic energy is converted to potential energy.
According to the law of conservation of energy, the kinetic energy plus the potential energy equals a constant.
Here given kinetic energy as 10 J, so this energy will get converted to potential energy.
We know that, potential energy is
[tex]P.E=m\cdot g\cdot h[/tex]
where,
m is the mass, g is the acceleration due to gravity and h is the height.
Putting the values,
[tex]\Rightarrow 10=1\times 10\times h[/tex]
[tex]\Rightarrow 10=10 h[/tex]
[tex]\Rightarrow h=1\ m[/tex]
Jerome finds that (3x6) ÷ 2 and 18÷2 are equal explain why this is true
Answer:
because 3x6=18 so it will be the same problem
Step-by-step explanation:
5x+2(3+x) x =4 I
don't know
Answer:
34
Step-by-step explanation:
5x+2(3+x)
The first step is to distribute the 2
5x+2*3 + 2x
5x+6+2x
Combine like terms
7x+6
Now substitute x=4
7*4+6
28+6
34
what is a cell? Also how is the cell made
Leila wrote an equation to represent the revenue of a parking lot for one day. She let x represent the number of cars that paid to park and y represent the number of trucks that paid to park. If a car costs $8 per day, a truck costs $10 per day, and the total revenue for the day was $830, which equation could Leila use to represent the number of cars and trucks that paid to park that day?
Answer:
8x + 10y = $830
Step-by-step explanation:
8x + 10y = total revenue
if the total revenue is 830 then you can equate the above formula to 830 to give
8x + 10y = $830
Answer:
The required equation is [tex]8x+10y = 830[/tex].
Step-by-step explanation:
Consider the provided information.
As it is given that variable x represents the number of cars that paid to park and variable y represents the number of trucks that paid to park.
The cost of parking a car is $8 per day, the expression to represent the cost of parking x cars per day is 8x.
The cost of parking a truck $10 per day, the expression to represent the cost of parking y trucks per day is 10y.
The total revenue for the day was $830.
Thus, the equation represent the number of cars and trucks that paid to park that day is:
[tex]8x+10y = 830[/tex]
Hence, the required equation is [tex]8x+10y = 830[/tex].
evaluate the expression 4!×3!
If you mean 4 x |3| =12
If it's 4 = 3x => 0.75
I'm sorry if I didn't help, I don't understand what you mean with " ! "
Answer is 144
4! = 4*3*2*1 = 24
3! = 3*2*1 = 6
6*24 = 144