Answers
Answer:
[tex]a. \ \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
[tex]b. \ \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
Step-by-step explanation:
The question relates with rules of indices
(a) The give expression is presented as follows;
[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}[/tex]
By expanding the expression, we get;
[tex]\dfrac{m^3 \times n^{-8} \times 5^4 \times m^4}{\left 3^3 \times m^6 \times n^3}[/tex]
Collecting like terms gives;
[tex]\dfrac{m^{(3 + 4 - 6)} \times 5^4}{ 3^3 \times n^{3 + 8}} = \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}= \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
(b) The given expression is presented as follows;
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \div (x \cdot y^n)^4[/tex]
Therefore, we get;
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n}[/tex]
Collecting like terms gives;
[tex]x^{3 \cdot m + 2 - 4} \times \left (y^{3 \cdot n - 3 -4 \cdot n}} \right ) = x^{3 \cdot m - 2} \times \left (y^{ - 3 -n}} \right ) = x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right )[/tex]
[tex]x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right ) = \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n} =\dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
Related Questions
PLEASE ILL MAKE BRAINIEST!!!
If the dimensions of a rectangle ABCD are 15 x 12, what is the area of rectangle BEFD?
Answers
Answer:
The area of rectangle BEFD is 180 square units.
Step-by-step explanation:
After checking the figure given, we have the following information:
[tex]AD = 15[/tex], [tex]AB = 12[/tex], [tex]BC = 15[/tex], [tex]CD = 12[/tex]
By Pythagorean Theorem, we determine the length of the line segment BD:
[tex]BD = \sqrt{AB^{2}+AD^{2}}[/tex] (1)
[tex]BD = \sqrt{12^{2}+15^{2}}[/tex]
[tex]BD = 3\sqrt{41}[/tex]
In addition, we know the following characteristics of the rectangle BEFD:
[tex]BD = EF[/tex], [tex]EF = EC + CF[/tex], [tex]BE = FD[/tex] (2), (3), (4)
By Pythagorean Theorem:
[tex]BC^{2} = BE^{2}+EC^{2}[/tex] (5)
[tex]CD^{2} = CF^{2}+DF^{2}[/tex] (6)
By (3), (4), (5) and (6):
[tex]BC^{2} = BE^{2} + EC^{2}[/tex] (7)
[tex]CD^{2} = (EF-EC)^{2} + BE^{2}[/tex] (8)
By (7) in (8):
[tex]CD^{2} = (EF-EC)^{2}+ (BC^{2}-EC^{2})[/tex]
[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC + EC^{2}+BC^{2}-EC^{2}[/tex]
[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC +BC^{2}[/tex]
Then, we clear [tex]EC[/tex]:
[tex]2\cdot EF\cdot EC = EF^{2} + BC^{2} - CD^{2}[/tex]
[tex]EC = \frac{EF^{2}+BC^{2}-CD^{2}}{2\cdot EF}[/tex]
If we know that [tex]EF = 3\sqrt{41}[/tex], [tex]BC = 15[/tex] and [tex]CD = 12[/tex], then the length of the segment [tex]EC[/tex] is:
[tex]EC = \frac{75\sqrt{41}}{41}[/tex]
And the length of the line segment [tex]CF[/tex] is:
[tex]CF = EF - EC[/tex]
[tex]CF = 3\sqrt{41}-\frac{75\sqrt{41}}{41}[/tex]
[tex]CF = \frac{48\sqrt{41}}{41}[/tex]
And the length of the line segment [tex]DF[/tex] is determined by Pythagorean Theorem:
[tex]FD = \sqrt{CD^{2}-CF^{2}}[/tex]
[tex]FD = \sqrt{12^{2}-\left(\frac{48\sqrt{41}}{41} \right)^{2}}[/tex]
[tex]FD = \frac{60\sqrt{41}}{41}[/tex]
And the area of the rectangle is determined by the following formula:
[tex]A = FD\cdot EF[/tex]
[tex]A = \left(\frac{60\sqrt{41}}{41} \right)\cdot (3\sqrt{41})[/tex]
[tex]A = 180[/tex]
The area of rectangle BEFD is 180 square units.
The number n is doubled and then has y added to it. The result is then divided by 2 and has the number n subtracted from it, the final result is
Answers
Answer:
[tex]\frac{y}{2}[/tex]
Step-by-step explanation:
n is doubled: 2n
y added: 2n + y
divided by 2: n + [tex]\frac{y}{2}[/tex]
n subtracted -> final resutl: [tex]\frac{y}{2}[/tex]
Given point P=(2,-4), determine its transformation after it goes through the composite transformation
Show all your work. P"=(
)
PLEASE HELP
Answers
Answer:
(2,-7)
Step-by-step explanation:
The point moves down 3 units resulting in (2,-7)
Quadrilateral ABCD is inscribed in this circle. What is the measure of angle a?
Answers
Answer:
Step-by-step explanation:
The rule is that opposite angles are supplementary. Therefore, angle A plus angle C = 180:
angle A + 43 = 180 and
angle A = 180 - 43 so
angle A = 137
What is the range of the function on the graph?
Answers
Answer:
The range is the set of possible output values, which are shown on the y-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.
Step-by-step explanation;
The range of a function is the set of y-coordinates of all the points int he graph of the function.
Look at the graph. The vertex is point (2, -3).
The graph does not go lower than that point.
The lowest y-coordinate is -3.
The graph goes up forever on both sides until infinity.
The range is all numbers greater than or equal to -3.
1. Determine the measure of the unknown angles indicated by letters. Justify your answers with
the properties or theorems you used
Answers
Answer:
hello,
Step-by-step explanation:
a)
In an isocele triangle, base's angles have the measure:
42+2a=180
2a=180-42
a=69(°)
b)
in a triangle, an external angle has for measure the sum of the angles not adjacents.
55+b=132
b=77 (°)
c)
in a quadrilater the sum of the (interior) angles is 2*180=360 degrees.
90+90+68+c=360
c=360-90-90-68
c=112 (°)
Maritza is comparing cell phones plans and notices that verizon offers a plan that is $60 for 10GB of data and $12 for each extra GB of data ore month. Create an expression to model this situation
Answers
Answer:
60 + 12 * g, with g representing the number of extra gigabytes
Step-by-step explanation:
First, we know that Maritza has to pay $60 for 10GB of data, no matter what. Therefore, the base cost of the cell phone plan is 60 dollars, and all extra costs must be added to that. Currently, our expression is therefore 60 + something = cost of cell phone plan.
After that, the plan costs $12 for each gigabyte of data past 10 GB. This means that, for example, if Maritza uses 11 gigabytes, the plan will cost 60 (the base amount) + 12 for each gigabyte past 10 GB. There are 11-10=1 extra gigabytes, so the cost is 60 + 12 * 1 = 72 dollars. For each extra gigabyte, 12 dollars are added, so we can represent this as
60 + 12 * g, with g representing the number of extra gigabytes
Please help me with my Geometry.
Answers
Answer:
it should be 6
Step-by-step explanation:
I could be wrong
Solve the triangle. Round to the nearest tenth when neccesary or to the nearest minute as appropriate.
Answers
Answer:
Here is the detailed answer below
Step-by-step explanation:
help me with this math question please
Answers
44+56+60+85= 245 Which is the least needed to cover the expenses.
Answer:
$44.00 + $85.00 = $129.00
Step-by-step explanation:
The least amount that she needs is $129.00 because we're summing the amount for food and House Rent.
Movies and Shopping are less important.
What 2 days did he decrease his walking
Answers
Answer:
4, 7, 14
Step-by-step explanation:
Because it's were it decreases
i need help plzzzz!!!!!
Answers
X>7-2
X>5
Hope this helps you
Step-by-step explanation:
x+2>7
x>7-2
x>5
2x+5>_ 15
2x>_ 15-5
2x>_ 10
2x/2>_ 10/2
x>_5
Given the functions below, find f(x) + g(x)
f(x) = 3x - 1
g(x) = x2 + 4
Answers
Answer:
x^2+3x+3
Step-by-step explanation:
f(x) = 3x - 1
g(x) = x^2 + 4
f(x) + g(x) = 3x-1+ x^2 +4
Combine like terms
= x^2+3x+3
What is 150% of 90?
please explain.
Answers
Answer: 135
Step-by-step explanation: Write 150% as 150/100
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have 150/100 of 90= 150/100 X 90
Therefore, the answer is 135
If you are using a calculator, enter 150÷100×90 which will give you 135 as the answer.
150 percentage of 90 is 135 which we obtained by multiplying 1.5 with 90.
"Percent" means "per hundred," so when we say "150%," it means 150 per hundred or 150 out of 100.
To find 150% of 90, we can use the following formula:
150% of 90 = (150/100) × 90
Convert 150% to a decimal.
To do this, divide 150 by 100:
150/100 = 1.5
Multiply the decimal value by 90:
1.5 × 90
= 135
So, 150% of 90 is 135 which means that 135 is 150% of 90, which is equivalent to saying that 135 is 1.5 times larger than 90.
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Given that h(x) = - (x - 1)^2 - 1, write an expression for f(x) in terms of x.
f(x) =
Answers
Answer: f(x) = -(x-1)^2+5
Explanation:
f(x) = h(x) + 6
f(x) = -(x-1)^2 - 1 + 6
f(x) = -(x-1)^2+5
Must click thanks and mark brainliest
The height h, in feet, of a projectile t seconds after launch is modeled by the equation h=32t-16t^2.
Answers
Complete question is;
The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32t – 16t². How long after launch does the projectile return to the ground?
Answer:
2 seconds
Step-by-step explanation:
We are told that the height function is given by;
h = 32t – 16t²
Now, the velocity will be the derivative of the height equation.
Thus;
v(t) = dh/dt = 32 - 32t
Now, for projectiles, at max height, v = 0.
Thus;
32 - 32t = 0
32t = 32
t = 32/32
t = 1 s
It will take the same time it took to get to Max height as it will to get to ground from that height.
Thus, total height = 1 + 1 = 2 seconds
HURRY PLEASEEEEE!!!!!!
Juan scored 24 points in the first half of the basketball game, and he scored p points in the second half of the game. Write this in variable/constant form.
Answers
Answer:
24+p=t
Step-by-step explanation:
If he scored 24 points in the first half, and p in the next half, he scored a total of t points.
A flag has a perimeter of 5 metres. The length of the flag is 600 mm more than the
width of the flag. The length is represented by L and the width is represented by W.
Which of the linear systems in the choices represents the description?
O2L + 2W = 5
L - 600 = W
O2L + 2W = 5000
L - 600 = W
OL+W = 5000
W + 600 = L
O L x W = 5000
L + 600 = W
Answers
Answer:
The first two.
Step-by-step explanation:
See that L is 600mm MORE than W.
From there, you can note that L = W+600
or rearrange the formula and get W= L-600
Then, see that the perimeter of a flag is 2L + 2W
(Because there are two four sides to a rectangle, 2 width, 2 length)
It must total to be 5 meters, or 5000mm
Thus,
2L + 2W = 5000
(PICTURE) please answer whatever you can Its really urgent
Answers
Step By Step Explanation:
I answered myself
someone answer this please
Answers
Answer:
720º
Step-by-step explanation:
To find the total amount of interior angles in any polygon, we have to use the formula, (n-2)*180.
Here, the n is the number of sides the polygon has. In this case, your polygon has 8 sides. Therefore it would be (8-2)*180 --> 4*180 = 720º.
Answer:
the answer is 720. Please give me brainliest
Se desea pintar un cuadrado inscrito en una circunferencia de radio R=3cm como se muestra en la figura. Calcular el área del cuadrado
Answers
El área del cuadrado es de 3 centímetros cuadrados.
Dado que se desea pintar un cuadrado inscrito en una circunferencia de radio R=3cm como se muestra en la figura, para calcular el área del cuadrado se debe realizar el siguiente cálculo:
Radio = diámetro / 2 3 = X/2 X = 6Hipotenusa del triángulo interno: 6 cmAplicando teorema pitagórico: lado al cuadrado mas lado al cuadrado es igual a hipotenusa al cuadrado.
L^2 + L^2 = 62L^2 = 6L^2 = 6/2L = √ 3L = 1.732Área de un cuadrado = L x L = L^2 = 3Por lo tanto, el área del cuadrado es de 3 centímetros cuadrados.
Aprende más en https://brainly.com/question/16405529
El área del cuadrado es de 18 centímetros cuadrados.
El procedimiento de resolución se basa en conocer que la Medida de la Diagonal de un Cuadrado inscrito es igual a la Medida del Radio del Círculo, lo cual permite determinar el valor de la medida del Cuadrado en función del Radio del Círculo. Finalmente, determinamos el Área del Cuadrado mediante su fórmula conocida.
Dado que existe un cuadrado inscrito en un círculo, la medida de la diagonal del cuadrado es igual a la medida del radio del círculo. Además, conocemos que un cuadrado está formado por 4 triángulos rectángulos con configuración angular 45-45-90. Entonces, la medida del lado del cuadrado se calcula mediante la siguiente relación geométrica:
[tex]l = \sqrt{2}\cdot R[/tex] (1)
Donde:
[tex]R[/tex] - Radio del círculo, en centímetros.
[tex]l[/tex] - Longitud del lado del cuadrado, en centímetros.
Por otra parte, la ecuación de área del cuadrado es igual a:
[tex]A = l^{2}[/tex] (2)
Donde [tex]A[/tex] es el área del cuadrado, en centímetros cuadrados.
Si sabemos que [tex]R = 3\,cm[/tex], entonces el área del cuadrado es:
[tex]l = \sqrt{2}\cdot (3\,cm)[/tex]
[tex]l = 3\sqrt{2}\,cm[/tex]
[tex]A = (3\sqrt{2}\,cm)^{2}[/tex]
[tex]A = 18\,cm^{2}[/tex]
El área del cuadrado es de 18 centímetros cuadrados.
He aquí una pregunta relacionada sobre el área del cuadrado: https://brainly.com/question/23915250
The definition of a circle
Answers
Answer:
a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)
Explanation:
Oxford dictionary definition
Step-by-step explanation:
a circle is a shape consisting of all points in a plane that are at a given distance from a given point the center
(4x-5y) is subtracted from (-10x-y)
Answers
Answer:
-14x+4y
this is the correct answer.
Combine and simplify these radicals.
Answers
Answer:
4 sqrt(3)
Step-by-step explanation:
sqrt(3) * sqrt(16)
sqrt(3) *4
4 sqrt(3)
Answer: d
Step-by-step explanation: I took the test
Divide 3x^2 + 4x - 4 by x + 2.
A. x-2
B.x+ 6
C.3х – 2
D. 3x + 6
Answers
Answer:
C.
Step-by-step explanation:
C. 3x-2 is the answer .
Answer:
C.3х – 2
Step-by-step explanation:
Explanation is in the attachment
Hope it is helpful to you
Tính giá trị của I = [tex]\lim_{x \to \infty}[/tex] ([tex]\frac{4^{n} - 5.3^{n} + 1}{2.4^{n} + 2}[/tex])
Answers
I assume you're supposed to find the limit as n approaches infinity, not x.
You have
[tex]\displaystyle \lim_{n\to\infty}\frac{4^n-5.3^n+1}{2.4^n+2} = \lim_{n\to\infty}\frac{\left(\dfrac4{5.3}\right)^n-\left(\dfrac{5.3}{5.3}\right)^n+\dfrac1{5.3^n}}{\left(\dfrac{2.4}{5.3}\right)^n+\dfrac2{5.3^n}} \\\\ = \lim_{n\to\infty}\frac{\left(\dfrac4{5.3}\right)^n-1+\dfrac1{5.3^n}}{\left(\dfrac{2.4}{5.3}\right)^n+\dfrac2{5.3^n}}[/tex]
For |x| < 1, we have lim |x|ⁿ = 0 as n goes to infinity. Then each exponential term converges to 0, which leaves us with -1/0. This means the limit is negative infinity.
On the other hand, perhaps you meant to write
[tex]\displaystyle \lim_{n\to\infty}\frac{4^n-5\times3^n+1}{2\times4^n+2}[/tex]
The same algebraic manipulation gives us
[tex]\displaystyle\lim_{n\to\infty}\frac{\left(\dfrac44\right)^n-5\left(\dfrac34\right)^n+\dfrac1{4^n}}{2\left(\dfrac44\right)^n+\dfrac2{4^n}} = \lim_{n\to\infty}\frac{1-5\left(\dfrac34\right)^n+\dfrac1{4^n}}{2+\dfrac2{4^n}}[/tex]
Again the exponential terms converge to 0, but this time we're left with the limit 1/2.
ailey is shopping at a department store during a 20% off everything sale. She also has a coupon for $5.00 off the sale amount. Hailey wants to keep her total under $65.00 before tax, so she creates this inequality:
0.80x − $5.00 ≤ $65.00.
Which inequality represents all possible solutions for x?
A.
x ≤ $75.00
B.
x ≤ $76.25
C.
x ≤ $86.25
D.
x ≤ $87.50
Answers
Answer:
D
Step-by-step explanation:
0.8x-5<=65
0.8x<=70
x<=700/8=87.5
Answer:
D
Step-by-step explanation:
Line m has no y-intercept, and its x-intercept is (3,0). line n has no x-intercept, and its y-intercept is (0-,4).
the equation of line m is ___ , and the equation of line n is ____.
type the correct answer in each box.
Answers
Answer:
x=3 and y=4
Step-by-step explanation:
please verify the answer
what is y=2x*2-6x-8 as a graph
Answers
Answer:
[tex] \bf \: y = 2 {x}^{2} - 6x - 8[/tex]
It is equation of a parabolla.
It is to be noted that the graph of y = 2x * 2-6x-8 which when simplified is y = -12x² - 12x. is attached accordingly.
What are the qualities of the graph of y = -12x² - 12x?The graph of y = -12x² - 12x is a downward-opening parabola.
It has a concave shape and its vertex is the highest point on the graph. The axis of symmetry is a vertical line passing through the vertex.
The graph may intersect or be tangent to the x-axis at two points, one point, or no points, depending on the discriminant.
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i need help with this question pls! :)
Answers
Hi there!
[tex]\large\boxed{\text{9 quarters}}[/tex]
We can let x = dimes and y = quarters.
We know that one dime = $0.10 and a quarter = $0.25, so:
$3.05 = $0.10x + $0.25y
And:
17 = x + y
Solve the system of equations. We can rearrange the bottom equation to create an expression equal to y:
17 - x = y
Substitute this into the top equation for y:
3.05 = 0.10x + 0.25(17 - x)
Distribute and simplify:
3.05 = 0.10x + 4.25 - 0.25x
3.05 = 4.25 - 0.15x
Solve for x:
-1.2 = -0.15x
x = 8
Find y using the above expression:
17 - 8 = y
y = 9
