The expression 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] is equivalent to 60 [tex]x^{8}[/tex] if x≠ 0 which is option B
We have to simplify the given equation 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] in order to find its equivalent
Which can be simplified using the basics of square and square roots
Square and square root gets cancelled for example [tex]\sqrt{x^{2} }[/tex] = x and powers get added when same bases are multiplied for example x² × x³ = [tex]x^{2+3}[/tex] =[tex]x^{5}[/tex]
Also √25 can be written as 5
At x = 0 the whole expression can be written as zero
4x² ×√[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex]
12x²×[tex]x^{2} \sqrt{5}[/tex] ×[tex]x^{4} \sqrt{5}[/tex]
12[tex]x^{8}[/tex] ×√25
60 [tex]x^{8}[/tex]
Hence, The expression 4x²×[tex]\sqrt{5x^{4} }[/tex] ×3[tex]\sqrt{5x^{8} }[/tex] is equivalent to 60 [tex]x^{8}[/tex] if x≠ 0 which is option B
The correct question is Select the correct answer.
Which expression is equivalent to 4x²√5x4 3√5x8, if x≠0?
OA. 12x¹0 √5
OB. 60x8
OC.35x18
O D. 7x¹⁰ √5
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Help for BRAINLIEST! Find BC
The length of the segment BC is equal to 5√3 π / 3.
What is the length of a missing side of a geometric system?
Herein we find the a geometric system formed by a circle and an inscribed right triangle formed by two right triangles. By a quick inspection we find the following measures:
AD = 10π, m ∠ BCD = 60°, m ∠ BDC = 30°, m ∠ BDA = 60°, m ∠ BAD = 30°
Then, by 30-60-90 right triangle theorem we find that:
DB = (1 / 2) · AD
DB = (1 / 2) · 10π
DB = 5π
DB = √3 · BC
BC = (√3 / 3) · DB
BC = 5√3 π / 3
The length of the segment BC is equal to 5√3 π / 3.
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4/9 es racional o irracional y porque?
Answer: 4/9 es racional - cualquier fracción adecuada x/y es un número racional. Expresado como un decimal, esto es igual a 0.4 recurrente (es decir, 0.44444...)
Step-by-step explanation: ¡Espero que esto ayude!
El número 4/9 es un número racional. Es una razón, o fracción, formada por dos números enteros, 4 y 9.
find the solution to this equation: 4x-2(x-3)=-7+5x+4
Answer:
x=3
Step-by-step explanation:
4x-2x+6=-7+5x+4
2x+6=-7+5x+4
2x+6-6=5x-3-6
2x=5x-9
-3x=-9
x=3
a translation along the directed line segment \overline{nb} nb start overline, n, b, end overline, then a reflection over the vertical line through point bbb.
A translation along the directed line segment NB then a reflection over the vertical line about B so sequence A is correct therefore option (A) will be correct.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
Reflection is a mirror image of a graph about any axis.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
Given the triangle MNO and ABC
Now,
If we translate MNO along the directed line segment NB and reflect over B then M will coincide with A and N with B and O with C.
In sequence B if we reflect on MO then M will not coincide with A and it will not form a triangle ABC.
Hence "A translation along the directed line segment NB then a reflection over the vertical line about B".
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The given question has missed an image, incomplete question is given in the image,
Find the measure of LAOC
m LAOC =
Classify LAOC
The measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.
What is an Acute Angle?An angle that has a measure that is less than 90 degrees is classified as an acute angle.
Given the diagram below, the angle that is formed by rays AO and CO is angle AOC. The instrument shows that angle AOC is exactly 30 degrees.
30 degrees is less than 90 degrees and can therefore be termed an acute angle.
Therefore, the measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.
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nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.
The given statement is true because it is the definition of nonlinear optimization.
it is the branch of mathematics with deals with the basic mathematical operators called arithmetic operators are addition, division, multiplication and subtraction.
Here,
The nonlinear optimization problem is an optimization problem in which at least one term in the objective function or a constraint is nonlinear, is true, Since its the basic definition of nonlinear optimization.
Thus, the given statement is true.
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2.5x17 pls some on solve it
Answer:
42.5
Step-by-step explanation:
You have to multiply 7 times 5 equals 35. Then you multiply 7 times 2 which is 14 plus 3 equals 5. So you have 175 as the first number. Then you put a 0 under that number. You multiply 5 times 1 which is 5 and 2 times 1 which is 2. Now you have 250 as your second number.
Add 175 plus 250 which is 425 but you have to put the decimal between 2 and 5. Now you have 42.5
Hope that helps
x3+y3+z3=k does anyone get this anyone?
Answer:
k = x^3+y^3+z^3
Step-by-step explanation:
Solve for k by simplifying both sides of the equation, then isolating the variable.
Hope this helps.
Describe the graph of the Celsius-Fahrenheit relationship
Using linear function concepts, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, we have that:
When the input is of 0, the output is of 32, hence the intercept is of 32.When the input changes by 10, the output changes by 18, hence the slope is of 18/10 = 1.8.Thus, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.
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A number z divided by 4 is 12
Answer:
z divided by 4 is 12
48 divided by 4 is 12
6. a.give the domain and range for the function graphed below. Explain why this graph represents a function.
b. what is the y intercept of the function shown in the graph.
c. identify any extrema of the function shown in the graph.
Answer:
A - Domain - [0,9] , Range - [0,3] , It represents a function because it passes the (vertical line test).
B - (0,0)
C - I'm not sure about this question but, If i would guess, (0,0) (9,3).
Step-by-step explanation:
For question C i think It means maximum and minimum points on the graph.
Im sorry if you get any of it wrong.
Carl used 24 blocks to build a tower. Each block is a cube with side length of 2 inches. Use the formula v = s3 to find the volume of a cube. What is the volume of the tower?
Answer:
184
Step-by-step explanation:
What is the result when the number 24 is increased by 25%?
Answer:
When i24 is increased by 25% the answer is 30
in college basketball, some teams get most of their points from just one player, and other teams are more balanced in scoring. consider the following facts about the scoring distributions for some ncaa division i basketball teams. each team has 121212 players. at baylor university, there are 666 players who each score 121212 points per game, and there are 666 players who each score 000 points per game. at the university of maryland, 111 player scores 585858 points per game, 111 player scores 141414 points per game, and the rest of the players score 000 points per game. at dartmouth college, 444 players score 555 points per game, 444 players score 666 points per game, and 444 players score 777 points per game.
At Maryland, the mean number of points per player per game is greater than the median number of points per player per game. The mean number of points per player per game is the same at all 3 schools.
Given that in Baylor's University that there are 6 players who each score 12 points per game, and 6 players who each score 0 points per game.
The scores are 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12.
Mean = Sum/Count = 72/12 = 6.
Median is the average between the nth and (n+1)th term.
(0+ 12)/2 = 6
In Maryland university 1 player scores 58 points per game, 1 player scores 14 points per game, and the rest of the 10 score 0 points per game,
58, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Mean = Sum/Count = 72/12 = 6.
Median is 0
In Dartmouth, university, 4 players score 5 points per game, 4 players score 6 points per game, 4 players score 7 points per game.
The scores are
5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7
Mean = Sum/Count = 72/12 = 6
Median =(6+6)/2= 6
At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.
The mean number of points per player per game is the same at all 3 schools.
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Find the average rate of change for the function f(x)=3^x+17
Using the intervals x=3 to x=6
The average rate of change for the function will be 234.
What is the average rate change of a function?It is the average amount by which the function is modified per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph that represents the function. The average rate of change of the function is given as,
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The function is given below.
f(x) = 3ˣ + 17
The value of the function at x = 3 will be
f(x) = 3³ + 17
f(x) = 27 + 17
f(x) = 44
The value of the function at x = 6 will be
f(x) = 3⁶ + 17
f(x) = 729 + 17
f(x) = 746
Then the average rate of change for the function will be
Average rate = [746 - 44] / [6 - 3]
Average rate = 702 / 3
Average rate = 234
The average rate of change for the function will be 234.
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in a poll conducted by a certain research center, 1046 adults were called after their telephone numbers were randomly generated by a computer, and were able to correctly identify the
In a poll conducted by a certain research center, 1046 adults were called after their telephone numbers were randomly generated by a computer, and were able to correctly identify the random sampling.
Each sample has an equal chance of being chosen as part of the sampling technique known as random sampling. A randomly selected sample is intended to be a fair representation of the entire population.
In statistics, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a procedure for randomly choosing a sample.
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BEED URGENT HELPPP!
(please help me answer these 3 questions, picture attached)
Questions:
1. what is the area of the whole rectangle?
( area = length * width )
2. what is the area of the shaded rectangle?
3. what is the area of the unshaded part of the rectangle? (area of the whole rectangle - area of the shaded part)
Answer: See below
Step-by-step explanation:
1) For the first question, we have to multiply the width by the length to find the area of the whole rectangle:
(4x-4)(x+1)= 4x^2 -4
2) For the second question, we have to multiply the width by the length to find the area of the shaded area in the rectangle:
(2x+2)(x-1)= 2x^2-2
3) The total area of the unshaded part of the whole triangle equals the area of the whole rectangle minus the shaded area:
4x^2-4 - 2x^2 -2 = 2x^2 - 6
Find the focus and the directrix for the parabola with the given equation.
Answer:
[tex]\mathrm{Focus:\;\;} \left(-\frac{5}{3},\:2\right)[/tex]
[tex]\mathrm{Directrix:\;\;}x=-\frac{1}{3}[/tex]
Step-by-step explanation:
The standard equation for a parabola is
[tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex]
with vertex at (h, k) and a focal length of |p|
[tex]\mathrm{Rewrite}\:x=-\frac{3}{8}\left(y-2\right)^2-1\:\mathrm{in\:the\:standard\:form}[/tex]:
[tex]\mathrm{Add\:}1\mathrm{\:to\:both\:sides}[/tex]
[tex]x+1=-\frac{3}{8}\left(y-2\right)^2-1+1[/tex] or
[tex]x+1=-\frac{3}{8}\left(y-2\right)^2[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-\frac{3}{8}[/tex]
[tex]\frac{x+1}{-\frac{3}{8}}=\frac{-\frac{3}{8}\left(y-2\right)^2}{-\frac{3}{8}}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-\frac{8x}{3}-\frac{8}{3}=\left(y-2\right)^2[/tex]
[tex]\mathrm{Factor\:}-\frac{8}{3}[/tex]
[tex]\left(-\frac{8}{3}\right)\left(x+\frac{-\frac{8}{3}}{-\frac{8}{3}}\right)=\left(y-2\right)^2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\left(-\frac{8}{3}\right)\left(x+1\right)=\left(y-2\right)^2[/tex]
[tex]\mathrm{Factor\:}4[/tex]
[tex]4\cdot \frac{-\frac{8}{3}}{4}\left(x+1\right)=\left(y-2\right)^2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]4\left(-\frac{2}{3}\right)\left(x+1\right)=\left(y-2\right)^2[/tex]
[tex]\mathrm{We\; can\; rewrite\:this\;as}[/tex]
[tex]4\left(-\frac{2}{3}\right)\left(x-\left(-1\right)\right)=\left(y-2\right)^2[/tex]
Comparing this with the standard form we get
[tex]\left(h,\:k\right)=\left(-1,\:2\right)[/tex]
[tex]\:p=-\frac{2}{3}[/tex]
The parabola is symmetric around the x-axis.
The focus lies a distance [tex]p[/tex] from the center [tex]\left(-1,\:2\right)[/tex] along the x axis
So focus is at
[tex]\left(-1+p,\:2\right)[/tex] [tex]=\left(-1+\left(-\frac{2}{3}\right),\:2\right)[/tex] [tex]=\bold{ \left(-\frac{5}{3},\:2\right)}[/tex]
The parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis at a distance -p from the center
[tex]x=-1-p[/tex]
[tex]x=-1-\left(-\frac{2}{3}\right) = \bold{-\frac{1}{3}}[/tex]
5. Reem paid £62 for a bicycle.
She sold it later for £46.
What was her percentage loss?
Step-by-step explanation:
[tex] \frac{46}{62} \times 100 = 74.19 percent \\ 100 - 74.19 = 25.81 \: percent \\ her \: loss \: was \: 25.81 \: percent[/tex]
Solve the inequality for v.
-12+v<-10
Answer:
v < 2
Step-by-step explanation:
To solve this problem, start by adding 12 to each side of the inequality, to clear the -12 from the left side. 10 + (-12) is 2, so your answer is v < 2.
Hope this helps! Let me know if you have any confusion!
What is the perimeter of a rectangle with a length of 9x - 4 and a width of 5x + 2 ?
Answer:
28x-4
Step-by-step explanation:
Given
length (l)= 9x-4
Breadth (b) = 5x+2
Now
Perimeter (P) = 2(l+b)
=2(9x-4+5x+2)
=2(14x-2)
=28x-4
Johns weekly salary is $478.25. his employer is changing the pay period to semimonthly. What is johns annual salary?
What will johns semimonthly salary be to the nearest cent
Based on the fact that the employer is changing the pay period to semimonthly, John's semimonthly salary to the nearest cent is $956.50
John's annual salary can be found to be $24,869
How to find the semimonthly salary?If a person is paid semimonthly, it means that they are paid twice a month or every two weeks.
This means that John's semimonthly salary is:
= 478.25 x 2
= $956.50
In a year, John's annual salary will be:
= 478.25 x 52 weeks
= $24,869
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in a _____ sequence, the ratio between consecutive terms is constant.
Answer:
Geometric.
Step-by-step explanation:
For example
2, 4, 8, 16
where the common ratio is 4/2 = 8/4 = 16/8 = 2.
Simplify
-4+6/2=
wjjjj
Answer:
good luck broooooooooooo
Answer:
-1
Step-by-step explanation:
→ -4 + (6/2)
→ -4 +3 = -1
So, the answer is -1.
february $1$, $2008$ is a friday. the last friday of february $2008$ will be february $x$, $2008$. if $2008$ is a leap year, what is the value of $x$?
x= 29 which is Friday of that Month.
As 1st February 2008 is Friday
By adding 7 to the date we will get the next Friday Date of that month
i.e., 1 + 7= 8
i.e., 8 is Friday
Again if we will add 7 in 8 then we will get another Friday
so by adding again i.e., 8 + 7= 15 which is again Friday
Then 15 + 7 = 22 which is Friday.
adding again we will reach final to final answer 22+ 7 = 29 which is Friday
after adding 29 with 7 we will get 36 and as we know there are only 30/31 days in a month.
So, by adding 7 to the date we will reach the next week.
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Can someone please help me with proofs
[tex]\angle DAE \cong \angle DCF[/tex]
by CPCTC.
in a certain clothing store, the ratio of the number of full-time employees to the number of employees who are not full-time is 1 to 4. if 5 more full-time employees were hired, the ratio would be 2 to 3. how many employees are employed by the store?
Answer: Total number of employees are employed by the store = 15 employees.
Step-by-step explanation:
The ratio of Full time employees to Not Full time employees would be 1 to 4.
Let, Full time employees F =1
Not Full time employees N =4
We can write:
F/N = ¼
Cross multiply to get:
N=4F
If 5 more Full time employees were hired, then the ratio would be 2 to 3.
This would be mean there are no (F+5) Full time employees.
Also there are still Not Full time employees.
We can write:
(F+5) / N = 2/3
Cross multiply to get:
3(F+5) =2N
Expand to get:
3F+15=2N
Replace N with 4F to get:
3F+15=2(4F)
Solve to get:
3F+15=8F
15=8F-3F
15=5F
F=3
So, there are presently 3 Full time employees.
How many employees does the store have?
Since F=3,
we can use the equation N=4F
To help find the value of N Replace F with 3 to get:
N = 4(3)
Solve to get:
N=12
So, Full time employees F=3
Not Full time employees N=12
Then, Total number of employees = F+N
= 3+12
= 15.
Hence, Total number of employees = 15 employees.
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45,000 - (-800) = 45,800
Answer:
True
Step-by-step explanation:
I'm assuming this is a true or false question, and so the answer is true. Because two negatives (-) equal a positive. So, 45,000 - (-800) actually is 45,00 + 800 because there was as subtraction sign and a negative sign.
Answer:
Step-by-step explanation:
45,000-(-800)=45,800
45,000-(-800) does =45,800
Find the center and radius of 2x^2 + 2y^2 - 12x + 8y - 24 = 0
When the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.
The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]
The general equation of the circle is [tex]x^{2} +y^{2}+2gx+2fy+c=0[/tex]
Where (-g,-f) is the coordinates of the circle
The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]
Divide the equation by 2
[tex]x^{2} +y^{2}-6x+4y-12=0[/tex]
Compare the equation with general form
2g= -6
g= -3
2f= 4
f= 2
The center of the circle (-g,-f) = (3,-2)
The radius of the circle = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]
Substitute the values in the equation
r= [tex]\sqrt{(-3)^{2}+2^{2}- (-24) }[/tex]
[tex]=\sqrt{9+4+24} \\=\sqrt{37}[/tex]
=6.08 units
Hence, when the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.
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how many ways can a parent distribute five one-dollar bills to her three children? (b) how many ways can she accomplish this if each child gets at least one dollar?
By the concept of Permutations and Combinations, we get:
Number of ways to distribute 5 dollar bills among three children = 21
and
Number of ways to distribute 5 dollar bills such that each child gets at least one dollar = 6
What is permutations and combinations?A permutation is an orderly arrangement of the items or numbers. Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.Given:
Number of 1 dollar bills = 5Number of children = 3To find: (A) number of ways to distribute the dollar bills among the children
(B) number of ways to do the same if each child gets at least a dollar.
Finding:
By using the formula: [tex]\binom{n+r-1}{r-1}[/tex],
Number of ways to distribute 5 dollar bills among three children = [tex]\binom{5+3-1}{3-1} = \binom{7}{2}= \frac{7\times6}{2}[/tex] = 21 ways.
Similarly, upon modifying the above formula as: [tex]\binom{n-1}{r-1}[/tex],
Number of ways to distribute 5 dollar bills such that each child gets at least one dollar is =
[tex]\binom{5-1}{3-1}= \binom{4}{2}=\frac{4\times3}{2}[/tex] = 6 ways.
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