Answers
The final answer is 4x, which is the simplest form of expression.
What is the rational exponent?
A rational exponent is an exponent that is in the form of a ratio of two integers, such as a/b where a and b are integers and b is not equal to zero.
To rewrite the expression in simplest rational exponent form, we can first simplify the radicals and then combine any like terms. Here are the steps to simplify the given expression:
4√x* √x = 4 * 1 √x * √x = 4 * x^(1/2) * x^(1/2) = 4 * x^( (1/2)+(1/2) ) = 4 * x^(1)
x^(1) = x
So, the expression in simplest rational exponent form is 4x
x * 4x = 4x
Notice that 4 and x are in the same radical which means 4 is a coefficient of x.
Therefore, 4√x * √x can be written as 4x, which is in the simplest form.
hence, the final answer is 4x, which is the simplest form of expression.
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Related Questions
Consider the number . what happens when z is raised to successively increasing powers? use the drop-down menus to complete each sentence. the modulus increases by a factor of . the argument increases by π over 3.
Answers
The modulus increases by a factor of 10 and the argument increases by 5π/3.
Modulus of the complex number:
The modulus of a complex number is the square root of the sum of the squares of the complex number's real and imaginary parts. If z is complex, the absolute value of complex z is given by √{[Re(z)]2 + [Im(z)] and denoted by |z|. exclusive. The absolute value of a complex number z = a + ib is the distance between the origin (0, 0) of the complex plane and the point (a, b). The modulus of a complex number is a distance, so its value is always non-negative.
The absolute value of a complex number z = x + iy denoted by |z| is given by the formula |z|. Given = √(x2 + y2), where x is the real part of the complex number z and y is the imaginary part. The modulus of a complex number z can also be computed using the conjugate of z. Since
z. z = (x+ iy)(x −iy)
=x²+y² , we have
z. z = |z|²
⇒ |zI =√z. z.
Then,
The modulus of the z will be =|z|= √p²+q²
We have,
z = 5 – 5i √3
So,
Now rewrite this given equation in the form of z = r(Cosθ + iSinθ),
For this first calculate the modulus,
|Z| = √((5√3)² + 5²)
|Z| = √(25×3 + 25)
|Z| = √(100) = 10
And,
Argument, θ = tan⁻¹ (b/a)
θ = tan⁻¹ (5√3/5)
θ = tan⁻¹ (√3)
θ = 71
Therefore, the modulus increases by a factor of 10, and the argument increase by 5π/3.
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Answer:
The modulus increases by a factor of ✔ 10.
The argument increases by ✔ 5π over 3
Step-by-step explanation:
correct on edge 2023
What is the length of the hypotenuse of a 45 45 90 triangle with a leg of 12?
Answers
It is given that a 45-45-90 triangle whose each leg is 12 cm, then the length of the hypotenuse can be found out as 12/√2
since the hypotenuse is one of the legs multiplied by √2.
dividing the hypotenuse by √2 will get the length of one leg. since it is a 45 45 90 triangle, the length of the two legs are the same.
It is given that a 45-45-90 triangle whose each leg is 12 cm, then the length of the hypotenuse can be found out as:
By using the Pythagoras theorem, we have
a^2+b^2= c^2
Substituting the given values, we have
12/√2
Thus, the length of the hypotenuse will be
12/√2
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Ceramic tile is being used to cover two 6 ft-by-4 ft rectangular walls. The tiles
are in the shape of equilateral triangles with 6-in. sides. A box of tiles contains
20 tiles. How many boxes of tiles will be needed to cover both walls?
Answers
Answer:
Approximately 5 boxes
Step-by-step explanation:
6x4=24 ft
24x2=48 ft
48x12=576 in
576/6=96
96/20=4.8 boxes
If I'm wrong I'm sorry
Use the data for the books each class donated for a book drive and find the upper quartile. 28 15 40 45 27 19 50 36 42 37 21 25
A.35
B.18
C.41
D.23
Answers
Answer:
41
Step-by-step explanation:
when you find the median you split the numbers in half from the upper to lower parts of the data. then you find the median of the upper part and that is the upper quartile.
median: 32
32, 36, 37, 40, 42, 45, 50
add 40+42 then divide by 2 and you get 41
hopefully this helps
3m+2≤ 29
help.............................
Answers
Answer:
29-2 =27 divided by 3
m=9
Answer:
One option is:
m=3
Step-by-step explanation:
3x3=9
9+2=11
11<29
Before beginning a unit of frog anatomy, a seventh grade biology teacher gives each of the 24 students in the class a pretest to assess their knowledge of frog anatomy. The teacher wants to compare the effectiveness of an instructional program in which students physically dissect frogs with the effectiveness of a different program in which students use computer software that only simulates the dissection of a frog. After completing one of the two programs, students will be given a posttest to assess their knowledge of frog anatomy. The teacher will then analyze the changes in the test scores (score on posttest minus score on pretest). a) Describe a method for assigning the 24 students to two groups of equal size that allows for a statistically valid comparison of the two instructional programs. b) Suppose the teacher decided to allow the students in the class to select which instructional program on frog anatomy (physical dissection or computer simulation) they prefer to take, and 11 students choose actual dissection and 13 students choose computer simulation. How might that self-selection process jeopardize a statistically valid comparison of the changes in the test scores (score on posttest minus score on pretest) for the two instructional programs? Provide a specific example to support your answer.
Answers
The following method for assigning the 24 students to two equal-sized groups allows for a statistical valid comparison of the two instructional programmes.
What is instructional program?An instructional programme is a course of study that requires the completion of a specified number of course credits from a prescribed group of courses and results in a formal award.
A) Each student will be given a unique random number generated by a random number generator on a calculator, statistical software, or a random number table. The assigned numbers will be listed in ascending order. Students with the lowest 12 numbers on the ordered list will be assigned to the instructional programme that requires physically dissecting frogs.
Students with the highest 12 numbers will receive an instructional programme that simulates frog dissection using computer software.
B) By not randomizing and allowing students to self-select, there is the possibility of changes in the differences between pre test and post test scores for a specific group due to the characteristics of students who choose a particular instructional method, rather than the instructional method itself.
For example, suppose frog-loving students already know a lot about frog anatomy; these students would be less likely to show a large difference between pre and post test scores. Assume that the frog-loving students prefer the computer simulation method (perhaps because they do not like the notion of dissecting the frogs they love).
The possible low change in pre- and post-test scores for the computer simulation group could then be attributed to the students' prior knowledge of frog anatomy, rather than to the instructional method itself. Because the students entering the frog dissection group have lower pre-test scores (less prior knowledge), they are more likely to show greater improvement between pre-test and post-test scores.
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5. Measure the length of each leg and the hypotenuse of this triangle: a.f = units ag units fg = units
Answers
To find the length of the side opposite the angle, multiply the hypotenuse by sin(). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos()
What is Hypotenuse triangle?The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, is opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles. When we study the right-angled theorem, Pythagoras Theorem, or Pythagorean Theorem, this is better understood.
Hypotenuse TheoramPythagoras theorem defines the hypotenuse theorem. This theorem states that the square of a right-angled triangle's hypotenuse side is equal to the sum of its base and perpendicular squares, so that;
Hypotenuse2 = Base2 + Perpendicular2
The square root of the sum of the base and perpendicular squares of a right-angled triangle provides the formula to get the hypotenuse. The hypotenuse formula is represented as follows:
Hypotenuse = √[Base2 + Perpendicular2]
Length of the hypotenuse:Hypotenuse length: In the scenario where the square root is not a perfect square, we take an approximation of the root here in order for the solution to appear.Additionally, the squares of the base and the height should always be added to establish the value, however this does not provide a perfect square.Due to the imperfect square-root number, we must therefore approximation the solution.To know more about Hypotenuse Triangle refer to:
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We have a drawer with 30 pairs of different socks. How many (individual) socks do we need to pull from the drawer before getting one pair for certain
Answers
Answer:
60 because their a 2 induivedinal in 1 sock.
Step-by-step explanation:
30 x 2 = 60
Find the midpoint between p and q.
p = (12,-3,6)
q = (-9,2,0)
Answers
Answer:
A on edge
Step-by-step explanation:
( 3/2, -1/2, 3)
Factor each polynomial completely.
a. 5a²c - 3a²d + 5b²c-3b²d
b. x^2n+ 6x^n +9
Answers
A = (a^2 + b^2) (5c - 3d)
B = (x^n + 3)^2
Explanation for A:
1. Factor out a^2 from (5a^2c - 3a^2d). This should look like a^2 (5c - 3d).
2. Factor out b^2 from (5b^2c - 3b^d). This should look like b^2 (5c - 3d).
3. Now multiply a^2 (5c - 3d) with b^2 (5c - 3d), by factoring out (5c - 3d) and writing a^2 + b^2 in parentheses like (a^2 + b^2) (5c - 3d)
Explanation for B:
1. Factor out x^n for x^2n + 6x^n, which should look like x^n (x^n + 6).
2. Write 9 as 3^2. The equation should look like x^n (x^n + 6) + 3^2. You can notice that the equation can be factored like (x^n + 3)^2 since you can get 6x^n by
(x^n + 3) multiples by 2, x^2n by squaring if, and 9 by squaring 3.
Pls help me solve this
Answers
(5-2x)(2-2x)(x)
4x^3-14x^2+10x
B
(1.5)(2)(1)
3
C
~2.67
A student-athlete can run 10 yards in 6 seconds. Which equation shows the number of yards that can be run in s seconds
Answers
The equation for the maximum number of yards per second that can be run is y = 5/3 s.
Define the term Direct Variation?Two quantities are said to be fluctuating directly if they are coupled in a way that an increase for one quantity suggests an increase in the other and a drop in one implies a decrease in the other. The direct variation equation, which connects the two values y and x, looks like this: y=kx, where k is the variational constant.A direct variation measurement between distance covered and time taken can be composed as:
y=kx,
where,
y stands for the number of yards, s stands for the number of seconds, and k is really the constant of variation.This is because the athlete's distance travelled directly varies with the amount of time it takes.
Find k using the given values:
y=kx,
10 = k(6)
k = 10/6
k = 5/3
As a result, the equation for the maximum number of yards per second is y = 5/3 s.
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Need help please ?!!!
Answers
Answer:
should be C. No, there are no y-values that have more than one x-value
but if i'm wrong let me know!
For what value of k do the pair of linear equations KX − 4y 3 and 6x − 12y 9 have an infinite number of solutions?
Answers
The pair of linear equations KX − 4y = 3 and 6x − 12y = 9 have an infinite number of solutions when K = 0.
This can be shown by solving the two equations for K. Solving the first equation for K yields K = (4y/X) + 3. Substituting this into the second equation yields: 0 = (4y/X) + 3 - (12y/6x). Simplifying this yields 0 = (2y/X) - (9/6x). This equation simplifies to 0 = (2y - 9x)/X. Since the denominator of the right side of the equation is not equal to 0, the only way to get 0 = 0 is if the numerator is equal to 0 as well. This happens when 2y - 9x = 0. Since y and x are variables, the only way that this equation can be true for all values of x and y is if the coefficient of both of them is equal to 0. Thus, K = 0 is the only value for which this pair of linear equations has an infinite number of solutions.
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Does a hyperbola have an inverse?
Answers
If the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
What is a hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
A hyperbola is made up of two mirror images of one another that resemble two infinite bows.
These two sections are known as connected components or branches.
The hyperbola's equation is expressed as (y−k)2b2−(x−h)2a2=1.
The transverse axis is defined by b, the conjugate axis by a, and the center is defined by (h,k).
The section of a line that a hyperbola's vertices form.
The inverse of the hyperbola is a Limaçon with an inner loop if the circle's center is in one of the foci.
Therefore, if the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
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What is the slope of the line perpendicular to the line y = 3x+1
Answers
Answer:
-1/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
to find perpendicular you need to reverse the slope
How many solutions does the system of linear equations represented in the graph below have?
Answers
Answer:
b. one solution
Step-by-step explanation:
two lines are intersecting.
i hope this helps :)
Answer:
B. One Solution.
Step-by-step explanation:
Two linear lines are intersecting at one point. (One point = One solution).
A parabola has a maximum value of 4 at x = -1, a y-intercept of 3, and an x-intercept of 1.
Which graph matches the description?
Answers
Answer:
Step-by-step explanation:
The second graph is the right one. Note that when x = 1, y (the maximum) is 4, and that the x-intercepts are -3 and 1.
The x-intercepts are -3 and 1.
We have given,
A parabola has a maximum value of 4 at x = -1,
A y-intercept of 3, and an x-intercept of 1.
What is the maximum point of the graph?The maximum value of a graph is the point on the graph where the y-coordinate has the largest value.
A maximum graph is one that represents the largest value of the y-coordinate.
The second graph is the right one.
Note that when x = 1, y (the maximum) is 4,
and that , The x-intercepts are -3 and 1.
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HELP DUE IN 15 MINS!
Determine if the figure is a parallelogram. Justify your answer by picking the property that verifies it is a parallelogram or the one the property that it fails to meet the criteria for.
1. Is the figure a parallelogram? Yes or NO??
2. Why?? A. Both Diagonals Bisect Each Other, B. One set of Opposite Sides are parallel and congruent, C. Both sets of opposite sides are parallel, D. Both sets of opposite sides are congruent, E. Both Pairs of opposite angles are congruent.
Answers
Answer:
B and D both lead to failure. I have no idea how to pick which one is right. I guess D but don't be surprised if it is B. The question tries to do too much.
D
Step-by-step explanation:
No.
You need one more fact.
You can't pick A. Angles are not noted.
B: there is no mention of parallel sides. This is why the proposition fails to give a parallelogram.
C: you haven't got both sides being parallel. You haven't even got one set of opposite sides being parallel
D: This is probably another alternative. You don't know anything about 1 set of opposite sides.
E: No angles are marked.
The half-life of radium is 1620 years. If a laboratory has 12 grams of radium, how long will it take before it has 8 grams of radium left?
a 947.6 years
b 804.3 years
c 797.5 years
d 849.5 years
Answers
Step-by-step explanation:
A = A02^(-t/hl) ---> ln(A/A0) = -(t/hl)ln2
solving for t,
t = -(hl)ln(A/A0)/ln2
= -(1620 yrs)×ln(8/12)/ln2
= 947.6 yrs
974.6 years It will take before it has 8 grams of radium left,
Given that,
The half-life of radium is 1620 years
Laboratory has 12 grams of radium,
We have to determine,
How long will it take before it has 8 grams of radium left.
According to the question,
Laboratory has radium = 12 grams
Left radium = 8 grams
Half life of radium [tex]_t_\frac{1}{2}[/tex] = 1620 years.
[tex]N = N_o [\frac{1}{2}]^{n} \\\\8 = 12 [\frac{1}{2}] ^{n}\\\\\frac{8}{12} } =[ \frac{1}{2} ]^{n}\\\\ log2 - log3 = n( log1 - log2)\\\\0.30-0.47 = n (0 - 0.30)\\\\-0.17 = -0.30 n\\\\n = 0.56[/tex]
It will take before it has 8 grams of radium left,
[tex]t = n \times t_\frac{1}{2} \\\\t = 0.56 \times 1620\\\\t = 974.6 \ years[/tex]
Hence, 974.6 years It will take before it has 8 grams of radium left,
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√(4/7)² solve for points
Answers
Answer:
unless I'm confused this morning, the square root of a squared number is equal to the number, so:
4/7 would ne my answer
Step-by-step explanation:
The ratio of the measures of the three angle in a triangle is 15:8:13. Find the measure of the three angles.
Answers
Answer:
a=15x; b=8x; c=13x
180°=a+b+c=15x+8x+13x=36x
=> x=180÷36=5
=> a=15×5=75°; b=8×5=40°; c=13×5=65°
Identify the term(s), coefficient(s), and
constant(s) in the expression
52 + 6 + ya.
Term(s) Coefficient(s) Constant(s)
Answers
In the expression 52 + 6 + ya,
"ya" is a term,The coefficient of "ya" is 1,"52" and "6" are constants.Describe Term(s), Coefficient(s), Constant(s).The terms are the individual parts of the expression that are being added together. The coefficient is the numerical factor that is multiplied by a variable in a term, and the constant is a term that has no variable.
Any expression with variables will either add or delete one or more variables. Any one of a variety of numbers to represent a generic idea. An absolute number is a constant. A constant is a number, whereas a coefficient is a number that is "in front of" a variable.
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Please help
Find the value of x
Find the measure of the two marked angles
PLEASE ALSO FIND X
Answers
The value of x is 8 and the measure of the two marked angles is 60°.
Which angles are corresponding and adjacent?When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.
we know that ,
10x-20=7x+4 (it is corresponding opposite angle)
3x=24
x=8
the value of x is 8.
the measure of the two marked angles is 10*8-20= 80°-20°= 60°.
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help on hw NEED ASAP WILL SEND 90$
Answers
Answer:
what's the question
Step-by-step explanation:
what's the question and no it will be for free <3
Please help! will give brainlist if correct answer. NO LINKS
find the unknown side length x. round your answer to the nearest tenth
A) 21.5
B) 12.8
C) 58
D) 48
Answers
Answer:
58 Use pathagreon theorem
Step-by-step explanation:
a^2 + b^2 = c^2
Answer:
58
Step-by-step explanation:
The Pythagorean theorem says
[tex]40^{2} + 42^{2} = x^{2}[/tex]
[tex]x^{2}[/tex] = 1600 + 1764
= 3364
x = [tex]\sqrt{3364}[/tex] = 58
Which expression is equivalent to cos (62)?
Answers
Answer:
The trigonometric value is equal to cos 62° is sin 28°
5. QRST is a Rhombus. The diagonals intersect at point 0. mZROS = 7x1, mzSTO= 4x - 22, QT = 4y + 2, ST = 8y-8 R T S X= y = mZTOQ = mzQRS = Perimeter QRST=_
Answers
The value of x is 18.45°.
The value of y is 2.5 units.
The measure of the angle TOQ is 128.15°.
The measure of the angle QRS is 90°.
The perimeter of QRST is 36 units.
What is a rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
Given, m∠ROS = 7x - 1, m∠STO= 4x - 22.
We know the sum of linear pair of angles is 180°.
Therefore,
7x - 1 + 4x - 22 = 180.
11x = 203.
x = 203/11.
x = 18.45°.
Also given that line segment QT = 4y + 2 and ST = 8y - 8.
We know the sides of a rhombus are of equal length.
Therefore,
4y + 2 = 8y - 8.
- 4y = - 10.
4y = 10.
y = 10/4.
y = 2.5.
We know vertically opposite angles are equal hence m∠ROS = m∠TOQ.
= 7(18.45) - 1.
= 128.15°.
m∠QRS is 90° as all four interior angles of a rhombus are right angles.
The perimeter of QRST is 4×(QT).
= 4×(10 + 2).
= 4×12.
= 36 units.
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a) 3.2÷0.8 explain pls b) 7.5÷0.5 also explain pls
Answers
7.5 divided by 0.5 is the same as 7.5x2=15
Find the measure of the missing angles.
Answers
Answer:
Y:64
X:15
Hope this helps
pls give me brainliest