(01.02 HC)
Write each expression with a single rational exponent. Show each step of your process. Which expressions are equivalent? Justify your reasoning.
Answers
By applying radical, power and rational properties we have the following results after simplifying expressions:
[tex]x^{\frac{3}{4} }[/tex]x[tex]x^{\frac{11}{10} }[/tex]xHow to reduce radical and rational expressions into a single power expression with rational exponent
In this question we need to simplify four given expressions by using the following radical and power properties:
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex] (1)[tex]x^{m+n} = x^{m}\cdot x^{n}[/tex] (2)[tex]x^{m-n} = \frac{x^{m}}{x^{n}}[/tex] (3)[tex](x^{m})^{n} = x^{m\cdot n}[/tex] (4)Now we proceed to simplify each of the four expressions:
[tex]\sqrt[4]{x^{3}} = x^{3/4}[/tex][tex]\frac{1}{x^{-1}} = (x^{-1})^{-1} = x[/tex][tex]\sqrt[10]{x^{5}\cdot x^{4}\cdot x^{2}} = \sqrt[10]{x^{11}} = x^{\frac{11}{10} }[/tex][tex]x^{\frac{1}{3} }\cdot x^{\frac{1}{3} }\cdot x^{\frac{1}{3} } = x[/tex]To learn more on power functions: https://brainly.com/question/18719083
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Related Questions
What is 3^-2 in evaluate expression
Answers
The evaluate expression of [tex]3^{-2}[/tex] is 1/9
What is exponents and powers?Exponent refers to the number of times a number is used in a multiplication. Power can be defined as a number being multiplied by itself a specific number of times. Exponent is the number to which a number is raised so as to define its power as a whole expression.
Given: [tex]3^{-2}[/tex]
Now evaluate this we have to use
[tex]x^{-2}[/tex]= 1/x²
So,
[tex]3^{-2}[/tex] =1/3²
[tex]3^{-2}[/tex] =1/9
Hence, the evaluate form is 1/9.
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The line x = 2 is the axis of symmetry for a parabola. the focus of the parabola is located 3 units from the vertex. which could be the equation for the parabola? (x – 2)2 = 12(y – k) (x – h)2 = 12(y – 2) (x – 2)2 = 3(y – k) (x – h)2 = 3(y – 2)
Answers
The correct answer is (x - 2)² = 12(y - k) so option A is the correct answer.
What is a parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A point and a line are used in one definition of a parabola.
Given data is as follows:-
The line x = 2 is the axis of symmetry for a parabola.vertex of parabola = (2,0)The equation of the parabola will be given as:-
The focus of the parabola is located at 3 units from the vertex.
The equation of the parabola can be:-
y - k = 12 ( x - 2 )²
Therefore the correct answer is (x - 2)² = 12(y - k) so option A is the correct answer.
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The vector ab has a magnitude of 20 units and is parallel to the
vector 4i + 3j.
find ab.
Answers
The vector ab has a magnitude of 20 units and is parallel to the
vector 4i + 3j. Hence, The vector AB is 16i + 12j.
How to find the vector?If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
Given;
The vector ab has a magnitude of 20 units and is parallel to the
vector 4i + 3j.
magnitude
[tex]\sqrt{4^2 + 3^2} \\\\\sqrt{16 + 9} \\\\= 5[/tex]
Unit vector in direction of resultant = (4i + 3j) / 5
Vector of magnitude 20 unit in direction of the resultant
= 20 x (4i + 3j) / 5
= 4 x (4i + 3j)
= 16i + 12j
Hence, The vector AB is 16i + 12j.
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There were 20 pumpkins in a garden. One fourth of the pumpkins were too small, one tenth were too large, and one half were just the right size. The rest were not ripe yet. How many of the pumpkins were too small?
Answers
Answer: 5 pumpkins
Step-by-step explanation:
Since one-fourth of the pumpkins were too small, we will find one-fourth of 20 by dividing, then multiplying.
One fourth = [tex]\frac{1}{4}[/tex] = 0.25
20 * 0.25 = 5
5 pumpkins were too small.
Answer:
5 pumpkins
Step-by-step explanation:
It is said that one fourth of the pumpkins is too small, so:
[tex]\frac{pumpkins-that-are-too-small}{total-amount-of-pumpkins}=\frac{1}{4}[/tex]
This means one out of every four pumpkins is too small.
But we have a total of 20 pumpkins, not four, so we just need to multiply our real total amount of pumpkins with the ratio given and then we find the amount of pumpkins that are too small:
[tex]\frac{pumpkins-that-are-too-small}{total-amount-of-pumpkins}*total-amount-of-pumpkins[/tex]
[tex]=pumpkins-that-are-too-small[/tex]
So; filling in the numbers:
[tex]\frac{1}{4} *20 = \frac{1*20}{4}=\frac{20}{4}=5[/tex]
someone help me out on this asap please and thank you!
Answers
Answer:
The answer is D
Step-by-step explanation:
If you minus 8 for x on (2,3) and plus 2 to the y on (2,3) you get (-6,5).
A student ran a distance of miles each day for 5 days. Then the student ran a distance of 44 miles each day for the next 5 days.
What was the total distance in miles the student ran during these 10 days?
F 23 mi
G 38 3/4
H 42 1/2
J 35 mi
Answers
Answer:
its 38 3/4
Step-by-step explanation:
d₂ = distance covered each day in the next 5 days From the question, Given: d₁ = 3 miles = 7/2 miles T = 5 Days d₂ = 4 miles = 17/4 miles Substitute these values into equation 1 D = [ (7/2)×5]+ [ (17/4)×5] D = 17.5+21.25 D = 38.75 miles
reflection across y = x
Answers
Answer:Reflecting over y=x means [tex](x, y) \longrightarrow (y,x)[/tex]. So, the coordinates of the image are:
[tex]V(-3, 0) \longrightarrow V'(0,-3)\\\\W(-1,0) \longrightarrow W'(0, -1)\\\\U(-2,-5) \longrightarrow U'(-5,-2)\\\\X(3,-3) \longrightarrow X'(-3, 3)[/tex]
Are the slats next to each other parallel?
Pls explain
Answers
The slats next to each other parallel to each other. This is further explained below.
What are slats?Generally, slats is simply defined as a very thin plank of wood, plastic, or metal used to make a fence or a Venetian blind.
The slats are parallel to each other
Since the total, the Interior angle of one side is 180 In and each alternative interior angle is identical in each pair
130 + 50 = 180
130 = All interior angles of slate
50 = All exterior angles of state.
states are parallel next to each other.
In conclusion, states are parallel next to each other.
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A group of people were asked which of three ice cream flavors they prefer. The results are shown in the table.
Ages Vanilla Strawberry Chocolate
20 years and younger 8 10 6
Over 20 years 8 6 12
What is the probability of a person being over 20 years old and preferring strawberry ice cream?
6%
10%
12%
16%
Answers
Using it's concept, it is found that the probability of a person being over 20 years old and preferring strawberry ice cream is of 12%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 8 + 10 + 6 + 8 + 6 + 12 = 50 people, and of those, 6 are over 20 years old and prefer strawberry ice cream, hence the probability is given by:
p = 6/50 = 0.12 = 12%.
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Answer:
12%
Step-by-step explanation:
I got it correct on test
please give person above me brainiest
Which expression is equivalent to StartRoot 128 x Superscript 8 Baseline y cubed z Superscript 9 Baseline EndRoot? Assume y greater-than-or-equal-to 0 and z greater-than-or-equal-to 1
Answers
The expression √(128x⁸y³z⁹) is equivalent to the expression 8x⁴yz⁴ √(2yz). Then the correct option is C.
The missing options are given below.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
⇒ √(128x⁸y³z⁹)
Then the expression is given below.
⇒ √[(64 × 2)(x⁴)²(y²y)(z⁸z)]
⇒ 8x⁴yz⁴ √(2yz)
Then the correct option is C.
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Find the area of a circle with radius, r = 66cm. give your answer rounded to 3 sf.
Answers
The area of a circle with a radius of 66 is 68.45.1cm^2.
We have given that,
The area of a circle with a radius, r = 66cm.
What is the formula for the area of the circle?
[tex]A=\pi r^2[/tex]
Use the given value in the above formula
[tex]A=\pi (66)^2\\A=6845.1cm^2[/tex]
The area of a circle with a radius of 66 is 68.45.1cm^2.
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PLEASEEEEEEEEEEEEEEEEEEEEEE Edgar rolls two six-sided number cubes. What is the probability that he rolls a 2 on
the first cube and a number less than 5 on the second cube? Use the diagram 1of
the sample space to help you.
a. 3/36=1/12
b. 2/36=1/18
c. 4/36=1/9
d. 7/36
Answers
Answer:
The probability that he rolls a sum of 9 given the sample space is . 9/36, or 1/4.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that he rolls a sum of 9 = cubes that have a sum of 9 / total number of cubes
9/36 = 1/4
Tell whether the system has no solution, one solution, or infinitely many solutions.
y = 3 x – 5
y = 3 x + 5
Answers
Step-by-step explanation:
y = 3x - 5
y = 3x + 5
a solution to this means, there is at list one value of x, for which both equations deliver the same y.
to find this we are saying both y are equal and solve for x :
3x - 5 = 3x + 5
-5 = 5
that is not true in any case and for any values of x.
therefore, there is no solution.
graphically you can imagine :
both functions are lines with the same slope or inclination. so, they are parallel. but have an offset from each other.
parallel lines will never cross (but they need a crossing point to have a common solution).
so, again, no solution.
Find the domain of the following piecewise function
Answers
The domain of the function will be [-4, 6). Then the correct option is B.
The complete question is attached below.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
[tex]f(x) = \left\{\begin{matrix}x+4, & if & -4\leq x < 3 \\\\2x-1, & if & 3 \leq x < 6 \\\end{matrix}\right.[/tex]
Then the domain of the function will be [-4, 6).
Then the correct option is B.
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A particle travels along a straight line, in a given direction, with constant acceleration. At instant t0 = 0, the magnitude of its velocity is v0 = 5 m/s; at time t = 10s, v = 25m/s. determine:
a) The type of motion of the particle
b) Acceleration
c) The function of velocity in relation to time
d) The velocity at time t = 8.0 s
e) The instant of time in which the velocity module is v = 15m/s
Answers
a) The motion described by the particle is undoubtedly a uniformly accelerated rectilinear motion, since the trajectory is rectilinear and the acceleration is constant.
b) In order to calculate the acceleration, we must apply the formula mentioned above, in such a way that the acceleration gives us:
[tex]\boldsymbol{a=\dfrac{v-v_{o}}{t-t_{o} }=\dfrac{25-5}{10-0 }=\dfrac{20}{10}=2 \ m/s^2 }[/tex]
Our acceleration is 2 meters per second squared.
c) We are asked to calculate the function of velocity in relation to time, we simply substitute in the formula.
[tex]\boldsymbol{v=v0+at }\\\boldsymbol{v=2+5t }[/tex]
Very easy!!.
d) To know what speed the particle will have at the instant of t = 8s, it is enough to substitute the value of “t” in the previous formula.
[tex]\boldsymbol{v=5+2(8)=5+16=21 \ m/s }[/tex]
So the speed at time t = 8s is 21 m/s²
e) In this case we are asked to determine at what instant of time the particle will have a speed of 15 m/s, we replace this value in the formula, simply clearing the variable "t", that is:
[tex]\boldsymbol{v=v_{0}+at }[/tex]
Clearing "t"
[tex]\boldsymbol{t=\dfrac{v-v_{o}}{a} }[/tex]
Substituting the speed value
[tex]\boldsymbol{t=\dfrac{v-v_{o}}{a}=\dfrac{15-5}{2}=\dfrac{10}{2}=5 \ seg }[/tex]
That is to say that when the particle has a speed of 15 m/s, it will happen exactly at 5 seconds.
Jeremy is shopping online for skating equipment. He buys a longboard complete with trucks and wheels for $146.25. At checkout, Jeremy gets a discount of $21 on his purchase. The final amount that Jeremy will be billed is $
.
Answers
Answer:
$125.21
Step-by-step explanation:
Select the correct answer.
Which data set has the widest spread?
A.
data set A: 3, 1, 2, 6, 7, 2, 5
B.
data set B: 4, 9, 4, 5, 3, 6, 8
C.
data set C: 1, 4, 6, 5, 7, 8, 5
D.
data set D: 4, 3, 4, 7, 2, 3, 1
E.
data set E: 5, 1, 4, 2, 6, 9, 2
Answers
Answer:
E.
data set E: 5, 1, 4, 2, 6, 9, 2
Step-by-step explanation:
Which graph represents exponential decay?
80
형
40
20
-
O
2
x
80
60
LI
1401
20
1 2 3
2 3
80
60
40
20
x
80
60
40
20
2 3
Answers
Answer:
(d) -- see attached
Step-by-step explanation:
A graph that shows exponential decay is one that tends toward a horizontal asymptote as x gets large.
__
A basic (parent) exponential decay curve is concave upward and tends toward zero as x gets large. The fractional change in any interval is the same as for any other interval of equal size. The curve attached decreases by a factor of 2 when x increases by 1.
Mrs.Butter works at HEB. Last month she sold more than 2 more than 10 min times the number of apples that she sold this month. Mrs.Butter sold a total of 200 apples over the last 2 months.How many apples did she sell?
Answers
Answer:
182 apples
Step-by-step explanation:
x+2 times 10= 200 apples sold this month
×+2=200/10
×=18
200-18=182 apples
A 15 foot ladder is leaning against a wall of a house. The base of the ladder is pulled away from the wall at a rate of 2ft/sec. Find the rate at which the area of the triangle is changing when the base of the ladder is 9ft from the wall
Answers
The rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall will be the negative 8/3.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A 15-foot ladder is leaning against a wall of a house.
The base of the ladder is pulled away from the wall at a rate of 2ft/sec.
Then the equation will be
x² + y² = 15²
x² + y² = 225
Differentiate with respect to time. Then we have
2x (2) + 2yy' = 0
y' = -2x / y
Then the rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall will be
Then the value of x will be
x² + 9² = 15²
x² + 81 = 225
x² = 144
x = 12 ft
Then the rate will be
y' = -2x / y
y' = – 2 × 12 / 9
y' = – 8/3
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Give the slope of y+ 2 = 3(x-7) and a point on the line.
A. The slope is 2 and (7, 3) is on the line.
B. The slope is 3 and (-7, 2) is on the line.
C. The slope is 3 and (7, -2) is on the line.
D. The slope is 7 and (3, 2) is on the line.
Answers
Answer:
C. The slope is 3 and the point (7,-2) is on the line.
A rectangle has a length of 12.4 yards and a width of 13.6 yards.
What is the area of the rectangle?
Enter your answer as a decimal in the box.
yd²
Answers
Answer: Your answer is 168.64
Step-by-step explanation: I did the k12 quiz, here's proof
Hope it helped :D
How much will you have saved after 6 years by contributing 1200 at the end of each year if you expect to earn 11 % on the same investment
Answers
Answer:
2244.50
Step-by-step explanation:
A= P(1+r/n)^nt
A= 1200(1+(.11/1))^6
Answer:
you have saved $7332 after 6 years
Step-by-step explanation:
11% of 1200, 1200 x 0.11 = 132
initial investment after 6 years: 1200 x 6 = 7200
initial + earn: 7200 + 132 = 7332
need in depth explanation please
Answers
Answer:
Y = 18
X = 9
Step-by-step explanation:
all the steps are in the picture. comment if you have any doubts.
PLEASE HELP ME I AM REALLY BAD AT WORD PROBLEMS!
A website offers free shipping to customers who order at least $75 dollars worth of merchandise. Della is ordering 2 flashlights at $10.00 each and plans to order packs of $5.00 batteries until her total is at least $75. Which statement best describes how many packs of batteries she must order to qualify for free shipping?
Answers
Answer:
Della must buy 11 packs of batteries to get free shipping
if an object is dropped from a height of 38 feet, the function h(t) = -16t square + 38 gives the height of the object after t seconds. Graph the function.
Answers
The graph of the quadratic equation can be seen below.
How to graph the quadratic equation?
Here we have a quadratic equation that represents the height:
[tex]h(t) = -16t^2 + 38[/tex]
Where this represents the height in ft.
This is just a quadratic function, so to graph it we can just get some points and then connect them, by evaluating the function we will get:
[tex]h(0) = -16*0^2 + 38 = 38\\\\h(1) = -16*1^1 + 38 = 22\\\\h(2) = -16*1.5 + 38 = 2[/tex]
So we have the 3 points (0, 38), (1, 22) and (2, 2), we graph them and connect them with a parabola. The graph can be seen below.
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Use the following regular polygon to answer the question.
E
F
D
.0
G
A
B
©2019 Strong Mind. Created using GeoGebra.
What is the angle of rotational symmetry for the figure?
C
Answers
(8x^2 - 3x +3) + (2x^2 -4x +6)
Answers
if f(x)=3/x+2- √x-3
f(19)=
Answers
Answer: f(19) = 29/7.
Step-by-step explanation: 1. Replace x with 19 in the function. This gives you:
[tex]\frac{3}{19+2} - \sqrt{19-3}[/tex]
2. Reduce these items to get:
[tex]\frac{3}{21} - \sqrt{16} \\[/tex]
3. Reduce again:
[tex]\frac{1}{7} + 4 = \frac{1}{7}+\frac{28}{7} = \frac{29}{7}[/tex]
4. However, be cautious. The full answer for this has a negative component ([tex]\frac{-27}{7}[/tex]) because the square root of 16 can be either 4 or -4.
identify an equation in point slope form for the line parallel to y=-2/8x+8 that passes through (4,-5)
Answers
Step-by-step explanation:
the point-slope form is
y - y1 = m(x - x1)
where (x1, y1) is a point on the line.
m is the slope of the line, which is always (in any form) the factor of x.
the parallel line has -2/8 as factor of x, which is therefore also the slope of our new line (after all, it has to be parallel, so it must have the same slope).
so, we have
y + 5 = -2/8 × (x - 4)
which can be simplified, of course, to
y + 5 = -1/4 × (x - 4)
