(1 point) The expression 64g4y2 64gʻy2 equals kg"ys where r, the exponent of g, is: and s, the exponent of y, is: and k, the leading coefficient is:
Answers
We are asked to find the final expression in exponent for, of the product of two radical expressions as shown below:
We will be addressing each factor at a time, first in the cubic root, and second in the square root.
Cubic root:
notice that the pure number (64) can be written as the perfect cube of the number 4 since 4^3 = 64. That means that a factor 4 will come out of the cubic root, and no factor 4 will be left in the root.
Now we are going to address the variables g and y which are inside the root, and try to find if they contain any perfect cube expression (perfect cubes will cancel out of the cubic root simplifying then the notation).
We notic that g^4 can be written as g^3 times g, so g^3 will come out of the cubic root as "g", and a factor "g" would be left inside the cubic root. Similarly, the factor y^2 cannot get out of the cubic root because it doesn't have a perfect cube in it.
We are then left with the following expression:
[tex]4g\sqrt[3]{g\cdot y^2}[/tex]Now, we recall the property of fractional exponents associated with roots of a factor:
[tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]Using this, the cubic root can be expressed as fractional exponents, as we show below:
[tex]4g\sqrt[3]{g\cdot y^2}=4g\cdot g^{\frac{1}{3}}\cdot y^{\frac{2}{3}}=4g^{\frac{4}{3}}\cdot y^{\frac{2}{3}}[/tex]Now we proceed to simplify the expression with the square root. This is much simpler, since all factor inside can be written as perfect squares:
64 = 8^2
g^4 = (g^2)^2 (the double square of g)
y^2 is already a perfect square.
Therefore, the square root is simplified entirely and we are left with the following factors:
8 g^2 y
Now we combine via the multiplication what we found for the cubic root and what we found for the square root:
[tex](4\cdot g^{\frac{4}{3}}\cdot y^{\frac{2}{3}})\cdot(8\cdot g^2\cdot y)=32\cdot g^{\frac{10}{3}}\cdot y^{\frac{5}{3}}[/tex]Therefore the power (r) of the factor g is the fraction: 10/3
The power (s) of the factor y is the fraction 5/3
and the constant number "k" is 32.
Related Questions
A ship leaves port on a bearing of 34.0 degrees and travels 10.4 mi. The ship then turns due east and travels 3.9 mi. How far is the ship from port, and what is its bearing from port?
Answers
→
r
=
13.5
mi
, at a bearing angle of
50.4
o
Explanation:
We're asked to find the total displacement, both the magnitude and direction, of the ship after it leaves the port with the given conditions.
First, I'll explain what a bearing is.
A bearing is NOT a regular angle measure; normally, angles are measured anticlockwise from the positive
x
-axis, but bearing angles are measured clockwise from the positive
y
-axis.
Therefore, a bearing of
34.0
o
indicates that this is an angle
90.0
o
−
34.0
o
=
56.0
o
measured normally. We'll use this angle in our calculations.
We're given that the first displacement is
10.4
mi
at an angle of
56.0
o
(as calculated earlier). Let's split this up into its components:
x
1
=
10.4
cos
56.0
o
=
5.82
m
y
1
=
10.4
sin
56.0
o
=
8.62
m
Our second displacement is a simple
4.6
mi
due east, that is, the positive
x
-direction. The components are thus
x
2
=
4.6
mi
y
2
=
0
mi
To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:
Δ
x
=
x
1
+
x
2
=
5.82
mi
+
4.6
mi
=
10.42
mi
Δ
y
=
y
1
+
y
2
=
8.62
mi
+
0
mi
=
8.62
mi
r
=
√
(
x
total
)
2
+
(
y
total
)
2
=
√
(
10.42
mi
)
2
+
(
8.62
mi
)
2
=
13.5
mi
The direction of the displacement vector is given by
tan
θ
=
Δ
y
Δ
x
so the angle is then
θ
=
arctan
(
Δ
y
Δ
x
)
=
arctan
(
8.62
mi
10.42
mi
)
=
39.6
o
The question asked for the bearing angle, which is just this angle subtracted from
90
o
:
Bearing angle
=
90
o
−
39.6
o
=
50.4
o
24 Finding Cylinder Dimensions < Next > 14.2: What's the Dimension? Volume formula for cylinder V=12h The volume of this cylinder with radius 5 units is 50T cubic units. Volume=undefined i cubic unit What does the height of this cylinder have to be? Explain how you know. radius=1.5 unit height:4 unit Submit and Explain height slid radius slid Igal DIN-
Answers
Explanation:
The volume formula is:
[tex]V=\pi r^2h[/tex]We know that the radius is r = 5 and the volume is V = 50pi. We have to replace these values into the formula above and solve for h:
[tex]\begin{gathered} 50\pi=\pi5^2h \\ 50\pi=25\pi h \\ h=\frac{50\pi}{25\pi}=\frac{50}{25}=2 \end{gathered}[/tex]Answer:
h = 2
HELP PLEASE
Review the objective below, and rate your knowledge of the topic from 0-4, with 0
being the lowest rating and 4 being the highest rating.
"I can factor an expression using the GCF."
0
1
2
3
4
Answers
Answer:
Step-by-step explanation:
Comment
Well my response is, I know how it is done and most of the time I get it right, but mistakes make me give myself about a 3.4.
I hope this answers your question. It will likely be taken down.
If f(x) = 2x + 1, find f(1).
Answers
Answer: 3
Step-by-step explanation:
if x = 1 then 2(1) +1 is 2+1 which is 3
f(1) means that in the place of x you plug in 1 and simplify.
[tex]f(1) = 2(1) + 1 \\ f(1) = 2 + 1 \\ f(1) = 3[/tex]
ATTACHED IS THE SOLUTION
A box contains 13 large marbles and 20 small marbles. Each marble is either green or white. 5 of the large marbles are green, and 13 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
The probability of selecting a small or white marble is 10/13
Step-by-step explanation:
The total number of marbles is 15 + 11 = 26 marbles
The probability that we want to calculate is if the marble selected is small or white.
So we need to find the number of small marbles as well as the number of white marbles
We can construct a table to see the distribution of the marbles. Please check the attachment for this.
From the table , we can see that there are 11 small marbles and a total of 9 white marbles
The probability of selecting a white marble is;
number of white marbles/total number of marbles = 9/26
The probability of selecting a small marble will be ;
number of small marbles/total number of marbles = 11/26
In probability, whenever we have or, we tend to add
So therefore, the probability of selecting a white or small marble = Probability of selecting a white marble + Probability of selecting a small marble
Mathematically, that would be 9/26 + 11/26 = 20/26
So the probability is 10/13
A shipping container will be used to transport several 150-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 26500 kilograms. Other shipments weighing 12100 kilograms have already been loaded into the container. Which inequality can be used to determine x, the greatest number of 150-kilogram crates that can be loaded onto the shipping container?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given values
[tex]\begin{gathered} \text{constant + Variable = Output} \\ \text{constant}=12100 \\ \text{Variable}=x \\ \text{Output}=\text{greatest value} \end{gathered}[/tex]STEP 2: Get the inequality
[tex]\begin{gathered} \text{ If }26500kg\text{ is the greatest value, this means that;} \\ \text{the addition of constant and variable must be less than or equal to 26500} \\ So\text{ we have;} \\ \\ 150x+12100\le26500 \end{gathered}[/tex]Hence, the answer is:
[tex]150x+12100\le26500[/tex]A teacher records the cost in dollars, y, of purchasing and maintaining a classroom aquarium for x months. Theequation shown models the data.y = 48x + 250What does 250 represent in this situation?A the monthly cost of the aquariumB the purchase cost of the aquariumC the total cost of the aquarium after x monthsD the cost of maintaining the aquarium for x months
Answers
B the purchase cost of the aquarium
Explanation
we have the equation
[tex]y=48x+250[/tex]this is a linear equation in the form
[tex]\begin{gathered} y=\text{ mx+b} \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]hence
[tex]\begin{gathered} y=48x+250\rightarrow y=mx+b \\ \text{slope}=48 \\ y-\text{intercept}=250 \end{gathered}[/tex]so, if we have the sentence
the cost in dollars, y, of purchasing and maintaining a classroom aquarium for x months
let
cost in dollars = y
as x is the variable, let x for the variable in the text, in this case, what changes is the number of months,so
number of months= x
the factor of x ( 48), is the value for the mainting the classroom ( as we can see it depends on the number of months , x)
so
the monthly cost of the aquarium=48
finally , we have 250, this values is a constant, it does not depend on the number of months, so it is
the purchase cost of the aquarium=250
so,the answer is
B the purchase cost of the aquarium
I hope this helps you
A rectangle has a length that is 7 less than 4 times the width. The perimeter is 100 in. Find the length and the width.
Answers
Answer:
136 m
Step-by-step explanation:
Let w = the width of the rectangular field.
Let l = the length of the rectangular field.
The formula for the perimeter P of the rectangular field is:
P = 2w + 2l
Since the length l is 7 m less than 4 times the width w, then we can write the following equation that relates l and w:
l = 4w - 7 m
Since l = 4w - 7 and it's given that perimeter P = 136 m, then we can substitute this information into the perimeter formula as follows:
P = 2w + 2l
136 m = 2w + 2(4w - 7 m)
136 m = 2w + 2(4w) - 2(7 m)
136 m = 2w + 8w - 14 m
136 m + 14m = 10w - 14 m + 14 m
150 m = 10w + 0
10w = 150 m
(10w)/10 = 150 m/10
(10/10)w = 150 m/10
(1)w = 15 m
w = 15 m
Therefore, l = 4w - 7 m
l = 4(15 m) - 7 m
l = 60 m - 7m
l = 53 m
CHECK:
P = 2w + 2l
136 m = 2(15 m) + 2(53 m)
136 m = 30 m + 106 m
136 m = 136 m
jeanscah estimates that 475 songs will fit on her iphone.the actual amount of the songs that fit Is 380.find the percent error.
Answers
Data:
Estimate: E= 475 songs
Actual amount: A=380
To find the percent of error you use the next formula:
[tex]\text{error}=\frac{\mleft|E-A\mright|}{A}\cdot100[/tex][tex]\begin{gathered} \text{error}=\frac{\mleft|475-380\mright|}{380}\cdot100 \\ \text{error}=\frac{\mleft|95\mright|}{380}\cdot100 \\ \text{error}=0.25\cdot100 \\ \text{error}=25 \end{gathered}[/tex]Then, the percent error is 25%Please help on how I would start these
Answers
Answer:
a) -15 (b)25/2 (c)-31.2 (d)15
Step-by-step explanation:
(a)f(-24)=5/6×24+15
-15
(b)f(9)=5/6×9+15
25/2
(c)f(x)=5/6x+15
5/6x+15=-11
5x+90=-66
5x=-66-90
5x=-156
5x/5=-156/5
x=-31.2
(d)f(0)=5/6×0+15
0+15
15
Solve the systems of equations Y= 6x+35Y= 9x+14X=Y=
Answers
y = 6x + 35
y = 9x + 14
Combining these equations, we get:
6x + 35 = 9x + 14
35 - 14 = 9x - 6x
21 = 3x
21/3 = x
x = 7
Substituting this result in the first equation:
y = 6*7 + 35
y = 42 + 35
y = 77
7x + 4 + 8x + 6. equals
Answers
Answer: [tex]15x + 10[/tex]
Step-by-step explanation:
[tex]7x + 4 + 8x + 6[/tex]
First you have to combine like terms. You combine like terms by adding them so u would add 7x and 8x and get 15x. Then u would add 4 and 6 and get 10.
[tex]15x + 10[/tex]
15x + 10 would be your final answer in simplest form.
The side of a square is represented by (s - 4);1. Write an expression that could represent the perimeter of the square.2. If the perimeter of the square is no more than 80 ft, what is the maximum value of s?
Answers
We have a square with sides (s-4).
The perimeter of a square is 4 times the length of the side, so we can write:
[tex]P=4\cdot(s-4)=4s-16[/tex]If P is no more than 80 ft, we can find the maximum value for s as:
[tex]\begin{gathered} P<80 \\ 4s-16<80 \\ 4s<80+16 \\ 4s<96 \\ s<\frac{96}{4} \\ s<24 \end{gathered}[/tex]Answer:
1) The perimeter is P = 4s-16
2) The maximum value for s, if the perimeter is no more than 80 ft, is 24 ft.
The height of a tree increases as time passes. Your friend says that time is the dependent variable because size depends on time. Is your friend correct?
Answers
Given that the height of a tree increases as time passes.
Your friend says that is dependent because size deemds on time.
Leet's determine if your friend is correct.
Here, since the height of a tree increases as time passes, the height of the tree depends on the time.
Hence, size is the dependent variable while time is the independent variable.
Therefore, your friend is NOT correct.
ANSWER:
No, your friend is NOT correct.
Select the correct answer.
What is the simplest form of this expression?
x-3/x-1 + 6/x-3
A. x²+12x+15 / (x-1)(x-3)
B. x²+3 / (x-1)(x-3)
C. x+3 / (x-1)(x-3)
D. x²-6x+3 / (x-1)(x-3)
Answers
x² + 3 / (x-1)(x-3) is simplest form of the given expression
What will the expression be?Given: x-3/x-1 + 6/x-3
First, find the LCM of x-1 and x-3. The LCM is c
(x-3)(x-3) + 6(x-1) / (x-1)(x-3)
Remove the bracket of the numerator
x² - 6x + 9 + 6x - 6 / (x-1)(x-3)
Add and subtract like terms
x² + 3 / (x-1)(x-3)
Therefore, the expression has the simplest form of x² + 3 / (x-1)(x-3). This shows the concept of expression.
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influence of education on south african economy
Answers
Children's academic success, literacy, numeracy, and scientific knowledge are all directly impacted by their schooling. A child's education in school helps them learn all the fundamentals that will benefit them in the future.
Explain about influence of education on south African economy?The study confirmed that reducing the proportion of people with lower levels of education, as in primary school or no education at all, has a positive effect on economic growth. In that regard, South Africa has done a good job of lowering the proportion of people with Grade 7 education or less to under 20%.Families with educated members have a better probability of improving their living situations than families without educated members. The working class, their families, and their communities are all assured of financial stability when a stable income is supplied to them.Children in South Africa struggle to enter the workforce without even a basic education, making it impossible for them to escape poverty. Education fosters the development of critical abilities like effective communication and social skills in addition to teaching fundamental skills like reading and writing.To learn more about education on south African refer to:
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0.04 divided by 0.628
Answers
Answer:
0.1 also 0.0636942675
A corporation reported profits of approximately 3,500 million with approximately 67000 million in revenues. Compare the profit to revenue by writing a fraction in lowest terms
Answers
The profit for te corporation is 235,00 million.
The revenue for the corporation is 6700e million.
ExplanationTo determine th fractio in lowest terms for thr e profit and revenue is
[tex]\begin{gathered} \frac{3500}{67000}=\frac{35}{670} \\ \frac{35}{670}=\frac{7}{134} \end{gathered}[/tex]AnswerHencenthe answer s [tex]\frac{7}{134}[/tex]We are working on integers, and I just don’t get the concept, if you could do an EXAMPLE problem for me that would be great I understandan this I just need further instruction
Answers
The history of integers begins with the natural numbers (1,2,3,...), which are also called the counting numbers. They arise naturally by the need of counting things. But there is a problem. "There is a missing number". If you have a number n of things and you subtract all of them, what remains? Intuitively, it must be a number, a number representing nothing (to have nothing). This is the origin of zero.
Now, as time passes, the man began to do trades and arose the money. This leads to a problem. Other numbers are missing now. How do you express how much money you owe someone? counting numbers are not useful here, for they mean "the money you have". Th
7 Write the numbers in order from
GREATEST to LEAST.
-71.1 -71 1/2
Answers
-71.1, then -71 1/2
When referring to negatives, the number closer to the origin is the greatest. -71 1/2 = -71.5, so it is the least.
Find the midpoint of AB given A (-3,-5) and B (-1,8)
Answers
A: (-3,-5)
B: (-1,8)
To find the midpoint we have to add each coordinate and divide by 2:
Midpoint: (-3-1)/2 , (-5+8)/2 = -4/2, 3/2 = -2,1.5
Midpoint: (-2, 1.5)
the equilateral triangle has a side length of 14. find the area of the triangle. round to the nearest tenth.
Answers
Answer: 85
To solve this, we need to calculate the height of the triangle. To do this, we divide the triangle verticaly, in two right triangles.
So, we have the hypotenuse of the two smaller triangles is 14. The short leg is half the side of the big triangle: 14/2=7 and the long leg is the height of the triangle and what we want to know.
By the pythagorean theorem:
[tex]14^2=7^2+x^2[/tex][tex]x=\sqrt[]{14^2-7^2}=7\sqrt[]{3}[/tex]And now we use the formula for the area of a triangle:
[tex]A=\frac{b\cdot h}{2}=\frac{7\cdot7\sqrt[]{3}}{2}=\frac{49\sqrt[]{3}}{2}[/tex]This is the area of each of the smaller triangles. To get the area of the big triangle, we add up the two smaller areas:
[tex]\frac{49\sqrt[]{3}}{2}+\frac{49\sqrt[]{3}}{2}=49\sqrt[]{3}[/tex]rounded to the nearest tenth is 85
Astronomers oftenmeasure largedistances usingastronomical units(AU) where 1 AU isthe average distancefrom Earth to theSun. In the image, drepresents thedistance from a starto the Sun. Using atechnique called"stellar parallax,astronomers determinedO is 0.00001389degrees.1. How faraway isthe starfrom theSun inastronomical units?Showyourreasoning.2. Write anexpression tocalculated for anystar.
Answers
In the given right triangle of the figure
we have that
sin(O)=1/d ----> by the opposite side divided by the hypotenuse in a right triangle
solve for d
d=1/sin(O)
[tex]d=\frac{1}{sin\left(0.00001389^o\right?}[/tex]d=4,124,966.13 AU -----> two decimal places
the expression to calculate d for any star is equal to
[tex]d=\frac{1}{sin\left(O\right)}[/tex]Complete sheet given
Answers
Answer:
20 hyenas
Step-by-step explanation:
locate number of lions 28 on the horizontal axis , then go up vertically to meet the line, then cross horizontally to meet the vertical axis at 20
that is 20 hyenas are contained
the first step in determining the solution to the system of equations, y=-x² - 4x-3 and y= 2x + 5, algebraically isthe two equations equal as -x² - 4x - 3= 2x + 5. What is the next step?et y = 0 in y=-x2 - 4x-3.actor each side of the equation.se substitution to create a one-variable equation.ombine like terms onto one side of the equation.
Answers
Given -
Equations:
y = -x² - 4x -3 and y = 2x + 5
To Find -
Next step =?
Step-by-Step Explanation -
We know first step:
-x² - 4x - 3= 2x + 5
-x² - 4x - 3 - 2x - 5 = 0
-x² - 6x - 8 = 0
-(x² + 6x + 8) = 0
x² + 6x + 8 = 0
x² + 2x + 4x + 8 = 0
x(x+2) +4(x +2) = 0
(x+4)(x+2) = 0
So,
x = -4 or x = -2
So,
The next step is to combine like terms onto one side of the equation.
Final Answer -
Option (d)
Combine like terms onto one side of the equation
Estimate the average rate of change from x = 4 to x = 7.
Answers
The average rate of change of the function from x = 4 to x = 7 is: -1/3.
How to Estimate the Average Rate of Change of a Function?The formula used to estimate the average rate of change of a function is given as:
f(b) - f(a) / b - a.
Given the function as shown in the diagram below, we are required to find the average rate of change of the function within the interval, x = 4 to x = 7, therefore:
a = 4
b = 7
f(a) = f(4) = 4
f(b) = f(7) = 3
To find the average rate of change of the given function for the interval of x = 4 to 7, substitute the above stated values into the formula for the average rate of change, f(b) - f(a) / b - a:
Average rate of change = 3 - 4 / 7 - 4
Average rate of change = -1/3
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What is the equation of a circle with radius 2 and center (3, 1)? (x - 3)2 – (y - 1)2 = 4 O (c - 3)2 + (y - 1)2 = 4 (x ) O (x + 3)2 + (y + 1)2 = 4 (x - 3)² + (y - 1)2 = 2
Answers
Given the radius of a circle as r = 2 and centre = (3,1)
We want to find the equation
Solution
First, the equation of a circle centre (a,b) and radius r is given by
[tex](x-a)^2+(y-b)^2=r^2[/tex]From the question
[tex]\begin{gathered} a=3 \\ b=1 \\ r=2 \end{gathered}[/tex]We put the parameters into the equation ans simplify
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-3)^2+(y-1)^2=2^2 \\ (x-3)^2+(y-1)^2=4 \end{gathered}[/tex]Therefore the correct option is Option B
Federal standards require that the angle ramp for the wheel chair to be less than 5 degrees, if the length of the ramp is 20 feet and vertical rise is 15 inches, does it meet federal standards?
Answers
ANSWER:
The ramp does meet federal standards
STEP-BY-STEP EXPLANATION:
The first thing we must do is sketch the situation of the statement in order to better understand it.
Now, we need to convert feet to inches, so they are the same units. We know that 1 foot is equal to 12 inches, so:
1 ft = 12 in
20 ft = 20 ft *12 in/ft = 240 in
Now, we calculate the angle of the ramp by means of the trigonometric sine function that relates the side opposite the angle to the hypotenuse.
Therefore:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{ opposite = 15} \\ \text{ hypotenuse = 240} \\ \text{ Replacing} \\ \sin \theta=\frac{15}{240} \\ \theta=\arcsin \mleft(\frac{15}{240}\mright) \\ \theta=3.58\text{\degree} \end{gathered}[/tex]The value of the angle is 3.58°, which is less than 5°, which means that it meets federal standards.
Please help solve the problem.
-2/5x+3=2/3x+1/3
Answers
Answer: -6/5=2/9
Step-by-step explanation:
Describe a series of transformations Matt can perform to device if the two windows are congruent
Answers
The three transformations—rotations, reflections, and translations—can be combined to produce congruent shapes. The truth is that any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.
Explain transformations.A point, line, or geometric figure has four different transformations that can be applied to alter its appearance. While the term "Image" refers to the position and final shape of the object, "Pre-Image" refers to the object's shape before transformation.
Given Information
The size and shape of the figures are preserved during stiff transformations, as we already know (reflections, translations, and rotations). Always in harmony with one another is the pre-image.
These transformational skills are all possessed by Matt:
Reflection
The reason a reflection maintains its original form Similar spots from the pre-image to the image remain apart from the line of reflection.
The transformation of rotations into congruence
Any rotating figure will twist. Although it is the same size and shape as before, the figure appears to have toppled over. A clock is a perfect example of how rotation works in real life. A clock's connecting arms turn around its axis every hour or every day. A rotation's degree determines what kind of rotation it is; typical rotations include 90, 180, and 270 degrees. Before turning around and going back to where it started, the figure does a full 360-degree turn. the direction of a rotation, whether it be clockwise or counterclockwise. The degree, amount, and other factors can be determined using this information .a revolution's speed, direction, etc.
Transformative translational congruence
When an object or shape is moved without altering its size, shape, or orientation, the movement is referred to as a translation. When doing a translation, also known as a slide, every point on an object or shape is moved uniformly and in one direction.
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