Which of the following expressions are equivalent? Justify your reasoning.Question 5
Answers
Answer:
Explanation:
A) Given the below expression;
[tex]\sqrt[4]{x^3}[/tex]The above can be written as;
[tex]\sqrt[4]{x^3}=(x^3)^{\frac{1}{4}}[/tex]Recall the below law of exponent;
[tex](a^n)^m=a^{nm}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex](x^3)^{\frac{1}{4}}=x^{\frac{3}{4}}[/tex]B) Given the below expression;
[tex]\frac{1}{x^{-1}}[/tex]Recall the below law of exponent;
[tex]\frac{1}{a}=a^{-1}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]\frac{1}{x^{-1}}=x^{-1(-1)}=x^1=x[/tex]C) Given the below expression;
[tex]\sqrt[10]{x^5\cdot x^4\cdot x^2}[/tex]Recall the below laws of exponents;
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^n)^m=a^{^{nm}} \end{gathered}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]\begin{gathered} \sqrt[10]{x^{5+4+2}}=\sqrt[10]{x^{11}}^{}^{} \\ =(x^{11})^{\frac{1}{10}}=x^{\frac{11}{10}}^{}^{} \end{gathered}[/tex]D) Given the below expression;
[tex]x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}[/tex]Recall the below law of exponents;
[tex]a^n\cdot a^m=a^{n+m}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}=x^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=x^{\frac{1+1+1}{3}}=x^{\frac{3}{3}}=x^1=x[/tex]We can see from the above that the below expressions are equivalent because they both yield the same result as x;
[tex]\begin{gathered} A)\sqrt[4]{x^3} \\ D)x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}} \end{gathered}[/tex]Related Questions
For the function f(x)=x2−9, find (a) f(x+h), (b) f(x+h)−f(x), and (c) f(x+h)−f(x) h.
Answers
Step-by-step explanation:
a)
[tex]f(x+h) = 2(x+h)-9[/tex]
[tex]f(x+h)=2x+2h-9[/tex]
b)
[tex]f(x+h)-f(x)=2x+2h-9-(2x-9)[/tex]
[tex]f(x+h)-f(x)=2x+2h-9-2x+9[/tex]
[tex]f(x+h)-f(x)=2h[/tex]
c)
[tex]f(x+h)-f(x)h=2x+2h-9-h(2x-9)[/tex]
[tex]f(x+h)-f(x)h=2x+2h-9-2hx+9h[/tex]
[tex]f(x+h)-f(x)h=-2hx+11h+2x-9[/tex]
Find the product. Write your answer as a mixed number in simplest form.
4 × 1 8/9
Answers
Answer: 68/9 which simplifies into 7 6/9
50 POINTS HELP PLEASE
Write the equation of the line given the following slope and y-intercept
m=4
b=−1
y=
(note for people answering and admins the y is supposed to be blank and its the answer box dont take it down pls,thank you)
Answers
Answer:
y = 4x - 1===========================
Given Slope m = 4,y-intercept b = - 1Equation of a line in slope-intercept formy = mx + bSubstitute the values to gety = 4x - 1word problem for 4x - 3 = 17?????
Answers
Answer: My bill was 17 dollars. I gave four tokens of equal monetary value to the cashier who gave me in return 3 one dollar bills. How much was each token worth?
Step-by-step explanation: 4x - 3 = 17.
add 3 to both sides
4x = 20
x = 5. Each token was worth $5.
Eight billion eighty-one million, one hundred and one thousand, five hundred and thirty-one in figures
Answers
Answer:
8,081,101,531
Step-by-step explanation:
8,081,101,531
What is the slope of the line on the graph
Answers
m= rise/run
The y intercept formula will be
Y=-1/3x+4
I don't know what any of this means for my son's homework please help
Answers
All we simply need to do is to apply the law of indices that states;
[tex](a^b)^c=a^{bc}[/tex]Hence;
[tex](\frac{x^2}{y^4})^3=\frac{x^6}{y^{12}}[/tex]The correct option is
Solve for x. Below is the equation.
Answers
x = 110
Angle 4 is a vertical angle to the 115 degrees angle. Therefore, it must be the same in degree measure. So, we know angle 4 is 115 degrees.
Additionally, angle 4 and angle (x+5) are co-interior angles. This means that they should add up to 180 degrees.
Applying these concepts, we can create an equation:
115 + (x+5) = 180.
When we solve, we end up with x = 110
Write an equation for the line point slope form and slope intercept formSlope= -6Passing through -3,-7
Answers
For this question, we recall the point-slope form of the equation of a line:
[tex]y-y_0=m(x-x_0)[/tex]and the slope-intercept form:
[tex]y=mx+b[/tex]Therefore for the given data, the point-slope form is:
[tex]\begin{gathered} y-(-7)=-6(x-(-3)) \\ y+7=-6(x+3) \end{gathered}[/tex]and the slope-intercept form is:
[tex]\begin{gathered} y=-6x-18-7 \\ y=-6x-25 \end{gathered}[/tex]if point c divides a directed line segment from point A to point B in a 1 : 5 ratio, what are the coordinates of point B?
Answers
The location of the point B on the line with the endpoints is 63
How to determine the coordinates of the segment?On the segment, we have the following endpoints
A = -3
C = 8
Rewrite the endpoints of the line segment as
A = (-3,0) and C = (8,0)
The ratio of the line is given as
Ratio, A : B = 1 :5
This means that
Point C = A/A + B
So, we have
C = 1/1 + 5
Evaluate
C = 1/6
The coordinate of point C on the line segment is calculated using
Point C = C * (B - A) + A
So, we have
8 = 1/6 * (B + 3) - 3
This gives
1/6 * (B + 3) = 11
So, we have
B + 3 = 66
Subtract 3
B = 63
Hence, the coordinate of the point B on the line segment is 63
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Possible question
if point c divides a directed line segment from point A to point B in a 1 : 5 ratio, what are the coordinates of point B?
A = -3 and C = 8
0.25 meses en días y horas.
Answers
Answer:
0.25 Months =7.6099 Days= 7 Days, 14 Hours, 38 Minutes and 19 Seconds
In Spanish
0.25 Meses =7.6099 Días= 7 Días, 14 Horas, 38 Minutos y 19 Segundos
Forever Flowers, the nursery that sells the peony plants, has an app that uses
equations to help customers order the correct number of plants. The function rule for
peony plants is P = 1.5n where P represents the number of plants needed for n yards.
a. What type of representation is a function rule?
b. State at least one reason why using this type of representation may be more useful
than other representations
Answers
a. A function rule is a representation of dependent variable, here n, in terms of the independent variable, here P, and is expressed as ƒ(P) = 1.5n.
b. This type of reason is useful because functions in an equation can take input from many variables, but always give the same result, which is unique to that function.
What is a function rule?The connection between the input or domain and the output or range is called a function rule. When there is exactly one value in the range for each domain value, a relation is a function.
f(x), where x is the input value, is how functions are expressed.
All functions have the general form y = f(x)
On any part of the function, a vertical line is drawn. It is a function if and only if it crosses the function at that single point. It is not a function if the line crosses itself more than once.
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URRGENT PLEASE HELP!!!! DOC ATTACHED
Answers
1. A conditional statement can be written as
If it is sunny then there is daylightThe hypothesis is: It is sunny
The conclusion is: there is daylight
2. The converse of the conditional statement
If there is daylight then it is sunny3. The inverse of the conditional statement
If it is not sunny then there is no daylight4. The contrapositive of the conditional statement
If there is no daylight then it is not sunny5. The biconditional statement and can be written because the statement and the converse are both true
6. The biconditional statement is
it is sunny if and only if there is daylightHow to identify a conditional statementA conditional statement is a term used in logic that refers to the type of statement that has "if-then". It is sometimes called if-then statements. Conditional statement are of two parts the hypothesis required to ensure that the conclusion. Other forms of conditional statements are
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Which of the following could be a real-world description of the quantity three times x end quantity divided by 8?
A. The cost of a pizza split by 8 people plus a $3 tip
B. The cost of a pizza plus a $3 tip divided by 8 people
C. The cost per pizza for 3 pizzas divided by 8 people
D. The cost per pizza for 8 pizzas divided by 3 people
Answers
3x / 8
This means that 3x is 3 times variable and then divided by 8.
A. is NOT correct because there is no addition and 8 is not being divided.
B. is NOT correct because there is no addition and the tip is not divided because it does not exist.
C. is CORRECT because it translates to the cost of a pizza times 3 and then eaten (divided) by 8 people.
D. is NOT correct; it should be switched.
Hope this helped and good luck! :)
A simple random sample of 20 items resulted in a sample mean of 15. The population standard deviation is = 9. Round your answers to two decimal places.
Answers
Based on the number of items in the simple random sample, and the sample mean, the standard error of the mean can be found to be 1.12
How to find the standard error?The standard error of a simple random sample can be found by the formula:
= Population standard deviation / √Number of items in simple random sample
Solving for the standard error gives:
= 5 / √20
= 5 / 4.4721359549995793928183473374626
= 1.118
= 1.12
We can therefore conclude that the standard error of this sample is 1.12.
Rest of the question:
What is the standard error of the mean?
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ONLY #11 please show work THANK YOU
Answers
The sketch of the given parametric equations is as appended.
Given parametric equations,
x(t) = 1+2t
y(t) = [tex]t^{2}[/tex]
y = [tex]\frac{(x-1)^{2}}{4}[/tex]
For bounding range of -2 ≤ t ≤ 2, corresponding values of x are as follows,
x = 2t + 1
For t = -2, x = 2(-2) + 1 = -3
For t = 2, x = 2(2) + 1 = 5
Hence the graph has been drawn with bounding limits of -3 ≤ x ≤ 5
The outcome is a parabola with vertex at (1,0) and open upwards. The curve moves towards infinity in upwards direction if there are no bounds / range.
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1,-4,16 what is the 15th term
Answers
The sequence has its 15th term to be 268435456
What is the 15th term of the sequence?From the question, the given parameters are
1, -4, 16
The above sequence is a geometric sequence, with the following parameters
First term, a = 1Common ratio, r = -4/1Evaluate the quotient
So, we have
r = -4
The nth term of a geometric sequence is
Tn = a * r^(n-1)
Where
a = 1 and r = -4
Also, we have n = 15
Substitute a = 1 and r = -4 in the equation Tn = a * r^(n-1)
So, we have
Tn = 1 * (-4)^(n-1)
Substitute 15 for n
Tn = 1 * (-4)^(15-1)
Evaluate
Tn = 268435456
Hence, the 15th term of this sequence is 268435456
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One dealer in sports shirts offers a dozen at 5000 list price, less a 15% discount. A second offers the same shirts for 5200 pesos a dozen less a 20% discount. Which is the better offer and by how much?
Answers
Call the two offers offer A and B respectively.
For offer A, the list price is 5000 pesos with a 15% discount. So you will pay:
[tex]A=5000(0.85)=4250\text{ pesos}[/tex]For offer B, the list price is 5200 with a 20% discount. So you will pay:
[tex]B=5200(0.8)=4160\text{ pesos}[/tex]So the first deal is costing 4250 pesos and second one costs 4160 pesos.
Hence the second deal is better by 4250-4160= 90 pesos.
The second deal is the better deal by 90 pesos.
i need help, please
Answers
Answer:
[tex]\frac{51}{4}[/tex]
Step-by-step explanation:
Since they are similar we can set up direct proportions
FE:CB=DE:AB
y:6=17:8
[tex]\frac{y}{6} =\frac{17}{8}[/tex]
cross multiply
8y=17*6
divide by 8 each side
[tex]\frac{51}{4}[/tex]
n
22
When two musical notes are a "fifth" apart, the frequency of the lower
note is the frequency of the higher note. Using f as the frequency of
the higher note, write an expression for the frequency of the lower
note.
Answers
A physics concept called frequency describes how many cycles a wave completes each second. As a result, the following expression is used to get the lower note's frequency [tex]\frac{2}{3}[/tex] f
What is wave ?A wave is a phenomena that moves through a physical medium without leaving any lasting impression on the molecules therein. Energy is transferred from one end of the medium to the other. Sound waves, light waves, electromagnetic waves, etc. are some examples.
Frequency develops during wave propagation. This can be characterized as the number of cycles a wave makes in a second. It's also measured in Hertz.
Let f stand for the upper note's frequency and for the lower note's frequency we have [tex]f_{1}[/tex]. We therefore have;
[tex]f_{1}[/tex] =[tex]f\frac{2}{3}[/tex]
Therefore, the expression for the frequency of the lower notes is [tex]\frac{2}{3}[/tex] f.
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Determine the value for m in the equation 1.4m = 0.42.
0.30
0.03
5.88
2.80
Determine the value for j in the equation 13 over 20 equals j plus 9 over 20.
4 over 20
4 over 40
2 over 20
22 over 40
Which statement correctly applies mathematical reasoning to find the possible values for x in the equation x − 1.3 = 1.5?
x is greater than 1.5
x is less than 1
x is between 0.1 and 1.5
x is less than 0.1
Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
23.04
19.2
10.0
2.8
Determine the value for k in the equation k − 173.54 = 294.57.
121.03
589.14
347.08
468.11
Answers
Answer:
1. 0.30
2.4 over 20
3. x is greater than 1.5
4. 19.2
5. 468.11
Step-by-step explanation:
1) 1.4m = 0.42.
Divide both sides by 1.4
1.4m/1.4 = 0.42/1.4
m = 0.30
2) 13/20=j+9/20
Flip equation
j + 9/20 = 13/20
Substract 9/20 from both sides
j + 9/20 - 9/20 = 13/20 - 9/20
j = 13 - 9/20
j = 4/20
3) x − 1.3 = 1.5?
Add 1.3 to both sides
x - 1.3 + 1.3 = 1.5 + 1.3
x = 2.8
So, x is greater than 1.5
4) x/6 + 0.4 =3 + 0.6
Substract 0.4 from both sides
x/6 + 0.4 - 0.4 = 3 + 0.6 -0.4
x/6 = 3 + 0.2
x/6 = 3.2
Multiply both sides by 6
x/6 • 6 = 3.2 • 6
x = 19.2
5) k − 173.54 = 294.57.
Add 173.54 to both sides
k - 173.54 + 173.54 = 294.57 + 173.54
k = 468.11
The value of m from the given equation is 0.3.
The given equation is 1.4m = 0.42.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
1) 1.4m = 0.42
⇒ m = 0.42/1.4
⇒ m = 0.3
2) 13/20 = j+9/20
⇒ j = 13/20 - 9/20
⇒ j = 4/20
⇒ j = 1/5
3) x - 1.3 = 1.5
⇒ x = 1.5 + 1.3
⇒ x = 2.8
4) x/6 + 4/10 = 3 + 6/10
⇒ x/6+0.4=3.6
⇒ x/6 = 3.2
⇒ x = 19.2
5) k − 173.54 = 294.57
⇒ k = 294.57+173.54
⇒ k = 468.11
Therefore, the value of m from the given equation is 0.3.
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A = $16,000, r= 11.0%, t = 5
Answers
Answer:
9495.221
Step-by-step explanation:
16000=Pe^(0.11x5)
Zachary has a container of worms for fishing. When empty, the mass of the container is 225 grams. With the worms in it, the container has a total mass of 751.4 grams. Each worm has a mass of 11.2 grams. How many worms are in the container? Write and solve an equation to model this equation.
Answers
Solving a linear equation we will see that there are 47 worms in the container
How many worms are in the container?We know that the mass of the container is 225 grams, and the mass of each worm is 11.2 grams.
Then if there are x worms on the containers, the total mass is:
M(x) = 225g + x*11.2g
In this case, we know that the total mass is 751.4 grams, then we can write:
751.4 g = 225g + x*11.2g
Solving this linear equation we get:
751.4g - 225g = x*11.2g
526.4g = x*11.2g
526.4g/11.2g = x = 47
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The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
Answers
The pressure is 672 pounds per square foot at a depth of 10.5 feet.
When a force is delivered to an object's surface perpendicularly to the region across which it is applied, the force is known as pressure (symbol: p or P).
The pressure in relation to the surrounding air is known as gauge pressure, also spelled gage pressure.Pressure is expressed using a variety of units. The standard unit of pressure in the imperial and U.S. customary systems is the pound-force per square inch (psi), which is equal to one newton per square meter (N/m²) in the SI. Some of these conclusions come up as a result of dividing a unit of force by a unit of area.a. The given formula is is P=64d
or , d = P ÷ 64
b. at a pressure of 672
d = 672 ÷ 64
or, d = 10.5 feet
Hence the water pressure on the submerged object is given by
d = P ÷ 64
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someone help pleasee
Answers
no answer for this question
Sketch the graph of of the linear inequality: y<2x
Answers
Ive attached it on this photo. ur welcome :)
Answer:
Step-by-step explanation:
What is the surface area of the pyramid?
Answers
Answer:
d
Step-by-step explanation:
becuase you multiply leght times width then multiply height so it turns out to be
6x6=36
36x6=180
Use the Distributive Property and mental math to find the product.
5(88)
Please Explain how to do it. Everyone else is saying the answer is 440, which I know.
Answers
You can split it up into 80 and 8
so it becomes a lot easier
80•5=400
8•5=40
Then combine them again to get
400+40=440
If you need more of an explanation let me know!!
A square swimming pool is surrounded by a cement sidewalk that is 3 feet wide. Enter two different function representations for the total area that the swimming pool and sidewalk enclose, A(x), if the length of the pool is x feet long
Answers
Step-by-step explanation:
the area function for the square pool itself is
A(x) = x² ft²
the area function for the pool and its sidewalk is
A(x) = (x + 6)² = x² + 12x + 36 ft²
simply because in this case the side length of the square is x+3+3 ft long (3ft added on both edges).
in evaluating the expression 8+ 9/4 (-2) jenny found the volume to be 25/2. she thinks that the number is too great, but is not sure what she did wrong
Answers
In evaluating the expression 8+ 9/4 (-2) Jenny found the volume to be 25/2. The mistake she made was
volume = 8 1/4.
What is an expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
8+ 9/4 (-2) = ?
Hence we solve
(8 – 2) + (9/4 - 0)
6+9/4
The number four is the Least Common Multiple (LCM) of the number one. Multiply each fraction's numerator and denominator by whichever number will result in the denominator of each fraction being equal to the LCM, and then subtract that value from 1.
Subtract the numerators now that the fractions have the same denominators.
9 - 0/4 = 9/4
As we convert to whole numbers we have
9/4 = 2 1/4
Hence
=6 +2(1/4)
=8 1/4.
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