Which shows the following expression after the negative exponents have been eliminated?
Answers
Answer:
[tex]\frac{a^3b^4}{ab^2}[/tex] which is the last choice in the question
Step-by-step explanation:
Simplify
[tex]\frac{a^3b^{-2}}{ab^{-4}} = \frac{a^3}{a}\frac{b^{-2}}{b^{-4}}[/tex]
Using the fact that [tex]\frac{x^m}{x^n} =x^{m-n}[/tex]
We get
[tex]\frac{a^3}{a} = a^{3-1} = a^2[/tex]
[tex]\frac{b^{-2}}{b^{-4}} = b^{-2-(-4)} = b^2[/tex]
So
[tex]\frac{a^3b^{-2}}{ab^{-4}} =a^2b^2[/tex]
Multiplying numerator and denominator by [tex]ab^2[/tex] gives
[tex]a^2b^2 \frac{ab^2}{ab^2}[/tex]
= [tex]\frac{a^3b^4}{ab^2}[/tex] ANSWER
Hint:
We can eliminate first choice since negative exponents still remain
We can eliminate third choice because the expression has a minus sign which is not possible
That just leaves second and fourth choices to work with
Related Questions
Solve for x. You must show all your work to receive credit.
Answers
Step-by-step explanation:
since the 2 arc angles cover the full circle, we know their sum must be 360°.
so,
23x - 5 + 37x + 5 = 360
60x = 360
x = 6
and so the angle at V = 5×6 + 17 = 30+17 = 47°
Please help me on this one I wrote it out :(
Answers
Answer:
D) 3
Step-by-step explanation:
22 * 2 = 44
To have a remainder 3, the number should be 44 + 3 = 47
47 ÷ 22 , leaves a remainder 3.
47 +22 = 69
69 ÷ 3 leaves a remainder 3.
69 +22 = 91
91 ÷ 3 leaves a remainder 3.
Answer: 47 , 69 , 91
Answer:B:1
Step-by-step explanation:
Write each number out and divide by 22 until you get one that’s answer is 3
What is the value of an AP: 50+45+40
Answers
Answer:
135 is correct answer of this question
Given 8 different toppings to choose from, how many 3-topping pizzas are possible?
Answers
Answer:
336 ways
Step-by-step explanation:
Use nPk which is [tex]\frac{n!}{(n-k)!}[/tex]. This is [tex]\frac{8!}{5!}[/tex]. This becomes 8×7×6 as the 8! and 5! cancel out. 8×7×6 is 336.
Total number of possible 3-topping pizzas are 336 ways.
How do you calculate the number of possible ways something can be arranged?In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n (n – k)!
Given that,
Total number of items n = 8
number of picking item k = 3
Now,
p(n,k) = [tex]\frac{n!}{(n -k)!}[/tex]
p(8,5) = [tex]\frac{8!}{(8 -3)!}[/tex]
= [tex]\frac{8!}{5!}[/tex]
= [tex]\frac{8.7.6.5! }{5! }[/tex]
= 8 × 7 ×6
p(8,5) = 336 ways
Hence, Total number of possible 3-topping pizzas are 336 ways.
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By which number -7÷25 should be divided to get -1÷15
Answers
Answer:
Step-by-step explanation:
Set it up like an equation first:
[tex]\frac{\frac{-7}{25} }{x}=-\frac{1}{15}[/tex] and then bring up the lower fraction, flip it, and multiply:
[tex]-\frac{7}{25}*\frac{1}{x}=-\frac{1}{15}[/tex]
Simplify to
[tex]-\frac{7}{25x}=-\frac{1}{15}[/tex] and cross multiply to get
-25x = -105 and divide both sides by -25 to get that
[tex]x=\frac{105}{25}=\frac{21}{5}[/tex]
Create a visual plot of the data in the table by constructing a bar graph.
3. What is the average view of the dress code? How did you come to this
conclusion?
4. The dress code will be changed if more than 60% of the school feels like a
change is needed. If 40% of this majority agrees on the same change, that will
be what is done with the dress code. Will the dress code change? Do we know
which option will occur? Be sure to explain your reasoning.
Answers
The average view of the dress code is that this dress is not good
Explain how Rashad could collect data to ensure that it is a random sample of the population.For Rashad's sample to be a random sample gotten from the population, the following must be considered.
First, he must have a defined population. In this case, his population is all the students in his high school (non students are not to be considered)Next, he must have a defined sample size (say 10% or 20% of the total number of students in the school)Next, he must select students at random (a perfect example of this is one of every five or ten students that enters the school gate.Lastly, he must collect data for his sampleCreate a visual plot of the data in the table by constructing a bar graph.To do this, we simply create a bar graph.
The response would go into the x-axis, while the number of people would go into the y-axis
See attachment for bar graph
What is the average view of the dress code? How did you come to this conclusion?The average view of the dress code is that this dress is not good
It is considered the average view of the dress code because it is the opinion with the most frequency
Will the dress change?The number of students that do not like the dress as:
210 + 206 + 770 = 1186
Their percentage is
Percentage = 1186/(210 + 206 + 770 + 358)
Percentage = 77%
This means that
Yes, the dress will change
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The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Answers
Lower quartile= 29+29/2=29
Median= 43 (middle number)
Upper quartile= 49+51/2=50
Maximum=56
A parent made x cupcakes for each of the 109 students in the fourth grade. Which expression could be used to determine the total number of cupcakes made?
Answers
109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade. This can be obtained by forming the algebraic expression for the given conditions.
Find the required expression:Algebraic expression is made up of numbers, operations and variables.Algebraic expression is true for all values of x. For example, 2x, 5x + 9 etc.
Given that,
A parent made x cupcakes for each of the 109 students in the fourth grade.
The total number of students in the class = 109
The number of cupcakes one student gets = 1 × x = x
⇒ The number of cupcakes 109 student gets = 109 × x = 109x
Hence 109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade.
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Lesson 1.6 Multiply by 1-digit numbers.
estimate then find the product
(only the circled ones)
Answers
The multiplication shows that the answers will be:
1. 3744
2. 8244
3. 3630
4. 2616
5. 20772
6. 7820
7. 3916
8. 3521
9. 21285
10. 54162
11. 4548
12. 2091
13. 17128
14. 55692
15. $895
16. 4300 miles
How to calculate the value?1. 416 × 9 = 3744
2. 1374 × 6 = 8244
3. 726 × 5 = 3630
4. 872 × 3 = 2616
5. 2308 × 9 = 20772
6. 1564 × 5 = 7820
7. 4 × 979 = 3916
8. 503 × 7 = 3521
9. 5 × 4257 = 21285
10. 6018 × 9 = 54162
11. 758 × 6 = 4548
12. 3 × 697 = 2091
13. 2141 × 8 = 17128
14. 7 × 7956 = 55692
15. From the information given, the cost of each ticket is $179. Also, there are 5 people that are flying.
Therefore, the total cost will be:
= $179 × 5
= $895
16. Also, for the second question, since the distance between the two cities is 2150 miles. The exact distance will be:
= 2150 × 2
= 4300 miles.
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Complete the proofs, ASAP!!! (Geometry)
Answers
1) [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{AB} \parallel \vec{CE}[/tex] (given)
2) [tex]\angle A \cong \angle B[/tex] (base angles theorem)
3) [tex]\angle A \cong \angle 1[/tex] (corresponding angles theorem)
4) [tex]\angle B \cong \angle 2[/tex] (alternate interior angles theorem)
5) [tex]\angle 1 \cong \angle 2[/tex] (transitive property of congruence)
6) [tex]\vec{CE}[/tex] bisects [tex]\angle BCD[/tex] (if a ray splits an angle into two congruent parts, it is a bisector)
Please help.
Match the graph of the function with the function rule.
Answers
The exponential function represented on the graph is defined by the following rule:
[tex]y = 3 \times 2^x[/tex]
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value, which is also the y-intercept, that is, the value of y when x = 0.b is the rate of change.From the graph, we get that when x = 0, y = 3, hence the initial value is of a = 3. Then the temporary definition is:
[tex]y = 3b^x[/tex]
Also from the graph, when x = 1, y = 6, hence we can apply to the definition to find b.
[tex]6 = 3b^1[/tex]
3b = 6
b = 2.
Hence the function is:
[tex]y = 3 \times 2^x[/tex]
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Is the function y = 3x4 - 1 linear or nonlinear?
Answers
If the x is an x and not a multiplication sign then yes, the function is indeed linear.
Hope this helps!
What will be the area of adjoining Trapezium?
a. 240cm²
b. 225cm²
c. 276cm²
d.195cm²
Answers
The area of the adjoining trapezium is 276 [tex]cm^{2}[/tex].
Given the sides of trapezium be 16 cm, 15 cm, 30 cm, 13 cm.
We are required to find the area of adjoining trapezium.
Draw two perpendiculars on AD and the points will be E and F.
From triangles ABE and CFD.
let the length of AE=x, FD=30-16-x=14-x.
BE=[tex]\sqrt{169-x^{2} }[/tex], CF=[tex]\sqrt{225-(14-x)^{2} }[/tex]
BE=CF
[tex]\sqrt{169-x^{2} }[/tex]=[tex]\sqrt{225-(14-x)^{2} }[/tex]
Squaring both sides.
169-[tex]x^{2}[/tex]=225-196-[tex]x^{2}[/tex]+28x
140=28x
x=5 cm.
Put in BE=[tex]\sqrt{169-x^{2} }[/tex]
BE=[tex]\sqrt{169-25}[/tex]
=[tex]\sqrt{144}[/tex]
=12 cm.
Area of trapezium=1/2 (sum of parallel sides)*height
=1/2 (30+16)*12
=23*12
=276 [tex]cm^{2}[/tex]
Hence if the sides of trapezium are 16 cm, 15 cm, 30 cm, 13 cm then the area of the adjoining trapezium is 276 [tex]cm^{2}[/tex].
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In the student council elections, five students are running for president, two are running for vice president, two are running for treasurer and three are running for secretary. How many different possible student council teams could be elected from these students?
Answers
Using the Fundamental Counting Theorem, it is found that 60 different possible student council teams could be elected from these students.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering the number of options for president, vice president, treasurer and secretary the parameters are:
n1 = 5, n2 = 2, n3 = 2, n4 = 3.
Hence the number of different teams is:
N = 5 x 2 x 2 x 3 = 60.
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the concentration of a drug in a patient's bloodstream t hours after the drug was administrated presented by the equation c(t) = 5t-t²+1 (in mg/mL). construct a table of values for c(t) for t=1,2,5,10. Round off answer to tree decimal places. use use the table to sketch a graph and interpret the result by giving the (a) domain, (b) range, (c) vertical asymptote, and (d) horizontal asymptote.
Answers
The graph of the function has no asymptotes.
The table of values of c(t)The function is given as:
c(t) = 5t - t² + 1
When t = 1, 2, 5, 10;
We have:
c(1) = 5(1) - 1² + 1 = 5
c(2) = 5(2) - 2² + 1 = 7
c(5) = 5(5) - 5² + 1 = 1
c(10) = 5(10) - 10² + 1 = -49
So, the table of values is
t c(t)
1 5
2 7
5 1
10 -49
See attachment for the graph of the function
The domain
From the question, we understand that t represents time.
Time cannot be negative i.e. t ≥ 0 The time does not exceed 5.2 i.e. t ≤ 5.2So, the domain is 0 ≤ t ≤ 5.2
The range
From the graph, the maximum of the graph is 7.25
So, the range is 0 ≤ f(t) ≤ 7.25
Asymptotes
From the graph, we can see that the graph has no asymptotes.
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What is the five-number summary for this data set?
17, 21, 22, 26, 28, 31, 33, 41, 46, 52
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.
Answers
Step-by-step explanation:
17, 21, 22, 26, 28, 31, 33, 41, 46, 52
min: 17
Q1: 26
median: 28
Q3: 31
max: 52
The Quadratic Formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a, was used to solve the equation 3x2 + 4x − 2 = 0. Fill in the missing denominator of the solution.
negative 2 plus or minus the square root of 10, all over blank
Answers
Answer:
3
Step-by-step explanation:
The quadratic formula is used to solve a quadratic equation in standard form, based on the values of the coefficients.
SolutionThe standard-form quadratic ax² +bx +c = 0 has solutions given by the quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
For the quadratic 3x² +4x -2 = 0, we have a=3, b=4, c=-2 and the formula gives ...
[tex]x=\dfrac{-4\pm\sqrt{4^2-4(3)(-2)}}{2(3)}=\dfrac{-4\pm\sqrt{16+24}}{6}\\\\x=\dfrac{-4\pm 2\sqrt{10}}{6}=\dfrac{-2\pm\sqrt{10}}{3}[/tex]
The denominator in the solution is 3.
Answer:
The answer is x=(-2±√10)/3
Step-by-step explanation:
11. Find the value of x. x=______
Answers
Answer: x = 3.5
Step-by-Step Solution:
Let us first label the figure.
Let the Triangle be ABC with a line DE || BC.
Now, in ∆ABC,
DE || BC (given)
=> AD/DB = AE/EC (by B.P.T)
Substituting the given values,
AD/DB = AE/EC
2/4 = x/7
1/2 = x/7
2x = 7
x = 7/2
=> x = 3.5
Therefore, x = 3.5
Let x be a discrete random variable. if pr(x<9) = 1/6, and pr(x>9) = 1/3, then what is pr(x=9)?
Answers
Answer: 1/2
Step-by-step explanation:
The probabilities must add to 1, so:
[tex]P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}[/tex]
Wes can paint a certain room in 8 hours. Sally can paint the same room in 5 hours. How long will it take them working together to paint the room? Give a rational expression to solve the problem,(5 points) then solve the problem.(5 points) Round your answer to the nearest hundredth if necessary.
Answers
The time it takes them working together to paint the room is 3.08 hours
Rational expressionRational expression are equation written as a ratio of two expressions or equations.
If Wes can paint a certain room in 8 hours, she can paint 1/8 of the room in 1 hr
Similarly, if Sally can paint the same room in 5 hours, , she can paint 1/5 of the room in 1 hr
Determine the time it takes them to paint the room altogether.
Time together = x
Using the expression below to determine the value of x
1/x = 1/8 + 1/5
1/x = 5+8/40
1/x = 13/40
x = 40/13
x = 3.08
Hence the time it takes them working together to paint the room is 3.08 hours
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Halfway through the season, the USF Bulls football team had the highest average final score. What was the USF Bulls' average score if their final
scores were 31, 36, 28, 52, and 27
Answers
Answer:
D 34.8
Step-by-step explanation:
[tex]\frac{31+36+28+52+27}{5}[/tex]
Is anyone really good at math?
Answers
Answer: 12 cm
Step-by-step explanation:
[tex]\mathtt{Using\ the \ pythagorean \ theorem: \\}[/tex]
[tex]a^2+b^2=c^2, \\\ we\ can\ plug\ in\ values\ for\ a,\ b,\ and\ c[/tex]
[tex]L=a\ and\ M=b\ and\ N=c[/tex]
Therefore,
[tex]L^2+35^2=37^2\\L^2+1225=1369\\L^2=144\\\sqrt{L^2} =\sqrt{144} \\L=\pm12\\Taking\ only\ the\ positive\ answer,\ we\ get:\\\large\boxed{L = 12cm}[/tex]
We have: L² + M² = N²
=> L² = N² - M² = 37² - 35² = 144 = 12²
=> L = 12
ANSWER: B.12
OK done. Thank to me :3
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173
miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
Answers
Using the law of cosines, the ship turned 72 degrees northwest when it changed direction.
What is the law of cosines?The law of cosines states that we can find the side c of a triangle as follows:
c² = a² + b² - 2abcos(C)
In which:
C is the angle opposite to side c.a and b are the lengths of the other sides.For this problem, the parameters are given as follows:
a = 94, b = 119, c = 173.
Hence the internal angle C is found as follows:
c² = a² + b² - 2abcos(C)
173² = 94² + 119² - 2 x 94 x 119cos(C)
22327cos(C) = -6932
cos(C) = -6932/22327
C = arccos(-6932/22327)
C = 108º.
The turning angle is the outside angle, which is supplementary with C, hence:
T = 180 - C = 180 - 108 = 72º.
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i need help with this
Answers
The value of the x from the given equation is 1 and 6/7.
According to the statement
we have given that the quadratic equation and we have to find the solve for the value of the x.
So, For this purpose we know that the
A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers.
So, The given equation is
7x^2 -x -6 =0
Find the factors of the equation
7x^2 -7x + 6x -6 =0
7x(x-1) -6(x-1) = 0
(x-1)(7x-6) =0
here the values of x becomes 1 and 6/7.
So, The value of the x from the given equation is 1 and 6/7.
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Diego wants to paint his room purple. He bought one gallon of purple paint that is 30% red paint and 70% blue paint. Diego wants to add more blue to the mix so that the paint mixture is 20% red, 80% blue.
1. How much blue paint should Diego add? Test the following possibilities: 0.2 gallons, 0.3 gallons, 0.4 gallons, 0.5 gallons.
0.2 gallons
0.2 gallons,
0.3 gallons
0.3 gallons,
0.4 gallons
0.4 gallons,
0.5 gallons
0.5 gallons,
BoldItalicUnderlineImage (12 image limit)Increase indentDecrease indentFormula keypadUndoRedoBullet listNumbered list
Edit imageView imageDelete image
2. Write an equation in which x
represents the amount of paint Diego should add.
3. Check that the amount of paint Diego should add is a solution to your equation.
Answers
idrk but I hope you have a good day and good luck with ur answer
Representa situaciónes relativas a la aplicación de paz
Answers
A situation where peace is being enforced refers to a peacekeeping mission.
What are peacekeeping missions?Peacekeeping missions refer to actions by regional and global international bodies to maintain the peace in an area.
For instance, if there has been conflict in an area, a peacekeeping force will work to prevent further violence between the parties in conflict.
An example of such missions include the United Nations Peacekeeping mission to the Democratic Republic of Congo and the African Union Peacekeeping mission to Somalia.
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Ekaete collected 12 raffle tickets. Roseline collected twice as many. How many raffle tickets did they collect in all?
Answers
Answer:
36
Step-by-step explanation:
12 times 2 which is 24 then u add 12 cause it's the amount they have together so you get 36
If f(x) = 3x + 1 and f^-1 = x-1/3 , then the ordered pair of f(3) =
Answers
Answer:
10
Step-by-step explanation:
f(x) = 3x + 1
f^-1 = x-1/3 , it is known as inverse function.
f(3)= 3*3 +1
=9+1
=10
To find inverse,
x=3x + 1
y=3x+1
Exchanging the position or x and y
x=3y+1
x-1=3y
.•. y=x-1/3
hey im pretty bad at this homework stuff can someone please help me answer all this
Answers
Answer:
Step-by-step explanation:
1. $135
2. a. no
b. $340
3. a. 33
b. $135*33= $4455+340= $4795
4. a. $7630 = 135v + 340
b. 135v + 340 = 7630
135v = 7290
v = 54 vacuums
Question 10 of 10
The function F(x) = log5 x is decreasing.
A. True
B. False
SUBMIT
Answers
Answer: False
Step-by-step explanation:
The base is more than 1, so the function is increasing.