Ben simplified this expression (2x^-4y^7 / 3x^3y^2)^3 Analyze bens work. did he simplify the expression correctly? If not, what was his mistake? Yes, he is correct. No, he needed to add the exponents of powers of the same base in the first step. No, he needed to apply the exponent to all factors in the product in the second step.
-c
No , he needed to apply the exponents to all factors in the product in the second step .
Find the general solution of the homogeneous system below. Give your answer as a vector.
x1 + 2x2 - 3x3 = 0
4x1 + 7x2 - 9x3 = 0
-x1 - 3x2 + 6x3 = 0
Answer:
Step-by-step explanation:
Given the system of homogeneous equations
x1 + 2x2 - 3x3 = 0 ................. 1
4x1 + 7x2 - 9x3 = 0 ................... 2
-x1 - 3x2 + 6x3 = 0..................... 3
First we will reduce the equation to two equations and two unknowns;
add equation 1 and 3;
2x2-3x2 +(-3x3+6x3) = 0
-x2 + 3x3 = 0
x2 = 3x3 .......... 4
Multiply equation 3 by 4 and add to equation 2;
equation 3 * 4 will give;
-4x1 - 12x2 + 24x3 = 0..................... 5
add equation 5 to equation 2;
7x2-12x2-9x3+24x3 = 0
-5x2 - 15x3 = 0 .......... 6
5x2 = 15x3
x2 = 3x3
Let x2 = k
From equation 4;
k = 3x3
x3 = k/3
substitute x2 = k and x3 = k/3 into equation 1 to get x1 in terms of k
From 1, x1 + 2x2 - 3x3 = 0
x1+2k-3(k/3) = 0
x1 +2k-k = 0
x1 +k = 0
x1 = -k
Writing the answer in vector form will give (x1. x2. x3) = (-k, k, k/3)
k(-1, 1, 1/3)
Hence the answer to the system of equation in vector form is k(-1, 1, 1/3) where k is any constant.
-56.5 as a mixed number
Answer:
-56 1/2
Step-by-step explanation:
Answer:
-5.6
Step-by-step explanation:
Tracey paid $165 for an item that was originally priced at $450. What percent of the original price did Tracey pay? Round your percentage answer to two decimal places.
Answer:
36.67%
Step-by-step explanation:
To find the percent, divide 165 by 450 (part over whole) and multiply by 100
(165/450) x 100
= 36.67
So, Tracey paid 36.67% of the original price
Help me please I do not understand this question
Answer:
<KNM = 131
Step-by-step explanation:
<KNM + <MNJ= 180 so,
8x - 5 + 4x - 19 = 180-----> collect like terms----> 12x - 24 =180-----> add 24 on each side----> cancels out on the left-----> 12x = 204-----> divide by 12 on each side-----> x = 17------> plug in-----> < KNM = 8(17)-5 ---> <KNM = 131
Did this help?!?!?
Density is calculated by dividing the mass by volume. A student measures the mass of an 8 cm3 object as 12.9g. What is the density of the object to the nearest tenths with proper units?
a.) 2 g/cm3
b.) 1.61 g/cm3
c.) 1.5 g/cm3
d.) 1.6 g/cm3
round 6893.209 to the nearest whole number
Answer:
6893
Step-by-step explanation:
Answer:
6893 is the nearest whole number
what is the opposite of the opposite of 8
Answer:
8
Step-by-step explanation:
The opposite of the opposite of 8 is just 8
Answer:
-8
Step-by-step explanation:
the opposite of 8 is -8 because of positive and negative numbers
7(-8)-2y=-52
help...
Answer:
y=-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
7x - 2y = -52
7(-8) - 2y = -52
-56 - 2y = -52
-2y = 4
y = -2
Best of Luck!
Cameron bought a used car for $4,500. He made a down payment of $1,200 and agreed to pay the remaining balance in monthly payments of $300 each.
Which equation can be used to find m, the number of months it will take Cameron to pay off his car? (7.10A)
F 4,500 = 1,200 + 300m
F 4,500 = 1,200 + 300m
G 4,500 = –300 + 1,200m
G 4,500 = –300 + 1,200m
H 4,500 = 300 + 1,200m
H 4,500 = 300 + 1,200m
J 4,500 = 1,200 – 300m
J 4,500 = 1,200 – 300m
Answer:
[tex]4500 = 1200 + 300m[/tex]
Step-by-step explanation:
Given
[tex]Total = 4500[/tex]
[tex]Base\ Amount = 1200[/tex]
[tex]Payment = 300[/tex] monthly
Required
Write an expression to determine the number of months
The total can be expressed using:
[tex]Total = Base\ Amount +Payment * Number\ of\ months[/tex]
Substitute value for each term
[tex]4500 = 1200 + 300 * m[/tex]
[tex]4500 = 1200 + 300m[/tex]
Hence:
Option F answers the question
Which choice correctly expresses the number below in the scientific notation?
What is the density of Iron Ore (Hematite)? Mass = 30g: Volume = 3.02
cubic cm. Round to TWO decimal places.
Answer:
9.93g/cb cm
Step-by-step explanation:
Density = mass/volume
= 30g/3.02cb cm
= 9.93g/cb cm
Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama}, A = {Math, History, Chemistry, English}, B = {Psychology, Drama, French, Chemistry, English}, and C = {Physics, History, French}. Find the following. n(B) + n(C)
Answer:
b. psychology drama French chemistry English
i need help please answer quickly this is due tomorrow
Step-by-step explanation:
elsian 69 pls help me with my latest question i will gove u anything u want pls its due today i am so stuck
Answer: see below
Step-by-step explanation:
Graph the points and rotate the graph as follows:
90° = 1 turn left180° = 2 turns left (or right)270° = 3 turns left (or 1 right)or use the following formulas:
90°: (x, y) → (-y, x)180°: (x, y) → (-x, -y)270°: (x, y) → (y, -x)1) 180°: (x, y) → (-x, -y)
D: (1, 4) → (-1, -4)
E: (7, 6) → (-7, -6)
F: (8, 3) → (-8, -3)
G: (2, 1) → (-2, -1)
2) 270°: (x, y) → (y, -x)
L: (1, 6) → (6, -1)
M: (8, 7) → (7, -8)
N: (5, 2) → (2, -5)
3) 90°: (x, y) → (-y, x)
Q: (2, 6) → (-6, 2)
R: (5, 7) → (-7, 5)
S: (7, 3) → (-3, 7)
T: (1, 1) → (-1, 1)
4) 180°: (x, y) → (-x, -y)
D: (3, 0) → (-3, 0)
E: (6, 1) → (-6, -1)
F: (7, -4) → (-7, 4)
G: (1, -6) → (-1, 6)
simplify 5-(-1) Quickly answer pls
Answer:
5-(-1)
5+1
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
5-(-1)
5+1
= 6
Using the distance formula, find the distance between these two points. Round to the nearest tenth. (8,9) and (3,2)
Answer:
The answer is
8.6 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(8,9) and (3,2)
The distance between them is
[tex]d = \sqrt{( {8 - 3})^{2} + ( {9 - 2})^{2} } \\ = \sqrt{ {5}^{2} + {7}^{2} } \\ = \sqrt{25 + 49} \\ = \sqrt{74} \: \: \: \: \: \: \: \: \: \: \\ = 8.60232...[/tex]
We have the final answer as
8.6 units to the nearest tenthHope this helps you
The dot plot shows the number of touchdowns a football team scored in 10 games
Answer:
Step-by-step explanation:
5
Can somebody help and crAck the code this is 100 points if you get it right your are gonna be the brainliest
Answer:
RECORD TIME
Step-by-step explanation:
RECORD TIME
Answer:
record time
Step-by-step explanation:
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Does someone have this kind of problem?
Answer:
Yes :<
Step-by-step explanation:
Hmm.. maybe f-1 (x) has a y-intercept of (0,-36).
Vishal was interested in the relationship between a person's age and their musical preferences. He called all
the numbers listed in his city's telephone directory, and whenever someone answered and agreed to be
surveyed, he asked them for their age and interviewed them about their musical preferences.
Once he was done, he analyzed his results and found that younger people prefer pop and hip-hop music
while older people prefer jazz and classical music.
What type of statistical study did Vishal use?
Choose 1 answer:
Sample study
Experiment
Observational study
Answer:
Sample study
Step-by-step explanation:
Sample study is a type of statistical study that is done by taking samples from respondents for any research purpose.
In this type of statistical study, a group of people are selected and asked some questions or data collected.
The type of statistical study that Vishal used was Sample Study because he collected data from a group of respondents to arrive at a hypothesis.
Vishal study of relationship between people's age & musical preferences is 'Observational Statistical Study'
Given : Vishal approached all people in city, enquired willing ones about age & musical preferences, & analysed conclusion thereafter.
Vishal used Observational Statistical Study, as :
Sample study denotes - component step of choosing few representatives ie sample units from all ie population units. It is a part of all statistical studies, & not a type of study in itself. Observational Study - involves studying the sample units in natural uncontrolled or un intervened setup , based on the variable/ traits or relationship study needed by nature of study. Experimental Study - involves studying & analysing variables traits or relationships, in manipulated, controlled or artificially treated experiment setup.Vishal collects sample from his city & studies them as it is, without any artificial intervention. Hence this natural enquiry based study of age & musical preferences is Observational Study
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Does anyone know how to figure this out? can you please explain it to me?
Answer:
x=108'
y=25'
Step-by-step explanation:
180 = 72+x
so,
x = 180-72
= 108'
x = 5y-17 ( but we know x is 108')
so 108 = 5y -17
108+17 = 5y
5y = 125
y = 25
Answer:
x = 108 degree
y = 25 degree
Step-by-step explanation:
You can use law of transversal to get these
9. The maximum value of a data set
consisting of 25 positive integers is 84. A
new data set consisting of 26 positive
integers is created by including 96 in the
original data set. Which of the following
measures must be 12 greater for the new
data set than for the original data set?
Answer:
Let m be the minimum value of original data set.
Given -
The range of original data set = 84 -mA new data set consists of 26 positive integers and 96 original data set.Therefore, the range of new data set is 96-m.
Now, we can find the difference between two ranges by subtracting the ranges -
[tex] \\ \implies \sf \: (96 - m) - (84 - m) \\ \\ \\ \sf \footnotesize \: using \: \: distributive \: \: property \: - \\ \\ \\ \bf \: it \: \: will \: \: be \: \: equal \: \: to \: \: 12. \\ [/tex]
Therefore, the range of the new data set must be greater than the range of original data set.
A dog walking along some train tracks meets a train every 4 minutes and the train catches up the dog every 12 minutes. Find the value of x if the trains leave the endpoint of the route every x minutes.
Answer and Step-by-step explanation:
Dog meets the train in = 4 minutes
Train catches up the dog in = 12 minutes
Let x be the time when train leave the route,
Train catch up the dog in 12 minutes, the endpoint of route is x and the dog meet up the train in 4min, so the equation becomes:
12 - x = 4
To find out the value of x, subtract 12 from both sides, we get
x = 4 – 12
-x = -8
Which gives x = 8, when train leaves the endpoint of route.
What temperature is 24° warmer than-12 °C?
Answer:
12 °C
Step-by-step explanation:
x = -12 + 24x = 12 °C12 °C is 24°C warmer than -12°C
Solve 5x - 4< 2x + 5. Enter your answer as an inequality.
Answer:
x < 3
Step-by-step explanation:
5x - 4 < 2x + 5
Subtract 2x from both sides
5x - 4 - 2x < 2x + 5 - 2x
5x - 2x - 4 < 2x - 2x + 5
3x - 4 < 0 + 5
3x - 4 < 5
Add 4 to both sides
3x - 4 + 4 < 5 + 4
3x < 9
Divide both sides by 3
3x/3 < 9/3
x < 3
640 - 40 = A.600 B.640 C.360 D.784 answer and you will get 45 points if you get correct and used paper and pencil.
Answer:
A. 600
Step-by-step explanation:
Answer:
A.............................,.
For what value of the variable will the expression 2b−3 be equal to the following: −11
make the numbers from 1 to 20 using the numbers 1 9 8 4
Answer:
9-1+8+4
Step-by-step explanation:
9-1=8
use that 8 and add the other 8 to make 16
now add the 4. 16+4=20
Answer:
1, 4, 8, 9, 11, 14, 18, 19
Suppose LCM(a,b) = 20160, a=60. Find the smallest possible value of b.
Answer:
see below
Step-by-step explanation:
given:
LCM(a,b) = 20160, a=60
find:
smallest possible value of b
solution;
60, b = 20,160
b = 20,160 / 60
b = 336
60 x 336 = 20,160
= 2⁶ x 3² x 5 x 7
= (2² x 3 x 5) x (2⁴ x 3 x 7)
= (60) x (336)
LCM(60,336) = 1680
consider the 2² x 3 to get the prime number:
= 336 x 12
= 4032
therefore,
LCM(60,4032) = 20160
The smallest possible value of b is 336.
What is Prime Factorization?Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.
We have been given that
LCM(a,b) = 20160 and a = 60
We have to determine the smallest possible value of b
Since the product of two numbers equals the product of their HCF and LCM.
⇒ 60 × b = 20,160
⇒ b = 20,160 / 60
⇒ b = 336
⇒ 60 × 336 = 20,160
We need to write 20160 as the product of its prime factors, which is 20160.
⇒ 2⁶ × 3² × 5 × 7
⇒ (2² × 3 × 5) x (2⁴ × 3 × 7)
⇒ (60) × (336)
⇒ LCM(60,336) = 1680
Therefore, the smallest possible value of b is 336.
Learn more about the Prime Factorization here:
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5
Quita bought a jacket priced at $88. The sales tax rate on the jacket was 7.5%.
How much was the sales tax in dollars and cents on this jacket?