Answers
Explanation:
I’m not entirely sure if it’s the right answer but please have a look
Answer:
[tex] \huge{ \boxed{ \tt{1 }}}[/tex]
❁ Question : Simplify :
[tex] \sf{( {x}^{a} ) ^{b - c} \times ( {x}^{b} ) ^{c - a} \times ( {x}^{c} )^{a - b}} [/tex]❁ Solution :
First , Use power law of indices.
Remember : If [tex] \sf{ {a}^{m} }[/tex] is an algebraic term , then
[tex] \sf{( {a}^{m} ) ^{n} } = {a}^{m \times n} = {a}^{mn} [/tex] , where m and n are positive integers.
➝ [tex] \sf{ {x}^{a(b - c)} \times {x}^{b(c - a)} \times {x}^{c(a - b)}} [/tex]
➝ [tex] \sf{ {x}^{ab - ac} \times {x}^{bc - ba} \times {x}^{ca - cb}} [/tex]
Now , Use product law of indices :
Remember : If [tex] \sf{ {a}^{m} }[/tex] and [tex] \sf{ {a}^{n}} [/tex] are the two algebraic terms , where m and n are the positive integers then [tex] \sf{ {a}^{m} \times {a}^{n} = {a}^{m + n}} [/tex]
➝ [tex] \sf{ {x}^{ab - ac + bc - ba + ca - cb}} [/tex]
Since two opposites adds up to zero , remove them :
➝ [tex] \sf{ {x} \: ^{ \cancel{ab} \: - \cancel{ac} \: + \cancel{bc} \: - \cancel{ba} \: + \cancel{ca} \: - \cancel{cb} } }[/tex]
➝ [tex] \sf{ {x}^{0} }[/tex]
Use Law of zero index
Remember : If [tex] \sf{ {a}^{0}} [/tex] is an algebraic term , where a ≠ 0 , then [tex] \sf{ {a}^{0} = 1}[/tex]
➝ [tex] \boxed{ \sf{1}}[/tex]
And we're done !
Hope I helped ! ♡
♪ Have a wonderful day / night ツ
~~
Related Questions
If x and (x+50°) are complementary angles. find the angles
Answers
Step-by-step explanation:
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
So
x + x + 50° = 90°
2x = 90° - 50°
2x = 40°
x = 40°/2
x = 20°
x + 50 = 20 + 50 = 70°
Hope it helps :)
Answer:
let 1st angle be x
and another angle be x+50°
two angles are said to be complementary,if the some of their measures is 90°
so,
x+x+50=90
2x+50 =90
2x=90-50
x=40/2
:-x= 20 ....... 1st angle
another angle (x+50)=20+50=70°
Phoebe knit a hat for a friend. She started with 197 meters of yarn. When she finished, she had 8,200 centimeters of yarn left over. How much yarn did Phoebe use to knit the hat? Write your answer in centimeters.
Answers
Answer:
Phone used 11,500 centimeters of yarn
Step-by-step explanation:
So first we know that 1 meter is equivalent to of 100 centimeters
Now lets convert everything into centimeters
197*100=19700
And thats it
Now we know she started with 19700 centimeters of yarn and has 8200 centimeters left over.
We can make an equation
We can make “x” stand for amount of yarn used.
19700-x=8200
Minus x becuase thats how much she used and equal 8200 becuase Thats what was left over
Now use inver operations
-x=-11,500
Now divide - on both sides
x=11,500
She used 11,500 centimeters of yarn
Answer: 11,500 centimeters of yarn
Step-by-step explanation:
Solve. Show your work in the sketchpad. Don't forget your dollar sign and to round to the nearest hundredth. You have to do this, it's money. For every hour that John works he earns $8.55. If John works 13.5 hours, how much money did he make?
Answers
Answer:
$115.43
Step-by-step explanation:
From the above question:
1 hour of work = $8.55
13.5 hours of work = x
Cross Multiply
x = 13.5 × $8.55
x = $115.425
Approximately to the nearest hundredth = $115.43
If John works 13.5 hours, the amount of money he makes = $115.43
Write the expression as a single multiplication sentence without
parentheses.
11 × (15 + 5)
Answers
Answer:
11x20
Step-by-step explanation:
15=5 equals 20 so 11x20 is 220
Hello! Can someone please help me with these 2 questions! thank you so much! (i’ll give brainlist)
Answers
Answer:
1) 4 2)1/5 X=10
Step-by-step explanation:
Small to large is a fraction
Large to small is a whole number
please help me with this
Answers
Answer:
The equation in the point-slope form for the line that passes through point (-1, -4) and has a slope of -3 is y+4=-3(x+1).
Step-by-step explanation:
Given that:
Line passes through the point = (-1, -4)
Slope of the line = -3
Point slope form of a line is given by;
[tex]y-y_1=m(x-x_1)[/tex]
Here,
x1 = -1 , y1 = -4 and m = -3
Putting the values in the point-slope form of the equation,
y-(-4) = -3(x-(-1))
y+4= -3(x+1)
Hence,
The equation in the point-slope form for the line that passes through point (-1, -4) and has a slope of -3 is y+4=-3(x+1).
Pls help me ill give brainliest.
Pls do all 3 to get brainliest
Answers
Answer:
5. 8(a-5)= -40
8a-40= -40
8a= -40+40
8a=0
a=0/8
a=0
option c is correct.
6. for d,
-1<d<1
I think the answer is option d , which is missing in the attachment.
the 4 question is missing.
so I am not able to answer that
What is the area of this ILL GIVE BRAINLIEST!!!!!!!
Answers
Answer:
Area = 56mm²
Step-by-step explanation:
Area of a trapezium/trapezoid
[tex] = \frac{1}{2} \times h \times (a + b)[/tex]
[tex] = \frac{1}{ 2} \times 7 \times (4 + 12)[/tex]
[tex] = \frac{7}{2} \times16[/tex]
[tex] = 7 \times 8[/tex]
[tex] = 56[/tex]
Write the equation of the line that connects the set of data points!helppp
Answers
Given:
The set of data points on the graph.
To find:
The equation of line that connects the set of data points.
Solution:
From the given graph it is clear that the data points are (20,40), (35,50), (50,60), (65,70).
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Let as consider the line passes through (20,40) and (50,60), then the equation of line is
[tex]y-40=\dfrac{60-40}{50-20}(x-20)[/tex]
[tex]y-40=\dfrac{20}{30}(x-20)[/tex]
[tex]y-40=\dfrac{2}{3}(x-20)[/tex]
Multiply both sides by 3.
[tex]3(y-40)=2(x-20)[/tex]
[tex]3y-120=2x-40[/tex]
Isolate variable terms.
[tex]-2x+3y=120-40[/tex]
[tex]-2x+3y=80[/tex]
Therefore, the standard form of the required line is [tex]-2x+3y=80[/tex].
A computer that cost 1099 last year cost 9999 this year. What is the percent change in price rounded to the nearest tenth
1%
0.1%
9.1 %
10 %
Answers
Type into a calculator as 1098 • 0.1
What's the next number? 0 , 1/3 , 1/2 , 3/5 , 2/3
Answers
Answer:
The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 is 5/7
Step-by-step explanation:
The given numbers are;
0, 1/3, 1/2, 3/5, and 2/3
The number sequence is formed adding [tex]\dfrac{1}{\left (\dfrac{n^2 + n}{2} \right ) }[/tex] to each (n - 1)th term to get the nth term number in the sequence, with the first term equal to 0, as follows;
For the 2nd term, the (n - 1)th term is 0, and n = 2, gives;
The
[tex]0 +\dfrac{1}{\left (\dfrac{2^2 + 2}{2} \right ) } = 0 + \dfrac{1}{3} = \dfrac{1}{3}[/tex]
For the 3rd term, the (n - 1)th term is 1/3, and n = 3, gives;
[tex]\dfrac{1}{3} +\dfrac{1}{\left (\dfrac{3^2 + 3}{2} \right ) } = \dfrac{1}{3} + \dfrac{1}{6} = \dfrac{1}{2}[/tex]
For the 4th term, the (n - 1)th term is 1/2, and n = 4, gives;
[tex]\dfrac{1}{2} +\dfrac{1}{\left (\dfrac{4^2 + 4}{2} \right ) } = \dfrac{1}{2} + \dfrac{1}{10} = \dfrac{3}{5}[/tex]
For the 5th term, the (n - 1)th term is 3/5, and n = 5, gives;
[tex]\dfrac{3}{5} +\dfrac{1}{\left (\dfrac{5^2 + 5}{2} \right ) } = \dfrac{3}{5} + \dfrac{1}{15} = \dfrac{2}{3}[/tex]
For the next or 6th term, the (n - 1)th term is 2/3, and n = 6, gives;
[tex]\dfrac{2}{3} +\dfrac{1}{\left (\dfrac{6^2 + 6}{2} \right ) } = \dfrac{2}{3} + \dfrac{1}{21} = \dfrac{15}{21} = \dfrac{5}{7}[/tex]
The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 = 5/7.
Asia can rake her yard's leaves in 2 hours. It takes Isaac 6 hours to rake the yard's
leaves by himself. How long would it take if Asia and isoac work together?
Is will be 1 hour and 30 minutes
Answers
Answer:
I think i would be 2hours and 30 mins. Srry if it's wrong
Step-by-step explanation:
In a class of 29 students, 20 play an instrument and 18 play a sport.
There are 11 students who play an instrument and also play a sport.
What is the probability that a student chosen randomly from the class
plays a sport and an instrument?
Can someone please help me
Answers
Answer:11/29
Step-by-step explanation:
The numerator is alredy given as 11 students play both an instrument and a sport. Denominator is how many students in the class which is 29.
a A persen sold on article at a profit of 15% If he
sold it for Rs. 81 less, his loss would love been
12% Find the cost price of the article
Answers
Answer:
cost price (cp)=RS.300
sorry for asking all these questions, this is just really confusing
Answers
Answer:
-31
Step-by-step explanation:
hope this helped! <3
NOW! Which division problem does the diagram below best illustrate?
0000
OC
30-5-6
35-7-5
021-7-3
40-5-8
Answers
1 pts
Identify the ordered pair (point) and the slope for the point-slope form Y-3 = 7(2 – 4).
[Type in integers only.]
Point:(
I
Slope:
« Previous
Next >
Answers
Point: (4,3)
Mark has 380 coins Casey has 2x more than Albert Lilly has 5 coins more than Casey Logan has 3x more than Casey and Albert How many coins does Logan have
Answers
Answer:
141 coins
Step-by-step explanation:
Given that Mark has a total of 380 coins(assumed to be shared amongst Albert,Casey, Lily and Logan)
Albert= x
Casey= 2x
Lily= 2x+5
Logan=3x
There's a total of 380 coins
x+2x+2x+5+3x= 380
8x+5=380
8x=380-5
x=375/8
x= 46.9
Therefore Logan's coins = 3x= 3×46.9= 140.61 coins
Approximately Logan's coins =141 coins
Which of the following are the coordinates of a rectangle with a length of 4 units and a width of 3 units in the coordinate plane?
A- (−2, 1), (−2, −2), (2, 1), (2, −2)
B- (4, 3), (0, 3), (4, 7), (0, 7)
C- (1, −4), (−1, −4), (1, 0), (−1, 0)
D- (5, 6), (−3, 6), (5, 1), (−3, 1)
Answers
-2 and 2 are the x values of the coordinates which are 4 units apart, being 4 units in LENGTH
1 and -2 are 3 units apart and them being in the y part of the coordinate it’s 3 units wide
Which of the following is a perfect square ?
A. - 4
B. 1 over 4 over 19 (1/4/19)
C. 0.9
D. 100
Answers
There are 30 students in the class and 270 apples. if the apples are divided equally among the students, how many does each student get?
Answers
Answer:
9
Step-by-step explanation:
270/30=9
Katelyn ate ⅓ of an apple pie, and Chad ate ⅜ of the same pie. What fraction of the pie was eaten?
Answers
Answer:
17/24
Step-by-step explanation:
1. This is an addition problem. Remember, when adding fractions, you first need to find a common denominator.
What is a number that both 3 and 8 go into? (If you don't know, then you can just multiply the numbers and use that as the denominator)3 x 8 = 24The new denominator is 24.2. To find the numerator, multiply the current numerators by the number of times the original denominators divide into 24.
For example, 3 divides into 24 a total of 8 times. So, multiply 1 by 8 to turn 1/3 into 8/24.Do the same for 3/8, except multiply it by 3 because 8 goes into 24 three times. This makes the fraction equal 9/24.3. Now that the denominators are the same, add the numerators and keep the denominator for now.
8/24 + 9/24 = 17/244. Usually, you would have to reduce the fraction, but since 17/24 is already reduced to its simplest form, 17/24 is your answer.
if x= (4/5)^-2 divided by (1/4)^2,find the value of x^-1
Answers
Answer:
[tex]\displaystyle x^{-1}=\frac{1}{25}[/tex]
Step-by-step explanation:
We are given the value of x:
[tex]x= (4/5)^{-2}[/tex] divided by [tex](1/4)^2[/tex]
We need to find the reciprocal of x or:
[tex]\displaystyle x^{-1}=\frac{1}{x}=\frac{\frac{1}{4}^2}{\frac{4}{5}^{-2}}[/tex]
Operating:
[tex]\displaystyle x^{-1}=\frac{1}{4}^2*\frac{5}{4}^{-2}[/tex]
[tex]\displaystyle x^{-1}=\frac{1}{16}*\frac{16}{25}[/tex]
[tex]\mathbf{\displaystyle x^{-1}=\frac{1}{25}}[/tex]
-4x+9-x<-3 can someone give me the answer olease
Answers
Answer:
Yes I will always help someone in need. Your answer is x= >12/5
Step-by-step explanation:
Add me and ask any question.Please give me Brainiest
help please btw last part of d it is 6
Answers
Answer:
Ans is C
Step-by-step explanation:
Answer: the answer is b!
Step-by-step explanation: Hope this helps! Merry Christmas!
11. In the diagrams below the rows of green tiles are surrounded by white tiles
Find a formula for the number of white tiles which would be needed to
surround a row of n green tiles.
Hii please help!!! Show work
Answers
Step-by-step explanation:
There are 12 white tiles surrounding 3 green tiles, and 16 white tiles surrounding 5 green tiles.
Common difference = (16-12)/(5-3) = 2.
Hence number of white tiles = 2n + 6.
I have no idea how to do this
Solve 3 x < 6
Answers
Answer:
X < 2
If you need an explanation, feel free to leave a comment
Cheers! :)
Find the base angles of the figure below.
A.) 72°
B.) 108°
C.) 36°
D.) 54°
Answers
Answer:
36
Step-by-step explanation:
The angles of a triangle have a sum of 180 degrees. This is an isosceles triangle indicated by the red markers on sides ED and EF. This means that the sides and angles are congruent.
Subtract 108 from 180 and divide that by 2.
180-108 = 72
72/2 = 36
y=6x+1
y=1/6x+1
y=1/6x-5
y=6x-5
which one
Answers
Answer:
y=6x+1
Step-by-step explanation:
count from your first point (0,-5) then count up to positive 1 on the y-axis, then go over 1 and you are at your other point. when you count up that is your slope. when you count over that is your b
ASAP!!! Will give brainliest!!! Solve for X
Answers
Answer:
h=√p^2+b^2
13 = √x^2+(x+7)^2 now you can solve
Answer:
x = 5
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + (x + 7)² = 13² ← expand and simplify left side
x² + x² + 14x + 49 = 169 ( subtract 169 from both sides )
2x² + 14x - 120 = 0 ( divide through by 2 )
x² + 7x - 60 = 0 ← in standard form
(x + 12)(x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 12 = 0 ⇒ x = - 12
x - 5 = 0 ⇒ x = 5
But x > 0 , thus x = 5