Answers
The given expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex].
What are Exponents?
The exponent of a number indicates how many times to multiply the number.For example, three to the power of two is represented as, [tex]3^{2}[/tex]. Here, 3 is the base number and 2 is the exponent. Also, [tex]3^{2} =3 \times 3[/tex].What are the Laws of Exponents?
There are major seven Laws of Exponents as follows:
Product Rule of Exponents: [tex]a^{m} \times a^{n} =a^{m+n}[/tex]Quotient Rule of Exponents: [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex]Power of a Power Rule: [tex](a^{m} )^{n} =a^{m \times n}[/tex]Product of a Power Rule: [tex]a^{m} \times b^{m} =(ab)^{m}[/tex]Power of a Quotient Rule: [tex]\frac{a^{m} }{b^{m} } =(\frac{a}{b})^{m}[/tex]Zero Power Rule: [tex]a^{0} =1[/tex]Negative Exponent Rule: [tex]a^{-m} =\frac{1}{a^{m}}[/tex]From the given question, we have the expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] -----(1)
Here, we can use the power of a power rule to simplify the expression.
The power of a power rule is of the form, [tex](a^{m} )^{n} =a^{m \times n}[/tex]
Solving expression (1) using the power of a power rule, we get
[tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-2 \times 3} }{(x^{6} y^{3} z)^{2 \times 3} }\\\implies [\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]
Therefore, the given expression is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]
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Related Questions
What is the expression in factored form?
5x² - 7x-6
O
(5x-2)(x-3)
(x + 3)(5x - 2)
O (5x + 3)(x - 2)
O (5x + 3)(x + 2)
Answers
(5x+3)(x-2)
(5x+3)(x-2)= 5x^2-10x+3x-6= 5x^2-7x-6
Increasing intervals for cubic function
Answers
Answer:
it is basic and .........
A discount of 25 % is allowed on an article marked at rs 17 500. calculate the discount
.
Answers
Answer: 4,375 rs
Step-by-step explanation:
25% × 17,500 = 4,375
Answer:
$4375
Step-by-step explanation:
25 percent *17500 =
(25:100)*17500 =
(25*17500):100 =
437500:100 = 4375
Now we have: 25 percent of 17500 = 4375
Divide usando un modelo de área
6426 ÷ 9
Answers
Three students in the Math Club are analyzing 1/410 x+8) and -(1/2 x +13)+3(x +5), for all the values of x. Each student claims the expressions are related according to the results shown in the table. Which student is correct?
Answers
Student 1 expression is correct 1/4(10 x+8) = -(1/2 x +13)+3(x +5)
Algebra is defined as a generalization of arithmetic in which numbers are represented by letters that are combined according to arithmetic rules. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are some of the sub-branches.
Given that 1/4(10 x+8) and -(1/2 x +13)+3(x +5)
Student 1: 1/4(10 x+8) = -(1/2 x +13)+3(x +5)
Student 2: 1/4(10 x+8) > -(1/2 x +13)+3(x +5)
Student 3: 1/4(10 x+8) < -(1/2 x +13)+3(x +5)
We have to find which student is correct for all values of x
Let us take x =1
Now substitute the x vale in student 1 expression
1/4(10 x+8) = -(1/2 x +13)+3(x +5)
1/4(10 (1)+8) = -(1/2 (1)+13)+3(1 +5)
1/4(18) = (-1/2 -13)+3(6)
18/4 = -1/2 -13 + 18
9/2 = -1/2 + 5
9/2 = (-1+10)/2
9/2 =9/2
So Student 1 expression satisfies
If student 1 expression is correct two are wrong
Therefore Student 1 expression is correct
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The acute angle meaure of a triangle are (x 20)°, (2x 10)°,
and (4x - 60)°. What are the angle meaure of the triangle?
A. 45°, 65°, 70° C. 40°, 60°, 80°
B. 50°, 60°, 70° D. 60°, 60°, 60°
Answers
The angles of the triangle will be 50°, 70°, 60° .
let the 3 angles of a triangle be A, B and C
The first acute angle A is given by = x + 20
The second acute angle B is given by = 2x + 10
The third acute angle C is given by = 4x - 60
Now we know that the sum of the angles of a triangle is 180°
So ,
A + B + C + = 180°
x + 20 + 2x + 10 + 4x - 60 = 180°
7x - 30 = 180°
7x = 210°
x = 30°
So, from the value of x , we can calculate the value of each angle
Therefore, the required angles are :
angle A = (x + 20)° = 30° + 20° = 50°
angle B = (2x + 10)° = 60° + 10° = 70°
angle C = (4x - 60)° = 120° - 60° = 60°
verification : sum of the angles = 50° + 70° + 60° = 180°
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rita and tina each make 11$ an hour
Answers
The expressions that represent the total weekly wages of Rita is 11r + 32 and of Tina is 11t.
We are given;
Rita and Tina each make $11 an hour working as cashiers at a supermarket.
Last week, Rita worked r hours while Tina worked t hours.
Rita also worked overtime hours during the week, for which she was paid an extra $32 flat wage.
We need to find the expressions that represent the total weekly wages of both Rita and Tina.
Let us form an algebraic expression for both one by one;
For Rita:
Number of hours Rita worked for = r
Cost per hour = $ 11
The amount for overtime Rita earned = $32
So, the equation expressing the total weekly wage for Rita = 11r + 32.
For Tina :
Number of hours Tina worked for = t
Cost per hour = $ 11
So, the equation expressing the total weekly wage for Tina = 11t.
Thus, the expressions that represent the total weekly wages of Rita is 11r + 32 and of Tina is 11t.
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A prefect is to be chosen from 15 girls and 8 boys. What is the probability that the prefect is a girl?
Answers
Answer:
0.6522 or 65.22%Step-by-step explanation:
Total number of candidates is:
15 + 8 = 23Probability of a girl to be chosen as prefect:
P(girl) = number of girls / total number of candidatesP(girl) = 15/23 = 0.6522 or 65.22%Answer:
Probability = 15/23
Step-by-step explanation:
Now we have to,
→ find probability that prefect is a girl.
The total members are,
→ 15 girls + 8 boys
→ s = 15 + 8
→ [ s = 23 ]
Then the probability will be,
→ P = 15/s
→ [ P = 15/23 ]
Hence, the answer is 15/23.
everyday a person uses about 90 liters of water at home 6 gallons is about 23 liters about how many liters of water does a person use at home daily?
Answers
The volume in liters a person uses daily is about 90 liters which is equivalent to 23.48 gallons
How to find the amount of water the person uses dailyInformation given in the question
everyday a person uses about 90 liters of water at home
6 gallons is about 23 liters
how many liters of water does a person use at home daily = ?
Volume is a three dimensional calculation, the formula depends on the object. how ever the calculation is usually done by area * height or thickness
the unit for volume can liters, gallons, cubic meters, and so on
The question have it that a person uses about 90 liters of water daily converting this quantity in gallon is done by
= 90 liters * 6 gallons / 23 liters
= 90 * 6 / 23
= 23.48 gallons
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the graph below represents the total number of cups of coffee and the total amount of sugar required to make coffee what is the constant of proportionality'
Answers
a. Constant of proportionality is equal to 5.
b. Point (12, 60) represents that 12 pounds of sugar required to make 60 cups of coffee.
What is graph ?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
We have the relation between total number of cups of coffee and the total amount of sugar:
Let y represents the number of cups of coffee
and, x represents the amount of sugar
y ∝ x
y = kx
a. 'k' is the constant of proportionality
When y = 20 , x = 4
20 = k × 4
k = 20/ 4
k = 5
b. From the graph point (12, 60) represents 12 is on the x-axis and y is on the y-axis.
12 represents amount of sugar and 60 represents the number of cups of coffee.
Hence, the Constant of proportionality is equal to 5.
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what is the probability that a family of two children has two boys given that the first child is a boy
Answers
Since the first child is a boy, this means we need to find the probability of another boy. This is 1/2 since we assume each gender has the same chance of happening.
10. (Modeling) Height of a Projectile A projectile is fired vertically upward, and its
height s(t) in feet after t seconds is given by the function defined by
s(t) = -16t² + 800t + 600.
(a) From what height was the projectile fired?
(b) After how many seconds will it reach its maximum height?
(c) What is the maximum height it will reach?
(d) Between what two times (in seconds, to the nearest tenth) will it be more than
5000 ft above the ground?
(e) How long to the nearest tenth of a second will the projectile be in the air?
fuel
Answers
The answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5).
A projectile is fired vertically upward, and its height s(t) in feet after t seconds is given by the function defined by
s(t) = -16t² + 800t + 600.
To find out
(a) From what height was the projectile fired
Given height functions: s(t) = -16t² + 800t + 600
Now,
[tex]s^{'}(t)[/tex] - -32t+800
(b) Now, to find the time it will attain maximum height,
[tex]s^{'}(t)[/tex] = 0
-32t = -800
t = 25 seconds
(c) The maximum height it will reach
= [tex]-16*(25)^{2} + 800*25+600[/tex]
= -10000+20000+600
= 10,600 feet
(d) Between what two times (in seconds, to the nearest tenth) will it be more than 5000 ft above the ground
By putting x = 3
[tex]P(3) = 4*(3)^{3}-50 * (3)^{2}-8*3+6[/tex]
= 108-90-24+6
= 114-114
= 0
Therefore x = 3 is a zero of P(x)
(e) How long to the nearest tenth of a second will the projectile be in the air
Now, factoring,
[tex]f(x) = x^{3}+3x^{2} -13x-15\\ \\= x^{3}+x^{2} +2x^{2}+2x-15x-15\\ \\ = (x+1)(x^{2} +5x-3x-15)\\\\= (x+1)(x(x+5)-3(x+5))\\\\=(x+1)(x-3)(x+5)[/tex]
Hence the answer is a) 0 height, b) 25 seconds c) 10,600 feet d) 3 times e) (x+1)(x-3)(x+5)
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a. Create a quadratic expression in standard form. An expression does NOT have an equal sign. Quadratic has the form ax^2+bx+c where you pick numbers for a, b, and c. You will need to find (b/2)^2; what will make that easier? LOOK (Links to an external site.)Links to an external site. here is a short video that demonstrates how to do this, please do not use x2 +16x in your example.
b. Rewrite the expression by completing the square. Explain your work using complete sentences.
Use the order of operations to turn the expression back into standard form. Explain your work using complete sentences.
Explain why completing the square will always result in a perfect square trinomial.
Answers
f(x) = ax? + bx + c
(b) To complete the square:
Divide the equation through by a , the equation then becomes
At this point, you are require to
(i) multiply the coefficient of x by 1/2
(I) square the result
(ili) add the result to both sides , we have
4(x) =27+ + (2) + + (2a) by completing the square, we have
4x) = (a + da) + & - *. We did this in order to make the expression balance
(c) Using the order of operation to turn the expression back into standard
form
Help meeeeeeeeeeee pleaseee
Answers
Answer:
25%
Step-by-step explanation:
A ubmarine travel 4. 2 km due Eat from it bae and then turn and travel due North for 6. 5 km. How far away i the ubmarine from it bae?
Give your anwer rounded to 1 DP
Answers
The Submarine is 7.74 Km away from its base .
In the question ,
it is given that ,
the distance travelled by Submarine from base in East direction = 4.2 Km
let the distance from base to east direction be denoted by AB ,
that means AB = 4.2 Km
the distance travelled by Submarine from East to North direction = 6.5 Km
let the distance from east to north direction be denoted by BC .
that means BC = 6.5 Km
the given situation form a right triangle ,
So , the distance from submarine to its base is the hypotnuse of the right triangle , that is AC .
So By Pythagoras Theorem ,
AC² = AB² + BC²
Substituting the values , we get
AC² = 4.2² + 6.5²
AC² = 17.64 + 42.25
AC² = 59.89
AC = √59.89
AC = 7.7388
AC = 7.74
Therefore , The Submarine is 7.74 Km away from its base .
The given question is incomplete , the complete question is
A Submarine travel 4. 2 km due Eat from it base and then turn and travel due North for 6. 5 km. How far away is the submarine from it base ?
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Once an antibiotic is given, number of bacteria decreases at a rate of 15% /day. There
were about 15,000 bacteria prior to the treatment. The graph models the number of
bacteria after x days of treatment.
W
What are the key features of the exponential function modeled in terms of this
situation and how can they be interpreted?
Answers
Asymptote indicates that as time increases, the number of bacteria approaches 0.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
Once an antibiotic is given, number of bacteria decreases at a rate of 15% /day.
There were about 15,000 bacteria prior to the treatment.
The line y = 0 is an asymptote of the graph.
The y-intercept is 15,000.
The y-intercept represents the number of bacteria when treatment began.
The asymptote indicates that as time increases, the number of bacteria approaches 0.
Hence, asymptote indicates that as time increases, the number of bacteria approaches 0.
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What is the value of sin(A)?
Answers
Answer: 3/5
Step-by-step explanation:
Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse: The other trigonometric functions of the angle can be defined similarly; for example, the tangent is the ratio between the opposite and adjacent sides. As stated, the values and.
PLSS HELP AASP I NEED THIS LIKE RNN
Answers
Answer:
4/6 and 6/9
Put 6 in both the boxes as the both ratios will be equal to 2/3 if 6 is put.
Answer:
[tex] \frac{4}{6} \: and \: \frac{6}{9} [/tex]
(a) a box contains 3 red balls, 2 white balls, and 5 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second? (enter your probability as a fraction.)
Answers
Answer:2
Step-by-step explanation:i did it
Find the common difference of the arithmetic sequence -13, -22, -31,.
Answers
The common difference of the arithmetic sequence -13, -22, -31, is -9.
What is an arithmetic sequence?An arithmetic sequence is a set of numbers that are ordered and have a common difference between each consecutive term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.
To find a specific term in an arithmetic sequence, we use the nth term formula. Step 1: An = a + (n - 1)d gives the nth term of an arithmetic sequence.
Some arithmetic sequence examples using this expression are:
1, 5, 9, 13, 17, 21, 25, 29, 33, ...
2, 4, 6, 8, 10, 12, 14, 16, 18,...
In this case, the difference will be:
= 2nd term - 1st term
= -22 - (-13)
= -22 + 13
= -9
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4x-4y=8
5x-3y = 18
Find X
Answers
Let's solve your system by substitution.
4x−4y=8 and 5x−3y=18
Step: Solve 4x−4y=8 for x:
4x − 4y = 8
4x − 4y + 4y = 8 + 4y (Add 4y to both sides)
4x = 4y + 8
[tex]\frac{4x}{4} = \frac{4y + 8}{4}[/tex]
x = y + 2
Step: Substitute y + 2 for x in 5x − 3y = 18:
5x − 3y = 18
5(y+2) − 3y = 18
2y + 10 = 18 (Simplify both sides of the equation)
2y + 10 + (−10) = 18 + (−10) (Add -10 to both sides)
2y = 8
y = 4
Step: Substitute 4 for y in x = y + 2:
x = y + 2
x=4+2
x=6 (Simplify both sides of the equation)
Answer:
x = 6 and y =4
4x-4y=8
+4y +4y
————— << equals
4x=4y+8
—- = —— << divide
4 4
—————- << equals
x=y+2
5x-3y=18
—————
5(y+2)-3y=18
———————- << equals
2y+10=18 << simplified
+-10 +-10
—————- << equals
2y=8
—-=— << divide
2 2
——— <y=4
x=4+2
———- << equals
x=6
The distance between the school and the park is 6 km. There are 1.6 km in 1 mile.How many miles apart are the school and the park
Answers
Answer:
3.7miles
Step-by-step explanation:
divide the length value by 1.6
Please help me please i beg you can someone tell me if my answer is right or not
Answers
Answer:
Absolutely correct. you got the answer
Find the 8th term of the geometric sequence 10, -20, 40, ...
Answers
Answer:
a₈ = - 1280
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 10 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-20}{10}[/tex] = - 2 , then
a₈ = 10 [tex](-2)^{7}[/tex] = 10 × - 128 = - 1280
The 8th term of geometric sequence is -1280
Step of calculate geometric sequence
This is a geometric sequence. The geometric number sequence is characterized by the presence of a ratio (the ratio between the next term and the previous term). The next term is the product of the previous term with the ratio. Another sequence called arithmetic sequence is characterized by the presence of difference (the difference between the next term and the previous term).
10, -20, 40, ...
We will first analyze the things that can be found in the three numbers in the sequence. The thing to look for is the first term (a) and also the ratio (r). The first term can also be written as U1, where the 2nd term is U2, and the n-th term is Un.
[tex]a = 10[/tex]
[tex]r=\frac{U2}{U1}[/tex]
[tex]r=\frac{-20}{10}[/tex]
[tex]r=2[/tex]
When the first term (U1) and ratio (r) have been obtained, then we can find the 8th term by substitute it in the formula.
[tex]Un=ar^{n-1}[/tex]
With that formula, let's find the 8th term.
[tex]U8=10(-2)^{8-1}[/tex]
[tex]U8=10(-2)^{7}\\U8=10(-128)\\U8=-1280[/tex]
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A man has extra digits (six fingers on each hand and six toes on each foot). His wife and their daughter have a normal number of digits. Having extra digits is a dominant trait. The couple's second child has extra digits. What is the probability that their next (third) child will have extra digits?.
Answers
The probability that their next (third) child will have extra digits is 0.5
Polydactyly refers to the presence of extra fingers in the human body. It is a hereditary condition that is passed down from parents to children. The thumb, middle, and little fingers are the most commonly affected by this condition. Polydactyly refers to the presence of extra fingers in the human body. It is a hereditary condition that is passed down from parents to children. The thumb, middle, and little fingers are the most commonly affected by this condition.
A trait is a distinguishing characteristic that a person possesses. Dominant traits are defined as having only one copy of a gene on a chromosome that expresses a specific trait.
Individuals exhibit the dominant traits most prominently. Polydactyly is the dominant condition in this case.
The father has six fingers and six toes, while the mother is in normal condition. In this particular condition, polydactyly is a dominant trait. Twelve percent of the couple's children are expected to have extra digits.
Because the father has the dominant trait and the mother is in normal condition, there is a 50% chance that this deformity will be passed down to children.
The probability that their next child will have extra digits is 0.5
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Otto used 5. 5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that otto used in the recipe, and what are the constraints on the values of x and y? y=5. 5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. Y=5. 5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5. 5. Y=x+5. 5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. Y=x+5. 5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5. 5.
Answers
From the given data , equation which can be formed to get the value of y that is the total amount of flour Otto used in his recipe is given by :
y = x + 5.5
With the constraints x and y where,
x is any real number ≥ 0,
y is any real number ≥ 5.5
As given in the question,
Number of cups of wheat flour used by Otto = 5.5.cups
Number of cups of white flour used by Otto = x cups
Let y represent the total amount of flour used by Otto in the recipe
Required equation to represent the total amount of flour used by Otto in the recipe is given by :
y = x + 5.5
Where x is any real number which is greater than or equal to 0.
As cups of flour can be in fractions.
And y is any real number which is greater than or equal to 5.5.
As y = x + 5.5, and x ≥0 and cups of flour can be in fractions.
Therefore, from the given data , equation which can be formed to get the value of y that is the total amount of flour Otto used in his recipe is given by :
y = x + 5.5
With the constraints x and y where,
x is any real number ≥ 0,
y is any real number ≥ 5.5
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what is the gcf of 140 and 180
Answers
The GCF of 140 and 180 in the question can be expressed as 20.
What is Prime factorization?The concept that will be used in the calculation is the concept of the Prime factorization.
Prime factorization can be described as the way that can be used to find the prime factors of a number , making sure that the original number is evenly divisible by these factors.
Prime factorization of 140 and 180 are:
40: (2 × 2 × 5 × 7)
180: (2 × 2 × 3 × 3 × 5)
Then the common prime factors which are common that can be associated with 140 and 180 which is the GCF of 140 and 180 is ( 2 × 2 × 5 )= 20.
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Which is the better buy?
6 pounds of kitty litter for $3.84
231 ounces of kitty litter for $6.93
Answers
HELP! PLEASE ASAP!!!!!!
Answers
The sales tax is $2 and the total cost of the item is $42.
Given:
selling price = $40
rate of sales tax = 5%
sales tax = 40*5%
= 40*5 / 100
= 200/100
= $2
Total cost = 40+2
= $42.
Therefore the sales tax is $2 and the total cost of the item is $42.
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A printing company calculates its costs using the function e(x) 0.3²-125x+100 and calculates its revenue using the function (x) -
function is p(x) r(x) - c(x)
Which function represents the company's profit?
A p(x)= 0.7x² + 35x + 190
B
(x) 0.7x² - 285x + 100
CP(x)= -0.7x² + 35x + 190
D p(x)= -0.7x² + 285x - 190
0.4x + 160x The company's profit
Answers
Answer:yes
Step-by-step explanation:
yes