The simplified form of the given expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is option d 49.
Given,
The expression = [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]
We can simplify this expression by using Laws of Indices;
The first rule: [tex]a^{n}[/tex] × [tex]a^{m}[/tex] = [tex]a^{m+n}[/tex]
The second rule: [tex](a^{n}) ^{m}[/tex] = [tex]a^{mn}[/tex]
The third rule: [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]
The fourth rule: [tex]a^{0}[/tex] = 1
The fifth rule: [tex]a^{-1}[/tex] = [tex]\frac{1}{a}[/tex] ; [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
The sixth rule: [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex] ; [tex]a^{\frac{1}{m} }[/tex] = [tex]\sqrt[m]{a}[/tex] ; [tex]a^{\frac{n}{m} }[/tex] = [tex](a^{\frac{1}{m} } )^{n}[/tex] = [tex](\sqrt[m]{a} )^{n}[/tex]
Here we can use First, Second, Fifth and Sixth rule:
[tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]
= [tex](7^{5} )^{\frac{1}{6} }[/tex] ×[tex](7^{7} )^{\frac{1}{6} }[/tex]
= [tex]16807^{\frac{1}{6} }[/tex] × [tex]823543^{\frac{1}{6} }[/tex]
= 5.061140185 × 9.68161288
= 49
That is, the simplified form of the expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is 49.
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what does UIF stand for ?
UIF stands for Unemployment Insurance Fund.
When workers become unemployed or are unable to work due to maternity, adoption, or parental leave, or illness, the Unemployment Insurance Fund (UIF) provides them with short-term assistance. It also helps the dependents of a deceased contributor.South Africa's unemployment insurance system is governed by the following legislation: 2001 Unemployment Insurance Act (the UI Act). 2002 Unemployment Insurance Contributions Act (the UIC Act)These Acts, which went into effect on April 1, 2002, provide for the benefits to which contributors are entitled, as well as the imposition and collection of contributions to the UIF.Contributions to the UIF are due from all employees and their employers. However, an employee is not eligible to contribute to the UIF if he or she: is employed by the employer for less than 24 hours per month; is employed as an officer or employee in the national or provincial spheres of government; or is employed as an officer or employee in the national or provincial spheres of government. Is a traditional leader, a member of the province House of Traditional Leaders, and a member of the Council of Traditional Leaders.Thus this is the full form of UIF.
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I'm having problems with this can someone help asap pls
Answer:
C I think good luck brother bye bye
Simplify -3r(-12r + 4r - 16) please!!
Answer:FIRST ONE
Step-by-step explanation:
Assume that 632 people purchased pies that day. Explain how you could determine exactly how many people bought each type of pie.
In order to determine exactly how many people bought each type of pie, one will have to multiply the percentage by 632.
How to illustrate the information?It should be noted that this is a pie chart and the information shows the percentage for each group.
In this case, to determine exactly how many people bought each type of pie, one will have to multiply the percentage by 632.
For example, berry will be:
= 15.4% × 632
= 97
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Sam flipped a coin 20 times. He got heads 12 times. What was the experimental probability of getting heads in Sam's coin toss experiment?
Answer: 60%
Step-by-step explanation:
12/20=.6
.6 is 60%
Answer:
21
Step-by-step explanation:
You are helping your friend with his math homework. He made an order of operations mistake. Which part did he do in the wrong order
write 658. 129 and expanded form
Answer:
Six hundred fifty eight and one hundred twenty nine thousandths
Hans will run 27 miles this week. so far, he has run 18 miles. what are the possible numbers of additional miles he will run? use t for the number of additional miles he will run.
Hans will run additional 9 miles to the 18 miles he has run to complete 27 miles in wants to run for the week.
If Hans is to run 27 miles this week and he has run 18 miles, the additional miles he has to run in the week is t. Meaning that t plus eighteen is equal to 27, which is expressed mathematically below
t + 18 = 27
To solve the equation above, use balancing method. To use balancing method, subtract 18 from both side of the equation.
t +18 -18 = 27-18
t + 0 = 27-8
t = 27 -18
t = 9
Therefore, Hans will run additional 9 miles to complete 27 miles for the week.
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What are the factor pairs of 63
Which expression is equivalent to log₅32 ?
(A) log 5+ log 32 (B) log 5- log 32 (C) (log 5)(log 32) (D) log 32/log 5
The given expression log₅32 is equivalent to the expression (D) log32/log5.
What do we mean by an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent rules. To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.To find which expression is equivalent to log₅32:
Law of logarithms:
The law of logarithms states that: log(a) b = log(10)b/log(10)aGiven the log function, which is written as log₅32
a = 5b = 32Substitute as: log₅32 = log32/log5
Therefore, the given expression log₅32 is equivalent to the expression (D) log32/log5.
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Find X, pls show the steps on how to do this equation
Answer:
perpendicular angle are=90
so there for: (4x-2)+(3x+8)=90
4x-2+3x+8=90
7x+6=90
7x=90-6
7x=84
so there for:x=12
alicia bought 2 1/2 dozen donuts for $8.10 . what was the cost per dount
Answer: $3.70
Step-by-step explanation:
30 divided by 8.10 equals 3.70
Write 7380 to the nearest thousand
Answer:
7000
Step-by-step explanation:
Your answer is 7000.
On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .
b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?
The height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² = 2 m
What is gravitational acceleration ?Gravitational acceleration can be defined as the acceleration of any object when the object is in free fall. or we can say that the gravitational acceleration is the quantity which describes the acceleration of free falling object within vacuum. It is denoted by g .
What is Potential Energy ?Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy.
Formula of potential energy :
U = mgh
where, U = gravitational energy
m = mass of object
g = gravitational acceleration
h = vertical height of object
In the question given,
g= -9.8m/s² , U = -39.2 kg m² /s²
as, U = mgh
h = U / mg
put the values in this equation
h = -39.2 / 2 (-9.8 )
h = 2
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The complete question is :
On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .
a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?
b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?
Q 100+ 10+ 20 ÷4-5 x 2 + 8
Answer:
113 explanation I just took the test
Answer: 113
Step-by-step explanation:
100 + 10 +5 -10 +8 = 113
If 21 and 22 are vertical angles, <2 and <3 are complementary angles
and m/3 = 56°, find m/1.
Answer:
........................................
Use the table to answer the table Input: 2, 3, 6.
Output: 6, 9, 18 what ratio is represented in the table?
A: 1:3
B: 1:4
C: 1:5
D: 1:13
Thanks to whoever answers this. :D
The required ratio of the input value to the output value is 1:3. option D is correct.
The table has been shown with input and output data we have to determine the ratio of the input value to the output values.
Here,
1) for input 2 there is output 6
Ratio = input / output = 2 / 6 = 1 : 3
2) for input 3 there is output 9
Ratio = input / output = 3 / 9 = 1 : 3
2) for input 6 there is output 18.
Ratio = input / output = 6 / 18 = 1:3
Thus, the required ratio of the input value to the output value is 1:3. option D is correct.
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The figure shown is composed of a triangle within
a trapezoid. Determine the area of the
shaded region.
The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²
What is the Area of a Trapezoid?Area of ay trapezoid is determined using the formula:
Area = 1/2 × (a + b) × h, where a and b are the lengths of the bases of the trapezoid that are parallel, and h is the height or distance between the bases of the trapezoid.
What is the Area of a Triangle?
To find the area of a triangle, use:
Area = 1/2 × base × height of the triangle.
The area of the shaded region = area of the trapezoid - area of the triangle
Area of the trapezoid:
a = 5 m
b = 9 m
h = 6m
Substitute
Area of the trapezoid = 1/2 × (5 + 9) × 6
Area of the trapezoid = 1/2 × (14) × 6
Area of the trapezoid = 7 × 6
Area of the trapezoid = 42 m²
Area of the triangle:
Base = 7 m
Height = 6 - 4 1/2 = 1.5 m
Substitute
Area of triangle = 1/2 × 7 × 1.5
Area of triangle = 5.25 m².
The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²
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Multiply 4.5x and 3x please!!
Answer:
13.5x
Step-by-step explanation:
Move all terms containing x to the left, all other terms to the right.
Cross multiply.
Answer: 13.5x
Step-by-step explanation: all that needs to happen is the numbers multiplied. after, put the x on the
Ivan bought a new television. He was able to pay $120 at the time he received the television,
He will pay $44 each month on the balance. The original cost of the television was $736. Ilow
many months will it take Ivan to pay off the television?
29) Explain the difference of the two expressions in the question.
What is the difference between (f g)(x) and (fog)(x)?
The function fg(x) seems to be the product of f and g, whereas the function fog(x) is the composition of f and g.
Definition of a composite function:A function whose values are discovered by applying another function to an independent variable and then applying that second function to the result, and whose domain consists of those possible values for which the result yielded by the first function lies inside the domain of both the second.
What kind of math are composite functions?A composite function is one that is dependent on another. When one function is swapped for another, a composite function is formed. For example, f(g(x)) is the composite function created when g(x) is replaced for x in f. (x). f(g(x)) can be translated as "f of g of x."
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Find the area of this circle.
Use 3.14 to approximate .
A = πr²
14 ft
A = [?] ft²
The area of the circle, using 3.14 to approx. The area of this circle is 615.44[tex]ft^{2}[/tex].
How to find the area of circle?The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = [tex]\pi r^{2}[/tex], where r is the circle's radius, is the formula for calculating a circle's surface area.
The square unit—for instance, [tex]m^{2}, cm^{2}, in^{2}[/tex] etc.—is the unit of area. In square units, the area of a circle is equal to [tex]\pi r^{2}[/tex]or [tex]\frac{\pi d^{2} }{4}[/tex]where (Pi) = [tex]\frac{22}{7}[/tex] or 3.14. The ratio of a circle's circumference to its diameter is known as pi (π). This unique mathematical constant exists.
Area = [tex]\pi r^{2}[/tex]
3.14×14×14 = 615.44[tex]ft^{2}[/tex].
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John is driving to his office to attend a meeting. In the first 10 minutes, he covers a distance of 1 mile every minute. Then he stops at a local restaurant for 15 minutes to have breakfast. After that, he covers a distance of 0.5 miles every minute in the next 10 minutes to reach his office.
Which graph models the piecewise function for the given situation?
Answer:
Letter D is the correct answer.
Step-by-step explanation:
In the graph, the first line is an increasing diagonal and it stops in 10, meaning that John travelled 10 miles in 10 minutes.
After that, there is a horizontal line that indicates how much time he spent at the restaurant.
Finally, the last diagonal shows the distance travelled (5 miles) and the time it took (10 minutes.)
had the same question a couple minutes ago
hope it helps you;)
please help me quick
the answer is pyramid or cone
Factor this expression completely.
6x^2- 13x - 28
Answer: (2x-7)(3x+4)
Step-by-step explanation:
There is a technique called the “Slide Method” that can make this easier to solve.
The first step is to slide the coefficient of the 1st term and multiply it to the last term; which becomes:
X^2-13x-28(6) or x^2-13x-168
Next, factor this equation normally. The two factors that go into this are -21 and 8, so we can set this up as: (x-21)(x+8)
After that, divide both sides by the 6 that you previously slid:
(X-21/6)(x+8/6)
Then, reduce the fractions:
(X-7/2)(x+4/3)
After this is the last step. Take the denominator of the fraction, and make it the coefficient of the x variable: (2x-7)(3x+4)
Checking our Work; we get: (6x^2+8x-21x-28)=(6x^2-13x-28)
So, we know that (2x-7)(3x+4) is correct.
The minimum distance from Earth to the Sun is 91.4 million miles. The maximum distance is 94.5 million miles. represent these 2 distances on a number line.
The required number line representation is attached
To solve this question we need to know the concept of number line :
Number lines are a horizontal straight lines in which the integers are placed in equal intervals all this numbers in a sequence can be represented in a number line . this line extends infinitely in both sides.
the numbers on the number line increases as one move right and decreases on moving from right to left . A number line can be used to depict both positive and negative integers. Writing numbers on a number line facilitates number comparison. The numbers on the left of the number line are smaller than the numbers on the right.
A number line can also be used to carry out addition , subtraction , multiplication and division . We move right to add move left to subtract and skip count to multiply .
The required number line is attached in the picture below :
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In the given right-angled triangle ABC, ∠B = 90°. Find the value of x.
Given - Sides of a triangle
Find - Value of x
Solution - The value of x is 3.
The sides of the right angled triangle are calculated by the Pythagoras theorem. As per the theorem,
Hypotenuse² = Base² + Perpendicular²
In the given triangle, Hypotenuse is (x+2), Perpendicular is 5 and Base is (x-3).
(x+2)² = 5² + (x-3)²
x² + 4x + 4 = 25 + x² - 6x + 9
On solving, the equation will be -
6x + 4x = 25 + 9 - 4
Performing addition and subtraction to find the value of x
10x = 30
x = 30/10
Performing division to find the value of x
x = 3
So, the value of x is 3.
24 -7.2(-4x + 3) ≤-26.4
Answer:
x [tex]\leq[/tex]-1
Step-by-step explanation:
first distribute
24+28.8x-21.6[tex]\leq[/tex]-26.4
add like numbers
2.4+28.8x[tex]\leq[/tex]-26.4
move the constant to the right
28.8x[tex]\leq[/tex]-26.4-2.4
calculate
28.8x[tex]\leq[/tex]-28.8
divide both sides by 28.8
x[tex]\leq[/tex]-1
Solve each equation. Round to the nearest ten-thousandth. Check your answers.
8+10x=1008
8 + [tex]10^x[/tex] = 1008 => x = 3, by exponentiation.
What is exponentiation?Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as [tex]b^n[/tex].Its pronunciation is "b (raised) to the (power of) n."Given: 8 + [tex]10^x[/tex] = 1008
=> [tex]10^x[/tex] = 1000
=> [tex]10^x[/tex] = 10³
=> x = 3
Hence, 8 + [tex]10^x[/tex] = 1008 => x = 3, by exponentiation.
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savannah is working two summer jobs, making $10 per hour washing cars and making $22 per hour tutoring. In a given week she can work at most 8 total hours and must earn no less that $110. Of x represents the number of hours washing cars and y represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities are 10x + 22y ≥ 110 and x + y ≥ 8 and values of x and y are 5.5 and 2.5 respectively.
What is inequality?In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
Total amount by washing cars = 10x
Total amount by tutoring = 22y
Total hours should be no less than 8
So,
x + y ≥ 8
And,
Total amount ≥ 10
10x + 22y ≥ 10
By substitution,
10(8 - y) + 22y ≥ 10
y ≥ 2.5
And x ≥ 5.5
Hence "The system of inequalities is 10x + 22y ≥ 110 and x + y ≥ 8 and values of x and y are 5.5 and 2.5 respectively".
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