Simplify each expression. (-8x³)⁻⁴/₃

The expanded form of 3(2x -3y -2) is given by the equation 6x -9y -6

The equation given is a linear equation in two variables and to simplify the equation 3(2x -3y -2), we need to use algebraic properties

The algebraic property used here is distributive property which says that a (b+ c) = ab + ac.

So, let us expand the equation using the algebraic property mentioned above

As a= 3, b=2x and c=3y+2

  3(2x -3y -2)

  3 (2x) -3(3y+2)

Using the property again with a=3, b=3y and c=2

     3 (2x) -3(3y+2)

     6x -3(3y) -3(2)

     6x - 9y -6

Hence, the expanded form of 3(2x -3y -2) is given by the equation 6x -9y -6

What are the 4 algebraic property?

There are four primary houses of numbers: commutative, associative, distributive, and identification. You ought to be acquainted with every of these. it's miles specifically important to understand these houses when you attain advanced math together with algebra and calculus.

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Answer:

I'm from California I'm new to this

The expanded form of the expression log m² n⁵ is

2 log m +5 log n.

Given that the expression is log m² n⁵.

We are required to find the expansion form of the given expression.

Product property of logarithm says that the logarithm of a product is equal to a sum of logarithms. Because logs are exponents, and we multiply like bases, we have to add the exponents.

The expression is log m² n⁵.

log m² n⁵=log [tex]m^{2}[/tex]+ log [tex]n^{5}[/tex]

=2 log m +5 log n

Hence the expanded form of the expression log m² n⁵ is

2 log m +5 log n.

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Answer:

4.: 15.84

5.: 193.2

6.: 10.7*5, 8.4*6, 7.5*7.5, 2.1*24

7.: 6, 5.75

Step-by-step explanation:

4.: 6.6*2.4=15.84

5.: 27.6*7=193.2

6.: 10.7*5=53.5, 8.4*6=50.4, 7.33*6=43.98, 7.5*7.5=56.25, 2.1*24=50.4

7.: 1.6*6.25=10, all numbers higher than 6.25 will return products higher than 10, all numbers lower than 6.25 will return products lower than 10.

Answer:

They are not equal

Step-by-step explanation:

the first one equals 0

the second one equals 12

Given that you are in the 88th percentile for GPA, there are 72 students that have a GPA greater than or equal to yours.

Percentile refers to the measure used to indicate the value below which a certain percentage of data lies.

If a data is said to be in the nth percentile, this means that n% of the data in the distribution are equal to or lower than that data.

If you are in the 88th percentile, then 88% of all the 600 students have a GPA equal or lower than yours.

88% of 600 = 0.88(600) = 528

students that have a GPA greater than or equal to yours = 600 - 528

students that have a GPA greater than or equal to yours = 72

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When the product of a number m and 1.7 is 6.63 the required value of m is 3.9

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given statement is,

The product of a number m and 1.7 is 6.63

Thus, converting it into numerical form we get,

1.7m = 6.63

Dividing both the side by 1.7 we get,

1.7m/1.7 = 6.63/1.7

Solving we get,

m = 3.9

this is the required value of m.

Thus, when the product of a number m and 1.7 is 6.63 the required value of m is 3.9

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Using proportions, it is found that 7.2q and q/6 are different terms, due to the different numeric coefficients.

A fraction is converted to decimal by the division of the numerator by the denominator, that is, we apply the proportion of the numerator by the denominator.

For this problem, we have two terms, given as follows:

7.2q and q/6.

To verify if they are equal terms, we have to look at the numeric coefficients, hence:

Hence 7.2q and q/6 are different terms, due to the different numeric coefficients.

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We get that when the expression 5 ∛ 9 y² . ∛ 24 y is simplified using multiplication, we get the result as 30 y.

We are given the expression:

5 ∛ 9 y² . ∛ 24 y

We need to multiply to simplify the expression.

First, we know that:

9 = 3 × 3

24 = 2 × 2 × 2 × 3

So,

∛ 24 = 2 ∛ 3

So, we get the expression as:

5 ∛ 9 y² . 2 ∛ 3 y

Multiply the terms, we get that:

10 ∛ 27 y³

= 30 y

Therefore, we get that when the expression 5 ∛ 9 y² . ∛ 24 y is simplified using multiplication, we get the result as 30 y.

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Answer: yes

Step-by-step explanation: In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Answer:

Yes it is a function bc no number repeats 2x

Step-by-step explanation:

Y

Two expressions with an equal sign is called as Equation. If the difference between two numbers is 12. The first number is 5 less than twice the second number then the two numbers are 29 and 17.

Two expressions with an equal sign is called as Equation.

Let the two numbers be a and b.

Given equation is a-b=12 .....(1) and

The first number is 5 less than twice the second number i.e a=2b-5

Substitute a in (1)

2b-5-b=12

b-5=12

b=17

b=17 is the second number.

Now we have to find first number so

a=2b-5...(2)

Substitute b=17 in (2)

a=2(17)-5

=34-5

=29

Therefore the two numbers are 29 and 17.

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The rate of falling temperature is 5 1/3 degrees per hour.

What do you mean by the rate of temperature?

This indicates the sensitivity of the reaction to change in temperature.

Given that;

The temperature fell 4 degrees in 3/4 of an hour.

So, we can set up a proportion to see how much temperature fell in an hour,

[tex]\frac{4}{3/4} = \frac{x}{1}[/tex]

4 /0.75 = x

x = 5 1/3

Hence, The rate of falling temperature is 5 1/3 degrees per hour.

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Answer:

Hello,

Step-by-step explanation:

0=x²+17x+72=x²+8x+9x+72=x(x+8)+9(x+8)=(x+8)(x+9)

x=[-9,-8]

Answer:

[tex]x = - 8 \: - 9[/tex]

Step-by-step explanation:

[tex]1. \: {x}^{2} + 72 + 17x = 0 \\ 2. \: (x + 8)(x + 9) = 0 \\ 3. \: x = - 8 \: - 9[/tex]

The coordinates of the midpoint M of the segment AD is ( -1, 1 ).

Hence, option A)( -1, 1 ) is the correct option.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point A(3,−2)

Point D(−5,4)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 3 + (-5) )/2, ( (-2) + 4)/2 )

M = ( ( 3 - 5 )/2, ( -2 + 4)/2 )

M = ( ( -2 )/2, ( 2)/2 )

M = ( -1, 1 )

The coordinates of the midpoint M of the segment AD is ( -1, 1 ).

Hence, option A)( -1, 1 ) is the correct option.

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Candles we light total in all 120 birthdays is 7260.

Arithmetic Progression is defined as the sequence of numbers where the difference is constant .

According to the given question

No of candle on 1st birthday = 1

no of candle on 2nd birthday =2

.

.

No of candle on 120th birthday= 120

The given situation can be represented in the form of sequence .

1,2,3,4,5,...,120.

The above sequence forms an Arithmetic Progression as the common difference is same that is 1.

To find the total candles we need to find the sum of the above AP.

Sum of AP [tex]=\frac{n}{2}[2a+(n-1)d][/tex]       ...where a=first term , n=total number of terms , d=common difference  .

a=1 , d=1 , n=120

Substituting the value we get

[tex]=\frac{120}{2} [2(1)+(120-1)1]\\ \\ =60[2+119] \\ \\ =60*121\\ \\ =7260[/tex]

Therefore , Total of 7260 candles  will be light in all 120 birthdays.

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Answer:

0.7

Step-by-step explanation:

add like you would normally

Step-by-step explanation:

f (x) = 7

Slope: 0

y-intercept: (0,7)

x   y

0   7

1    7

Graph x

Slope: 1

y-intercept: (0,0)

x   y

0  0

1    1

Plot each graph on the same coordinate system.

f (x) = 7

x

Answer: The value is −34.234

Step-by-step explanation:

The equation of the line that passes through (2, -6) and is perpendicular to the given line is y = -x -4

From the question, we are to determine the equation of a line that passes through (2, -6) and it perpendicular to y = x + 4

If two lines are perpendicular, the product of their slope is -1.

That is,

m₁m₂ = -1

First,

We will determine the slope of the line that the equation was given

y = x + 4

Comparing with the slope-intercept form of the equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison

m = 1

The slope of the line that the equation was given is 1

Thus,

The slope of the line that is perpendicular to this line is -1

From the given information,

The line passes through the point (2, -6)

Using the point-slope form of the equation of a line

y - y₁ = m(x - x₁)

Then,

y - -6 = -1(x - 2)

y + 6 = -x + 2

y = -x + 2 - 6

y= -x -4

Hence, the equation of the described line is y = -x -4

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Answer:

y = -x -4

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

1

f(4) means what is the value of f(x) when x = 4

substitute x = 4 into f(x)

f(4) = 2(4) - 5 = 8 - 5= 3

-----------------------------------

2

substitute x = - 1 into g(x)

g(- 1) = 3(- 1)² + 5 = 3(1) + 5 = 3 + 5 = 8

--------------------------------------

3

substitute x = 4 into h(x)

h(4) = 3(4) + 2 = 12 + 2 = 14

--------------------------------------

4

(f + g)(- 2)

= f(- 2) + g(- 2)

= 2(- 2) - 5 + 3(- 2)² + 5

= - 4 - 5 + 3(4) + 5

= - 9 + 12 + 5

= - 9 + 17

= 8

-----------------------------------------

5

(f + h)(2)

= f(2) + h(2)

= 2(2) - 5 + 3(2) + 2

= 4 - 5 + 6 + 2

= - 1 + 8

= 7

-------------------------------------------------

6

(f - g)(- 3)

= f(- 3) - g(- 3)

= 2(- 3) - 5 - (3(- 3)² + 5)

= - 6 - 5 - (  3(9) + 5)

= - 11 - ( 27 + 5)

= - 11 - ( 32)

= - 11 - 32

= - 43

------------------------------------------------

7

(g + h)(- 2)

= g(- 2) + h(- 2)

= 3(- 2)² + 5 + 3(- 2) + 2

= 3(4) + 5 - 6 + 2

= 12 + 5 - 4

= 17 - 4

= 13

Answer:

B. 8 x 10^3

Step-by-step explanation:

(1.6 x 10^5)/(0.2 x 10^2)

= (1.6/0.2)x(10^5/10^2)

= 8x10^(5-2)

= 8 x 10^3

Based on the expression the number of grid squares in a character of size 7 is 55

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression for the number of grid squares in a character of size s is given as

6 + s^2

Rewrite the expression as a function

So, we have

f(s) = 6 + s^2

To find the number of grid squares in a character of size 7, we set s to 7

i.e. s = 7

So, we have

f(7) = 6 + 7^2

Evaluate the exponent

So, we have

f(7) = 6 + 49

Evaluate the sum

So, we have

f(7) = 55

Hence, the number of grid squares in a character of size 7 is 55

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Answer:

A all values are solutions

Step-by-step explanation:

we have the absolute value of an expression (in this case 13x).

that means the result is always (ALWAYS) positive, no matter what happens in the included expression.

the minimum result value is 0.

it cannot get below 0.

so, |13x| > -5 is always true, no matter what value you pick for x.

Answer: 31.9 USD

Step-by-step explanation: 6.70x4=26.8. 26.8+5.10=31.9

Answer:

Answer: 31.9 USD

Step-by-step explanation:

6.70 x 4 = 26.8

26.8 + 5.10 = 31.9

The new function for f(x) = (x – 3) is g(x) = x/2 – 3

Given,

The function, f(x) = (x – 3)

Horizontal stretch by a factor of 2

The quadratic parent function f(x) = (x – 3) is the simplest form of a quadratic function.

If the function is multiplied by the factor b and:

|b| > 0  the function is stretched.

If 0 < |b| < 1 the function is compressed.

Then the new function will be in the form:

g(x) = (1/b)x - 3

Therefore, keeping the above on mind, if b=2, then the new function is:

g(x) = (1/2)x - 3

g(x) = x/2 - 3

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The inverse function returns the original value for which the output of a function was given.

[tex]y^{-1}[/tex] = -1 ± √(x - 5) /2 be the inverse the function y = (1 - 2x)² + 5.

The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value. The inverse of f is then g(y) = (y - 5)/2 = x.

An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.

Let the equation be y = (1 - 2x)² + 5

simplifying the above equation, we get

√(x - 5) y = (1 - 2x)² + 5

x = (1 - 2y)² + 5

The function of x be x = (1 - 2y)² + 5

x - 5 = (1 - 2x)²

± √(x - 5) = (1 - 2y)

± √(x - 5) - 1 = 2y

Divide both sides of the equation by 2, we get

[± √(x - 5) - 1]/2 = 2y/2

[± √(x - 5) -1] /2 = y

[tex]y^{-1}[/tex] = -1 ± √(x - 5) /2

Therefore, the inverse of the function be [tex]y^{-1}[/tex] = -1 ± √(x - 5) /2.

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Answer:(1,800 - 12g) / 30 = m

Step-by-step explanation:

answer is 36

Step-by-step explanation:

good right?

The answer to the given logarithm expression is log₄₉7  = 1/2

Another technique to clarify exponents in mathematics is through logarithms. A base number's logarithm equals another number.

For instance, log10 100 = 2 if 102 = 100. A logarithm is defined as an influence by which variety must be raised to receive another value. this is often the foremost convenient thanks to represent large numbers. Logarithms have several important properties that prove that logarithmic multiplication and division is written because the logarithm of addition and subtraction. The log is named the logarithm of base e. The logarithm is represented by ln or loge. where 'e' represents Euler's constant,  approximately capable 2.71828. as an example, the log of 76 is written as ln 76. The log defines what percentage times 'e' must be multiplied to induce the required output.

We need to evaluate log₄₉7

Using Property

logₙ (a) = 1 / logₐ (n)

log₄₉7 = 1/ log₇ 49

Using the properties of log again logₐ (mⁿ) = n logₐ m

49 = 7²log₇ 49

can be written as

log₇ 49 = 2 log₇ 7

We know that logₐ a = 12 log₇ 7= 2

Value of log₄₉7 = 1/ log₇ 49= 1/ 2 log₇ 7= 1/2

Hence,  we evaluated the logarithm which is log₄₉7  = 1/2

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