Expand each logarithm.
log m² n⁵

The numeric values of the expressions are given as follows:

3. 36.

5. 38.

7. 16/61.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

In item 3, we have that:

4|m - n|, m = -7, n = 2.

Hence the numeric value is:

4|-7 - 2| = 4|-9| = 4 x 9 = 36.

In item 5, we have that:

s²t - 10 with s = -8, t = 3/4.

Hence the numeric value is:

(-8)² x 3/4 - 10 = 48 - 10 = 38.

In item 7, we have that:

(a + b)^5/(a - 2b²), a = 6, b = -8.

Hence the numeric value is:

(-2)^5/(6 - 128)

-32/-122 (negative divided by negative is positive).

32/122 (simplify by 2).

16/61.

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(12x^5 + x² + 4) /4.

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

Given equation

x²/4+3x^5+1

Find common denominator

x²/4+3x^5 . 4/4+4/4

Combine fractions with common denominator

(x²+3x^5 . 4+4)/4

Multiply the numbers

(x²+12x^5 +4)/4

Rearrange terms

(x²+12x^5 +4)/4

(12x^5 + x² + 4) /4

Thus , solution of the given polynomial is (12x^5 + x² + 4) /4. we can also write it as -

3x^5 + x² / 4 + 1.

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Answer: 2/189

Step-by-step explanation:

Step-by-step explanation:

f(x) = x² - 3x + 3

f(4) = 4² - 3.4 + 3

f(4) = 16 - 12 + 3

f(4) = 7

Answer:

Step-by-step explanation: 37 times 1000 equals 37000 if you times anything by 1000 just add 2 zeros to the end

The equivalent expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given:

(p^3)(2p^2 - 4p)(3p^2 - 1)

Now further solving

(p^3)(2p^2 * 3p^2 - 2p^2 * 1 - 4p * 3p^2 + 4p)

=(p^3) (6p^4 - 2p^2 - 12 P^3 + 4p)

=(p3)(6p^4 - 12p^3 - 2p^2 + 4p)

Hence, the value of expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).

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The name of each midpoint and the segment it bisects include the following:

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

In this scenario, the name of each midpoint and the segment it bisects include the following:

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Complete Question:

Name each midpoint and the segment it bisects.

By option verification,

i.e., substituting the options by given equation and verifying

Given -2x + 3y > = 1  and - 5x + 6y <= 1

Substituting option A i.e., ( x , y ) = ( 6,6)

-2x + 3y >=1 --> -2 * 6 + 3 * 6 >= 1

                   --> -12+ 18 >= 1    

                  ---> 6>=1

-5x + 6y<=1--> -5 * 6 + 6 *6 <=1

                 --> -30+ 36 <=1

                -->6<=1

False

Substituting option B i.e., (x ,  y)= (7 ,8)

-2x + 3y>=1  --> -2* 7 + 3 * 8>=1

                   --> -14 + 24>=1

                  --> 10>=1

-5x + 6y<=1 --> -5 *7 + 6* 8<=1

                  --> -35 + 48<=1

                  --> 13<=1

False

Substituting option C i.e., (x, y) = ( 8 ,7)

-2x + 3y >=1 --> -2* 8 + 3* 7>=1

                    --> -16 + 21>=1

                   --> 5>=1

-5x + 6y <=1 --> -5 * 8 +  6 * 7 <=1

                   --> -40 + 42<=1

                  --> 2<=1

False

Substituting option D i.e., (x ,y ) = (9, 7)

-2x + 3y >= 1 --> -2* 9 + 3 * 7 >=1

                    --> -18 +21>=1

                   --> 3>=1

-5x + 6y <=1 --> -5* 9 + 6 * 7 <=1

                    --> -45 + 42<=1

                   --> -3<=1

True

Therefore (x ,y ) = (9, 7) is the solution of the given equation -2x + 3y>=1 and -5x = 6y <=1

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Answer: For the people who were just as confused with the answer above, the answer is D-

Step-by-step explanation:

Answer: The answer is B. a||b and l||m

Step-by-step explanation: I hope this helps.

Answer: Everything lol

Step-by-step explanation:

Tonya's total earnings for a month where her total sales were $80,000 is $5,450

What made up Tonya's total earnings?

Tonya's total earnings in any month comprises the basic salary of  $650 , 3% of sales as sales commission on sales revenue of up to $32,000 and 8% as commission on sales in excess of $32,000

total earnings=basic salary+(3%*sales of up to $32,000)+(8%*sales of above $80,000)

basic salary=$650

3%*sales of up to $32,000=3%*$32,000

3%*sales of up to $32,000=$960

8%*sales of above $80,000=8%*($80,000-$32,000)

8%*sales of above $80,000=8%*$48,000

8%*sales of above $80,000=$3,840

Tonya's total earnings for a month=$650+$960+$3,840

Tonya's total earnings for a month=$5,450

Note that the total earnings based on the basic salary of $650 and sales revenue of $80,000 is $5,450

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Answer:

2

Step-by-step explanation:

8-4=4

4/2=2

Answer:

so you take 2×4=8 and 2×2=4 I think that's how to do it

Answer:

10 hours

$352

Step-by-step explanation:

Given costs:

Define the variables:

Create a system of equations using the given costs and defined variables:

[tex]\begin{cases}y=132+22x\\y=152+20x \end{cases}[/tex]

To find how many hours Ryan would need to rent the boat in order for the cost of both companies to be the same, substitute equation 1 into equation 2 and solve for x:

[tex]\begin{aligned}132+22x & = 152+20x\\132+22x-20x & = 152+20x-20x\\132+2x & = 152\\132+2x-132 & = 152-132\\2x & = 20\\\dfrac{2x}{2} & = \dfrac{20}{2}\\x & = 10\end{aligned}[/tex]

Therefore, the number of hours Ryan would need to rent the boat in order for the cost of both companies to be the same is 10 hours.

Substitute x = 10 into one of the equations to find the cost at both companies if Ryan rented a boat for this many hours:

[tex]\begin{aligned}x=10 \implies y & = 132+22(10)\\& = 132+220\\& = 352\end{aligned}[/tex]

Therefore, the cost at both companies if Ryan rented a boat for 10 hours would be $352.

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Answer:

3 = x ÷ 4

Step-by-step explanation:

Given expressions:

8 = x - 2 ⇒ x = 8 + 2= 10

3 = x ÷ 4  ⇒ x = 3*4 = 12

x - 6 = 5  ⇒ x = 5 + 6 = 11

x - 3 = 9  ⇒ x = 9 + 3 = 12

3 of them involves addition, one of them - multiplication

The second expression doesn't belong

Answer:

0.025

Step-by-step explanation:

Divide 4 by 139 and get the number as a decimal

The given function is a linear function because variable have first degree power.

The terms "linear function" in mathematics refer to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

A linear function is a function that represents a straight line on the coordinate plane. As an illustration, the equation y = 3x – 2 represents a linear function because it is a straight line in the coordinate plane.

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The minutes when the scenes have the same amounts rendered is 14 minutes.

The expression for the kitchen is illustrated as 540 + 90t.

The expression for the garden is illustrated add 960 + 60t.

Therefore, for the same amount, this will be:

540 + 90t = 960 + 60t.

Collect like terms

90t - 60t = 960 - 540

30t = 420

Divide

t = 420 / 30

t = 14 minutes

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The number that can be equal to 2x² -50 =  2(x + 5)(x - 5).

For the given equation;

= 2x² -50

Take 2 common;

= 2(x² - 25)

This could be written as;

= 2(x² - 5²)

Now use per the property of (a² - b²)  = (a + b)(a - b).

= 2(x + 5)(x - 5)

Thus, the given expression 2x² -50 can be represented as 2(x + 5)(x - 5).

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let's firstly convert the mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}} ~\hfill \stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}~~ - ~~\cfrac{14}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~ - ~~(2)14}{6}}\implies \cfrac{51~~ - ~~28}{6}\implies \cfrac{23}{6}\implies {\LARGE \begin{array}{llll} 3\frac{5}{6} \end{array}}[/tex]

The domain of the function C(t) is R - { -5. -2}.

The domain of a function is the set of all values for which the range of the function is defined.

To achieve an immediate response to a particular drug's effects the concentration, C, in mg/L, of a particular medication after being injected into a patient is given by the function

C(t) = [tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex] where t represents time in hours.

We know that a function is undefined when its denominator becomes zero.

∴ We have to factor the quadratic equation t² + 7t + 10 which is,

t² + 5t + 2t + 10 = 0.

t(t+5)+2(t+5) = 0.

(t+5)(t+2) = 0.

So, t = -5 or t = -2 are the two values of this equation which makes the function c(t) undefined.

∴ The domain of the function [tex]\frac{-18t^2 + 54t}{(t+5)(t+2)}[/tex] is all real numbers except -2 and - 5 which can be written as

Domain of C(t) is R - { -5, -2}, where R represents all real numbers.

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The constant of proportionality for the paints portraits is estimated as 5.

For, the given question;

The relation between the portraits and the time for their drawing made by Drew is-

In 5 hours ----> 1 portrait

Thus, 5/1 = 5

In 10 hours ------> 2 portrait

Thus, 10/2 = 5

In 15 hours -----> 3 portrait

Thus, 15/3 = 5 .....and so on.

Therefore, the constant of proportionality is found as 5.

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The solution for y is given as :  y = (34+x)/36

According to the question we have been the linear equation in two variable as :

                       2y - x = 34 (-y + 1)

We need to solve the above equation for y. For that we will do step by step.

First we will open the brackets on the right hand side of the equation we get

                        2y - x = -34y + 34

then we will combine the terms on the left hand side of the equation.

                        2y + 34y = 34 + x

                          36y  = 34+x

dividing both the sides by 36 we get

                         36y/36 = (34+x)/36

                             y = (34+x)/36

Hence the solution for y is given as :  y = (34+x)/36

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Answer:

12'

Step-by-step explanation:

Pythagoras theorem = a² = b²+c²

*a² is always the hypothenuse (the longest side if the triangle)

you could use b² as the base and c² as the height

to find the height i.e., c² you transpose and substitute what we know so that'll be

13'² = 5'² + c²

you expand which will then give you

169 = 25 + c²

you then take over the 25+ which when addition goes over the equal sign becomes subtraction so that'll now give you

169 - 25 = c²

144 = c²

we want to find for c not c² so to do that we find the square root of 144 which is equal to 12.

so the height is equal to 12'

hope this helps

After solving the equation ln x = -2, x is the value of equal to  [tex]e^{-2}[/tex]

We have been asked to find x in ln x = -2

⇒ ln x = -2

⇒ x = [tex]e^{-2}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Using operations with functions, we have that:

a) w(t) = -3t + 5.

b) The pool will leak all the water in 1.67 hours.

c) 1.67 hours.

d) Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.

e) The domain of the function is 0 ≤ t ≤ 1.67.

The amount of water in the pool is determined by the subtraction of the amount flowing into the pool by the amount being drained out the pool.

For this problem, these following functions are given:

Hence the amount of water in the pool is given by:

w(t) = f(t) - d(t)

w(t) = t² + 8t + 9 - t² - 11t - 4

w(t) = -3t + 5.

Hence:

The function is: w(t) = -3t + 5.

The pool will have leaked all the water when:

w(t) = 0.

Hence:

-3t + 5 = 0.

3t = 5

t = 1.67.

The pool will leak all the water in 1.67 hours.

Equaling f(t) and d(t), we have that:

t² + 8t + 9 = t² + 11t + 4.

3t = 5.

t = 1.67.

Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.

The domain of a function is the set that contains all input values of the function. For this problem, the input is the time, hence:

Hence:

The domain of the function is 0 ≤ t ≤ 1.67.

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Greetings from Brasil...

90X - 128 = 24X + 50

90X - 24X = 50 + 128