Example 1:
If f(x) = 3x-4, find each value. Show all work.

a) ƒ(4)

b) f(-5)

c) f(2-x)

We can buy 9 programs after buying the laptop if we want to spend $ 500 at most on the laptop.

The cost of the laptop = $ 319

The maximum money we have = $ 500

Money left after purchasing the laptop will be calculated by using subtraction.

Money left = $ 500 - $ 319 = $ 181

Now, cost of each program = $ 20

The number of programs we can buy = $ 181 / $ 20

The number of programs we can buy = 9.05

That means 9 programs.

Therefore, we get that, we can buy 9 programs after buying the laptop if we want to spend $ 500 at most on the laptop.

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The radical expression of the term (x⁻¹⁰ / x⁵)²/⁵ is ⁵√(1/x¹⁰)

 A radical is a number that is denoted by a root and can be easily identified because before the number is the symbol √, which lets us know that it is a root.

In this case we have an exponential number since it is raised to a number, radicals can be expressed as powers raised to fractions as follows:

√a = a¹/²

 We reduce the fraction value

(x⁻¹⁰ / x⁵) = x⁻⁵ = 1/x⁵

 If our term is raised to 2/5, it can be expressed as:

(1/x⁵)²/⁵ = ⁵√(1/x⁵)² = ⁵√(1/x¹⁰)

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The required ratio of the input value to the output value is 1:3.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given:

Input   Output

 2             6

 3             9

 6             18

Now, the ratio is

2/6 = 1/3

and,  3/9 = 1/3

6/18 = 1/3

Hence, the ratio is 1:3.

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The common rate of both expressions are equal, so the expressions 64,96 and 60,90 are proportional

The expressions are given as

64,96 and 60,90

Rewrite the expressions as

(x, y) = (64,96) and (60,90)

As a general rule

Proportional expressions have the same constant rate

The constant rate (r) of the expressions is then calculated as

r = y/x

For the expression (64, 96), we have the following computation

r = 96/64

Evaluate the quotient

So, we have

r = 1.5

For the expression (60, 90), we have the following computation

r = 90/60

Evaluate the quotient

So, we have

r = 1.5

The common rate of both expressions are equal i.e. 1.5

Hence, the expressions 64,96 and 60,90 are proportional

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An expression for the combined total dollar amount he earned this month:

Total Earning = 15b + P(N - b)

where, b is the total hours worked as a tutor

P is the amount earned by Ryan per hour as a waiter

N is the total number of possible hours Ryan can work in a month

In this question,

Ryan works as a tutor for $15 an hour and as a waiter for $10 an hour. This month, he worked a combined total of 81 hours at his two jobs.

Let the number of hours Ryan works daily as a waiter be x

and the number of hours worked daily as a tutor be y

Ryan earns $15 per hour as tutor.

So, we get an expression for the daily earnings on tutoring = 15y

Let Ryan earns $P per hour as waiter.

so, we get an expression for the daily earning as a waiter = Px

The total possible hours Ryan can work in a month is dependent on conditions not specified.

Assuming 24 working days (6 days weekly for 4 weeks) in a month with maximum approved work hours of 12 hours daily, the total hours Ryan can work will equal 24 x 12 = 288 hours

This 288hrs is an estimate and can change based on applicable hours of work daily and number of working days in a month; it can also be represented as N

If b is the total hours Ryan worked as a tutor this month, the hours Ryan can work as a waiter in a month is equal to 288 - b

So, in a month, Ryan will earn 15b as a tutor and P(288-b) as a waiter or optionally P(N - b)

So, the combined dollar amount earned in a month is:

Total Earning = 15b + P(N - b)

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The exponential expression [tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6² is equivalent to the exponential expression is 3² / [tex]6^{5}[/tex] which is option 2 and not option 1

The Exponential expression given to us is 6^-3/3^-2x6^2 or we can write it as

[tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6²

There is a rule for solving exponents that when we reciprocate the fractions with exponential powers the signs of powers get changed from negative to positive and positive to negative

for example

[tex]x^{-2}[/tex] is written as [tex]\frac{1}{x^{2} }[/tex]

So, we can write the above  exponential expression as

3² / 6³ × 6²

Also, when two same numbers with different powers then the base remains same and powers get added.

3² / [tex]6^{3+5}[/tex]

3² / [tex]6^{5}[/tex]

So, the exponential expression [tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6² is equivalent to the exponential expression is 3² / [tex]6^{5}[/tex] which is option 2 and not option 1

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n-2 is the next larger odd integer if the number represented by n-3 is an odd number.

Parity, in mathematics, is the characteristic of an integer that determines whether it is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd. For instance, 4, 0, and 82 are even. 3, 5, 7, and 21 are odd numbers in comparison.

Whole numbers that cannot be divided perfectly into pairs are referred to as odd numbers. When two is divided by an odd number, one is left over.

based on the available facts;

Formulate based on the conditions stated:

(n-3)+1

Rearrange and group related terms:

n+(-3+1)

Calculate the sum or difference:

n-2

Answer is n-2

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The only graph that has a slope of -¹/₃ and a y-intercept of -4 that represents the inequality y > -¹/₃x - 4 is the graph represented by option C.

We want to find the graph that represents the inequality;

y > -¹/₃x - 4

Now, the general form of equation for a linear equation is;

y = mx + c

where;

m is slope

c is y-intercept

Now since the inequality is greater than, it means that it must be shaded at the top and must be a broken or dashed line. Thus, the only graph that has a slope of -¹/₃ and a y-intercept of -4 is the graph represented by option C.

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The action that is an example of someone taking action to accept personal responsibility for eating right is writing down foods consumed at each meal in a day.

There are several ways to take responsibility for our eating habits and one of them is to write down the foods that we consume during each meal that we take in a day.

This would enable us to keep track of the calories we consume and therefore give us a better idea of which foods to eat and which to avoid to maintain our recommended dietary intake.

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Answer:

Which action is an example of someone taking action to accept personal responsibility for eating right?

(A.) continuing to eat while watching television

(B.) consuming high-fat foods every day

(C.) writing down foods consumed at each meal in a day

(D.) going to the store on an empty stomach

Step-by-step explanation:

2022-2023 :)

Answer:

Standard notation/form

-1.91 × 10³

Hope this helps.

Answer:

6._ _ is the hundreth.

Since the diget after 6 is infact greater than or equal to 5.. (8>5).

We can round up to 6.17

Answer:

Hi the answer to that question is 2

Answer:

$29.40

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

To solve [tex]\frac{ab^2-4}{10}[/tex]

We need to know what [tex]ab^2[/tex] is.

[tex]ab^2 = a*b^2 = 4 * 6^2 = 4*36 = 144[/tex]

[tex]\frac{144-4}{10} = 140/10 =14[/tex]

Hope this helps :)

Have a great day!

Answer: 1/23

Step-by-step explanation:

x=multiplicative inverse of 23

23*x=1

23x=1

23x/23=1/23

x=1/23

The linear equation in slope intercept form is y = -2x + 1

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The table represents the given parameters

On the table, we have the following points

(x, y) = (0, 1) and (1, -1)

A linear equation is represented as

y = mx + c

Substitute (x, y) = (0, 1) and (1, -1) in y = mx + c

So, we have

1 = 0 * m + c

-1 = 1 * m + c

This gives

1 = c

-1 =m + c

Rewrite 1 = c as

c = 1

Substitute c = 1 in -1 =m + c

-1 =m + 1

Evaluate

m = -2

Substitute m = -2 and c = 1 in y = mx + c

y = -2x + 1

Hence, the linear equation in slope intercept form is y = -2x + 1

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The percent of surface sunlight intensity that reaches a depth of 370 feet is 0.0017%

We have been given the function which models the intensity of sunlight beneath the surface of the ocean which is

                    y = [tex]20 * (0.975)^{x}[/tex]    (1)

where, y = the percent of surface sunlight intensity that reaches a depth of    x feet.

            x = depth in feet

b) We need to find the percent of sunlight at a depth of 370 feet that is we have been given, x = 370feet.

putting the required values in equation (1) we get

                [tex]y = 20*(0.975)^{370}[/tex]

                y = 20* 0.000085

                y = 0.0017%

Hence 0.0017% of sunlight intensity reaches a depth of 370 feet

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The required zeros of the polynomial f(x) are  2, -2, and ±√-4.

What are zeros of the polynomial?

All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.

Solving for the zeros of a polynomial

f(x)=x⁴ - 16

Let, f(x) = 0

x⁴-- 16 = 0

(x²)² - 4² = 0

(x² + 4) (x² - 4) = 0

(x² + 4)(x - 2)(x + 2) = 0

i.e. x² + 4 = 0, x - 2 = 0, x + 2 = 0

x = 2, -2, ±√-4

Hence, the required zeros of the polynomial f(x) are  2, -2, and ±√-4.

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The equation of the line is y = -(1/3)x + 5,

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

We have,

The line is perpendicular to y = 3x - 2 and passes through (3, 4).

The slope of the line and the slope of y = 3x - 2 is:

[tex]m_{1} m_{2}[/tex] = -1

Where [tex]m_{2}[/tex] = 3

[tex]m_{1}[/tex] = -1/3

The equation for the line that passes (3, 4) is given by:

y - 4 = -1/3 ( x - 3)

y = -1/3x + 1 + 4

y = -(1/3)x + 5

Thus the equation of the line is y = -(1/3)x + 5,

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The complete question is:

What is the equation of the line perpendicular to y = 3x − 2  and passes through point (3,4)?

There are 24 possible arrangements that begin with letter R

Combinations are used to determine the number of selections of an item within another while permutation is used for arrangements

The arrangements of the digits is an illustration of factorials

The word is given as: SHREK

If the first letter begins with the letter R, then we have the following possible arrangements

The number of arrangement is the product of the above values

So, we have

Arrangement = 1 * 4 * 3 * 2 * 1

Evaluate

Arrangement = 24

Hence. there are 24 possible arrangements that begin with letter R

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Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(10,8)

Equation Form:

x=10,y=8

Step-by-step explanation:

Answer:

2x>8

Step-by-step explanation:

this should be right

Caroline and Rodney, on their way to the canoe livery, stopped to eat lunch at the point on their map with coordinates of (-2, -1).

The coordinates of a point on a two dimensional plane are two numbers that define its location.

The given coordinates of the journey are;

Required; The coordinates of the map where Caroline and Rodney stopped for lunch.

Solution:

The coordinates of a point (x, y), which is a proportion, t, of the distance between two points (a, b), and (c, d) is given by the formula;

x = a•(1 -t) + c•t

y = b•(1 -t) + d•t

The location where they had lunch is therefore;

x = -4×(1 - (1/3)) + (1/3)×2 = -2

y = -3×(1 - (1/3)) + (1/3)×3 = -1

The points is therefore; (-2, -1)

The coordinates on the map where Caroline and Rodney stopped for lunch is (-2, -1)

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Answer:

[tex]\sf x^{13}[/tex]

Step-by-step explanation:

If bases are same, add the exponents.

   [tex]\sf \boxed{a^m*a^n =a^{m+n}}[/tex]

[tex]\sf x^{10}*x^3} = x^{10+3}\\[/tex]

            [tex]\sf = x^{13}\\[/tex]

Hey there!

x^10 * x^3

x^10

= x * x * x * x * x * x * x * x * x * x

x^3

= x * x * x

x * x * x * x * x * x * x * x * x * x + x * x * x

= x^13

Or

10 + 3 = 13

Therefore, your answer should be:
x^13

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Using the properties of logarithm the value of the expression is  [tex]log_{6} 12 + log_{6} 3 = 2[/tex]

A logarithm is the power to which a number must be raised in order to get some other number.

According to the question we have been given the logarithmic expression as

                        = [tex]log_{6} 12 + log_{6} 3[/tex]

The properties of logarithm that we are going to use are :

  [tex]log(x*y) = logx + logy[/tex]   and   [tex]log_{a} a = 1[/tex]

Also we can see that the base are same so we can use the property of logarithm in the given equation.

Now solving it step by step using the properties of logarithm we get

                    [tex]= log_{6} (12*3)\\= log_{6} 36\\= log_{6} 6^{2} \\= 2* log_{6} 6\\= 2*1\\ = 2[/tex]                      

Hence using the properties of logarithm the value of the expression is [tex]log_{6} 12 + log_{6} 3 = 2[/tex]

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Answer:The answer to your question is

I bought

12

hardcover books and

24

softcover books.

Explanation:

We shall represent the hardcover books purchased by

x

and the softcover books purchased by

y

. From the details we can write two equations:

x

+

y

=

36

8

x

+

2

y

=

144

From the first equation we can calculate the value of

y

.

x

+

y

=

36

Subtract

x

from each side.

y

=

36

−

x

Now, in the second equation, substitute

y

with

(

36

−

x

)

.

8

x

+

2

y

=

144

8

x

+

2

(

36

−

x

)

=

144

Open the brackets and simplify.

8

x

+

72

−

2

x

=

144

6

x

+

72

=

144

Subtract

72

from both sides.

6

x

=

72

Divide both sides by

6

.

x

=

12

Now in the first equation, substitute

x

with

12

.

x

+

y

=

36

12

+

y

=

36

Subtract

12

from both sides.

y

=

24

Step-by-step explanation:

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