One of Ted’s jobs at home is to pump gas for his family’s sedan and truck. When he fills up the sedan with 12 gallons of gas, he notices that it costs him $50.04. Write an equation using the unit rate from #27. #27 is $4.17.

log(x) - log (3) = 8 => x = 299916251.899, by properties of logarithm.

Now,

log (x) - log (3) = 8

=> log (x) = 8 + log (3) = 8 + 0.477

=> log (x) = 8.477

Since, generally the base of log is 10, raising them to 10.

=> [tex]10^{log_{10}x} = 10^{8.477}[/tex]

=> x = 299916251.899 (as  [tex]a^{log_a(x)} = x[/tex])

Hence, log(x) - log (3) = 8 => x = 299916251.899, by properties of logarithm.

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The intercepts and the standard form of each polynomial are listed below:

In this case we need to find the intercepts of each quadratic equation and transform each quadratic equation into standard form. The x-intercept correspond with each of the roots of the polynomial and the y-intercept is found by evaluating the expression at x = 0.

Now we proceed to find each element:

Case 1

x-Intercept

x = - 4 or x = 6

Standard form

f(x) = (x + 4) · (x - 6)

f(x) = x² - 2 · x - 24

y-Intercept

f(0) = - 24

Case 2

x-Intercept

x = 1 / 4 or x = 3

Standard form

f(x) = (2 · x - 4) · (x - 3)

f(x) = 2 · (x - 2) · (x - 3)

f(x) = 2 · (x² - 5 · x + 6)

f(x) = 2 · x² - 10 · x + 12

y-Intercept

f(0) = 12

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Answer:

x = 30

Step-by-step explanation:

To find the x intercept, you need to substitute [tex]y = 0[/tex], as all points on the x axis's y-coordinate is 0.

[tex]0 = 30000 - 1000x\\ \\ \to 0 + 1000x = 30000 \cancel{- 1000x + 1000x} \\\\ \to 1000x = 30000 \\ \\\to \frac{1000x}{1000} = \frac{30000}{1000} \\ \\\to x = 30[/tex]

Answer: Its x= 30

Step-by-step explanation:

Answer:

50 meters

Step-by-step explanation:

Width is x

So length will be x + 20

Perimeter = 2 (W + L) = 2 (x + x + 20) = 2 (2x + 20) = 4x + 40

so 4x + 40 = 160

4x = 120

x = 30

so length = x + 20 = 30 + 20 = 50

Answer to this question is:

Domain of given function is (-∞,0)∪(0,∞),{x|x≠0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is √x/x,-√x/x

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation:(-∞,0)∪(0,∞)

Set-Builder Notation:{x|x≠0}

The set of all valid y values constitutes the range.Graph may be used to find the values.

Interval Notation:(0,∞)

Set-Builder Notation:{y|y>0}

For calculation of inverse:

∴Domain of given function is (-∞,0)∪(0,∞),{x|x≠0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is √x/x,-√x/x

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The domain and range of the function f(x) is [1, ∞) and (0, ∞) and g(x) is (0,∞) and [-1, ∞).

Domain of function f(x) :

√ (x - 1) ≥ 0

So, we get that:

x ≥ 1

= [1, ∞)

Range = (0, ∞) as square of a number is always positive.

Domain of function g(x):

√ x ≥ 0

on adding 1 both sides we get

x ≥ 0

= (0,∞)

Range = [-1, ∞).

Therefore, the domain and range of the function f(x) is [1, ∞) and (0, ∞) and g(x) is (0,∞) and [-1, ∞).

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Answer:

a sin(bθ−c)+d

→ Using this, find the amplitude based off of the given formula. Use the expression as a reference to help you identify a.

a = 3

b = 4

c = 0(no defined value)

d = 0(impossible to identify)

→ Find a.

→ Since a is already given, we know that a = 3, therefore, the amplitude is 3

Option C: Samantha is correct because when using x=2, the resulting values in both expressions are equal.

Consider, 4x + 2

When x = 2,

=> 4x + 2 = 4*2 + 2

=> 10

Now consider, x + 17 + 3x - 15

When x = 2,

=> 2 + 17 + 3*2 - 15

=> 10

Therefore, Samantha is correct as both expressions equal 10 when x=2.

In other words, if we consider, x + 17 + 3x - 15

=> x + 17 + 3x - 15

=> x(1+3) + 17 - 15

=> 4x + 2

This shows that for any value of x, the expression x + 17 + 3x - 15, simplifies to 4x + 2.

Therefore, both the expressions, 4x + 2 and x + 17 + 3x - 15, are equal.

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The simplest form of the expression is √2 .

We have given an expression  √128/8 .   .....(1)

Factors of 128 is given by

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2  

Put this factors in equation (1) , we get

√128/8 = [tex]\frac{\sqrt{2\times2\times2\times2\times2\times2\times2} }{8}[/tex]

On simplifying , we get

√128/8 = 2 ×2 × 2√2 / 8

            = 8√2 /8

           = √2

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Given that Angles A and B are complementary to each other, the numerical value of x is 15.

Complementary angles are angles that sum up to 90 degrees.

Given the data in the question;

Since Angles A and B are complementary to each other, the sum of angle A and B is 90 degrees.

Measure of angle A + Measure of angle B = 90°

Plug in the given values and solve for x.

41 + (2x + 19) = 90

41 + 2x + 19 = 90

2x + 60 = 90

2x = 90 - 60

2x = 30

x = 30/2

x = 15

Given that Angles A and B are complementary to each other, the numerical value of x is 15.

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Answer: A is the answer

Step-by-step explanation: i took the test and got it right

Answer:

number 0

Step-by-step explanation:

The identity property of addition states that when zero is added to any real number, the number does not change. Thus, the number "0" is called the additive identity of a matrix.

Answer:

Step-by-step explanation:

ok so go on a new tab and put if I  earn $9.15 per hour painting a fence. it takes 6.75 hours to paint the fence. did you earn enough to buy the jersey show? is so how much money do you have left? if not how much money do you need to earn? easy. -5 start pls-

Answer: y=kx

Step-by-step explanation:

The standard form will be

1/10 x⁴-2x²-4x-1

Polynomials in standard form can also be referred to as the standard form of a polynomial which means writing a polynomial in the descending order of the power of the variable. To write a polynomial in a standard form, the degree of the polynomial is important as in the standard form of a polynomial, the terms are written in decreasing order of the power of x. The standard form of polynomial is given by, f(x) = anxn + an-1xn-1 + an-2xn-2 + ... + a1x + a0, where x is the variable and ai are coefficients.

A mathematical expression of one or more algebraic terms in which the variables involved have only non-negative integer powers is called a polynomial. The terms have variables, constants, and exponents. The standard form polynomial of degree 'n' is

aₙxⁿ+aₙ₋₁xⁿ⁻¹+aₙ₋₂xⁿ⁻²+.......

To write a polynomial in standard form ,simplyfy and then arrange the terms in descending order.

ax²+bx+c

move -1

-4x+x⁴/10-2x²-1

Reorder terms

1/10x⁴-2x²-4x-1

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Answer:

Step-by-step explanation: 14 minutes

Answer:

√20, 4.5, √45, 45

Step-by-step explanation:

find your square roots first, then group based on the value of the square roots

Expression as a single natural logarithm is ln 64/64 = ln 1.

ln 1 is the converted from 2 ln 8-3 ln 4 to a single natural logarithm.

We need to convert 2 ln 8-3 ln 4 as a single natural logarithm.

First apply power property

⇒ ln 8² - ln 4³

⇒ ln 64 - ln 64

Now, applying quotient property

⇒ ln 64/64 = ln 1

Here, we finally converted 2 ln 8-3 ln 4 to a single natural logarithm ln 1.

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Answer:

C.

Step-by-step explanation:

C describes theta moving +5 units. In math, negative goes left, negative goes left. However, since there are no negative values involved, we can assume that theta will move 5 units to the left in terms of absolute value, which excludes the need for the negative to be moved left. Therefore, the answer is C due to this change.

I hope this helps, let me know if anything confuses you, and I will try my best to make it less confusing.

Answer:   To find the HCF, find any prime factors that are in common between the products. Each product contains two 2s and one 3, so use these for the HCF. Cross any numbers used so far off from the products. To find the LCM, multiply the HCF by all the numbers in the products that have not yet been used.

Step-by-step explanation:

Answer:

[tex]\frac{5}{1}[/tex]

Step-by-step explanation:

45 : 9

= [tex]\frac{45}{9}[/tex] ← divide numerator and denominator by 9 )

= [tex]\frac{5}{1}[/tex] ← in simplest form

Answer: B. 10A + 7B

Step-by-step explanation:

     To find the correct binomial, we will factor the given expression. I assume that by "-498²" you mean "-49B²".

This is a difference of squares:

     (10A + 7B)(10A - 7B)

The binomial 10A + 7B is an answer option, so our answer is:

     B. 10A + 7B

The equation of the translated graph from the parent function is g(x) = |x + 2| + 1

The parent function is given as

f(x)= |x|

From the graph, we can see that the parent function f(x) is translated as follows:

The above sequence of translation is represented as

(x, y) = (x + 2, y + 1)

So, we have

g(x) = |x + 2| + 1

Hence, the equation of the translated graph is g(x) = |x + 2| + 1

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The expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.

It follows from the task content that the expression which is equivalent to that given in the task content be determined.

On this note, by distributing the coefficient of.tne parents; we have;

-1/2 ( 1/4x - 3/8)

= {(-1/2) × (1/4)x} + {-1/2 × -3/8}

= (-1/8)x + 3/16

Ultimately, the expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.

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Answer:

5a+2b+10

Step-by-step explanation:

Let's simplify step-by-step.

a(6−1)+3b−b(2−1)+10

=5a+3b+−b+10

Combine Like Terms:

=5a+3b+−b+10

=(5a)+(3b+−b)+(10)

=5a+2b+10

Completing the Automatic grading is used for empty questions. If a student's response corresponds to the right response you give, you will receive credit for that answer. The technique you use to assess the responses is up to you.

100% exact

Comprised comprises a portion of the right response

meets the criteria you define for a pattern

Enter your query in text form, then enclose the response in brackets. To format the text and add formulas, files, photos, and links, utilize the editor's formatting options.

Using a semicolon, divide several right responses.

Example: Red, blue, and yellow are three examples of primary colors.

A regular expression might also be used. Each blank will only accept one expression at a time. Remember to enclose both the regular expression and the solution in brackets.

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Answer: 7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)

                              J(-3, 1) = J'(4, 0)

                              F(-2, 3) = F'(5, 2)

                              N(-2, 0) = N'(5, -1)

Step-by-step explanation:

If you want to translate a point 7 units right, you'll need to add 7 to its x-coordinate. If you want to translate a point 1 unit down, you'll need to subtract 1 from its y-coordinate. Do both of these things to perform a translation 7 units right and 1 unit down.

So, we can write,

            7 units right means add the +7

             1 unit down means subtract the -1

Then,

                  J(-3, 1) = J'(-3 + 7, 1 - 1)

                  J(-3, 1) = J'(4, 0)

                  F(-2, 3) = F'(-2 + 7, 3 - 1)

                  F(-2, 3) = F'(5, 2)

                  N(-2, 0) = N'(-2 + 7, 0 - 1)

                  N(-2, 0) = N'(5, -1)

Therefore,

These points to make sure they have shifted 7 units right and 1 unit down.

   7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)

                              J(-3, 1) = J'(4, 0)

                              F(-2, 3) = F'(5, 2)

                              N(-2, 0) = N'(5, -1)

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The solution of the compound inequality are:

| x - 3  | < 4              -1 < x < 7

| x + 2 | > 8             -10 < x or  x >6

Given data

| x - 3  | < 4 and | x + 2 | > 8

Solution the first inequality | x - 3  | < 4

| x - 3  | < 4

x < 4 + 3  OR  x >  - 4 + 3

x < 7        OR  x >  - 1

-1 < x < 7

Solution for the second inequality  | x + 2 | > 8

| x + 2 | > 8

x < -8 - 2  OR  x >   8 - 2

x < - 10        OR  x >  6

-10 < x or  x >6

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