Question 9 Every day when commuting to and from work, Stefanie drives her car a total of 143 miles for 2.5 hours. Her car already has 45,300 miles on it. a. Write a function that shows the total number of miles, f(x), Stefanie's car will have been driven after x more days. Explain how you know where each number goes in the equation. b. If Stefanie works 4 days a week, how many miles will her car have been driven after 3 weeks? Show and explain all your work.

Answer: 4

Step-by-step explanation:

9/6=3/2(1.5)

6/1.5= 4

To check whether the lines are perpendicular or parallel, we will use the following rules:

1) For parallel lines, the slopes are equal.

2) For perpendicular lines, the product of the slopes is equal to -1.

Slope of line AB:

Using

The slope is given as

Slope of line CD:

Using

The slope is given as

Comparing both slopes, we can observe that

Therefore, both lines are PERPENDICULAR.

The probability that everyone will get a red card is 0.5.

So, the probability that everyone gets a red card:

Then,

Therefore, the probability that everyone will get a red card is 0.5.

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Answer:

y-int = (0,-3)

slope = 2

Step-by-step explanation:

The slope is found by the number before x. If its just x then the slope is 1. The y-int is found by the number all the way at the end. In this case its -3. So the y-int is (0,-3)

Answer:

Step-by-step explanation:

y

=

2

x

+

3

The slope-intercept form is

y

=

m

x

+

b

, where

m

is the slope and

b

is the y-intercept.

y

=

m

x

+

b

Find the values of

m

and

b

using the form

y

=

m

x

+

b

.

m

=

2

b

=

3

The slope of the line is the value of

m

, and the y-intercept is the value of

b

.

Slope:

2

y-intercept:

(

0

,

3

)

The expression is equivalent to option A, 8x[tex]\sqrt[6]{x}[/tex].

Option A is correct

Variables, constants, and mathematical operators make up an expression, which is a mathematical statement.

Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation. The x-term is typically put before constants when arranging the terms in the same sequence. It is said that two expressions are equivalent if every phrase in them is the same.

The expression is 2[tex]\sqrt[3]{x^2}[/tex]

The expression can be simplified as

= 2.4[tex]x^{2/3}[/tex][tex]x^{1/2}[/tex]

= 8[tex]x^{7/6}[/tex]

= 8x[tex]x^{1/6}[/tex]

= 8x[tex]\sqrt[6]{x}[/tex]

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The number of roses that the florist sold who sold 125 daisies is; 200

Scatter plots are the graphs that present the relationship between two variables in a data-set.

From the given scatter plots, we see that the x and y axes are marked in intervals of 50 like 0, 50, 100, 150, 200,...e.t.c

Now, from the scatter plot, we see a couple of coordinates and we are told that the x-axis shows the number of roses sold at a flower show while the y-axis shows the number of daises sold at the flower show.

Now, from the scatter plot, we see that when the number of daises sold is 125, we can trace that the number of roses sold was 200 roses.

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Answer: 3

Step-by-step explanation:

6 - 2, 3

15- 3, 5

Simplifying the given logarithmic equation, the expression is obtained as log([tex]\frac{x^{4} }{v^{2} y^{3} }[/tex]).

The objective is to find the resultant expression for 4 × logx -(2 × logv + 3 × logy)

According to logarithmic results,

The product of an integer constant and a logarithm term of a number is equivalent to the logarithm of the number raised to the power of the particular integer constant.

That is, b × log(a) = log([tex]a^{b}[/tex])

Hence, 4 × log(x) = log([tex]x^{4}[/tex]),

2 × log(v) = log([tex]v^{2}[/tex])

and, 3 × log(y) = log([tex]y^{3}[/tex])

So, the equation can be rewritten as log([tex]x^{4}[/tex]) - (log([tex]v^{2}[/tex]) +  log([tex]y^{3}[/tex]))

The sum of the logarithms of two numbers is equivalent to the logarithm of their product.

That is, log(a) + log(b) = log(a×b)

Hence, log([tex]v^{2}[/tex]) +  log([tex]y^{3}[/tex]) = log([tex]v^{2}[/tex][tex]y^{3}[/tex])

So, the equation can be rewritten as log([tex]x^{4}[/tex]) - log([tex]v^{2}[/tex][tex]y^{3}[/tex])

The difference in the logarithms of two numbers is equivalent to the logarithm of their fraction.

That is, log(a) - log(b) = log(a÷b)

Hence, log([tex]x^{4}[/tex]) - log([tex]v^{2}[/tex][tex]y^{3}[/tex]) = log([tex]\frac{x^{4} }{v^{2} y^{3} }[/tex])

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It is to be noted that an equation is formed of two equal terms. As per the literal equation m=5/4n-7, the value of m when the value of n is 7 is 42.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.

The value of m from the given equation can be found by substituting the value of n as 7 in the given equation as shown below.

m = (5/4)n - 7

Substitute the value of n as 40,

m = (5/4)40 - 7

m = (5/1)10 - 7

m = 50 - 7

m = 42

Therefore, as per the literal equation m=5/4n-7, the value of m when the value of n is 7 is 42.

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Full Question:

Use the literal equation m=5/4n-7 to find m when n =40

For the given equation 2x+3y≥6 and 3x=2y≤6, the solution is (1.5, 1). Option A is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

3x=2y<=6

3x =2y

y=1.5x

3x≤6

x≤2

2y≤6

y≤3

As a result, we found that y is 1.5 times x, the value of x should be less than 2, and y should be less than 3.

We analyze each option one by one we obtained the correct values is,

(y,x) = (1.5, 1)

The values follow all the obtained condition

Thus, for the given equation 2x+3y≥6 and 3x=2y≤6 the solution is (1.5, 1). Option A is correct.

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Answer:

(0.5, 2) and (-2, 4)

Step-by-step explanation:

I did the assignment it is the correct answer.

Answer: 24 units

Step-by-step explanation:

If you are multiplying a shape by a scale factor, the dimensions are also multiplied by the scale factor.

QR= x

Q'R'= (1/2)(X)

12=(1/2)(X)

(2)12= 1/2x(2)

24=X

If you're multiplying QR by 1/2 you would get 12. 12 is a half of QR. Therefore, QR is 24.

Answer:

[tex]\sf y =\dfrac{-1}{4}x+\dfrac{17}{2}[/tex]

Step-by-step explanation:

        where m is slope and b is y-intercept.

y = 4x + 9

Slope = m₁ = 4

[tex]\sf \text{Slope of the perpendicular line = $\dfrac{-1}{m_1}$}[/tex]

                                                [tex]\sf \boxed{m = \dfrac{-1}{4}}[/tex]

  [tex]\sf y =\dfrac{-1}{4}x +b[/tex]

The point (2,8) passes through the line. Substitute in the above equation to find 'b'.

     [tex]\sf 8 = \dfrac{-1}{4}*2+b\\\\\\ 8 = \dfrac{-1}{2}+b\\\\[/tex]

[tex]\sf 8+\dfrac{1}{2}=b\\\\ \dfrac{16}{2}+\dfrac{1}{2}=b\\\\ \boxed{b=\dfrac{17}{2}}[/tex]

     Equation of the line:

                    [tex]\sf y =\dfrac{-1}{4}x + \dfrac{17}{2}[/tex]

The common ratio of the geometric sequence with 8th term of -7^32 and first term is of 28 is of:

q = -4535.

In a geometric sequence the result of the division of consecutive terms is always the same, called common ratio q.

Hence, the nth term of a geometric sequence is obtained according to the rule presented as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the first term and the 8th term are given as follows:

[tex]a_1 = 28, a_8 = -7^{32}[/tex]

Hence the common ratio can be obtained as follows:

[tex]a_8 = a_1q^{7}[/tex]

[tex]-7^{32} = 28q^{7}[/tex]

[tex]q^7 = -\frac{7^{32}}{28}[/tex]

[tex]q = -\sqrt[7]{\frac{7^{32}}{28}}[/tex] (the 7th root is calculated with a calculator, elevating the number to 1/7).

q = -4535.

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The solution set of the inequality x ≥ - 4 using set builder notation and interval notation is {x | x ∈ Z, - 4 ≤ x ≤ ∞ } and [ - 4, ∞ ) respectively.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.

Interval Notation: A set of real numbers known as an interval contains all real numbers that fall inside any two of the set's numbers.

Consider the inequality,

x ≥ - 4

In the number line, the value of x is equal to and greater than - 4 increasing to infinity.

Therefore,

The solution set using the set builder notation is:

{x | x ∈ Z, - 4 ≤ x ≤ ∞ }

The solution set of the inequality using the interval notation is:

[ - 4, ∞ )

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We need to determine a few characteristics of the following linear equation:

The first step we need to take is to isolate the "y" variable on the left side.

Now we need to analyze this function and provide the necessary characteristics.

First is the Domain. The Domain of a function is the group of all numbers that can be used as an input (x), in this case the Domain is the whole Real group.

Second is the Range, which is the group of numbers that can be the output of the function (y), for this case we also have the whole Real group as Range.

Then we need to find the "Zero". Which is the value at which the function crosses the x-axis, to calculate it we must make "y=0" and solve for x.

The zero is equal to 12.

The slope of the function is the number multiplying "x", in this case it is -1/2.

The slope is negative, decrescent.

To find the value of f(8), we need to replace x by 8 and solve for y.

The value of f(8) = 2.

To determine the value of x where f(x) is equal to 5, we need to replace f(x) by 5 and solve for x.

The value of x for which f(x) is equal to 5, is 2.

Now we need to graph the equation, for that we have to use two of the points we found before, we will use (8, 2) and (2,5). We need to mark these points at the coordinate plane and draw a line between them:

3012 +

4624

-------

7636

Answer:

Step-by-step explanation:

3.012+4.624=7.636

how to solve this is to line them up with the decimal point.

decimal point to decimal point. look at the example below.

3.012 plus

4.624 equals

7.636

the first one is 99 and the second one is 72

Hope this helped

Answer:

33% of 300 is about 99, and 24% of 300 is about 72

Step-by-step explanation:

Hope this helps.

8y - 2y = 24

a)

The x intercept is when y = 0; if we use the equation when y = 0:

8x - 2(0) = 24 ==> 8x = 24 ==> x = 24/8 ==> x = 3

So the fist answer is TRUE

b)

The y intercept is when x = 0; if we use the equation with x = 0:

8(0) - 2y = 24 ==> -2y = 24 ==> y = 24/(-2) ==> y = -12

So the second answer is FALSE

c)

if we take the equation and solve it for y:

8x - 2y = 24 ==> 8x - 24 = 2y ==> (8x - 24)/2 = y ==> 4x - 12 = y ==> y = 4x -12

So the third answer is TRUE

Answer:

linear equations;15m+10=w

15 pages written for every month for 5 months plus the 10 pages she has already written is equal to the total number of pages written in 5 months m=number months written in this case it is 5 months.

w=number of pages written in 5 months 15(5)+10=w

75+10=w

85 Pages written=w

will have written 85 Pages in 5 months

Answer:

1/3+2 2/3=3/2=1 1/2 yards or x=3/2

The fraction of students who chose power other than flight and invisibility are 18/100.

Researchers surveyed the students and obtained different kind of data, the data found is,

The number of male students wanting superpower of fight are 26.

The number of female students wanting superpower of fight are 11.

The number of male students wanting superpower of invisibility are 14.

The number of female students wanting superpower of invisibility are 31.

The number of male students wanting other superpower are 10.

The number of female students wanting other superpower are 8.

Total number of students wanting the power other than flight and invisibility are 18.

So,

The fraction of student wanting power other than invisibility and flight = student wanting other power/total number of students.

= 18/100

The fraction of student wanting power other than invisibility and flight is 18/100

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Two angles form a linear pair.

so, the sum of the angles are 180

the measure of the angles are z and (2.4 * z + 10)

so,

z + (2.4 * z + 10) = 180

solve for z

so,

z + 2.4 * z + 10 = 180

3.4 z = 180 - 10

3.4 * z = 170

divide both sides by 3.4

so, z = 170/3.4 = 50

so, the angles are 50 and 130

The revenue is given as:

R = 40x

The cost of producing x units is given as:

C = 20x + 6600

The profit P is given as:

P = R - C

P = 40x - (20x + 6600)

P = 40x - 20x - 660011111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222

The quadratic equation that Olivia is solving is y = x² + 4x + 6

Any expression that can be changed into standard form, such as the ones below, is considered to be a quadratic equation in algebra:

y = ax² + bx +c

Now from the given step and by using the quadratic formula we can ascertain that the values of a ,b and c are 1 ,4 and 6 respectively.

hence the quadratic equation is y = x² + 4x + 6.

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The answer is 3 1/3 feet

Solution :

Total length of material : 13 1/3 feet

Number of sections needed : 4

so the length of new sections = Total length ÷ No. of section

                                                  = 13 1/3 ÷ 4

             13 1/3 = 40/3

so,         40/3 ÷ 6

that is    40/3 × 1/6

            = 40/12

            = 3.33 or  3 1/3

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Answer:

A     and      d

Step-by-step explanation:

Answer:

false 1/10 false 80 13/1

The total earning of the store from the formed equation is: 15,500 dollars.

What is equation?

In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.

According to the question, the given parameter states that the music store sold 1000 CDs and 100 CD players. And the cost of each CD is $12 and each CD player is $35.

Now, to calculate the total earning by forming the equation for the given statement and it is as follows:

(1000)(12) + (100)(35) = 12,000 + 3500 = 15,500 dollars

Hence, the total earning of the store from the formed equation is: 15,500 dollars.

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The value of x and y using the substitution method are 5/4 and 5/4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Two equations:

3x + 5y = 10 _____(1)

9y + 3x = 15 ______(2)

From (1) we get,

3x = 10 - 5y

x = (10 - 5y) / 3 ______(3)

Putting (3) in (2) we get,

9y + 3 x [(10 - 5y) / 3] = 15

9y + 10 - 5y = 15

4y = 15 - 10

4y = 5

y = 5/4

Putting y = 5/4 in (3) we get,

x = (10 - 5 x 5/4) / 3

x = (10 - 25/4) / 3

x = (40 - 25) / (4 x 3)

x = 15 / 12

x = 3x5 / 3x4

x = 5/4

Thus,

The value of x and y using the substitution method are 5/4 and 5/4.

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