The price of a gallon of gasoline has increase, on average from $2.50 in 2006 to $4.00 in 2008. What is the percentage of increase?

Answer:

Step-by-step explanation:

It is convenient to use technology to plot the points and the functions to see what lies where. The first attachment shows such a plot.

_____

Of course, you can do the function evaluations. For example, testing answer B, we find ...

... 3·6 ≤ -2·1 +18 . . . . false for the first equation — not a solution

Checking all the points requires 10 function evaluations. When things get repetitive like that, I like to use a graphing calculator or spreadsheet.

_____

Using a calculator

The second attachment shows a calculator evaluating the viability of each point as a solution. The equations have been rearranged to ...

This makes it easy to look at the evaluation results to see if the solution is viable or not.

The x-values of the points are entered into list L₁ and the y-values into L₂. The result of the first inequality above is in L₃ and the result for the second inequality is in L₄. Any negative value in L₃ or L₄ shows a point that is not part of the solution set. Points B and D fail to match problem requirements.

Points A, C, and E are in the solution set.

The simplified expression is [tex]\( \frac{x - 2}{x + 2} \)[/tex].

To divide the expression [tex]\(\frac{x^3 - 8}{x^2 + 2x + 4}\) by \((x^2 - 4)\)[/tex], you first factor both the numerator and denominator.

Factor the numerator:

[tex]\[ x^3 - 8 \][/tex]

[tex]\[= (x - 2)(x^2 + 2x + 4) \][/tex]

This is based on the difference of cubes: [tex]\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\), where \(a = x\) and \(b = 2\).[/tex]

Now, factor the denominator:

[tex]\[ x^2 + 2x + 4 \][/tex]

[tex]\[= (x + 2)^2 \][/tex]

The expression becomes:

[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \][/tex]

Now, divide by [tex]\((x^2 - 4)\)[/tex]:

[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \div (x^2 - 4) \][/tex]

Factor [tex]\(x^2 - 4\)[/tex] further:

[tex]\[ x^2 - 4 = (x + 2)(x - 2) \][/tex]

Now, cancel out common factors:

[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \div (x^2 - 4) = \frac{x - 2}{x + 2} \][/tex]

Therefore, the simplified expression is [tex]\( \frac{x - 2}{x + 2} \)[/tex].

Complete question:

Simplify: X^3-8/x^2+2x+4 divided by (x^2-4)

Answer:27

Step-by-step explanation:

See Mrs. Ryan plants 3 flowers along 4 in. of a garden row.

The garden row is 3 ft long.

We know 1 ft = 12 inches

So, 3 ft = 36 inches

No. of flowers Length

3 4

x 36

So our equation becomes 4x = 36*3

equation, we get x = 36*3/4

= 27

Therefore, Mrs. Ryan can plant 27 flowers along the garden row.

Hope it helps!!!

Answer:

$3.13

Step-by-step explanation:

We assume you mean the tax rate is 4.4%. Then the tax on $3 is ...

... tax = (tax rate) × (item cost)

... = 4.4/100 × 3.00 = 4.4 × .03 = 0.132 ≈ 0.13

The amount paid is ...

... amount paid = tax + item cost = $0.13 +3.00

... amount paid = $3.13

yes

no

Doing what the directions say is generally a good idea.

Adding a number moves to the right; subtracting a number moves to the left. Subtracting a negative number is the same as adding its opposite.

The arrowhead end of the line in the figure is the end result. Two of them end up to the right of -8, that is, greater than -8.

Answer:

Answer:

yes

-6-(-6)

-4-(-7)

no

all others

Step-by-step explanation:

Answer:

C. Decreasing; Linear.

Step-by-step explanation:

We have been given a table that shows the relationship between two variables.

Let us find slope of our given values using slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let us find rate of change for points (1,5) and (2,-1)

[tex]m=\frac{-1-5}{2-1}[/tex]

[tex]m=\frac{-6}{1}=-6[/tex]

Let us find slope for points (3,-7) and (4,-13).

[tex]m=\frac{-13--7}{4-3}[/tex]

[tex]m=\frac{-13+7}{1}[/tex]

[tex]m=\frac{-6}{1}=-6[/tex]

We can see that rate of change is constant (-6), therefore, our function is a linear function. Since slope is negative (-6) and with each increase in x, our y is decreasing, therefore, our function is decreasing.

Answer:

Step-by-step explanation:

A) Use the distributive property to eliminate parentheses. Then combine like terms. (The only "like terms" are the constants.)

... = 12 +3·2y +3·(-3) . . . use the distributive property to multiply each term in parentheses by the factor 3 outside those parentheses

... = 12 +6y -9 . . . . . . . . simplify

... = 6y + (12 -9) . . . . . . group like terms together

... = 6y + 3 . . . . . . . . . . simplify

___

B) Look for factors of each term that are also found in the other term.

... 18b has factors 3×6×b

... 12 has factors 2×6

The only common factor is 6, so we factor that out using the distributive property.

... 18b -12 = 6(3b -2)

_____

Comment on factoring

For factoring problems, it helps immensely if you know your times tables and some of the rules for divisibility. (Even numbers are divisible by 2, numbers ending in 0 or 5 are divisible by 5, numbers whose sum of digits is divisible by 3 are divisible by 3, for example.)

Answer:

r+6

Step-by-step explanation:

r = marbles that Rory has

r+6 = marbles that Conrad has

Answer:

r+6

Step-by-step explanation:

r = marbles that Rory has

r+6 = marbles that Conrad has

you could also use c

Answer:

The sum of the measures of the angles in a triangle is equal to 180 degree.

In triangle FGH;

[tex]\angle F + \angle G + \angle H = 180^{\circ}[/tex]

or

[tex]\angle H = 180^{\circ} -{\angle F + \angle G}[/tex]

Substitute the given values from the given figure we have;

[tex]\angle H = 180^{\circ} -{33^{\circ} + 90^{\circ}}[/tex]

[tex]\angle H = 180^{\circ} -{123^{\circ}}[/tex]

Simplify:

[tex]\angle H = 57^{\circ}[/tex]

Given that:

[tex]\cos H = \frac{x}{y}[/tex]

Using Cosine ratio:

[tex]\cos \theta = \frac{\text{Base}}{\text{Hypotenuse}}[/tex]

In a given figure:

Base = GH = x and Hypotenuse = FH = y = 80 cm

Then;

[tex]\cos 57^{\circ}= \frac{x}{80}[/tex]

or

[tex]x = \cos 57^{\circ} \cdot 80[/tex]  

[tex]x = 0.54463903501 \cdot 80 \approx 43.57[/tex] cm

Therefore, the value of :

[tex]H = 57^{\circ}[/tex]

x = 43.57 cm

y = 80 cm

The value of H is 57 degrees, x is 43.57, and y is 80 cm.

The sum of the measures of the angles in a triangle is equal to 180 degrees.

The cosine is defined as the ratio of the base of the triangle and the hypotenuse of the triangle.

[tex]\rm Cosh= \dfrac{Base}{Hypotenuse}[/tex]

Where the value of base x  is and Hypotenuse = FH = y = 80 cm.

The sum of the measures of the angles in a triangle is equal to 180 degrees.

Then,

In triangle FGH;

[tex]= \rm \angle F+\angle G + \angle H =180\\\\=90+33+\angle H =180\\\\\angle H = 180-90-33\\\\\angle H =180-123\\\\\angle H =57[/tex]

Substitute all the values in the formula;

[tex]\rm Cosh= \dfrac{Base}{Hypotenuse}\\\\Cos57=\dfrac{x}{80}\\\\x = Cos57 \times 80\\\\x=43.57 \ cm[/tex]

Hence, the value of H is 57 degrees, x is 43.57, and y is 80 cm.

To know more about the Cosine function click the link given below.

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Answer:

The line will change its slope by a factor of -2 (line will now "point down" with twice the original steepness)

Step-by-step explanation:

f(x) = x    | replace f(x) --> (-1/2)f(x)

(-1/2)f(x) = x

f(x) = -2x

Answer:

(i)

Emily's score was 9

(ii)

e = m + 2

Step-by-step explanation:

Let's assume

Emily's score is e

Miguel's score is m

Valerie's score is v

Their combined score is 24

so, we get

[tex]e+m+v=24[/tex]

Emily and Miguel's combined score is twice that of Valerie

we get

[tex]e+m=2v[/tex]

Valerie scored only one more point than Miguel

we get

[tex]v=m+1[/tex]

(i)

we got system of equations as

[tex]e+m+v=24[/tex].............(1)

[tex]e+m=2v[/tex]..................(2)

[tex]v=m+1[/tex]......................(3)

we can plug second equation into first one

[tex]2v+v=24[/tex]

[tex]3v=24[/tex]

[tex]v=8[/tex]

now, we can plug this into second and third equation

[tex]v=m+1[/tex]

we can plug it and find m

[tex]8=m+1[/tex]

[tex]m=7[/tex]

now, we can find e

[tex]e+7=2\times 8[/tex]

[tex]e=9[/tex]

So, Emily's score was 9

(ii)

we  got

e=9

m=7

9=7+2

e=m+2

Answer: Emily's score is 9; Equation (D) v = m+1

Step-by-step explanation: To find Emily's score, let's represent each score with their own initials, i.e.: Emily's score is E; Miguel's score is M and Valerie's score is V.

Their combined score is 24, which means:

E + M + V = 24 (1)

Emily and Miguel's combined score is twice of Valerie, in other words:

E + M = 2V (2)

Valerie scored only one point more than Miguel:

V = M + 1 (3)

Substitute (3) into (2):

E + M = 2(M + 1)

E = 2M - M + 2

E = M + 2 (4)

With (3) and (4), use it to substitute into equation (1):

E + M + V = 24

M + 2 + M + M + 1 =24

3M = 21

M = 7

Using M=7 to find E:

E = M + 2

E = 7 + 2

E = 9

Emily's score is 9.

To represent the situation, the correct equation is V = M + 1, which means Valerie's score is 1 more than Miguel, which is exactly what's written in the question.

Answer:

See attached.

Step-by-step explanation:

The inequality x > 0 means the feasible region is to the right of the y-axis.

The inequality y > x means the feasible region is above the line y=x.

Only the first graph has these characteristics.

The feasibility region for the system of inequalities Y>X and Y<-1/4X+5 can be found by graphing both inequalities and finding the area that satisfies both at the same time. Y>X results in a line where the feasible region is above the line, while Y<-1/4X+5 produces a line where the feasible region is below it.

The question is asking for the best graphical representation of the feasibility region for the system of inequalities Y>X and Y<-1/4X+5. Feasibility region in mathematics often refers to the set of all feasible solutions, which are the solutions that satisfy all constraints of the problem. In this context, it means finding the area of the graph that satisfies both inequalities at the same time.

One way to approach this is by graphing each of the inequalities on a two-dimensional plane. The inequality Y>X means that the Y-values are greater than the X-values. This will result in a graph where the feasible region is above the line Y=X.

On the other hand, Y<-1/4X+5 means that the Y-values are less than -1/4 times the X-values, plus 5. This produces a line with a negative slope, indicating that the feasible region is below this line.

The area that satisfies both these conditions represents the feasible region for the system of inequalities.

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ANSWER:  

The candle was 12 inches tall to begin with.

After 2 hours (120 minutes), the height of the candle is approximately 9.9625 inches.

To start, let's define our variables:

t  represents time in minutes.

h  represents the height of the candle in inches.

First, we find the rate at which the candle is burning. The change in height over time is [tex]\( \frac{{11.2 - 10.75}}{{32}} \)[/tex] inches per minute.

Using point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and  m  is the slope, we can use the point [tex]\((32, 11.2)\)[/tex] and the calculated slope to find the equation of the line.

[tex]\( h - 11.2 = \frac{{11.2 - 10.75}}{{32}}(t - 32) \)[/tex]

Simplify to: [tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(t - 32) \)[/tex]

Next, we want to find the height after 2 hours (which is 120 minutes). Substituting t = 120  into the equation:

[tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(120 - 32) \)[/tex]

[tex]\( h - 11.2 = -\frac{{0.45}}{{32}}(88) \)[/tex]

[tex]\( h - 11.2 = -1.2375 \)[/tex]

Now, solving for  h :

[tex]\( h = 11.2 - 1.2375 \)[/tex]

[tex]\( h = 9.9625 \)[/tex]

So, after 2 hours (120 minutes), the height of the candle is approximately 9.9625 inches.

Answer:

All the answers are correct

Step-by-step explanation:

Any relation that is a function will pass the vertical line test, regardless of any other characteristic it may have (such as being the inverse of some other function).

The inverse of a function is that function reflected across the line y=x. If the inverse passes the vertical line test (is a function), then the original must pass the horizontal line test. The reflection of a vertical line is a horizontal line and vice versa.

Let m and b represent the numbers of math and biology books sold, respectively. The problem statement tells you ...

... m + b = 266

... m - b = 54 . . . . . . . 54 more math books were sold

Adding these two equations gives you ...

... 2m = 320

... m = 160 . . . . . divide by 2

... b = 160 -54 = 106 . . . . 54 fewer biology books were sold.

160 math textbooks and 106 biology textbooks were sold in a week.

x = 0.973

3e^(2x) +5 = 26

3e^(2x) = 21 . . . . . subtract 5

e^(2x) = 7 . . . . . . . divide by 3

2x = ln(7) . . . . . . . .take the natural log

x = ln(7)/2 ≈ 0.973 . . . . divide by 2 and evaluate

Answer:

x= .973

Step-by-step explanation:

3e^2x +5=26

Subtract 5 from each side

3e^2x +5-5=26-5

3e^2x =21

Divide by 3 on each side

3/3e^2x =21/3

e^2x =7

Take the natural log on both sides

ln (e^2x) =ln (7)

2x = ln (7)

Divide by 2

2x/2 = ln(7)/2

x = ln(7)/2

x is approximately .972955075

Rounding to the nearest thousandth

x = .973

Answer:2w + 20

Step-by-step explanation:

See, the carpet has a rectangular measure of 10 feet.

It's width is 'w'

We, know that perimeter is the sum of all sides.

Now there are two equal sides which we consider length and two other equal sides for width.

So, we have to add all sides which gives 20 +2w

Also general formula for perimeter is 2(length + breadth)

So, our ans. is 2w + 20

Hope it helps!!!

Answer:

2w + 20

Explanation:

As stated in the question, the perimeter is the sum of the lengths of all the sides. So a general expression for the perimeter of a four-sided shape could be written like this:

P = AB + BC + CD + DA

or

P = 2w + 2l; w = width and l = length

So, to write an expression to match this problem, all we have to do is substitute the given side lengths (the first form) or substitute the given values of w and l (the second form):

P = AB + BC + CD + DA

P = 10 + w + 10 + w

P = 20 + 2w

P = 2w + 20

OR

P = 2w + 2l

P = 2(w) + 2(10)

P = 2w + 20

Answer:

1. Equivalent: [tex]p(1+0.20),\ 1.20p;[/tex]

2. Not equivalent: [tex]2p+0.20,\ 0.80p,\ 2.20p,\ 1.02p.[/tex]

Step-by-step explanation:

Consider the expression [tex]p+0.20p.[/tex]

Use the distributive property

[tex]a\cdot (b+c)=a\cdot b+a\cdot c.[/tex]

Then

[tex]p+0.20p=p\cdot 1+p\cdot 0.20=p\cdot (1+0.20)=p(1+0.20).[/tex]

Expression [tex]p(1+0.20)[/tex] is equivalent to the expression [tex]p+0.20p.[/tex]

Since [tex]1+0.20=1.20,[/tex] then expression [tex]p(1+0.20)=1.20p[/tex]  is equivalent to the expression [tex]p+0.20p.[/tex]

All the rest expressions are not equivalent to the expression [tex]p+0.20p.[/tex]

Final answer:

The expressions equivalent to Paul's original expression p + 0.20p for calculating a meal's cost plus a 20% tip are p(1+0.20) and 1.20p. The other expressions provided do not accurately represent the original expression's intent to include a 20% tip.

Explanation:

The expression p + 0.20p can be simplified by combining like terms. As both terms contain 'p', we can add them together. Since 0.20 is the decimal form of 20%, this expression can be rewritten as 1p + 0.20p, which simplifies to 1.20p. This means that to find the total cost of the meal including the tip, you multiply the price of the meal 'p' by 1.20. Therefore, the equivalent expressions to p + 0.20p are p(1+0.20) and 1.20p, because both represent Paul adding a 20% tip to the cost of his meal.

Let's identify which of the given expressions are equivalent:

2p + 0.20 - Not equivalent, as it suggests doubling the price plus 20 cents.

0.80p - Not equivalent, as it represents only 80% of the original price.

p(1+0.20) - Equivalent; this is simply another way of writing the original expression.

1.20p - Equivalent; this is the simplified form of the original expression.

2.20p - Not equivalent, as it incorrectly represents an additional 220% of the meal cost.

1.02p - Not equivalent, as it only adds an additional 2% to the original price, not the 20% intended for the tip.

Answer:

There should be 120 peanuts

Step-by-step explanation:

We can use ratio's to solve this problem

5 bags

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

75 peanuts

5 bags           8 bags

---------------  = ------------------

75 peanuts      x peanuts

Using cross products

5x = 75*8

5x = 600

Divide each side by 5

5x/5 = 600/5

x = 120

Answer:

if 5 bags of peanuts = 75peanuts

Then 1 bag will be 15 peanuts beacause 75 divided by 5 is 15

8 bags of peanuts will then be 15 multiply by 8 which is 120 peanuts

Step-by-step explanation:

Answer:

I am 90% sure that the answer is M'N'O' is 90*

Step-by-step explanation:

A line segment MN is shown as M = -1,1 and N= -5,4 this makes a diagonal line across the grid. Another line segment NO is shown with O as ordered pair negative 1, 4. Angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′. this is where the angles meet, Rotating the shape (or the angles) does not change the degree of the angle of the shape. I am 99% sure that an 90* angle would be formed. but im just in middle school so what do i know?

Answer with explanation:

It is given that ,∠M NO is formed by segments MN and NO on the following coordinate grid.

Coordinate of Point M = (-1,1)

Coordinate of Point N= (-5,4)

Coordinate of Point O= (-1,4)

[tex]MN=\sqrt{(-1+5)^2+(1-4)^2}\\\\MN=\sqrt{16+9}\\\\MN=5\\\\NO=\sqrt{(-1+5)^2+(4-4)^2}\\\\NO=4\\\\MO=\sqrt{(-1+1)^2+(4-1)^2}\\\\MO=3[/tex]

MO²+NO²=MN²

So,By Pythagorean Theorem, ΔM NO is right Angled Triangle having ∠ O=90°.

Now, it is given that, ∠MNO is rotated 90 degrees counterclockwise about the origin to form ∠ M′N′O′.

⇒When we rotate a Triangle either Anticlockwise or Clockwise the triangle before Rotation and Triangle after rotation will be congruent to each other.

Option D:→

 m∠ M′N′O′ = m∠M NO

Answer:

[tex]\sqrt{3}[/tex]  :1

Step-by-step explanation:

Ratio of height of two cylinders are 3:1

Let C2 has the height x

then height of C1 is 3x

Let r1 is the radius of C1

and r2 is the radius of C2

As given that volume of both are equal

Also we know that formula for the volume of the cylinder is

V= π r²h

for C1

V= π (r1)²h

for C2

V=π (r2)²h

As volume of both are same so equating them

π (r1)²h1 = π (r2)²h2

as h1 =3x and h2=x

putting values

π (r1)²(3x) = π (r2)²(x)

cancelling out π and x from both side of the equation

3(r1)²= (r2)²

Taking square root of both sides give

[tex]\sqrt{3(r1)^{2} }=\sqrt{(r2)^{2} }[/tex]

r1 ( [tex]\sqrt{3}[/tex]) = r2

or

r1 : r2 =  [tex]\sqrt{3}[/tex]  :1

To find the total number of people who came to the three showings, divide the total amount collected by the average admission price. Set up equations using the given information for each night and solve simultaneously to find the values of x, y, a, b, p, and q. Add those values to find the total number of people.

To find the total number of people who came to the three showings, we need to divide the total amount collected by the average admission price. Let's calculate:

On the first night, let's assume there were x children and y adults. So, we can set up the equation.

9x + 17y = 541.

Similarly, for the second and third nights, we can set up two more equations:

9a + 17b = 541 and 9p + 17q = 541.

Solving these three equations simultaneously will give us the values of x, y, a, b, p, and q, which represent the number of children and adults present on each night. Adding those numbers together will give us the total number of people who came to the three showings.

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Answer:

[tex]3 \cdot 10^{-10}[/tex]

Step-by-step explanation:

[tex]\dfrac{1.2\cdot 10^{-3}}{4\cdot 10^{6}}=\dfrac{12\cdot 10^{-4}}{4\cdot 10^{6}}\\\\=\dfrac{12}{4}\cdot 10^{-4-6}=3\cdot 10^{-10}[/tex]

I like to adjust the operands so the quotient needs no adjustment. Here that means rewriting the numerator to an equivalent value with a mantissa between 4 and 40.

Answer:

Net pay =$ 308

Step-by-step explanation:

Net pay  is the gross pay minus taxes

Net pay = gross pay - gross pay * tax rate

Simplifying this equation by factoring out gross pay

Net pay = gross pay (1- tax rate)

Gross pay =  hours worked * hourly rate

Substituting this in

Net pay = hours worked * hourly rate (1- tax rate)

We know the

hours worked = 40

Hourly rate = 8.75

tax rate = .12

Net pay = 40 * 8.75 (1- .12)

Net pay = 350(.88)

Net pay =$ 308

$137,557.93

It is convenient to let a spreadsheet do the calculations. The number in the fourth column is the number in the first column divided by the number in the second column and multiplied by the number in the third column.

For example, the weighted average cost of Widgets is ...

... 135,320.00 × 866/2740 = 42,769.02

Then the total of all on-hand inventory is the sum of the inventory costs of the three items: $137,557.93.

Answer:

492,000

Step-by-step explanation:

Do 41,000x12. Pls mark me brainliest if im correct!

Answer:

-20x +52

Step-by-step explanation:

To solve this, we put the function g(x) into the function f(x) in the place of x

Put 5x-3 in for x in -4x

f(g(x)) = -4 (5x-13)

       = -4*5x -4(-13)

       = -20x +52

Answer:

D)180 mi/6 gal; by multiplying the numerator and denominator of the unit rate by 6.

Step-by-step explanation:

    30 mi/1 gal    Multiply numerator and denominator by 6

= 180 mi/6 gal

A) and C) are wrong because they have gallons in the numerator

B) is wrong. It should be either 90 mi/3 gal or 150 mi/5 gal.