The equation y = 13,000x + 65,000 can be used to determine the total number of miles driven, y, on Franklin's used car based on the number of months, x, after he purchased it. What is the meaning of the y-intercept of the function?
A.Franklin drove about 13,000 miles each month.

B.The car had been driven 65,000 miles when Franklin purchased it.

C.The car had been driven 13,000 miles when Franklin purchased it.

D.Franklin drove about 65,000 miles each month.

Answer:

1.5053412e+25

Step-by-step explanation:

use a calculator dude

The symmetry of a quadratic function is a vertical line that is x = − b/2a.

Quadratic function is defined as the function of the form f(x) = ax² + bx + c, where a, b and c are real numbers with a = 0 and it has the domain of a quadratic function is (−∞,∞).

Here we have given that we need to find the symmetry of a quadratic function.

As we all know that When a quadratic function is graphed in the coordinate plane, then the resulting parabola and corresponding axis of symmetry are vertical.

Here we have also know that in order to find the symmetry we have to  replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

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A linear equation in two variables is an equation that can be written in the form of:

ax + by = c,

where a, b, and c are constants, and x and y are variables.

Linear equations in two variables are also called a system of linear equations in two variables. In this type of equation, the variables are related linearly, meaning that the highest power of the variables is 1. This is in contrast to non-linear equations, which have variables with powers greater than 1.

For example,

2x + 3y = 6 is a linear equation in two variables.

4x - 6y = 10 is also a linear equation in two variables.

A system of linear equations in two variables can have one unique solution, infinitely many solutions, or no solution. The solution of the system can be found by different methods such as graphing, substitution, elimination, matrix method, and numerical methods, as mentioned in the previous answers.

Linear equations in two variables are used to model many real-world situations such as in finance, physics, economics, and many more. The study of linear equations in two variables is a fundamental part of algebra and is a stepping stone to more advanced mathematical concepts.

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The prime factorization of 36 is (2 2 3 3) while that of 49 is (7 7), respectively. As can be seen, the prime numbers 36 and 49 have no common prime factors, making them co-prime.

Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number. As an illustration, the prime number 2 contains two factors, 2 and 1.

The prime numbers that divide a positive integer exactly are said to be its prime factors. Integer factorization, often known as prime factorization, is the process of locating these integers. According to the basic theorem of mathematics, each positive integer has a distinct prime factorization.

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The curve's y-intercept is 4, and its slope is 2.

To depict the curve, we will make use of the idea of slope and intercept in linear equations.

A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.

When y = 2x - 4 is put into comparison with the generic form, we get

The curve has a slope of 2 and a y-intercept of -4.

Picking two points on the line y = 2x – 4 will make it easier for us to plot the graph.

Since the supplied line's y-intercept is 4, the line y = 2x - 4 must pass through (0, -4).

Put y = 0

0 = 2x - 4

x = 2

Line passes through (2,0).

Draw a line passing through (0,4) and (2,0) and we get the graph.

Correct question :

How do you graph y = 2x - 4 on a graph?

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Answer:

C

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = G (10, 1 ) and (x₂, y₂ ) = H (3, 5 ) , then

midpoint = ( [tex]\frac{10+3}{2}[/tex] , [tex]\frac{1+5}{2}[/tex] ) = ( [tex]\frac{13}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = ( [tex]\frac{13}{2}[/tex] , 3 )

The rule of parallel lines: they never intersect each other.

We know that two lines are parallel to each other if they lie in the same plane and never intersect each other.

Parallel lines are always equidistant from each other.

Also, the parallel lines are coplanar.

Mathematically, the parallel lines are represented by the symbol, ‘||‘.

If two lines l₁ and l₂ are parallel to each other then they are represented as l₁ || l₂.

Two lines parallel to a third line are parallel

As we know, the slopes of parallel lines are equal.

Let us assume that m₁ be the slope of line l₁ and m₂ be the slope of line l₂.

If line l₁ and l₂ are parallel to each other then m₁ = m₂

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The volume of each of the 3 samples is given as follows:

The density is given by the division of the mass by the volume, hence:

Density = Mass/Volume

The equation can be solved for the volume as follows:

Volume = Mass/Density.

The density of ice is given as follows:

0.9 g/ cm³.

Hence the volume of each sample is given as follows:

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Answer:

max : 2, min : -2

Step-by-step explanation:

this question is kinda hard and brain-intensive but i think i am right

Answer:

max : 2, min : -2

Step-by-step explanation:

max : 2, min : -2

The total length of the two boards is 9 inches.

An inch can be defined as a unit of length in the customary system of measurement. Length in inches is either represented by in or ''. For instance, 5 inches can be written as 16 in or 16''. of a foot.

as given, a carpenter has a board that is three and one fourth inches long

i.e. the carpenter has a board that is 3.25 inches long.

and a second board to the end that is five and three fourth inches long

i.e. another board that is 5.75 inches long.

When joined together, the total length of the two boards is 3.25 inches + 5.75 inches = 9 inches.

Therefore, the total length of the two boards is 9 inches.

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Answer:

18, 19, 20

Step-by-step explanation:

Let the integers be x - 1, x, x + 1.

x - 1 + x + x + 1 = 57

3x = 57

x = 19

x - 1 = 18

x = 19

x + 1 = 20

Answer: 18 , 19 , 20

Step-by-step explanation:

18+19+20=57

The total time that Tony bakes the casserole is calculated by adding the two times together.

The first time the casserole bakes for 25 5/12 minutes and the second time it bakes for 2 3/6 minutes. The two times can be written in fractions as 25 5/12 + 2 3/6. To add fractions with different denominators, the denominators must first be made equal.To accurately calculate the total amount of time the casserole bakes, the fractions must be converted to their equivalent value in the same unit. 5/12 minutes is equal to 10/24 minutes and 2 3/6 minutes is equal to 8/6 minutes. To add the two fractions, 10/24 and 8/6, they must be converted to have the same denominator. The least common denominator is 24, so 10/24 is equal to 5/12, and 8/6 is equal to 16/24.  To make the denominators equal, the common denominator of 12 must be used. 25 5/12 can be rewritten as 225/12 and 2 3/6 can be rewritten as 15/12. 225/12 + 15/12 = 240/12. The fraction 240/12 can be reduced to 20/1. Therefore, the total time that Tony bakes the casserole is 20 minutes. The formula used to calculate this time is (25 5/12) + (2 3/6) = (225/12) + (15/12) = (240/12) = (20/1).

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Answer:

Step-by-step explanation:

the degree of a polynomial is determined by the biggest exponent. For example, in this equation: 6x^4+3x^3+3x^2+2x+1, you can see that the biggest exponent is the 4, so it would be a polynomial of the 4th degree.

The required arcs that are shorter than the semi circle are  DA,DB,DC,AC,AB .

Minor arc: an arc that is less than a semicircle. A minor arc is named by using only the two endpoints of the arc.

Given here: Arcs of a circle.

An arc whose measure is less than 180 degrees is called a minor arc. An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two. And a semicircle subtends and angle of 180 at the center of the circle.

Thus all the arcs that measure less than 180 are shorter than the semi circle

∴DA,DB,DC,AC,AB are the arcs that measure less than 180 at the center of the circle.

Hence, The required arcs are DA,DB,DC,AC,AB .

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Answer:

$46

Step-by-step explanation:

We already have our first value of 34.5 and the second value of 75. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1

34.5 = 75% × Y

STEP 2

[tex]34.5 = \frac{75}{100} *Y[/tex]

Multiplying both sides by 100 and dividing both sides of the equation by 75 we will arrive at:

STEP 3

[tex]Y = 34.5 *\frac{100}{75}[/tex]

STEP 4

Y = 34.5 × 100 ÷ 75

STEP 5

Y=46

Answer:

The original price is 46

Step-by-step explanation:

The x be the original price of the item.

The discount is 25%

x - .25x = 34.50

.75x = 34.50

Divide each side by .75

x = 34.50/.75

x = 46

The original price is 46

Answer:

Yes. Since 8 - 11 is -3, -3= -3

Step-by-step explanation:

-3=8-b

-3=8-11

-3=-3

Answer:

Look Below ↓↓↓

Step-by-step explanation:

Let's solve it and see if it is:-

[tex]\bf -3=8-b[/tex]

Simplify both sides of the equation:-

[tex]\bf -3=8-b[/tex]

[tex]\bf -3=8+-b[/tex]

[tex]\bf -3=-b+8[/tex]

Flip the equation:-

[tex]\bf -b+8=-3[/tex]

Subtract 8 from both sides:-

[tex]\bf -b+8-8=-3-8[/tex]

[tex]\bf -b=-11[/tex]

Divide both sides by -1:-

[tex]\bf \cfrac{-b}{-1}=\cfrac{-11}{-1}[/tex]

[tex]\bf b=11[/tex]

Therefore, yes b = 11!!

_____________________

Hope this helps!

Have a great day!

To write a system of linear inequalities represented by the graph solution boundary line dashed for > and < and solid for ≤ and ≥ is used.

These steps will be used to graphically solve a set of linear inequalities:

1. Find y's inequality solution.

2. Represent the inequality as a linear equation and, depending on the inequality sign, graph the line as either a solid line or a dashed line.

a. Draw the line as a dashed line if the inequality symbol is missing an equals sign ( or >).

b. Draw the line as a solid line if the inequality sign contains an equals sign (or ).

3. Darken the area when the inequality is satisfied.

4. For every disparity, repeat steps 1 through -3.

5. The region where all of the inequalities intersect will be the solution set.

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Question 1: The value of the dependent variable given a value of the independent is 11.54 (thousands of people)

Question 2: The value of the independent variable given a value of the dependent is 1998 (5 years after 2000)

Real-life application problem: The population of a city is growing at a rate modeled by the equation y = log(5x + 10) + 8, where y is the population in thousands and x is the number of years since the year 2000.

To determine the key properties of the function and sketch its graph:

The function is a combination of a logarithmic and an exponential function.

The domain of the function is all real numbers (since the logarithm function is defined for all positive numbers)

The range of the function is all real numbers greater than or equal to 8 (since the minimum value of the function is 8)

The graph of the function will be a smooth, continuous curve that starts at the point (0,8) and increases without bound as x increases.

Question 1: Determine the value of the population (y) given a value of x = 5 (number of years since 2000)

Solution:

y = log(5x + 10) + 8

y = log(5(5) + 10) + 8

y = log(25 + 10) + 8

y = log(35) + 8

y = 3.54 + 8

y = 11.54 (thousands of people)

Question 2: Determine the value of x (number of years since 2000) given a population of y = 12 (thousands of people)

Solution:

y = log(5x + 10) + 8

12 = log(5x + 10) + 8

4 = log(5x + 10)

5x + 10 = 10^4

5x = 9990

x = 1998 (5 years after 2000)

Note that this is not a realistic scenario, as the population of a city cannot be negative except in the case of extinction.

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Answer:

$10.57

Step-by-step explanation:

$12.90

-  18%

----------

$10.57

Yes, the given set  A={x:x²=4 and 3x=9(0)}  is an empty set.

Given the set:

A={x:x²=4 and 3x=9(0)}

Consider the equation:

x²=4

Solve for x:

x²=4⇒x=±2

Consider the other equation:

3x = 9

Solve for x:

3x = 9⇒x = 3

Because the square of the set element should be 4, the element should be 2 or -2, but 2 or -2 multiplied by 3 gets 6 or -6, which is not equal to 9. As a result, no element exists that can meet both conditions.

The value of ‘x’ is not same in both cases, so this is a null set.

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The percent salinity of the resulting mixture is given as follows:

2.63%.

The percent salinity of the resulting mixture is obtained applying the proportions in the context of the problem.

The proportions are obtained applying the weighed mean, as follows:

0 x 1000 + 0.035 x 3000 = 105 gallons of salt.

Considering that the total mixture is of 1000 + 3000 = 4000 gallons, the percentage of salt in the resulting mixture is given as follows:

105/4000 x 100% = 2.63%.

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Eric and willow will have the same number of baseball cards (when they initially have 350 and 250 cards respectively ) after 20 weeks.

Given,

Number of baseball cards Eric has =  350

Eric collects 10 cards per week.

Number of baseball cards Willow has = 250

Willow collects 15 cards per week

Let after [tex]x[/tex] weeks both eric and willow have the same number of baseball cards .

According to the question,

                                     [tex]350 + 10x = 250 + 15x\\5x = 100\\x=20[/tex]

Therefore, after 20 weeks both eric and willow have the same number of baseball cards.

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Answer:

m = 5

Step-by-step explanation:

-12 + 3m=m - 2

3m = m + 10

2m = 10

m = 5

Let's check

-12 + 3(5) = 5 - 2

-12 + 15 = 3

3 = 3

So, m = 5 is the correct answer.

Fraction value for 1/4 plus 1/4 is 1/2.

The same denominator and different numerators are considered equivalent fractions in mathematics. For instance, since 2/4 and 3/6 both equal 1, they can both be considered similar fractions. A fraction is a portion of a whole. Equivalent fractions depict identical sections of the total.

It is possible to determine the equivalent fraction of any fraction by multiplying the numerator and denominator by the same integer. Equivalent fractions are those that represent the same value despite having different visual characteristics. For instance, if you cut a piece of cake in half and eat one of the pieces, you will have eaten half of the cake.

= 1/4+1/4

= 2/4

= 1/2

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Correct Question:

What is 1/4 plus 1/4 as a fraction?.

The amount on line 10 (total payments and credits) must be equal to the amount on line 11 (amount you owe) which is C: $4184.

How to calculate difference?

The difference is a mathematical operation used to find the amount by which one number is greater or smaller than another number. It is calculated by subtracting the smaller number from the larger number. The difference can be represented by the symbol "-" or the word "minus"

The dollar amount that could be on line 10 if $4184 is on line 11 and the taxpayer will neither receive a refund nor owe the IRS is $4184.

Line 10 on the 1040EZ form is for the "Total payments and credits" which is the sum of all payments made throughout the year, including any tax payments, estimated tax payments, and any credits the taxpayer is entitled to.

Line 11 is for the "Amount you owe" which is the difference between the total tax liability (calculated on the form) and the total payments and credits.

If the taxpayer will neither receive a refund nor owe the IRS, it means that the total payments and credits are equal to the total tax liability.

Hence, the amount on line 10 (total payments and credits) must be equal to the amount on line 11 (amount you owe) which is $4184.

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The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.

Whenever the ratio is found by using the opposite side and the hypotenuse, we call it sine ratio.

We then say that sine 45 degrees is equal to 0.707. In short, we can use the symbol sin instead of sine and write sin (45 degrees) = 0.707

In general, sine of angle A =   length of leg opposite angle A / hypotenuse

sin(A) =   opposite/hypotenuse

In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.

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The line of reflection is also known as the axis of symmetry. Then the correct option is C.

Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The reflection does not change the shape and size of the geometry. But flipped the image.

From the graph, if it is rotated by 72°. Then the figure will remain the same. And the line of reflection is also known as the axis of symmetry.

Thus, the correct option is C.

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The rise and run of the line may be determined using two of its points, and the slope can be calculated.

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The correct matches are: A. Slope = 1.56, B. Slope = 0.86, C. Slope = 3

D. Slope = -5.61, E. Slope = -0.44  

Given two line-side coordinates, use the slope formula to determine the slope of the line. Slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations.

Here are the correct matches of each pair of points to the slope of the line that joins them:

A. (9, 10) and (7.2) - Slope = (10 - 7.2)/(9 - 7.2) = 2.8/1.8 = 1.56

B. (-8,-11) and (-1,-5) - Slope = (-5 - (-11))/(-1 - (-8)) = 6/7 = 0.86

C. (5,-6) and (2,3) - Slope = (3 - (-6))/(2 - 5) = 9/3 = 3

D. (6.3) and (5,-1) - Slope = (-1 - 6.3)/(5 - 6.3) = -7.3/1.3 = -5.61

E. (4,7) and (6.2) - Slope = (6.2 - 7)/(4 - 6.2) = -0.8/1.8 = -0.44

So, the correct matches are:

A. Slope = 1.56

B. Slope = 0.86

C. Slope = 3

D. Slope = -5.61

E. Slope = -0.44      

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By using the formula, Quantity = Percent × Whole, 20 is 50% percent of 40.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the percentage which 20 is of a whole number (40), we would apply the following mathematical expression (formula);

Quantity = percent × whole number

Substituting the given parameters into the percentage and quantity formula, we have the following;

20 = percent × 40

Percent = 20/40

Percent = 0.5

Next, we would multiply the resulting decimal value by 100 as follows;

Percentage = 0.5 × 100

Percentage = 50%.

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Answer:

A. (x - 3)² + (y + 2)² = 16

Step-by-step explanation:

The formula for a circle plotted on the Cartesian coordinate system is:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

where [tex](a,b)[/tex] is the center of the circle, and [tex]r[/tex] is the length of the circle's radius.

Since the center of the circle in this problem is (3, -2), we know that the left side of the equation should be:

[tex](x - 3)^2 + (y - (-2))^2[/tex]

which can be simplified to:

[tex](x - 3)^2 + (y + 2)^2[/tex]

The radius of the circle is given as 4, so we know that the right side of the equation is:

[tex]4^2[/tex], which is the same as [tex]16[/tex].

Finally, to answer this question, we can put the two sides of the equation together to get:

[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]