If the domain of f is ( -1, 1), then the function g defined by g(x) = f((x + 1)/(x - 1)) has a domain of; (-2, 0)
What is the domain of the function?The domain of a function refers to the set of all possible intput values that make the function possible.
Now, we are given the function;
g(x) = f((x + 1)/(x - 1))
The domain would be a set of real numbers excluding 1 because at x = 1, the function is undefined.
Since the domain of f(x) is -1 < x < 1 ,
Then the domain of f(x + 1) is -1 < x + 1 < 1 .
domain of -1 < x + 1 < 1 will simplify to -2 < x < 0
Thus, we can say that the domain of f(x + 1) is (-2, 0).
Thus;
g(x) = f(x + 1) and as such, the domain of g(x) is (-2, 0) .
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0. Michael works in a supermarket. He is paid $10.80 per hour. How much will he earn if he works a 37 hour week?
Answer:
Michael will earn $399.60 for a 37-hour week.
Step-by-step explanation:
[tex]10.80 \times 37 = 399.60[/tex]
okay so this question is very easy you just supposed to multiple the paid per hour amount with the hours per week.
Data
paid per hour $10.80
find how much for 37 hours
Solution
37 * 10.80
=$399.6
Using the graph , find g (0) and find x such that g (x) =-1
In order to find g(0), we just need to find the value of the function for x = 0.
Looking at the graph, for x = 0 we have y = 7.
Therefore g(0) = 7.
To find the value of x for g(x) = -1, let's look for the value of x where y = -1.
Looking at the graph, for y = -1, we have x = -2.
Therefore g(x) = -1 for x = -2.
Myra is taking her first hot-air balloon ride! The balloon was at an altitude of 288 meters until an air current caused it to rise another 36 meters.
What is the altitude of the balloon now?
The altitude of the balloon now is 324 meters.
Altitude , height, or depth are terms used to describe the measurement between a reference datum and a location or item, usually in the vertical or "up" direction.
There are various definitions and reference points used depending on the circumstance (e.g., aviation, geometry, geographical survey, sport, or atmospheric pressure). The term "elevation" or altitude is commonly favored in the context of geography, despite the fact that the term "altitude" is regularly used to refer to a location's height above sea level.Vertical distance measurements conducted in the "down" direction are frequently referred to as "depth" and the vertical distance in the up direction is altitude.The height of the balloon is 288 meters.
The balloon rises by 36 meters.
The altitude of the balloon now = 288 + 36 = 324 meters
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The coordinates of the endpoints of line segment se are s(-7,3) and e(2,-6). if point m is on se, what are the coordinates of m such that sm:me is 1:2?
By applying the section formula between three points A, C and B we find that the coordinate of m is ( -4, 0)
Let's suppose we have a line on which we have 3 linear dots A, C, and B respectively, in this we have to use the section formula,
Where A = x1, y1
B = x2, y2
C = m:n
According to the section formula
C = (mx2 = nx1) / m+n * (my2 + ny1) / m+n
Sm/ Me = 1/2
Using section formula :
the coordinates of m = (2-14)/1+2 , (-6+6) / 1+2
the coordinates of m = ( -12/3 , 0/3)
the coordinates of m = ( - 4 , 0 )
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13. A jeweler wants to make a triangular pendant for a necklace using three pieces of wire. He
has two pieces of wire with lengths of 12 millimeters and 15 millimeters. Describe the possible
lengths for the third wire.
a. Find the length of each side of the quadrilateral. What do you notice?
b. Find the slope of each side of the quadrilateral. What do you notice? Are any sides parallel or perpendicular?
c. Find the length of each diagonal (the segment that goes from one vertex to an opposite verter), What do you notice?
d. Find the slope of each diagonal. What do you notice?
(1. List the properties that you find, (Ex. Are all sides congruent? Perpendicular? Etc)
(a) The lengths of RE, EC, CT, and TR are 8, 13, 8, and 13, respectively.
(b) The slopes of RE, EC, CT, and TR are 0, not defined, 0, and not defined, respectively.
(c) The lengths of RC and ET are √233 and √233, respectively.
(d) The slopes of RC and ET are -13/8 and 13/8, respectively.
The quadrilateral RECT is a rectangle.
The vertices of the quadrilateral are R(1, 7), E(9, 7), C(9, -6), and T(1, -6).The length of the side RE is √[(1-9)² + (7-7)²] = 8.The length of the side EC is √[(9-9)² + (7-(-6))²] = 13.The length of the side CT is √[(9-1)² + (-6-(-6))²] = 8.The length of the side TR is √[(1-1)² + (-6-7)²] = 13.The length of the diagonal RC is √[(1-9)² + (7-(-6))²] = √233.The length of the diagonal ET is √[(9-1)² + (7-(-6))²] = √233.The slope of the side RE is (7-7)/(9-1) = 0.The slope of the side EC is (-6-7)/(9-9) = Not Defined.The slope of the side CT is (-6-(-6))/(1-9) = 0.The slope of the side TR is (7-(-6))/(1-1) = Not Defined.The slope of the diagonal RC is (-6-7)/(9-1) = -13/8.The slope of the diagonal ET is (-6-7)/(1-9) = 13/8.The sides RT and EC are equal in length and parallel to each other.The sides RE and TC are equal in length and parallel to each other.All the sides are perpendicular to their adjacent sides.Hence, we conclude that the quadrilateral RECT is a rectangle.To learn more about rectangles, visit :
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C. Find the equation of a line passing through (2, 2) and having inclination 30º.
The equation of line is (y-2) = 1/[tex]\sqrt{3}[/tex](x-2)
What is Equation of line?
The equation of a line is the algebraic representation of a line using cartesian coordinates.
The general form of the equation of a straight line is written as y = mx + cy=mx+c.
Where m is the gradient of the straight line
and c is the y-intercept of the straight line.
And
The equation of line passing through point ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) is
(y-[tex]y_{1}[/tex]) = m (x-[tex]x_{1}[/tex])
Given line in the graph passes through (2,2).
We have to find the equation of the line.
Given, angle of inclination is 30.
m = tan (angle of inclination)
m = tan 30
m = 1/[tex]\sqrt{3}[/tex]
Therefore after substituting, equation of line
(y-2) = 1/[tex]\sqrt{3}[/tex](x-2)
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Here is a list of ingredients needed to make 6 pancakes.
Flour 140 grams
Eggs 2
Milk 220 millilitres
Complete the list of ingredients needed to make 9 pancakes.
Answer:
Flour: 210 grams
Eggs: 3 Eggs
Milk: 330 milliliters
Step-by-step explanation:
First we need to find the amount of ingredients needed for One pancake
Flour:
140 grams / 6 pancakes = [tex]\frac{70}{3}[/tex]grams
Eggs:
2 eggs / 6 pancakes = [tex]\frac{1}{3}[/tex] eggs
Milk:
220 milliliters / 6 pancakes = [tex]\frac{110}{3}[/tex] milliliters
Now we just multiply them by 9:
Flour: [tex]\frac{70}{3} *9 = 210[/tex] grams
Eggs: [tex]\frac{1}{3}*9 = 3[/tex] eggs
Milk: [tex]\frac{110}{3}*9 = 330[/tex] milliliters
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How many tiles measuring 20cm by 50cm are needed to completely cover a wall 4m by 8m?
320 Tiles of measuring 20cm*50cm will be needed to cover a wall 4m by 8m.
Let to cover the wall of dimension 4m * 8m completely with the tiles we need x number of tiles of size 20cm * 50 cm.
The area of wall must be that of total areas covered by tiles.
So,
Area of 1 Tile = 20cm * 50 cm = 1000sq. cm
Total Area of Tiles needed = 1000x sq.cm
Total Area of wall = 4m * 8m = 400 * 800 = 320000 sq. cm
So, We know that
Total Area of wall = Area of 1 Tile * x
320000 = 1000x
x = 320
Therefore, we can conclude that we will need 320 tiles to cover a wall of area 32sq. metres completely.
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Wally and drake both wanted to see the moons of jupiter. they each wanted to buy a telescope that sold for $62.48. together they had a total of $95. how much more money did they have left to save?
The amount of money Wally and Drake have left to save is equal to $29.96 if each one of them wanted to buy a telescope.
The amount of money left to be saved can be calculated by using an algebraic expression.
First, we determine the cost of two telescopes if each one of them wanted to buy a telescope to see the moons of Jupiter.
As the cost of one telescope is $62.48, the cost of two telescopes will be;
62.48 + 62.48 = 124.96
An algebraic expression can be given as;
95 + x = 124.96
where x is the money left to be saved.
Solving for x;
x = 124.96 - 95
x = 29.96
Hence, $29.96 is the amount left to be saved for each one of them to buy a microscope.
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1. Write a multiplication expression that you can use
to find 16 ÷ 4/5
Multiplication expression used is 16 ×[tex]\frac{5}{4}[/tex].
What is multiplicative inverse?A number that when multiplied by a number x results in the multiplicative identity, 1, is known as a multiplicative inverse or reciprocal, indicated by 1/x or x1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number. When a number is multiplied by its original number, the multiplicative inverse of that number, or x-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2-1 since it fulfils the formula: 2 x 2-1
2 x [tex]\frac{1}{2}[/tex]= 1. It is also known as a number's reciprocal.
Given Data
16 ÷ [tex]\frac{4}{5}[/tex]
Reciprocating,
16 × [tex]\frac{5}{4}[/tex]
Simplifying,
4(5)
20
Multiplication expression used is 16 ×[tex]\frac{5}{4}[/tex]
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C is in the interior of LABD. m/ABC=
(2x+12)°, m/CBD = (3x + 10)°, and
m/ABD = 72°. Find m/ABC.
Answer:
32°
Step-by-step explanation:
Using the angle addition postulate,
[tex]3x+10+2x+12=72 \\ \\ 5x+22=72 \\ \\ 5x=50 \\ \\ x=10 \\ \\ \implies m\angle ABC=2(10)+12=32^{\circ}[/tex]
What is the area of the gable if it is a triangle with two sides of 81 feet that meet at a 112° angle?
The area of the gable if it is a triangle with two sides of 81 feet that meet at a 112 degrees angle is 3041.22 square feet
The two sides of the triangle=81
AB=AC=81 feet
∠A=112 degrees
∠BAD=∠DA =56 degrees
Here we have to use trigonometric functions
To find the height of the triangle we have to use the cos function
cos θ=Adjacent side/Hypotenuse
cos 56=Height/81
Height=81×cos 56
=45.29 feet
To find the length of the DC, we have to use the sine function
sin θ=Opposite side / Hypotenuse
sin 56=Base / 81
Base DC=81×sin 56
=67.15 feet
The base of the triangle BC=BD+DC
=67.15+67.15
=134.3 feets
The area of the triangle=(1/2)×b×h
Where b is the base and h is the height
=(1/2)×134.3×45.29
=3041.22 square feet
Hence, the area of the gable if it is a triangle with two sides of 81 feet that meet at a 112 degrees angle is 3041.22 square feet
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Mrs. Dundee wants to sell the rights to her cajun cookbook. One publisher offered to pay $80,000 and a $3 royalty for every book sold. Publisher two offered to pay $30,000 and $5 for every book sold. Over what ranges of sales will Mrs. Dundee make more from the second publisher than from the first?
The range of sales for the given condition is (25000, +∞), Hence Mrs. Dundee makes more from the second publisher than the first.
As per the question statement, Mrs. Dundee wants to sell the rights to her Cajun cookbook so one publisher offered to pay $80,000 and a $3 royalty for every book sold and publisher two offered to pay $30,000 and $5 for every book sold.
We are supposed to find the range of sales for the given conditions.
Let's suppose Mrs. Dundee sold "x" books
30,000 + 5x > 80,000 + 3x
2x > 50,000
x > 25,000
So, the range of sales for the given condition is (25000, +∞), Hence Mrs. Dundee makes more from the second publisher than the first.
Range: When a function is applied to its whole set of outputs, its range is the set of outputs it produces.To learn more about range and functions, click on the link given below:
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Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
m arcPQR
In the illustration above, a circle with a few lines intersecting at various locations is shown. So, if we split the circle in half, the resulting semicircle has a vertical angle of 180 degrees. Since ∠ROP = 125°, ∠POS = 55° is obtained by taking 180° away from 125°. ∠POS and ∠QOR are equivalent terms. Also, ∠ROP = ∠QOS.
What is lines intersecting?
In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the crossing lines share a common point.
the characteristics of intersecting lines
The intersecting lines (two or more) never cross over at more than one location.
Any angle may be used to intersect the lines in any direction. Always larger than 0° and less than 180°, this angle is generated.
A pair of vertical angles are created by two intersecting lines. The vertical angles have the same vertex and are opposing angles (which is the point of intersection).
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Chris and jeff sold 15.5 pounds of trail mix. they sold trail mix for 3.98 per pound. how much money did they collect explain?
P.s please help!
Answer: $61.69
Step-by-step explanation: Since is say "per pound", it means for each 1 singular item/weight/etc. So for Each pound, you gain 3.98 dollars. Multiply 15.5 and 3.98 to get 61.69.
A new car worth $21,000 is depreciating in value by $3,000 per year. After how many years will the car's value be $3,000?
After__years, the car's value will be $3,000.
Answer:
After 6 years, the car's value will be $3000=================
GivenInitial value = $21000,Depreciation rate = $3000 per year.To findNumber of years to reach $3000 in value.SolutionThis is a linear relationship, with initial value being the y-intercept and depreciation rate being the slope of the line:
y = 21000 - 3000x, where y- the value of the car after x years.Since y = 3000, plug it in and find the value of x:
3000 = 21000 - 3000x3000x = 21000 - 30003000x = 18000x = 18000/3000x = 6Sara is multiplying two factors; one is a whole number and one has two decimal places. She says the product could have one decimal place. Is she correct? Give an example and explain your reasoning.
In relation to the division of a whole number by a decimal, Sarah made an incorrect claim.
What is whole number ?A number without fractions or decimals is said to be entire. Whole numbers include 1, 10, and 1000 as examples.
What is decimal ?A decimal number is one that is made up of both integers and non-integers. Decimal numbers include 1.1, 2.2, and 100.234. A number with two digits following the decimal point is said to have two decimal places. Examples include 10.23 and 1.23
Assume that 2 is the entire number and that 2.23 is the decimal. The final value would be 4.46.
Assume that 100 is the entire number and that 2.23 is the decimal. The item is 223.
This demonstrates that having two decimal places on a product is not always necessary.
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Order the numbers from least to greatest:
-8/9, 7/8, 1.7, -10/7, 0.3
Answer: -10/7 < -8/9 < 0.3 < 7/8 < 1.7
Step-by-step explanation:
20 Words -> 2 Minutes
Find how long will it take to type 1650 words
Answer:
165 minutes
Step-by-step explanation:
use the second derivative test for concavity and the phase line to produce a phase portrait and sketch one typical solution curves in each region determined by the equilibrium solutions
if the second derivative is negative, then the first derivative is decreasing, Graphically, we see this as the curve. of the graph being concave down, that is, shaped like a parabola open downward.
The second derivative tells whether the curve is concave up or concave down at that point. If the second derivative is positive at a point, the graph is bending upwards at that point. Similarly if the second derivative is negative, the graph is concave down.
When second derivative is positive concavity?
If the second derivative is positive at a point, the graph is concave up at that point. If the second derivative is positive at a critical point, then the critical point is a local minimum. If the second derivative is negative at a point, the graph is concave down.
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Montraie bought snacks for his team's practice. He bought a bag of popcorn for $2.45
and a 18-pack of juice bottles. The total cost before tax was $29.99. How much was
each bottle of juice?
Taxes can be paid in cash or labor and can be either direct or indirect.
Cost of juice bottle is $27.54.
What is tax?Tax compliance refers to policy actions and individual behavior aimed at ensuring that taxpayers are paying the right amount of tax at the right time and securing the correct tax allowances and tax reliefs. A tax is a mandatory financial charge or some other type of the levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and the various public expenditures (regional, local, or national). Around 3000–2800 BC, the first recorded taxation was enacted in ancient Egypt. Non-compliance with the law includes failing to pay on time as well as evading or resisting taxation. Taxes can be paid in cash or labor and can be either direct or indirect.
Most nations have a tax system in place to finance public, shared, or agreed-upon national necessities as well as governmental duties. While some scale taxes are progressive based on brackets of annual income amounts, most impose a flat percentage rate of taxation on personal annual income. The majority of nations impose taxes on both personal and business income. The Wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, usage taxes, payroll taxes, fees, and/or tariffs are frequently levied by nations or subunits.
A bag of popcorn = $2.45
Juice bottles =18
Total cost = $29.99
Cost of juice bottle = $29.99-$2.45= $27.54
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Jill wants to rent a car. Rental Company A charges $40 per day plus $0.10 per mile driven. Company B charges $35 per day plus $0.15 per mile driven. After how many miles driven will the price charged by each company be the same?
Considering the definition of an equation and the way to solve it, after 100 miles driven the price charged by each company will be the same.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the number of miles driven, and knowing that:
Rental Company A charges $40 per day plus $0.10 per mile driven. → Price of company A= 40 +0.10xRental Company B charges $35 per day plus $0.15 per mile driven. → Price of company B= 35 +0.15xThe price charged by each company is the same,the equation is:
Price of company A= Price of company B
40 +0.10x= 35 +0.15x
Solving:
40 - 35= 0.15x - 0.10x
5= 0.05x
5 ÷ 0.05= x
100= x
Finally, after 100 miles driven the price charged will be the same.
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Lucy used 3 3/4 cups of sugar for her lemonade stand. She divided the
sugar, in equal amounts, into 6 pitchers. How much sugar went into each
pitcher?
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
3 [tex]\frac{3}{4}[/tex] ÷ 6 Change 3 [tex]\frac{3}{4}[/tex] into an improper fraction
Another name for 1 is [tex]\frac{4}{4}[/tex] so another name for 3 is [tex]\frac{4}{4}[/tex] + [tex]\frac{4}{4}[/tex] + [tex]\frac{4}{4}[/tex] or [tex]\frac{12}{4}[/tex]
[tex]\frac{12}{4}[/tex] + [tex]\frac{3}{4}[/tex] = [tex]\frac{15}{4}[/tex] So we now have
[tex]\frac{15}{4}[/tex] ÷ 6 or
[tex]\frac{15}{4}[/tex] ÷ [tex]\frac{6}{1}[/tex] If I use the common denominator of 4, I can divide straight across.
[tex]\frac{15}{4}[/tex] ÷[tex]\frac{24}{4}[/tex] Now divide across and we get
[tex]\frac{\frac{15}{24} }{\frac{4}{4} }[/tex] = [tex]\frac{\frac{15}{24} }{1}[/tex]= [tex]\frac{15}{24}[/tex] Divide the top and bottom by 3 to simplify to [tex]\frac{5}{8}[/tex]
This is not the most traditional way to solve, but I think it is more intuitive.
Line G and lineH are complementary angles. If mlineG = (6x - 15)' and mlineH= (3r + 6)", find H
Since angle G and angle H are complementary angles, the value of x is 11 while angle H is equal to 39 degrees.
What is a complementary angle?A complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this formula:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
Substituting the given parameters into the formula, we have;
(6x - 15)° + (3x + 6)° = 90°
9x - 9 = 90°
9x = 90 + 9
9x = 99
x = 99/9
x = 11
Next, we would determine the value of H:
H = 3x + 6
H = 3(11) + 6
H = 33 + 6
H = 39 degrees.
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Complete Question:
Angle G and angle H are complementary angles. If G= (6x-15)° and H= (3x+6)° find the x value and H
A plane flew at a constant speed between Boston and Philadelphia. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is d=350t. How long will it take the airplane to travel 280 miles?
Based on the equation that relates the distance traveled by the plane going from Boston to Philadelphia, the time it would take for the plane to travel 280 miles is 48 minutes
How to find the time taken?You can use the formula given to find the amount of time taken by the plane to travel 280 miles.
The formula is;
d=350t
distance travelled = 350 x time
Solving for time taken gives;
280 = 350 x time
Time = 280 / 350
Time = 0.8 hours x 60 minutes per hour
Time = 48 minutes
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The annualized interest on Jill’s two investments amounted to 1560. The savings account earned 3% And the cd earned 5% interest. If the amount she deposited in the savings was twice the amount of her deposit in the cd, how much did she deposit into each account
Based on the annualized interest from the investments that Jill went into, the amount deposited in savings was $28,363.64 and the amount in the cd was $14,181.82.
How find the amount deposited?Assuming that the amount invested in the cd was x, then the amount invested can be modeled as:
= 5%x
= 0.05x
The amount invested in savings was:
= 2 x 3% x
= 2 x 0.03x
= 0.06x
The amount invested in cd was:
0.06x + 0.05x = 1,560
0.11x = 1,560
x = 1,560 / 0.11
x = $14,181.82
The amount in the savings was:
= 14,181.82 x 2
= $28,363.64
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A local pizza shop has a membership program for frequent buyers. The membership costs $25 per month and members get a discounted price of $1 per slice of pizza. Ava purchased a membership to this pizza shop. How much would Ava have to pay the pizza shop if she bought 18 slices of pizza this month? What would be the monthly cost for x slices of pizza? mx+b
The cost of 18 slices of pizza is $18.
The monthly cost for x slices of pizza is $25 + x
What is the monthly cost?The equation that represents the amount of money that Ava would have to pay when she buys 18 slices of pizza is a linear equation. A linear equation is an equation that has one variable raised to the power of one. The linear equation increases by a fixed amount. When drawn on a coordinate plane, a linear equation is a straight line.
The total monthly cost is a function of the membership fee, the cost per pizza and the number of pizzas bought.
The form of the linear equation is :
fx = mx + b
b = slope m = interceptTotal amount paid = membership fee + total cost of pizzas
Total amount paid for 18 pizzas = cost per pizza x number of pizzas bought
$18 x 1 = $18
Total monthly cost for x pizzas = membership fee + (discounted price x number of pizzas bought)
$25 + ($1 x x)
$25 + $1x = $25 + $1x
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Jada cuts an 11 inch strip of paper into 5 equal parts, how many inches long is each part?
Answer:
2.2
Step-by-step explanation:
11 / 5 = 2.2 inches
y = {(2, 6), (3, 1, 4), (1), (5, 6)} Is y a function and why? No, there is a limited number of ordered pairs in this list. Yes, there is more than one ordered pair in this list. Yes, no two ordered pairs in this list has the same second element. No, the elements of the set of y are not all ordered pairs.
The reason with respect to this function is: D. No, the elements of the set of y are not all ordered pairs.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable to an output variable.
Based on the ordered pairs shown above, we can reasonably infer and logically deduce that these ordered pairs does not represent a function because the elements of the set of "y" aren't all ordered pairs i.e (3, 1, 4).
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