The profit generated from selling x boxes of pencils is a linear function of x, with a slope of $0.80 and a y-intercept of -$12.60
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range) with the property that each input is related to exactly one output.
Let us first define the demand function as D(x), where x is the number of boxes of pencils sold. We know that the manager can sell 10 boxes of pencils at a price of $2.19 per box, which means that the revenue generated from this sale is:
10 * $2.19 = $21.90
Similarly, when the price is $1.70, she can sell 24 boxes of pencils, which gives a revenue of:
24 * $1.70 = $40.80
Now, we can use these two data points to find the equation of the demand function. Since we assume that the demand is linear, we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept. In our case, y represents the revenue generated by selling x boxes of pencils.
To find the slope, we use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the two data points we have.
m = ($40.80 - $21.90) / (24 - 10)
m = $18.90 / 14
m = $1.35
To find the y-intercept, we can use either of the two data points and solve for b:
$21.90 = $1.35 * 10 + b
b = $7.40
Therefore, the demand function for the pencils is:
D(x) = $1.35x + $7.40
This means that for each additional box of pencils sold, the revenue generated increases by $1.35. The y-intercept of $7.40 represents the revenue generated when no pencils are sold, which includes fixed costs such as rent, utilities, and wages.
We also have the cost function C(x) = 0.55x + $20, which represents the total cost of buying x boxes of pencils. The profit function P(x) is defined as the difference between the revenue and the cost:
P(x) = D(x) - C(x)
Substituting the expressions for D(x) and C(x), we get:
P(x) = ($1.35x + $7.40) - (0.55x + $20)
Simplifying this expression, we get:
P(x) = $0.80x - $12.60
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PLEASE ANSWER IMAGINE BELOW I NEED THE ANSWER IN 5 MINS PLEASEE
Question 8(Multiple Choice Worth 2 points) (09.06 LC) How many decimeters are in 3.6 millimeters? 0.036 decimeters O0.36 decimeters O 36 decimeters O 360 decimeters
The number of decimeters in 3.6 millimeters is 0. 0036 decimeters. Option D
How to convert the unitsConversion of units is simply defined as the conversion that is between different units of measurement for a particular quantity.
it is carried out mostly through multiplicative conversion factors.
It may involve multiple steps of multiplication or division by a conversion factor.
From the information given, we have that;
1 decimeter = 1000 millimeters
Then, x decimeter = 3.6 millimeters
Cross multiply the values
x = 3.6/1000
divide the values
x = 0. 0036 decimeters
Hence, the value is 0. 0036 decimeters
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Write and solve an equation to find the value of x. (x + 10) Equation: X= 55
Answer:
65
Step-by-step explanation:
X=55
55+10=65
so
X+10=65
I hope that's what you meant.
Question 13:
Christine had 0.8 times the amount of money Sarah had. They went shopping and spent
$684 altogether. Christine spent 0.25 of her money and had thrice as much money left
as Sarah. How much money did Sarah spend?
Answer: Let's call Sarah's original amount of money as x. Then, Christine had 0.8x.
After they spent $684 altogether, Christine had 0.8x - 0.25(0.8x) = 0.8x - 0.2x = 0.6x left.
Sarah had x - 684.
Since Christine had thrice as much money left as Sarah, we can write an equation:
0.6x = 3(x - 684)
Expanding the right side of the equation:
0.6x = 3x - 2052
Solving for x:
2.6x = 2052
x = 787.69
So Sarah originally had 787.69 dollars and spent 787.69 - 684 = 103.69 dollars.
Step-by-step explanation:
a theater charges $8 for main floor seats and $5 for balcony seats. for a full house, the ticket income is $4,200. at one show, only 25% of the main floor seats and 40% of the balcony seats were sold for a total of $1,200. how many main floor tickets and how many balcony tickets were sold for this show?
By solving a system of equations we can see that there are 400 main-floor seats and 200 balcony seats.
Let x = number of seats on the main-floor
y = number of balcony seats
We know that if all the seats are sold, then the total income is $4,200, we can write the equation:
x*8 + y*5 = $4,200
And if 25% of the main-floor and 40% of the balcony seats are sold, then we get an income of $1200, then we can write:
0.25*x*8 + 0.4*y*5 = $1,200
x*2 + y*2 = $1,200
2(x + y) = $1200
x + y = $600
x = 600 - y
putting the value of x in equation1)
8(600-y) + 5y = 4200
4800 - 8y + 5y = 4200
3y = 600
y = 200
and x = 600 - 200 = 400
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translate the following sentence into an equation "Twice the difference of M and 14 equals 64 ."
Answer:
2 * (M - 14) = 64
Step-by-step explanation:
Twice mean s two times the rest of M
your gross income is $4,000 per month. your federal state tax is 10%, state tax is 7%, city tax is 3%, and you pay 7% to social security. what is your monthly disposable income?
If the gross income per month is $4000 , then the monthly disposable income will be $2920 .
To find the monthly disposable income, we subtract the various taxes from the gross income.
The Federal tax is = 10% of $4000 = $400 ;
The State tax is = 7% of $4000 = $280 ;
The City tax is = 3% of $4000 = $120 ;
and the Social security tax is = 7% of $4000 = $280 ;
So , the Total monthly tax is = $400 + $280 + $120 + $280 = $1080 ;
We know that the Monthly disposable income = Gross income - Total tax ;
⇒ Monthly disposable income = $4000 - $1080 ;
⇒ Monthly disposable income = $2920 .
Therefore, the monthly disposable income after taxes is $2920.
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There are 10 people in a group. 3 are red and 7 are blue. They vote yes or no.
What is probability that all 3 red people vote no and all 7 blue people vote yes?
Answer:70% chance they vote yes
Step-by-step explanation:
Answer:
3/10 for red people and 7/10 for blue people.
Step-by-step explanation:
Solve and graph 11x+6<9x+10
We solved the given inequality and found the values of x lie in the interval ( -∞ , 4). This is graphed and shown on the number line as below.
What is meant by inequality?
A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.
Given inequality is:
11x + 6 < 9x + 10
Solving,
11x - 9x < 10 - 6
2x < 4
x < 4
The values of x is in the interval : ( -∞ , 4)
The above inequality is shown below on the number line as well as on the graph.
We can see that all the values to the left of 4 but not including 4 can be taken as the value of x.
Therefore we solved the given inequality which is graphed and shown on the number line.
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approximately how many acres are there in a lot 1/2 mile by 1/2 mile?
There are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.
To find the number of acres in a lot, you can use the following formula:
Number of acres = (length in feet) x (width in feet) / 43,560
First, convert the length and width from miles to feet. There are 5,280 feet in a mile, so:
Length in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet
Width in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet
Next, plug these values into the formula:
Number of acres = (2,640 feet) x (2,640 feet) / 43,560 = 174,240,000 / 43,560 = 160 acres
Therefore, there are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.
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The distance between Dallas and Houston is about 364 kilometers. There are approximately
measurement is closest to the number of miles between these two towns?
Answer
A 227.5 miles
B 582.4 miles
C 40 miles
D 372 miles
In a case whereby the distance between Dallas and Houston is about 364 kilometers the approximately measurement is closest to the number of miles between these two towns is A 227.5 miles.
How can the the approximately measurement be determined?The concept that will be used here is unit conversion. It should be noted that 1 Mile = 1.609344 kilometres.
Then Xmile = 364 kilometers
We can cross multiply to have
Xmile =364 kilometers/1.609344 kilometres.
=226.179
Hence the closest to the number of miles is A 227.5 miles
Therefore, option A is correct.
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Pls show your work thank you will mark the Brainliest
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's start with eliminating choices first ~
The value decreases as years pass by, so the value multiplied by initial value should be an exponent on the value that is less than 1.
So, only the choices with exponent on 0.9 should be qualified, eliminating the choices A and C
Next, the initial value of motorcycle is 12000 according to table. so at x = 0, v(x) should be equal to 12000.
Now, let's check option B
[tex]\qquad \sf \dashrightarrow \: v(x) = 12000(0.9) {}^{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: v(0) = 12000(0.9) {}^{0} [/tex]
[tex]\qquad \sf \dashrightarrow \: v(0) = 12000(1)[/tex]
[tex]\qquad \sf \dashrightarrow \: v(0) = 12000[/tex]
And since choice B satisfy each and every condition, that's the correct answer ~
You want to carpet your 12 ft. by 16 ft room. If the carpet you have chosen cost $10 per square foot, how much will it cost to carpet your room?
At a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.
What are the parameter for determining square foot?The rectangle's area in square meters The area's width and length should be measured in feet. To calculate area, multiply your length by your width. Use our length converter to convert your measures if they aren't already in feet.
Area is length times breadth, or 12 feet by 16 feet, or 192 square feet. The cost of the carpet is $10 per square foot. By dividing the square footage of the room by the price per square foot, we can get the overall cost to carpet it.
Total cost is equal to Area. Cost per square foot is $1920 or 192 square feet (around 18 m2) times $10 per square foot.
Therefore, at a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.
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The area is approximately enter your response here
▼
in squared .in2.
in.in.
in cubed .in3.
(Simplify your answer. Type a whole number or a decimal. Round to the nearest hundredth as needed.)
Step-by-step explanation:
this is a 14.4 in × 10.2 in rectangle, were 2 identical half-circles (= 1 full circle) are removed.
so, in other words, the shaded area is
rectangle area - circle area
the rectangle area is length × width.
the circle area is pi×r². with r (radius) being half the diameter. the diameter is 10.2 in, so, r = 10.2/2 = 5.1 in.
so, the shaded area is
14.4 × 10.2 - pi × 5.1² = 146.88 - 3.14 × 26.01 =
= 146.88 - 81.6714 = 65.2086 ≈ 65.21 in²
remember, an area is always expressed in square units. a volume in cubic units. and a length in simple units.
The human body produces about $4. 8\times10^6$4. 8×106 red blood cells in 4 times 10 to the negative 2 power$4\times10^{-2}$4×10−2 minute. How many red blood cells does the body produce each minute? Write your answer in scientific notation and in standard form
The total number of red blood cells produced by human body in each minute is given by [ 1.2 × 10^8 ] red blood cells
Number of red blood cells produced by human body = 4. 8 × 10^6
Time taken by human body to produce 4. 8 × 10^6 red blood cells
= 4×10^(−2) minute
Number of red blood cells produced by human body in one minute are :
4 × 10^(−2) minute = 4. 8 × 10^6 red blood cells
⇒ 1 minute = [ 4. 8 × 10^6 / 4 × 10^(−2) ] red blood cells
⇒ 1 minute = [ 1.2 × 10^( 6 - (−2) ) ] red blood cells
⇒ 1 minute = [ 1.2 × 10^( 6 + 2) ) ] red blood cells
⇒ 1 minute = [ 1.2 × 10^8 ] red blood cells
Therefore, total number of red blood cells produced by human body in one minute is equal to [ 1.2 × 10^8 ] red blood cells.
The above question is incomplete, the complete question is:
The human body produces about4. 8×10^6 red blood cells in 4×10^(−2) minute. How many red blood cells does the body produce each minute? Write your answer in scientific notation and in standard form.
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Expand and simplify
(3x + 4)(2x + 3)
Answer:
6x^2 + 17x + 12
Step-by-step explanation:
(3x + 4)(2x + 3) - Distribute
6x^2 + 9x + 8x + 12
6x^2 + 17x + 12
Choose the correct simplification of m to the seventh power times n to the fourth power all over m to the fourth power times n to the third power. a. m11n7 b. m11n c. m3n d. m to third power all over n to the seventh power
The expression [tex]m^{7} * n^{4}[/tex] divided by [tex]m^{4} * n^{3}[/tex] simplifies to [tex]m^{3} * n[/tex], meaning m raised to the power of 3 times n. This is found by subtracting the exponents in the denominator from the exponents in the numerator.
To simplify the expression [tex]\frac{m^{7} * n^{4}}{m^{4} * n^{3}}[/tex] , we need to divide the exponents of m and n. To do this, we subtract the exponents of m and n in the denominator from the exponents of m and n in the numerator.
Starting with m, we have:
[tex]\frac{m^{7}}{m^{4}}[/tex] = [tex]m^{(7-4)}[/tex] = [tex]m^{3}[/tex]
This means that we divided the exponent of m in the numerator (7) by the exponent of m in the denominator (4), and the result is m raised to the power of 3.
Next, we do the same thing with n:
[tex]\frac{n^{4} }{n^{3} }[/tex] = [tex]n^{(4-3)}[/tex] = [tex]n^{1}[/tex] = n
This means that we divided the exponent of n in the numerator (4) by the exponent of n in the denominator (3), and the result is n raised to the power of 1, which is just n.
Finally, we can combine the results:
[tex]m^{3}*n[/tex] = [tex]m^{3}*n[/tex]
So, the simplified form of the expression [tex]\frac {m^{7 }* n^{4}} { m^{4} * n^{3}}[/tex] is [tex]m^{3}*n[/tex].
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Answer:
m^3n
Step-by-step explanation:
m3n
Ok I know it’s late but I really need help with these problems and no one can help me so can someone please help and explain. I know it’s a lot but I’m really confused, thank you so much.
answers are on the picture
Step-by-step explanation:
#5
CONNECTING CONCEPTS You use 94 inches of plastic to frame the perimeter of a kite. One side of the kite has a
length of 18 inches. Find the length of each of the three remaining sides in order from least to greatest.
Length: in.,in., in
The length of each of the three remaining sides, in order from least to greatest, is x = 8, y = 18 and z = 3.
What is Perimeter?
Perimeter is the total length of the boundary of a two-dimensional shape or figure. It is the distance around the outside of a closed shape, such as a rectangle, triangle, circle, or any other polygon. To find the perimeter of a shape, you add up the lengths of all its sides. Perimeter is usually measured in units of length, such as centimeters, meters, feet, or inches. Perimeter is an important concept in geometry, and it is used to calculate the amount of material needed to surround a shape or to measure the distance around a path or track.
Let's denote the lengths of the three remaining sides of the kite as x, y, and z, where x is the shortest side.
The perimeter of the kite is the sum of the lengths of all four sides:
P = x + y + z + 18
We also know that the total length of plastic used to frame the perimeter is 94 inches:
94 = 2x + 2y + 2z + 36
Simplifying the equations by dividing both sides of the second equation by 2, we get:
47 = x + y + z + 18
47 = x + y + z + 18
Substituting the first equation into the second equation, we get:
x + y + z + 18 = 2x + 2y + 2z + 36
Simplifying this equation, we get:
x = 8
Substituting x = 8 into the first equation, we get:
y + z + 26 = 47
Simplifying this equation, we get:
y + z = 21
We want to find the values of y and z. Since we don't have enough information to solve for each of them individually, we'll use a bit of logic to determine their relative values.
The only combination that satisfies these conditions is:
y = 18
z = 3
Therefore, the length of each of the three remaining sides, in order from least to greatest, is:
x = 8
y = 18
z = 3
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Ayden is a salesperson who sells computers at an electronics store. He makes a base pay amount of $90 per day regardless of sales and he earns a commission of 1% of the dollar amount of all sales that he makes. Write an equation for the function P(x),P(x), representing Ayden's total pay on a day on which he sells xx dollars worth of computers
The function P(x) representing Ayden's total pay on a day on which he sell x dollar worth of computers is P(x) = 0.01x + 90
The base pay amount of Ayden per regardless of sales = $90
The commission of Ayden = 1% of the dollar amount of sales
Consider the total sales amount in a day as x
The function is the mathematical expression that shows the relationship between one variable and another variable. If one variable is dependent variable then the other variable will be independent variable.
Then the function will be
P(x) = 1% of x + 90
= 0.01x + 90
Therefore, the equation for the function P(x) = 0.01x + 90
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The area of a circular swimming pool is 154m2. Its radius will be:
Area of a circular swimming pool is 154m², So radius of the circular swimming pool is approximately 7.88 meters
The area of a circle is given by the formula:
A = πr²
where A is the area, r is the radius, and π is a mathematical constant approximately equal to 3.14.
We are given the area of the circular swimming pool as 154m². So we can set up the equation:
154 = πr²
Solving for r, we get:
r = √(154/π) ≈ 7.88 m
Hence,
The radius of the circular swimming pool is approximately 7.88 meters.
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Find the value of b if the graph of y=0.3+b goes through the point. N(5, d)
Answer:
the answer according to your question is that " b" is = -0.3
An AP has first term 7 and common difference 4. If the sum of all it's terms is 900,how many term are there?
If an AP has first term 7 and common difference 4. If the sum of all it's terms is 900, then there are 3 terms.
Let's use the formula for the sum of an arithmetic progression to solve this problem:
S = n/2[2a + (n-1)d]
where S is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.
We know that a = 7 and d = 4, and we're given that S = 900. Substituting these values into the formula, we get:
900 = n/2[2(7) + (n-1)(4)]
Simplifying the expression inside the brackets:
900 = n/2[14 + 4n - 4]
900 = n/2[10 + 4n]
Multiplying both sides by 2 to eliminate the fraction:
1800 = n[10 + 4n]
Simplifying the right-hand side:
1800 = 4n^2 + 10n
Rearranging to get a quadratic equation in standard form:
4n^2 + 10n - 1800 = 0
We can solve for n using the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 4, b = 10, and c = -1800, so:
n = (-10 ± √(10^2 - 4(4)(-1800))) / 2(4)
n = (-10 ± √(100 + 28800)) / 8
n = (-10 ± √(28900)) / 8
n = (-10 ± 170) / 8
n = 20/8 or n = -180/8
n = 2.5 or n = -22.5
Since the number of terms must be a positive integer, we can discard the negative solution and conclude that there are 2.5 terms. However, this doesn't make sense because the number of terms in an arithmetic progression must be a whole number. Therefore, we need to round up to the nearest whole number, which gives us:
n = 3
Therefore, there are 3 terms in the arithmetic progression with first term 7 and common difference 4, and the sum of these terms is 900.
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Garcia and Jim were shooting free throws. Garcia made 4 out of 15 free throws. Jim missed 6 out of 16 free throws. Who made the free throw a greater fraction of the time
If Jim missed 6 out of 16 free throws, then he made 10/16 free throws. At the same time Gracia made 4/15 free rows. The common denominator of those fractions (if we simplify 10/16 to 5/8) is 120, so:
Garcia made 4/15 = 32/120 free throws
Jim made 5/8 = 75/120 free throws
We can clearly see that Jim was more than two times better than Garcia
How many solutions does this system of equations have? y=-2x+2 and 2y+4x=4
The system of equations will have a unique solution.
What is a system of equations?A finite set of equations for which we searched for common solutions is referred to as a system of equations, also known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.
Given that the equations are:-
y=-2x+2 and 2y+4x=4
Convert the equations into general form,
2x + y = 2
4x + 2y = 4
If the ratio of a₁ / a₂ is not equal to the ratio of b₁ / b₂ the equation will have a unique solution. And if are equal than the equation will have infinitely many solutions.
2 / 4 = 1 / 2 = 2 /4
1 /2 = 1/ 2 = 1/ 2
The equation will have many solutions.
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Select the correct answer.
What is the value of x in the triangle?
7√3
60°
OA. 21
OB. 10
O C.
C. 7
O D. 7√3
30%
The value of x in the triangle is equal to: A. 21.
What is a 30-60-90 triangle?In Mathematics, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).
Note: x is the side opposite to the 60° angle.
The side opposite to the 60° angle, x = 7√3 × √3
The side opposite to the 60° angle, x = 7 × 3
The side opposite to the 60° angle, x = 21 units.
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Which of the following items has volume?
baseball diamond
floor rug
piece of paper
water bottle
The only option that represents an object with volume is; Option D: Water Bottle
How to find the volume of objects?An object that will have volume is a 3-D object which means that it has length, width and height. Thus, 2D objects cannot have a volume.
Let us access the given options;
A) Baseball diamond: This refers to the baseball field because of the shape of the infield. Thus, it has only length and width and is a 2D shape which doesn't have a volume.
B) Floor Rug: A floor rug, is a plane shape which means it s a 2D shape which doesn't have a volume.
C) A piece of paper: This is a plane shape which means it s a 2D shape which doesn't have a volume.
D) Water Bottle: This is a 3D shape that has length, width and height and as such it has volume.
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(no picture available) - Solid A is dilated using a scale factor of 2/5, resulting in Solid B. Solid B is also dilated using a scale factor of 2/5, resulting in Solid C. If the volume of Solid B is 72km^3, what is the volume of Solid A and Solid C?
The volume of the solids A and C will be 1,125 cubic km and 4.608 cubic km, respectively.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Solid A is dilated using a scale factor of 2/5, resulting in Solid B. Then the volume of solid A is given as,
(Scale factor)³ x (Volume of solid A) = Volume of solid B
(2/5)³ x Volume of solid A = 72
Volume of solid A = 1,125 km³
Solid B is also dilated using a scale factor of 2/5, resulting in Solid C. Then the volume of solid C is given as,
(Scale factor)³ x (Volume of solid B) = Volume of solid C
(2/5)³ x 72 = Volume of solid C
Volume of solid C = 4.608 km³
The volume of the solids A and C will be 1,125 cubic km and 4.608 cubic km, respectively.
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1. Write a linear equation based off the word
problem.
On Your Own 3
Chili's is running a special where you can buy a basket
of fries for $5, and each refill basket of fries is only $1.
Write an equation that shows the total bill y for x
baskets of fries.
PAMAY
2
Submit
2. Click the calculator icon at the top to open the
graphing calculator. Graph the equation.
How many times did you get a refill of fries if your bill
was $9?
E
Submit
The equation of the total bill with x number of refills is y = 5 + x and the refills if the bill is $9 is 4.
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
Let us consider the number of times we refill = x.
For every refill the cost will be = 1(x) = x.
Then, a basket of fries for $5, and each refill basket of fries is only $1 is:
y = 5 + x
The equation of the total bill with x number of refills is y = 5 + x.
The graph of the equation is obtained by substituting different values of x.
For x = 1:
y = 5 + 1 = 6
Similarly, x = 2:
y = 5 + 2 = 7
If the bill is $9 then,
y = 5 + x
9 = 5 + x
9 - 5 = x
x = 4
Hence, the equation of the total bill with x number of refills is y = 5 + x and the refills if the bill is $9 is 4.
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The slope-intercept form of a line is y=2/3x + 2. Which line is perpendicular and shifted down 8?
The slope-intercept form of a line is y=2/3x + 2, the line is perpendicular and shifted down 8 is y = -3/2x - 6.
The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. In the given equation, y = 2/3x + 2, the slope is 2/3 and the y-intercept is 2.
To find a line that is perpendicular to this line, we need to find a line that has a slope that is the negative reciprocal of the slope of the given line. The negative reciprocal of 2/3 is -3/2, so the slope of the new line will be -3/2.
Now we need to find the equation of the new line in slope-intercept form. We know the slope of the line (-3/2), so we can substitute this value for m in the slope-intercept form and get:
y = -3/2x + b
To find the value of b, which is the y-intercept of the new line, we need to use the fact that the line is shifted down 8 units. We can do this by subtracting 8 from the y-intercept of the given line (which is 2), to get:
b = 2 - 8 = -6
So the equation of the line that is perpendicular to y = 2/3x + 2 and shifted down 8 units is:
y = -3/2x - 6
This line has a slope of -3/2, which is the negative reciprocal of the slope of the given line, and a y-intercept of -6, which is 8 units lower than the y-intercept of the given line.
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