The correct answer is C. We can add and subtract terms regardless if they have the same base.
To add polynomials, we add the coefficients of the like terms together. For example, to add 2x^3 + 5x^2 + 6x + 3 and 3x^2 + 7x + 8, we would first identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then added together, so 2x^3 + (5+3)x^2 + (6+7)x + (3+8). The result is 2x^3 + 8x^2 + 13x + 11.
To subtract polynomials, we subtract the coefficients of the like terms. For example, to subtract 3x^2 + 7x + 8 from 2x^3 + 5x^2 + 6x + 3, we would identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then subtracted, so 2x^3 + (5-3)x^2 + (6-7)x + (3-8). The result is 2x^3 + 2x^2 - x - 5.
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Which trigonometric ratio is used to find the cosine of a right triangle?
Answer: Cosine ratios are exactly the same idea of sine ratios or tangent ratios. The only difference between it and the other two trigonometric ratios is that it is the ratio of the adjacent side to the hypotenuse of a right triangle.
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
Answer:
C) One solution-------------------------
Given system:
- x + 6y = 76x - 30y = - 34We can solve it by elimination.
Multiply the first equation by 6 and add up to get:
-6x + 36y + 6x - 30y = 42 - 346y = 8y = 8/6y = 4/3Without solving for x we can see there is one solution.
The last answer choice is the correct one.
Answer:
The given system of equations has exactly one solution (1, ⁴/₃).
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-x+6y=7\\6x-30y=-34\end{cases}[/tex]
To solve the given system of equations, multiply all terms of the first equation by 5:
[tex]\implies -x \cdot 5+6y \cdot 5=7 \cdot 5[/tex]
[tex]\implies -5x+30y=35[/tex]
Add this to the second equation to eliminate the term in y:
[tex]\begin{array}{crcccl}&6x & - & 30y & = &-34\\\vphantom{\dfrac12}+ & (-5x & + & 30y & = & \;\;\:35)\\\cline{2-6}\vphantom{\dfrac12}&x&&&=&\;\;\;\;\:1\\\cline{2-6}\end{array}[/tex]
Therefore, x = 1.
Substitute the found value of x into the first equation and solve for y:
[tex]\implies -(1)+6y=7[/tex]
[tex]\implies 6y=8[/tex]
[tex]\implies y=\dfrac{8}{6}[/tex]
[tex]\implies y=\dfrac{4}{3}[/tex]
Therefore, the given system of equations has exactly one solution (1, ⁴/₃).
The Leap of Faith water slide in Atlantis stands 60 feet high. If the base of the slide is 37 feet from the pool, then what is the length of the slide? Round your answer to the nearest tenth.
The Atlantis water slide measures 70.69 feet in length when the slide's base is 37 feet from the pool and it is 60 feet tall.
what is Pythagoras theorem ?The Pythagorean Theorem, often known as the Mathematicians, is the fundamental Euclidean geometry relation between the three sides of a right triangle. The area of a cube with the velocity vector side equals the sum of the areas of polygons with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the perfect distance equals a sum of the squares that span its sides. It is sometimes written as the basic algebra notation a2 + b2 = c2.
given
According to Pythagoras's Theorem, which states that
c2 = a2 + b2
c2 = 3600 + 1369
c2 = 4969
c = 70.49, the water slide in Atlantis is 60 feet high and has a base that is 37 feet from the pool.
The Atlantis water slide measures 70.69 feet in length when the slide's base is 37 feet from the pool and it is 60 feet tall.
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Why do we use the midpoint method?
The midpoint method is a numerical integration technique used to approximate the definite integral of a function over a given interval. It is a Riemann sum method.
What does the midway in math mean?The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them.
Here,
The midpoint method is used for a few reasons:
Simplicity: The midpoint method is relatively easy to understand and implement, compared to other numerical integration techniques.
Accuracy: The midpoint method is more accurate than some other Riemann sum methods like the left-hand rule or right-hand rule, which evaluate the function at the endpoints of each subinterval.
Efficiency: The midpoint method is more efficient than some other numerical integration techniques, especially for functions that are not smooth or have sharp changes.
Flexibility: The midpoint method can be used for both definite and indefinite integrals, and for functions that are not well-behaved.
Overall, the midpoint method is a simple, accurate, efficient and flexible numerical integration method that can be used to approximate the definite integral of a function over a given interval.
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Please help!! i included a picture as well not sure if it would help !Write the equation of a quadratic function given the transformations given below:
• Opens upwards
●
A = ½
● Horizontal shift right 5
• Vertical shift down 2
The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.
What is quadratic function?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form. The three graphs in the image below are all parabolas.
Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.You are aware that a line is defined by two points. This implies that there is only one line that contains both points if you are given any two points in the plane. Points and quadratic functions both fit this description.There is only one quadratic function f whose graph contains all three points when there are three points in the plane with distinct first coordinates and that are not on a line. This fact is demonstrated by the applet below. Three spots are shown on the graph, and a parabola passes through them all.The text box behind the graph displays the associated function. The function and parabola are updated if any of the points are moved.Using the methods of stretching/shrinking and moving (translation) the parabola y = x2 several quadratic functions can be graphed easily by hand.How do you determine if quadratic equation opens up or down?A quadratic function's graph takes the form of a parabola. The parabola will open upward if the value of the "a" term is positive, and downward if the value is negative
How to shift a function upwards?.A function can be raised by adding outside of it: f (x) + b raises f (x) by b units. The same principles apply for moving a function down, except instead of subtracting a positive integer, f (x) b represents f (x) moved down b units.
Shift Up and Down by Changing the Value of kYou can represent a vertical (up, down) shift of the graph of f(x)=x2 by adding or subtracting a constant, k.
f(x)=x2+k
Right- and down-shift of a functionBy increasing or decreasing the output or the input, you can change the direction of the function's graph to the right, left, up, or down. A function's output can be increased to move the graph up. The graph is shifted downward when a function's output is subtracted from.
Horizontal and vertical shift of a functionThe output has a constant added to it, which causes the vertical shift. For a positive constant, move the graph upward; for a negative constant, move it below. A constant supplied to the input causes a horizontal shift. For a positive constant, move the graph to the left; for a negative one, move it to the right.
Shift left and right by changing the value of hYou can represent a horizontal (left, right) shift of the graph of f(x)=x2 by adding or subtracting a constant, h, to the variable x, before squaring.
f(x)=(x−h)2
If h>0, the graph shifts toward the right and if h<0 , the graph shifts to the left.
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Camryn is moving 240 miles and will have to pay a travel fee. If she hires movers for 35 hours to pack all of her boxes it will cost $1221, including the travel fee. If she hires movers for only 10 hours to pack boxes, it will cost $546, including the travel fee. What is the hourly rate for the movers? What is the cost per mile? I I I I 19 i
The total cost of the move when hiring movers for 35 hours is $1221, and the total cost of the move when hiring movers for 10 hours is $546.
What is the hourly rate for the movers?Hourly rate for the movers = $54 ($1221 / 35 hours)Cost per mile = $5.11 ($1221 / 240 miles)The hourly rate for the movers is $35 per hour.If Camryn hires the movers for 35 hours to pack all of her boxes, it will cost $1221 including the travel fee.If she hires the movers for only 10 hours to pack boxes, it will cost $546 including the travel fee.This means that the cost per mile to move Camryn's belongings is $5.19. This cost includes the travel fee of the movers, so Camryn is paying $5.19 for every mile that the movers have to travel.This cost does not include the cost of any other services or supplies that the movers may need to complete the move, such as packing materials or fuel.Camryn should take these additional costs into account when deciding how many hours to hire the movers for.The hourly rate for the movers is $35 per hour. This fee includes the cost of the travel fee. The cost per mile is $5.10. This cost takes into account the travel fee, which is included in the total cost.This means that hiring movers for 35 hours will cost $675 more than hiring movers for 10 hours. The difference in cost is due to the travel fee and the number of hours spent packing and loading boxes.The hourly rate for the movers is constant and does not change based on the number of hours hired. This rate is $35 per hour and includes the cost of the travel fee. The cost per mile is determined by dividing the total cost for the move, including the travel fee, by the number of miles being moved. In this case, the cost per mile is $5.10. Overall, the cost of the move depends on the number of hours spent packing and loading boxes, as well as the travel fee. The hourly rate for the movers is the same regardless of the number of hours hired, but the cost per mile is determined by the total cost of the move, including the travel fee.To learn more about cost analysis of hiring movers to help with a move refer to:
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which is an equation with a degree of 3, a zero located at x=4 and a y-intercept located at (0,60)
The degree 3 polynomial equation is 1/2(4 - x)(x - 1)(x - 2).
What is a polynomial equation?A polynomial equation is one in which a polynomial is set to zero. It is an equation composed of variables, non-negative integer exponents, and coefficients, as well as operations and an equal sign. It has various exponents. The highest one represents the equation's degree.A third-degree polynomial is defined as p(x) = ax³ + bx² + cx + d, where 'a' is not equal to zero. Because it has a degree of three, it is also known as a cubic polynomial.Here given,
With zeros and a coefficient, the function is:
f(x) = a(x - 4)(x - 1)(x - 2)
Regarding the y-intercept:
f(0) = a(0 - 4)(0 - 1)(0 - 2)
4 = a(-4)(-1)(-2)
4 = -8a
a = -1/2
As a result, the function is:
f(x) = -1/2(x - 4) (x - 1)(x - 2)
= 1/2(4 - x)(x - 1)(x - 2)
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Here is a question on angle measures in real-life.
Angle FED is equal to what amount?
Answer:235
Step-by-step explanation: its because.......
Fred borrowed $38,000 for 5 years at an APR of 4%
a) find the monthly payment.
b) What is the total payment?
c) Find the Finance Charge
a) The monthly payment for a loan of $38,000 borrowed by Fred for 5 years at 4% APR is $699.83.
b) The total payment to be made is $41,989.80.
c) The finance charge is $3,989.80.
What is the finance charge?The finance charge is the difference between the sum of the monthly payments and the loan amount.
The monthly payments, total payment, and finance charge can be computed using an online finance calculator as follows:
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $38,000
FV (Future Value) = $0
Results:
PMT (Monthly Payments) = $699.83
Sum of all periodic payments (Total Payment) = $41,989.80
Total Interest (Finance Charge) = $3,989.80
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A district restaurant manager bought 4 cases of disposable cups for $150 each. Each case contained 3,600 cups. He wants to split the cups equally between 6 restaurants. Which calculation yields the number of cups for each restaurant?.
The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 number of cups.
The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 cups. The district restaurant manager purchased four cases of disposable cups, each costing $150 and containing 3,600 cups. He needed to split the cups among six restaurants. To determine how many cups each restaurant would receive, he divided 3,600 by 6. This gave him an answer of 600 cups for each restaurant.
3,600 ÷ 6 = 600 cups
The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 number of cups.
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9+ a/6=8
show work
solve a
Answer:
a = -6
Step-by-step explanation:
9+a/6=8 1. -9 both sides
(6)a/6= -1(6) 2. multiply 6 on both sides
a = -6
Solve the equation -8x < 32
Answer: x < -4
Step-by-step explanation: This is a question of an inequality. Here, everything proceeds like a normal equation that we solve. To obtain the value of x, we will divide 32 by 8.
-8x<32
x<-32/8
x<-4 (On dividing -32 by 8)
This means x can take any value less than -4 i.e. -5,-6,-7,......
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Is 3 2 an ordered pair?
Yes, (3, 2) is an ordered pair.
The combination of the x coordinate (abscissa) and the y coordinate (ordinate) is called an ordered pair, which has two values written in a fixed order within parentheses.
It can help us to locate a point on the cartesian plane for better visual understanding. The numerical values in an ordered pair can be both integers or fractions.
In the Cartesian plane, we can define a two-dimensional space with two perpendicular reference lines, the x-axis and the y-axis. The point where the two lines meet is the origin (O).
For example plot the point Q with the coordinates (3, 2)
According to the definition of ordered pair, the point Q will be written as:
Q = (3, 2)
The left number in the ordered pair shows the distance from the “x” axis which is 3
The right number shows the distance from the “y” axis which is 2.
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Help please, I don't understand any of this
The graph solution is in the attached images, for all the systems of inequalities.
What is the graph of a function?
The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.
The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.
we have the following inequalities:
i)
y > 3x - 17,
y ≤ -4x +11.
ii)
4x - 4y > -40,
-5x + 5y < 10.
iii)
x + 3y ≥ 31,
4x - 2y ≥ -2,.
iv)
5x + y < 3,
5x + y > 37
Hence, the graph solution is in the attached images, for all the systems of inequalities.
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helpppp asap !!!!!!!!!!!
The numeric value for the logarithmic expressions is given as follows:
1. [tex]\log_{6}{\left(\frac{5}{8}\right)} = -0.263[/tex]
2. [tex]\log_6{40} = 2.059[/tex]
3. [tex]\log_6{64} = 2[/tex]
4. [tex]\log_6{125} = 2.694[/tex]
a. [tex]\log_{5}{\left(\frac{11}{30}\right)} = -0.623[/tex]
b. [tex]\log_5{330} = 3.603[/tex]
c. [tex]\log_5{121} = 2.98[/tex]
How to obtain the numeric value for the logarithmic expressions?For the first expression, we have that the logarithm of the quotient is the subtraction of the logarithms, hence:
[tex]\log_{6}{\left(\frac{5}{8}\right)} = \log_6{5} - \log_6{8} = 0.898 - 1.161 = -0.263[/tex]
The same rule is applied for item a, hence:
[tex]\log_{5}{\left(\frac{11}{30}\right)} = \log_5{11} - \log_5{30} = 1.49 - 2.113 = -0.623[/tex]
For the second expression, we apply the logarithm of the product, which is the sum of the logarithms, hence:
[tex]\log_6{40} = \log_6{5 \times 8} = \log_6{5} + \log_6{8} = 0.898 + 1.161 = 2.059[/tex]
For item b, we have that:
[tex]\log_5{330} = \log_5{11 \times 30} = \log_5{11} + \log_5{30} = 1.49 + 2.113 = 3.603[/tex]
For the third expression, we have that the exponent is equals to the base, hence we just take the lower term, as follows:
[tex]\log_6{64} = \log_6{2^6} = 2[/tex]
For the fourth term, we have the rule for the logarithm of an exponent, hence:
[tex]\log_6{125} = \log_6{5^3} = 3\log_6{5} = 3 \times 0.898 = 2.694[/tex]
The same rule is applied for item c, as follows:
[tex]\log_5{121} = \log_5{11^2} = 2\log_5{11} = 2 \times 1.49 = 2.98[/tex]
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Will E. Wait works at Willy Wonka's Chocolate Factory. His annual salary is $58,500.
He is paid biweekly. What is Will's biweekly gross salary?
Your answer
Answer: 562.50
Step-by-step explanation:
The dimensions of a rectangle are 7 in by (x+2)in. Which expression represents its area?
The correct option for the area of rectangle is A: 7(x + 2) sq in.
Define the term rectangle and its area?The characteristics of a rectangle were just as follows:
It has a tight, flat form.There are 4 corners, 4 angles, as well as 4 sides (vertices).There are two dimensions to it: length and width.A rectangle has 90° angles on each side.The opposing sides are parallel and equal.It features two equal-length diagonals.An area is the amount of space a rectangle takes up.By calculating the product of a rectangle's length and breadth, one can get the area of the shape.
So,
Area of a rectangle = Length × Width
Dimension are-
length : 7 inBreadth : (x + 2)inSo,
Area of a rectangle = 7 × (x + 2) sq in..
Thus, the expression represents area of a rectangle is 7 × (x + 2) sq in.
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The complete question is-
The dimensions of a rectangle are 7 in by (x+2)in. Which expression represents its area?
A: 7(x + 2) sq in..
B: 7 + (x + 2) sq in..
There were 75 runners to start a race. In the first half of the race, 1/3 of them dropped out. In the second half of the race, 2/5 of the remaining runners dropped out. How many runners finished the race?
Just the photo, please help, the 9 weeks end today and I need these turned in soon as possible
Answer:
3/4 : 1 1/2 1 2/4 : 3. 5 : 10
Step-by-step explanation:
What is a infinitely many solution?
An infinite solution has both sides equal.
What number has an unlimited number of answers?
There are infinitely many possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable.
If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions. 2x and 2x should be combined.
Are all possible solutions parallel?
There are no answers when the lines are parallel, and occasionally the two equations will graph as the same line, in which case there are an endless number of solutions. These kinds of systems are occasionally described using specific words.
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A store buys a jacket for $20.00 and then sells it to customers for 80% more than that. what is the selling price of the ja
Answer: 36
Step-by-step explanation:
80% or 200 is 16
16+20=36
An object is dropped from 40 feet below the tip of the pinnacle atop a 716-ft tall building. The height h of the object after t seconds is given by the equation h=−16t2+676. Find how many seconds pass before the object reaches the ground.
Answer:
Below
Step-by-step explanation:
When it reaches the ground h = 0
h = 0 = -16t^2+676
16t^2 = 676
t^2 = 42.25 t = 6.5 s
The triangles below are similar. Identify the
appropriate similarity theorem that justifies the
similarity. Justify your reasoning.
AAA(Angle angle angle) Theorem can be used to prove given triangles as similar.
As we know we have to show all three angles equally.
so we have to show the similarities between T(DNM) and T(DFE) ....
(T Means Triangle.)
(A Means Angle)
As D is a common vertex in both the triangles
SO A(NDM) = A(FDE)................Angle D .......... 1A(DNM) = A(DFE) ------- by Alternative property exterior angles are equal...........2A(NMD)= A(FED) --------- BY Alternative property interior angles are equal .........3by equations 1, 2, and 3 we can conclude that all three angles of T(DFE) = T(DNM)
SO By the AAA rule, we can say that the two Triangles are similar.
Now we can say all the sides of T(DFE) will be in all propositions of T(DNM).
Like DN/DF=DM/DE=NM/FE
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How many children can you predict a family has if the amount spent on groceries per week is $169.47?
Answer: Well for a family of 6 we spend around 200-300$, so a family of 4-5 if older like teens, or 6-7 for young toddlers.
help pleaseee i can’t get it right
The compositions between functions f(x) = 3 · x - 2 and g(x) = x + 1 are f[g(x)] = 3 · x + 1 and g[f(x)] = 3 · x - 1, respectively.
How to use composition between two functions
Let be f(x) and g(x) functions, there is a composition of the form f[g(x)], when the independent variable of function f is substituted by function g. That is to say:
f ° g(x) = f [g(x)]
First, define functions f(x) and g(x):
f(x) = 3 · x - 2
g(x) = x + 1
Second, perform the required compositions and simplify the expressions:
f[g(x)] = 3 · (x + 1) - 2
f[g(x)] = 3 · x + 1
g[f(x)] = (3 · x - 2) + 1
g[f(x)] = 3 · x - 1
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If the length of a rectangle increases 2 times and the width decreses 3 times, then its area decreased by :
a) 66.6%
b) 66.(6)%
c) 33.(3)%
d) 33.3%
e) 30%
The statement which is correct about the Area of the rectangle in discuss as required is that the area decreased by; Choice C; 33.(3)%.
By what percent does the area of the rectangle decrease?As evident in the task content; the length of a rectangle increases 2 times and the width decreses 3 times;
Since the initial length can be said to be; l and the initial width can be said to be; w and Area A = l × w.
However, when the length and width change as described; the area of the rectangle is;
Area = 2l × ( w / 3 )
Area = ( 2/3 ) × lw
On this note, the new Area of the rectangle is two-third the initial area.
On this note, the area of the rectangle has decreased by one-third which is equivalent to; Choice C; 33.(3)%.
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For a part-time job, Jeannie conducted a survey with two questionnaires, Type A
and Type B. She chose 500 homes and mailed questionnaires at a cost of $.19 for
Type A and $.23 for Type B. If the total cost of the mailing was $106.20, how
many of each type did she mail?
Out of the 500 homes, 226 Type A forms were sent while 274 Type B forms were sent.
How many of the forms were sent?To determine the number of forms sent, we can begin by identifying how much Jeannie spent on mailing each of the questionnaires. The sum of $0.19 and $0.23 is $0.42. Now, we will find out how much of these were the total cost as follows:
Type A:
$0.19 / $0.42 × $106.20
= $48.
Type B:
$0.23 / $0.42 × $106.20
= $58.2
Next, we will determine how much of these went into the 500 homes as follows:
Type A:
$48 / 106.2 × 500
= 225. 9 ≈ 226 homes
Type B:
$58.2 / $106.2 × 500
= 274 homes
So, while Type A was sent to 226 homes, Type B was sent to 274 homes.
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- Hair grows at a rate of 1/64 inch per day. Write this number using negative exponents.
Answer:
[tex]4^{-3}[/tex]
Step-by-step explanation:
[tex]4^{3}[/tex] = 64
Take the reciprocal of both sides.
1/64 = [tex]4^{-3[/tex]
Where do we find value table?
The proper method of finding a value table has been mentioned and explained below.
Value tables are a part of domain definition. The value table is maintained at the domain level and thus, is also called domain-level validation. Whenever you create a domain, you can enter the required values. Whenever you use this Domain, the system will make it so that you are forced to enter only these values. This is a sort of master check.
This means that if you want to enter values into this table you have to create a development request & transport the same. The system, then, proposes the value table as a check table. The check against the value table only takes place when a foreign key is defined
.
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The price of strawberries at Fine Foods is shown in the graph. At best Market, the price y for x pounds of strawberries is given by y=2.90x. Which store sells strawberries at a cheaper unit price?
The store that sells strawberries at a cheaper unit price is Fine Foods.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represents the number of pounds of strawberries.y represents the price in dollars.k represents the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 2/1 = 6/3 = 10/5 = 14/7
Constant of proportionality (k) = 2.
Therefore, an equation for the price of strawberries at Fine Foods is y = 2x and as such, it sells strawberries at a cheaper unit price.
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