Fulton is building a doghouse. He cuts 5 equal-sized pieces from a board that is 15 feet long. After cutting the pieces, he has 2
Which of these equations and expressions will, when solved or simplified, give the length of the 5 pieces of wood Fulton cut?
Answers
Answer:
X=15 divided by 2
Step-by-step explanation:
Where X equals 5.
Answer:
[tex]5x + 2\frac{1}{2} = 15[/tex] and [tex]\frac{15 - 2\frac{1}{2} }{5}[/tex]
Step-by-step explanation:
Assume the length of each piece of wood is x feet.
We can say that the length of uncut board = (number of pieces × length of each piece) + length of leftover board, or [tex]15 = 5x + 2\frac{1}{2}[/tex].
Apply the Symmetric Property of Equality:
[tex]5x + 2\frac{1}{2} = 15[/tex]
Subtract [tex]2\frac{1}{2}[/tex] from both sides of the equation:
[tex]5x = 15 - 2\frac{1}{2}[/tex]
Divide both sides by 5: (See image)
Cancel out the common terms from the numerator and denominator:
[tex]x = \frac{5}{2}[/tex]
[tex]= 2\frac{1}{2}[/tex]
Related Questions
which equation is the slope intercept form of this equation?
y-4=-2(x-5)
A) y=-2x+14
B)2x+y=6
C)y-4=-2x+10
D)x=-1/2y+3
Please help me!!!!!!!!!!! ☆I will give brainliest if right☆
Answers
Answer:
A) y = -2x + 14Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation i point-slope form.
Convert to the slope-intercept form:
[tex]y-4=-2(x-5)[/tex] use the distributive property
[tex]y-4=-2x+(-2)(-5)[/tex]
[tex]y-4=-2x+10[/tex] add 4 t oboth sides
[tex]y-4+4=-2x+10+4\\\\y=-2x+14[/tex]
help me in math tasks please
Answers
Answer:
1. 3/5 c
2. 7 c
3. 2/5 b
4. $3.24 c
5. -3.2 b
Step-by-step explanation:
1.
2/5 + 1/5 = 3/5
2.
a negative + a negative = a positive
2+5 = 7
3.
terminating means the decimal ends. When u divide a & c they keep on going but 2/5 ends
4.
divide 16.8 by 5.19 = 3.23 round up so 3.24
5.
multiply the two together to get the answer
Determine whether y2=3x+1 is a function.
Answers
The equation y2=3x+1 is a function.
Explanation:Determine whether y2=3x+1 is a function
A function is a relation in which each input has exactly one output. To determine if the equation y2=3x+1 is a function, we need to check if each input value of x corresponds to exactly one output value of y.
In this case, the equation represents a quadratic curve, which passes the vertical line test, meaning that it is indeed a function.
For example, when x=1, we can substitute it into the equation as follows: y2 = 3(1) + 1 = 4.
Therefore, for every value of x, there is a unique value of y, indicating that the equation y2=3x+1 is a function.
-15x + 4 < 109 or -6x + 70 > - 2
Answers
For this case we must find the solution set of the given inequalities:
[tex]-15x + 4 <109[/tex]
We subtract 4 from both sides of the inequality:
[tex]-15x <109-4\\-15x <105[/tex]
We divide between 15 on both sides of the inequality:
[tex]-x <\frac {105} {15}\\-x <7[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x> -7[/tex]
The solution is given by all values of x greater than -7.
[tex]-6x + 70> -2[/tex]
Subtracting 70 from both sides of the inequality:
[tex]-6x> -2-70\\-6x> -72[/tex]
We divide by 6 on both sides of the inequality:
[tex]-x> - \frac {72} {6}\\-x> -12[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x <12[/tex]
Thus, the solution set is given by:
[tex]x> -7\ U\ x <12[/tex]
Therefore the solution is all real numbers.
Answer:
All real numbers.
is y=17 a linear function
Answers
Answer:
No.
Explanation:
The term linear function refers to two distinct but related notions. This is just one point.
Determine if each relation is a function. Explain your reasoning.
Answers
Answer:
The first picture is a function while the second one is not.
Step-by-step explanation:
Reason - first picture passed the vertical line test, the other didn't.
Find the coordinates of the center of the given circle
(x - 5)2 + (y + 3)2 = 25
(5,-3)
(5.3)
(-5,3)
Answers
Answer:
The coordinates are (5.3)
Step-by-step explanation:
change the subject of the formula to w help
[tex]d = w - r { }^{2} [/tex]
Answers
Answer:
w = d + r²
Step-by-step explanation:
Given
d = w - r² ( isolate w by adding r² to both sides )
d + r² = w
The area of a triangle is 80in^2. The ratio of the length of its base to its height is 5:2. What are the base and height of the triangle? ..... show work
Answers
Answer: base = 20 inches , height = 8 inches
Step-by-step explanation:
The formula fro calculating the area of a triangle , given the base and the height is given as ;
A = [tex]\frac{1}{2}[/tex]bh
The ratio of its base to the height is given as 5: 2 , this means that
2b = 5h , that is
b = [tex]\frac{5h}{2}[/tex]
Substitute this into the formula for finding area , that is
80 = [tex]\frac{1}{2}[/tex] X [tex]\frac{5h}{2}[/tex] X h
80 = [tex]\frac{5h^{2}}{4}[/tex]
Therefore :
[tex]5h^{2}[/tex] = 80 x 4
[tex]5h^{2}[/tex] = 320
[tex]h^{2}[/tex] = 320 / 5
[tex]5h^{2}[/tex] = 64
h = 8 inches
Substitute h = 8 into b = [tex]\frac{5h}{2}[/tex] , then
b = 20 inches
Therefore , the base of the triangle is 20 inches and the height is 8 inches
Draw to show the numbers write the number to solve. Charlie gathering apples pears and plums the number of apples and plums are 10 partners there are the same number of apples and pears how many pieces of fruit could Charlie gather?
Answers
Answer:
Charlie could gather 30 pieces of fruit.
Fetching Information:
As Charlie has gathered apples pears and plums, and the number of apples and plums are 10 partners, and also there are same number of apples and pears.
What to Determine?
How many pieces of fruit could Charlie determine?
Solution:
Let 'a' be the number of apples, 'b' be the number of plums, and 'c' be the number of pears.
As the number of plums and apples is same i.e both are 10 in numbers.
So, a = b = 10
Note that number of pears and apples is also same. So, the the total number of pears will be 10.
So, c = 10
Total number of pieces of fruit = number of apples + number of plums + number of pears
Hence,
Total number of pieces of fruit = a + b + c
= 10 + 10 + 10
= 30
Thus, Charlie could gather 30 pieces of fruit.
Keywords: number, total
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Graph a line with a slope of
that contains the point (6,3).
Answers
A rectangular field is 400 meters long and 350 M wide what is the area of the field in square kilometers do not round the answer and be sure to include the correct unit in the answer
Answers
Final answer:
The area of a rectangular field that is 400 meters long and 350 meters wide is calculated by multiplying the length and width in meters to get square meters and then converting to square kilometers. The field's area is 0.14 square kilometers.
Explanation:
To calculate the area of a rectangular field, you multiply the length by the width. The area is usually given in square units.
In this case, the field is 400 meters long and 350 meters wide. To find the area in square meters, we do the following calculation:
Area = Length × Width
Area = 400 m × 350 m
Area = 140,000 m2
To convert square meters to square kilometers, you need to remember that 1 square kilometer equals 1,000,000 square meters. Therefore, you divide the area in square meters by 1,000,000 to get the area in square kilometers:
Area in square kilometers = Area in square meters / 1,000,000
Area in square kilometers = 140,000 m2 / 1,000,000
Area in square kilometers = 0.14 km2
The area of the field is 0.14 square kilometers.
To find the area of the rectangular field in square kilometers, the measurements of 400 meters and 350 meters must first be converted to kilometers, resulting in an area of 0.14 square kilometers.
Explanation:To calculate the area of a rectangular field in square kilometers, we can use the formula for the area of a rectangle which is length × width. First, we need to convert the measurements into the same unit, so we will convert meters to kilometers. We know that 1 kilometer is equivalent to 1000 meters. Therefore, a field that is 400 meters long is 0.4 kilometers long (400 ÷ 1000 = 0.4 km), and a field that is 350 meters wide is 0.35 kilometers wide (350 ÷ 1000 = 0.35 km).
Now, with both measurements in kilometers, we can find the area:
To find the area of a rectangular field, you need to multiply its length by its width. In this case, the length is 400 meters and the width is 350 meters. So, the area of the field is 400 * 350 = 140,000 square meters.To convert this to square kilometers, we need to divide the area by 1,000,000 (since there are 1,000,000 square meters in a square kilometer). So, the area of the field in square kilometers is 140,000 / 1,000,000 = 0.14 square kilometers.Therefore, the area of the rectangular field is 0.14 square kilometers.A line passes through point A(10,15). A second point on the line has an x-value that is 125% of the x-value of point A and a y-value that is 75% of the y-value of point A. Use point A to write an equation of the line in point-slope form.
An equation is y− = (x− )
Answers
The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
Step-by-step explanation:
The point-slope form of a linear equation is [tex]y-y_{1}=m(x-x_{1})[/tex] , where
m is the slope of the line, where [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the line[tex](x_{1},y_{1})[/tex] is a point on the line∵ Point A = (10 , 15)
∵ The x-coordinate of the second point is 125% of x-coordinate
of point A
∴ x-coordinate of second point = [tex]\frac{125}{100}[/tex] × 10
∴ x-coordinate of second point = 12.5
∵ The y-coordinate of the second point is 75% of y-coordinate
of point A
∴ y-coordinate of second point = [tex]\frac{75}{100}[/tex] × 15
∴ y-coordinate of second point = 11.25
∴ The coordinates of the second point are (12.5 , 11.25)
Let us find the slope of the line by using the rule of it above
∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)
∵ [tex](x_{2},y_{2})[/tex] = (12.5 , 11.25)
∴ [tex]m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}[/tex]
Now we can write the equation
∵ The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex]
∵ [tex]m=-\frac{3}{2}[/tex]
∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)
- Substitute these values in the form of the equation
∴ y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
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what is greater 19/34, 19/36
Answers
Answer:19/34
Step-by-step explanation:
Which ordered pair is a solution to the system of inequalities?
y> 2x
y> 7
A. (4,8)
B. (0,0)
c. (3,7)
D. (1,9)
Answers
Answer:
D
Step-by-step explanation:
To determine which ordered pair is a solution.
Substitute the x and y values into the inequalities.
Note that both must be true for the pair to be a solution of the system.
(4, 8)
8 > 2(4) → 8 > 8 ← False
8 > 7 ← True
(0, 0)
0 > 2(0) → 0 > 0 ← False
0 > 7 ← False
(3, 7)
7 > 2(3) → 7 > 6 ← True
7 > 7 ← False
(1, 9)
9 > 2(1) → 9 > 2 ← True
9 > 7 ← True
Thus (1, 9) is a solution to the system of equations. → D
The ordered pair (1,9) is the solution to the system of inequalities.
Explanation:To determine which ordered pair is a solution to the system of inequalities, we need to check if each pair satisfies both inequalities. Let's check:
A. (4,8): For y > 2x, 8 > 2(4) = 8 > 8, which is false. For y > 7, 8 > 7, which is true. Therefore, (4,8) is NOT a solution to the system.
B. (0,0): For y > 2x, 0 > 2(0) = 0 > 0, which is false. For y > 7, 0 > 7, which is false. Therefore, (0,0) is NOT a solution to the system.
C. (3,7): For y > 2x, 7 > 2(3) = 7 > 6, which is true. For y > 7, 7 > 7, which is false. Therefore, (3,7) is NOT a solution to the system.
D. (1,9): For y > 2x, 9 > 2(1) = 9 > 2, which is true. For y > 7, 9 > 7, which is true. Therefore, (1,9) is a solution to the system.
Thus, the ordered pair (1,9) is the solution to the system of inequalities.
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A backpacker parked his car and hiked a distance of 1.2 km on the first day. On the second day, he continued hiking away from his car with an average speed of 2.3 km/hr. Write the equation that can be used to find the backpacker's distance in km (d) from his car as a function of time in hours (t) as he hiked on the second day.
d(t) =
Answers
Answer:
d = 1.2 + 2.3t
Step-by-step explanation:
A backpacker parked his car and hiked a distance of 1.2 km on the first day. On the second day, he continued hiking away from his car with an average speed of 2.3 km/hr.
Now, on the second day he started from distance 1.2 km from his car and continues to hike with an average speed of 2.3 km/hr.
Therefore, the distance of the backpacker from his car on the second day is given by
d = 1.2 + 2.3t
where d is the distance in km and t is the time in hours he hiked. (Answer)
Helllllllllppppppppp
Answers
Answer:
[tex]\frac{8}{5} x^{2} - \frac{16}{5} xy + 4x[/tex]
[tex]xy^{2} + \frac{2}{3}y - 8y^{2}z[/tex]
Step-by-step explanation:
We have to simplify the followings:
1) [tex]- \frac{4}{5}x (- 2x + 4y - 5)[/tex]
= [tex]- \frac{4}{5}x \times (- 2x) + - \frac{4}{5}x \times (4y) + - \frac{4}{5}x \times (- 5)[/tex]
{By distributive property of multiplication}
= [tex]\frac{8}{5} x^{2} - \frac{16}{5} xy + 4x[/tex] (Answer)
2) [tex]2y^{2}( \frac{1}{2} x + \frac{2}{6}y - 4z)[/tex]
= [tex]2y^{2} \times (\frac{1}{2} x) + 2y^{2} \times ( \frac{2}{6}y) - 2y^{2} \times (4z)[/tex]
{By distributive property of multiplication}
= [tex]xy^{2} + \frac{2}{3}y - 8y^{2}z[/tex] (Answer)
Write the equation of a line that is parallel to
y
=
9
y=9y, equals, 9 and that passes through the point
(
3
,
−
8
)
(3,−8)left parenthesis, 3, comma, minus, 8, right parenthesis.
Answers
Answer:
The equation of the line is [tex]y=-8[/tex]
Step-by-step explanation:
we know that
The equation of the line [tex]y=9[/tex] is a horizontal line (parallel to the x-axis)
The equation of a horizontal line is equal to the y-coordinate of the point that passes through it
In this problem, the line passes through the point (3,-8)
The y-coordinate is -8
therefore
The equation of the line is [tex]y=-8[/tex]
Use the rule 6x to write a sequence. Start your sequence with x = 0. Be sure to write a sequence of at least six numbers, each separated by commas: 0, ___, ___, ___, ___, ___
Answers
The rule 6x means that whatever number is next in the sequence, you multiply by 6
Seeing that you are counting up one by one, multiply each number by 6
6•0=0
6•1=6
6•2=12
6•3=18
6•4=24
6•5=30
And that is the end of your sequence! It becomes 0,6,12,18,24,30
Hope this helps comment below for more questions :)
Sequence by the given rule will be 0, 6, 12, 18, 24, 30, 36.
Given rule for the sequence to be formed,
Terms = 6xHere, x = 0, 1, 2, 3, 4, 5
To write the sequence, substitute the values of x in the rule given,
1st term → 6 × 0 = 0
2nd term → 6 × 1 = 6
3rd term → 6 × 2 = 12
4th term → 6 × 3 = 18
5th term → 6 × 4 = 24
6th term → 6 × 5 = 30
Therefore, sequence will be → 0, 6, 12, 18, 24, 30, 36.
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Find a bank account balance if the account starts with $100, has an anual rate if 4%, and the money left in the account for 12 years
Answers
Answer:
required bank balance=$148
Step-by-step explanation:
simple interest=[tex]( \right )P\times R\times T\left )\div 100[/tex]
where P=principle=$100
R=rate of interest=4%
T=time=12 year
simple interest=[tex]( \right )100\times 4\times 12\left )\div 100[/tex]
simple interest=[tex]\frac{4800}{100}[/tex]
simple interest=48
required bank balance=principle+simple interest
required bank balance=$100+$48=$148
required bank balance=$148
PLEASE PLEASE HELP ME SOMEONE I AM BEING TIMED
virgina has 1/2 of a cake leftover. she wants to serve each of her guests 1/10 of a whole cake. how many guests can she serve.
Answers
Answer:
5 guests
Step-by-step explanation:
10 slices per cake
half of that is 5 slices
1 slice = 1 guest
15-0 = 0-15. True or False. Justify your statement.
Answers
Answer:
False
Step-by-step explanation:
15-0=0
0-15=-15
15 ≠ -15 False.
Simplify the expression 2 × 36 − 24 ÷ 6
Answers
Answer:
68
Step-by-step explanation:
P- parentheses
E- exponential
M- multiplication
D- division
A- addition
S- subtraction
2 x 36 = 72
72 - 24 ÷ 6
24 ÷ 6 = 4
72 - 4 = 68
Answer:
68
Step-by-step explanation:
*Remember the order of operations PEMDAS*(Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)
2 x 36 = 7224 / 6= 4now, 72 - 4= 68hope it helps:)
Which of the following is the BEST summary of this
paragraph?
A tsunami is not like normal ocean waves. It's a series
OA) of waves. You need to wait several hours for all of
them to pass.
Because a tsunami is not one wave, but a series of
several waves that can be as far as two hours apart,
OB)
you must wait several hours after the last wave in
order to be sure the tsunami is over.
A tsunami consists of not one but many waves that
come in one after the other. Not knowing whether the
OC)
tsunami is over unless more than two hours have
Answers
Answer:
I THINK IT IS OB
HOPE IT HELPS!
Answer:
B
Step-by-step explanation:
PLZZZ HURRYYYY ITS TIMEDDDDD
Daniel expanded the expression as shown. What errors did he make? Select three options.
-2(-8x-4y+3/4)=-10x-8y-1 1/4
A. The first term should be positive.
B. The second term should be positive.
C.The last term should be -1 1/2, not -1 1/4.
D. He divided -8 by -2 instead of multiplying -8 by -2.
E. He did not simplify the expression completely.
Answers
Answer:
Step-by-step explanation:
-2(-8x - 4y + 3/4) =
16x + 8y - 3/2 ....(-3/2 is the same as - 1 1/2)
errors.....
A. the first term should be positive
B. the second term should be positive
C. the last term should be - 1 1/2
Daniel expanded the expression . The errors made by Daniel are
A. The first term should be positive.
B. The second term should be positive.
C. The last term should be -1 1/2, not -1 1/4.
Given :
Daniel expanded the expression as shown
[tex]-2(-8x-4y+3/4)\\-10x-8y-1 1/4[/tex]
Lets multiply -2 inside the parenthesis and see what happens
[tex]-2(-8x-4y+3/4) \\-2 (-8x)-2(-4y)-2(\frac{3}{4} )[/tex]
we know that negative times negative is positive
Also to simplify the fraction ,we can cancel out 2 and 4
[tex]-2 (-8x)-2(-4y)-2(\frac{3}{4} )\\+16x+8y-\frac{3}{2} \\+16x+8y-1\frac{1}{2} \\[/tex]
So the first and second terms are positive
Also the constant term is -1 1/2
So the errors he make are
A. The first term should be positive.
B. The second term should be positive.
C.The last term should be -1 1/2, not -1 1/4.
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y=-2x+5 was shifted down 7 units what equation is it now
Answers
Answer:
[tex]y=-2x-2[/tex]
Step-by-step explanation:
we have
[tex]y=-2x+5[/tex]
This is the equation of a line in slope intercept form
where
[tex]m=-2[/tex] ---> the slope
[tex]b=5[/tex] ----> the y-intercept
we know that
If the given line was shifted down 7 units, then the new y-intercept is equal to
[tex]b=5-7=-2[/tex]
The slope of the new line will be the same that the original line, because are parallel lines
so
The new equation is
[tex]y=-2x-2[/tex]
Systems of equations with different slopes and different y-intercepts have more than one solution. (5 points) Always Sometimes Never
Answers
Answer:
Never
Step-by-step explanation:
we know that
A system of linear equations with the same slope and the same y-intercept has infinite solutions (identical lines)
A system of linear equations with the same slope and different y-intercept has no solutions (parallel lines)
A system of linear equations with different slopes and different y-intercept has only one solution
Please help! I really need it!
Answers
Answer:
1. x > 4
2. m < 2
3. x > 2
4. x < -6
Step-by-step explanation:
These 4 inequalities will be solved the same way we solve equations. We take variables to one side and numbers to another and use algebra to solve. Each of them are solved shown below:
1.
[tex]4+6x<x+6x\\4+6x<7x\\4<7x-6x\\4<x[/tex]
so x is greater than 4, we can write (variable first):
x > 4
2.
[tex]m+16>8m+2\\16-2>8m-m\\14>7m\\\frac{14}{7}>m\\2>m[/tex]
so m is less than 2, we can write:
m < 2
3.
[tex]5x-1>13-2x\\5x+2x>13+1\\7x>14\\x>\frac{14}{7}\\x>2[/tex]
so x is greater than 2, we can write:
x > 2
4.
[tex]-3x-2>-x+10\\-2-10>-x+3x\\-12>2x\\\frac{-12}{2}>x\\-6>x[/tex]
so x is less than -6, we can write:
x < -6
Which input value produces the same output value for the
two functions on the graph?
O
O x=-1
Ox= 0
O
Ox=4
Answers
Answer: [tex]d)x=4[/tex]
Step-by-step explanation:
The missing graph is attached. And the options are:[tex]a)x=-1\\b)x=0\\c)x=3\\d)x=4[/tex]
By definition, a relation is a function if and only if each input value has one and only one output value.
It is important to remember that the input values are the values of "x" and the output values are the values of "y".
Observe the graph attached.
You can identify in the graph that the function f(x) and the function g(x) intersect each other at the following point:
[tex](4,3)[/tex]
Where the x-coordinate (input value) is:
[tex]x=4[/tex]
And the y-coordinate (output value) is:
[tex]y=3[/tex]
Therefore, you can conclude that the input value that produces the same output value for the two functions on the graph, is:
[tex]x=4[/tex]
3. Caleb has $25 to spend on prizes for a game at the school fair. Lip balm costs $1.25 each, and mini-notebooks cost $2.50 each.
a. Write a linear equation in STANDARD FORM that can be used to determine how many of each prize she can buy.
b. Graph the equation using x- and y- intercepts.
Answers
Answer:
linear equation in Standard form that can be used to determine how many of each prize Caleb can buy is [tex]1.25x+ 2.50y = 25[/tex]
Step-by-step explanation:
Given:
Total cost spent on prizes for games = $25
Cost of one lip balm = $1.25
Cost of one mini notebook = $2.50
A) linear equation in STANDARD FORM that can be used to determine how many of each prize she can buy.
Let the number of lip balms be x and the number of mini note books be y. Then
[tex]1.25x+ 2.50y = 25[/tex]
B. Graph the equation using x- and y- intercepts.
Now by trial and error method
[tex]1.25(0)+ 2.50(10) = 25[/tex]
[tex]1.25(2)+ 2.50(9) = 25[/tex]
[tex]1.25(4)+ 2.50(8) = 25[/tex]
[tex]1.25(6)+ 2.50(7) = 25[/tex]
[tex]1.25(8)+ 2.50(6) = 25[/tex]
[tex]1.25(10)+ 2.50(5) = 25[/tex]
[tex]1.25(12)+ 2.50(4) = 25[/tex]
[tex]1.25(14)+ 2.50(3) = 25[/tex]
[tex]1.25(16)+ 2.50(2) = 25[/tex]
[tex]1.25(18)+ 2.50(1) = 25[/tex]
[tex]1.25(20)+ 2.50(0) = 25[/tex]
Thus Caleb can buy 0,2,4,6,8,9,10,12,14,1,6,18,20 lip balms and
0,1,2,3,4,5,6,7,8,9,10 mini note books respectively
Now plotting these value in the graph, we get the below graph