The product of a rational number multiplied by itself is called as a perfect square.,we can easily find out the square root for a number which is a imperfect square
Step-by-step explanation:
using the following formula we can find a square root for a number which is a imperfect square
X = Non perfect square
√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )
[tex]√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )[/tex]Example
√38
the nearest perfect root is 36
36 (√36=6)
so √38 = √36 + (38-36)/2√36
= 6 + 2/12
=6 + 1/6 = 6.166 (answer)
[tex]√38 the nearest perfect root is 36 36 (√36=6)so √38 = √36 + (38-36)/2√36 = 6 + 2/12=6 + 1/6 = 6.166 (answer)[/tex]
To find the square root of a non-perfect square, use estimation techniques or the quadratic formula if in relation to an equation. Use the imaginary unit i for square roots of negative numbers, and simplify by removing perfect squares when adding or subtracting radicals.
Finding the square root of a number that is not a perfect square can be done using a few different methods. One simple non-calculator method is to use estimation and refinement; start with an approximate guess and improve it. When dealing with negative numbers, remember that we use the imaginary unit i to denote the square roots of negative numbers. For example, a₂ can be written as 2i. Adding and subtracting radicals involves simplifying each radical by removing perfect squares and combining like terms.
For equations where the square root is part of a quadratic equation, ax²+bx+c = 0, if a, b, and c are non-zero, we should use the quadratic formula to find solutions. Estimation also applies when dealing with cube roots or higher, where we can start with an initial guess and use methods like calculus to refine it.
To estimate a surd like a₃ without a calculator, consider its place on the number line between two integers, knowing that a₃ is about 1.732. This helps get an approximate value which is often sufficient for many applications.
Compare the numbers. Pick the correct sign.
7 ? 5
You can use the number line to help.
Submit
Answer:
7 > 5
Step-by-step explanation:
On a number line, 7 is to the right of 5.
On the number line, a number is greater than a number to its left.
7 is greater than 5
7 > 5
Select the expression that is equivalent to the given polynomial.
16r4 – 625
O A. (2x + 5)(2x - 5)(2x + 5i) (2x – 5i)
B. (2x - 5)(2x – 5)(2x – 5i)(2x – 5i)
C. (2x - 5)(2x – 5)(2x + 5i)(2x – 5i)
D. (2x + 5)(2x + 5)(2x + 5) (21 + 5i)
Observe that [tex]16r^4[/tex] is the square of [tex]4r^2[/tex], and 625 is the square of 25.
So, your expression is a difference of squares, and as such we can rewrite it as
[tex]16r^4-625=(4r^2+25)(4r^2-25)[/tex]
Now again, [tex]4r^2[/tex] is the square of [tex]2r[/tex], and 25 is the square of 5. So, we have a sum and a difference of squares.
But if we think of 25 as [tex]-(5i)^2[/tex], we have again the difference of two squares, so we have
[tex]4r^2+25=(2r+5i)(2r-5i)[/tex]
[tex]4r^2-25=(2r+5)(2r-5)[/tex]
Option A is the correct expression equivalent to 16r⁴-625.
The options in the question must have r in place of x.
What does the imaginary number i mean?The imaginary number 'i' is the solution of the algebraic equation x²+1.
Thus, x²+1=(x+i)(x-i).
How to factorize (a²+b²)?We can observe that (a+bi)(a-bi)=(a²+b²)+i(-ab+ba)=a²+b².
Hence the factorization of a²+b² is (a+bi)(a-bi)
How to factorize the given polynomial?16r⁴-625
=(4r²-25)(4r²+25)
=(2r-5)(2r+5)(2r+5i)(2r-5i)
So, option A is the correct expression equivalent to 16r⁴-625.
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what is the degree of 23x4
Answer:
92
Step-by-step explanation:
Answer:
92
Step-by-step explanation:
23 x 4 = 92
Suppose that h(x) varies directly with x and h(x) = 44 when x = 2.
What is h (2) when x = 1.5?
Ο 14.7
Ο
Ο 132
Ο
Ο 22
Ο
Ο 33
Value of h(1.5) is 33
Step-by-step explanation:
Step 1: Find the relation between h(x) and x. Given h(x) = 44 when x = 2. Then h(x) = 22 × x = 22xStep 2: Find h(x) when x = 1.5⇒ h(1.5) = 22 × 1.5 = 33
Final answer:
To find h(2) when x = 1.5, you first determine the constant of variation (k) using the given information h(x) = 44 when x = 2. This leads to k = 22. Plugging x = 1.5 into the direct variation equation h(x) = k*x, we get h(1.5) = (option D) 33.
Explanation:
If h(x) varies directly with x, then we can express this relationship as h(x) = k*x, where k is the constant of variation. We're given that h(2) = 44, so we can solve for k by plugging in the values:
44 = k*2 => k = 22.
Now that we have the value of k, we can find h(1.5) by multiplying k by 1.5:
h(1.5) = 22 * 1.5 = 33.
Therefore, the value of h(2) when x = 1.5 is (option D) 33.
There are 12 boys and 14 girls in a class. One of the students is selected at random to represent the class at student council. What is the probability that the student selected is a girl?
Final answer:
The probability of selecting a girl to represent the class on the student council, from a class of 12 boys and 14 girls, is 7/13 or approximately 53.85%.
Explanation:
This question demands basic understanding of probability
The question relates to determining the probability that a student selected at random to represent a class at student council is a girl. Given there are 12 boys and 14 girls in the class, the total number of students is 12 + 14 = 26. The probability of selecting a girl is therefore the number of girls divided by the total number of students, which is 14/26. Simplified, this probability is 7/13, which can be approximated to 0.5385 or 53.85%.
Therefore, as per the above explaination, the correct answer is 53.85%
In an equation what number do you subtract from 59 to get 31?
Answer:
x = 28
Step-by-step explanation:
Step 1: Make an equation to represent the words
In an equation what number do you subtract from 59 to get 31?
59 - x = 31
Step 2: Solve for x
59 - x - 59 = 31 - 59
-x / -1 = -28 / -1
x = 28
Answer: x = 28
3 1/25 into a decimal
Answer:
3.04
Step-by-step explanation:
(9)/(16) x^(2)+7.5x=-25
Answer:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Exact Form:
x= −20/3
Decimal Form:
x= −6.66...
Mixed Number Form:
x= −6 2/3
Step-by-step explanation:
What is the area of the parallelogram with a base of 1.75 cm and a height of 1.5 cm? 2.75 cm2 3.625 cm2 2.625 cm2 3.25 cm2
Answer:
Step-by-step explanation:
Area of parallelogram=base*height
So 1.75*1.5=2.625cm²
Answer:
2.625
Step-by-step explanation:
Use the quadratic formula to solve x2 - 5x - 2 = 0.
Answer:
x=-0.37 or 5.37
Step-by-step explanation:
The quadratic formula is;
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
The expression to be solved is
[tex] {x}^{2} - 5x - 2 = 0[/tex]
Comparing this to the general form of the quadratic equation,
[tex] a{x}^{2} + bx + c = 0 [/tex]
a=1, b=-5 and c =-2.
We substitute these values into the quadratic formula
[tex] \implies x = \frac{ - ( - 5)\pm \sqrt{ { (- 5)}^{2} - 4(1)( - 2)} }{2(1)} [/tex]
Simplifying we obtain,
[tex] x = \frac{ 5\pm \sqrt{25 + 8}}{2} [/tex]
[tex] \implies x = \frac{ 5\pm \sqrt{28}}{2} [/tex]
[tex] \implies x = \frac{5 + 2\sqrt{7} }{2}or \frac{5 - 2 \sqrt{7} }{2} [/tex]
[tex]\implies x = \frac{5}{2} + \sqrt{7} or \frac{5 }{2} - \sqrt{7} [/tex]
x=5.37 or -0.37
The solutions to the quadratic equation x² - 5x - 2 = 0 are:
x = (5 + √33) / 2
x = (5 - √33) / 2
To solve the quadratic equation x² - 5x - 2 = 0 using the quadratic formula, we can use the formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a, b, and c represent the coefficients of the quadratic equation.
For the equation x² - 5x - 2 = 0, we can identify the values of a, b, and c:
a = 1
b = -5
c = -2
Substituting these values into the quadratic formula, we have:
x = (-(-5) ± √((-5)² - 4 × 1 × (-2))) / (2 × 1)
Simplifying:
x = (5 ± √(25 + 8)) / 2
x = (5 ± √33) / 2
Therefore, the solutions to the quadratic equation x² - 5x - 2 = 0 are:
x = (5 + √33) / 2
x = (5 - √33) / 2
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Beverly is starting a new diet. Her current weight is 160 pounds. She expects to lose 4 pounds per month. If x represents the number of months Beverly is on the diet, which linear function models the situation?
What is the least common denominator of the equation StartFraction 2 Over 9 EndFraction x + two-thirds x = 7?
3
Answer:
9 is the least common denominator for the given equationStep-by-step explanation:
Given equation is StartFraction 2 Over 9 EndFraction x + two-thirds x = 7.
It can be written as [tex]\frac{2}{9}x+\frac{2}{3}x=7[/tex]
To find the least common denominator for the given equation :That is to find the Least common Multiple of the denominators.
[tex]\frac{2}{9}x+\frac{2}{3}x=7[/tex]
[tex]\frac{2x+2x(3)}{9}=7[/tex] ( here LCM of 9 and 3 is 9 so we take 9 as LCM )
Therefore 9 is the least common denominator for the given equationAnswer: the answer is 9
Step-by-step explanation: I took the test and its right
Annie is working furiously to knit scarves and beanies for a craft fair next weekend. Yesterday she completed 3 scarves and 2 beanies, using a total of 22 meters of yarn. The day before, she used 10 meters to knit 1 scarf and 2 beanies. Assuming Annie is using the same pattern and type of yarn for each scarf and beanie, how much yarn does each project require?
Annie uses 6 meters of yarn for each scarf and 2 meters for each beanie, based on creating a system of equations from the given data and solving it.
Explanation:The student is asking to solve a system of equations to find out how much yarn is required for each scarf and beanie that Annie is knitting. To determine the amount of yarn needed for each project, we will use the information given for two separate days. On the first day, 3 scarves and 2 beanies used a total of 22 meters of yarn. On the second day, 1 scarf and 2 beanies used a total of 10 meters of yarn. Let's denote the amount of yarn needed for a scarf by 'S' and for a beanie by 'B'.
We can set up the following system of equations:
3S + 2B = 22 (from the first day's work)1S + 2B = 10 (from the second day's work)Subtract the second equation from the first to eliminate 'B' and solve for 'S':
(3S + 2B) - (1S + 2B) = 22 - 102S = 12S = 6 metersNow, we can substitute 'S' back into the second equation to solve for 'B':
1(6) + 2B = 106 + 2B = 102B = 4B = 2 metersTherefore, each scarf requires 6 meters of yarn and each beanie requires 2 meters of yarn.
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On a field trip there are 18 chaperones supervising 81 children. If the children are broken into groups how many adults are needed for a group of 27 kids
Answer:
6
Step-by-step explanation:
you first divide 81 by 18 and get 4.5, that is the number of children per adult.
next you'll divide 27 by 4.5 and 6.
that's the answer.
Final answer:
With an initially provided ratio of 18 adults for 81 children, the simplified ratio is 1 adult for every 4.5 children. Hence, for a group of 27 kids, 6 adults are needed to maintain the same supervision ratio.
Explanation:
To determine the number of adults needed for a group of 27 kids on a field trip when there are 18 chaperones supervising 81 children, we can calculate the adult-to-child ratio. We start with the given total ratio of 18 adults for 81 children. This simplifies to 1 adult for every 4.5 children, as 81 divided by 18 equals 4.5. Therefore, for a group of 27 children, we divide 27 by 4.5 to find the number of adults needed.
27 kids
/ 4.5 kids/adult = 6 adults
Thus, 6 adults are needed for a group of 27 kids to maintain the same supervision ratio.
What’s the remainder of 84 divided by 25
Answer:
remainder is 9
Step-by-step explanation:
remainder of 84 divided by 25multiples of 25 are:
25 , 50 , 75
84-75 = 9
remainder is 9
Answer:
The remainder is 9
Step-by-step explanation:
Step 1: Find the remainder
84/25
25 goes into 84 3 times.
84 - 3(25)
84 - 75
9
Answer: The remainder is 9
could someone please help me with 20.7 divided by 1.5
Answer:
13.8
Step-by-step explanation:
First, lets convert to fraction
20.7 = 207/ 10
1.5 = 15/10
therefore,
20.7 / 1.5 becomes;
(207/10) / (15/10)
this becomes;
(207/10) * (10/15)
10 cancels out
= 207/15
Divide both numerator and denominator by 3
=69/5
=13.8
Which statement is true about the factorization of 30x^2 + 40xy + 51y^2
The factorization of 30x^2 + 40xy + 51y^2 over the integers appears not to be possible due to the coefficients and a discriminant that is unlikely to be a perfect square. Advanced methods may be needed to factorize it if at all possible.
Explanation:The factorization of the expression 30x^2 + 40xy + 51y^2 is a task in algebra, which involves breaking down the given quadratic expression into products of its factors. However, this specific expression does not factorize neatly over the integers. When factoring, one would typically look for two binomials that multiply to the quadratic expression, but in this case, due to the coefficients and the lack of a clear common factor or a pattern that matches a known factoring formula, it is likely that the quadratic expression cannot be factored over the rational numbers without resorting to more advanced techniques or numerical methods. To completely verify this, you would use the quadratic formula to find the roots of the corresponding quadratic equation and see if they are rational numbers. If they are not, then exact factoring over the rationals is impossible.
Remember, for a quadratic expression ax^2+bx+c to be factorizable over the rationals, the discriminant, which is b^2-4ac, must be a perfect square. In the case of 30x^2 + 40xy + 51y^2, calculating the discriminant may help determine the factorizability of the expression. If the discriminant is not a perfect square, the expression cannot be factored into rational factors.
What is the answer to 7x=3x+24
Answer:
7x=3x+24
4x=24
x=6
Answer:
[tex]x=6\\[/tex]
Step-by-step explanation:
[tex]7x=3x+24[/tex]
[tex]7x-3x=3x-3x+24[/tex]
[tex]4x=24[/tex]
[tex]\frac{4x}{4} =\frac{24}{4}[/tex]
[tex]x=6[/tex]
the answer to this equation is negative 6 but I don’t know to explain how I got the answer is word form.
The value of k is –6.
Solution:
Given equation:
[tex]$\frac{5 \cdot 5^{k}}{5^{-8}}=5^{3}[/tex]
To find the value of k:
[tex]$\frac{5 \cdot 5^{k}}{5^{-8}}=5^{3}[/tex]
Using exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]
[tex]$\frac{5^{1+k}}{5^{-8}}=5^{3}[/tex]
Using exponent rule: [tex]\frac{1}{a^{-m}} = a^{m}[/tex]
[tex]$ 5^{1+k} \cdot 5^{8}=5^{3}[/tex]
Using exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]
[tex]$ 5^{1+k+8}=5^{3}[/tex]
[tex]$ 5^{k+9}=5^{3}[/tex]
If the bases are same then, we can equate the powers of the bases.
i. e. If [tex]a^m = a^n[/tex] then m = n.
k + 9 = 3
Subtract 9 from both sides of the equation, we get
k = –6
Hence the value of k is –6.
$8 buys 40 ounces of ground turkey
We see here that $1 will buy 5 ounces of ground turkey.
To find out how much $1 will buy, we can set up a proportion using the given information.
We know that $8 buys 40 ounces of ground turkey. Let's set up the proportion:
$8/40 ounces = $1/x ounces
To solve the proportion, we can cross-multiply:
$8 × x ounces = 40 ounces * $1
Simplifying further:
$8x = $40
To isolate x (the number of ounces that $1 will buy), we can divide both sides of the equation by $8:
x = $40 / $8
x = 5 ounces
Therefore, $1 will buy 5 ounces of ground turkey.
Alternatively, we can set up a ratio using the given information:
$8 for 40 ounces
To find out how much $1 will buy, we can find the unit price:
Unit price = Total cost / Total quantity
Unit price = $8 / 40 ounce
Unit price = $0.20 per ounce
Since $1 is equal to 100 cents, we can divide $1 by the unit price:
$1 / $0.20 per ounce = 5 ounces
Therefore, $1 will buy 5 ounces of ground turkey.
Complete question:
$8 buys 40 ounces of ground turkey, how much will $1 buy?
A 2/3 foot board is cut to 7/16 of its original length. What is its new length?
Answer:
7/24 feet.
Step-by-step explanation:
That would be 7/16 of 2/3
= 2/3 * 7/16
= 14/48
= 7/24 feet.
The new length of the board after being cut to 7/16 of its original length is 7/24 foot.
Explanation:Yes, the thing you need to understand here is that you've to multiply the length of the board by the fraction given to find the new length. So, in this problem, the original length of the board was 2/3 foot and it was cut to 7/16 of its original length. Hence, to find the new length, you multiply 2/3 foot by 7/16.
This results in 14/48 foot, which when simplified/reduced gives 7/24 foot. Therefore, the new length of the board after it is cut is 7/24 foot.
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3x - 2y = 3; 6x – 4y = 1
How many solutions ?
Answer:
It has no solution
Step-by-step explanation:
3x - 2y = 3
6x - 4y = 1
To fond the number of solutions, we will first of all solve this system of equation.
We can solve this system of equation by either substitution method or elimination method or both method
We will be using both method to solve this system of equation.
3x - 2y = 3 ------------------------------------(1)
6x - 4y = 1 ------------------------------------(2)
we will first eliminate y, to do that, lets multiply equation (1) by 4 and then multiply equation(2) by 2
12x - 8y = 12 ----------------------------------(3)
12x - 8y = 2 ------------------------------------(4)
Subtract equation (4) from equation (3)
0 = 10
But 0≠ 10
This system of equation has no solution
Answer:
No solution.
Step-by-step explanation:
3x-2y=3
6x-4y=1, or 2(3x-2y)=1, 2×3=1, 6=1
Since 6 cannot be equal to 1, this system of equations has no solution
Find the slope of the line that passes through points (4,5) and (-1,3)
A.)5/2
B.) 1/6
C.)2/5
D.)-5/2
Answer:
C - 2/5
Step-by-step explanation:
Using the formula for slope
m = (y_2 - y_1) / (x_2 - x_1)
Given two points
( 4 , 5) (-1 , 3)
x_1 = 4
y_1 = 5
x_2 = -1
y_2 = 3
Insert the values into the equation
m = (y_2 - y_1) / (x_2 - x_1)
m = ( 3 - 5) / ( -1 - 4)
= -2 / -5
- $ - cancels out
m = 2/5
Slope = m = 2/5
if f(x)=2(x)^2+5sqrt(x+2) complete the following statement f(2)=
Solution:
Given that,
[tex]f(x) = 2x^2 + 5\sqrt{x + 2}[/tex]
We have to find f(2)
To find f(2), plug in x = 2 in given f(x) and solve to get the answer
Plug in x = 2 in f(x)
[tex]f(2) = 2(2)^2 + 5 \sqrt{2+2}\\\\f(2) = 2 \times 4 + 5\sqrt{4}\\\\Simplify\\\\f(2) = 8 + 5 \times 2\\\\f(2) = 8 + 10\\\\f(2) = 18[/tex]
Thus the value of f(2) is 18
please help me!!!!!!!
Answer:
-63
You say PEMDAS I say BIDMAS. So first you gotta do brackets. So -25 + 4². To do this you need to find out 4² = 16. -25 + 16 = -9. Now -9 x 7 = -63
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Roman reign vs Golberg who win match in wrestlemania
Answer:
Is this a book ????
Step-by-step explanation:
but roman
The winner of a match between Roman Reigns and Goldberg at WrestleMania is predetermined by WWE's creative team based on storytelling needs and is not an actual competitive event.
The outcome of a wrestling match between Roman Reigns and Goldberg at WrestleMania would depend on the storytelling and booking decisions made by the WWE's creative team.
Wrestling matches are choreographed and the winners are predetermined for entertainment purposes. Thus, it's not possible to predict who would win in a real competition since the outcomes are planned.
However, looking at both wrestlers' track records and their standing with the WWE at the time of your question could give us an idea of who the company might favor to write as the victor.
Ming throws a stone off a bridge into a river below.
The stone's height (in meters above the water), 3 seconds after Ming threw it, is modeled by:
h(x) = -5(x - 1)2 + 45
How many seconds after being thrown will the stone reach its maximum height?
Please help!
Answer:
In 1 seconds after being thrown will the stone reach its maximum height.
Step-by-step explanation:
Given : Ming throws a stone off a bridge into a river below. The stone's height (in meters above the water), 3 seconds after Ming threw it, is modeled by : [tex]h(x) = -5(x - 1)^2 + 45[/tex].
To find : How many seconds after being thrown will the stone reach its maximum height?
Solution :
The maximum height is attain by getting the vertex of the model.
The vertex form of the quadratic equation or parabola is
[tex]f (x) = a(x - h)^2+ k[/tex]
Where, (h,k) are the vertex.
On comparing with the given model, [tex]h(x) = -5(x - 1)^2 + 45[/tex]
a=-5, h=1 and k=45
The vertex of the equation is (h,k)=(1,45).
Now the maximum height is 45 m and number of second is 1 sec.
Therefore, In 1 seconds after being thrown will the stone reach its maximum height.
A circle has a radius of 14 feet. What it’s area
Answer:
6.157
Step-by-step explanation:
A=πr^2=π·14^2≈615.75216
Select all the complex numbers in the given table
The complex number from the table are
[tex]1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}[/tex]
Solution:
Let us solve and identify the complex number.
(A) [tex]5-\sqrt{\frac{9}{4}}[/tex]
[tex]5-\sqrt{\frac{9}{4}}= 5-\sqrt{\frac{3^2}{2^2}}[/tex]
[tex]= 5-\frac{3}{2}[/tex]
= 3.5
This is not a complex number.
(B) [tex]1+\sqrt{-3}[/tex]
[tex]1+\sqrt{-3}=1+\sqrt{-1\times 3}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]1+\sqrt{-3}=1+\sqrt{3}i[/tex]
This is a complex number.
(C) [tex]4-3 \sqrt{-16}[/tex]
[tex]4-3 \sqrt{-16}=4-3 \sqrt{-1\times 4^2}[/tex]
[tex]4-3 \sqrt{-16}=4-3\times4 \sqrt{-1}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]4-3 \sqrt{-16}=4-12i[/tex]
This is a complex number.
(D) [tex]\frac{2-\sqrt{12}}{5}[/tex]
[tex]\frac{2-\sqrt{12}}{5}=\frac{2-2\sqrt{3}}{5}[/tex]
There is no –1 in the root.
This is not a complex number.
(E) [tex]\frac{3+2 \sqrt{-9}}{7}[/tex]
[tex]\frac{3+2 \sqrt{-9}}{7}=\frac{3+2 \sqrt{-1\times 3^2}}{7}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]=\frac{3+6i}{7}[/tex]
This is a complex number.
(F) [tex]9 \sqrt{-\frac{7}{5}}[/tex]
[tex]9 \sqrt{-\frac{7}{5}}=9 \sqrt{-1 \times \frac{7}{5}}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]9 \sqrt{-\frac{7}{5}}=9 \sqrt{ \frac{7}{5}}i[/tex]
This is a complex number.
Hence the complex number from the table are
[tex]1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}[/tex]
Eduardo and Sarawong are selling wrapping paper for a school fundraiser. Eduardo sold 5 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for a total of $185. Sarawong sold 14 rolls of plain and 5 rolls of holiday for a total of $338. Find the cost per roll of plain wrapping paper and 5 rolls of holiday wrapping paper.
Answer: A roll of plain wrapping paper costs $17, while a roll of holiday wrapping paper costs $20.
Step-by-step explanation: First let us represent a roll of plain wrapping paper with letter p and a roll of holiday wrapping paper would be represented by d. If Eduardo sold 5 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for $185, then we can express this as
5p+ 5d= 185
Also if Sarawong sold 14 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for $338, then this too can be expressed as
14p + 5d = 338
Now we have a pair of simultaneous equations which are,
5p + 5d = 185 ———(1)
14p + 5d = 338 ———(2)
Since all the variables have coefficients greater than 1, we shall use the elimination method. Note that the coefficients of the d variable are both 5, so straight away we subtract equation (1) from equation (2) and we now have;
(14p - 5p) + (5d - 5d) = 338 - 185
9p = 153
Divide both sides of the equation by 9
p = 17
Having calculated p, we can now substitute for the value of p into equation (1)
5p + 5d = 185
5(17) + 5d = 185
85 + 5d = 185
Subtract 85 from both sides of the equation
5d = 100
Divide both sides of the equation by 5
d = 20
Hence, the cost per roll of plain wrapping paper is $17, while the cost per roll of holiday wrapping paper is $20.