Vector A and B are at right angles and have the same initial point. Find the magnitude and direction from vector A of the resultant vector.
Answers
We need to find the magnitude and direction from vector A of the resultanr vector.
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Write the equation, in standard form, of the parabola containing the following points: (0, 1), (1, 5), (2, 3). You must set up a system of three equations to get credit for this question.
Answers
The equation of the parabola for the given points is y = -3x² + 7x + 1
Equation of the parabola
The standard form of the equation of a parabola is expressed as
y = f(x) = ax² + bx + c
where a, b, and c are constants and a ≠ 0.
Given,
Here we have the points (0, 1), (1, 5), (2, 3).
Now, we have to find the equation of the parabola.
Here we are given three coordinates (0, 1), (1, 5), and (2, 3) which lie on the parabola and which means that it satisfies the parabolic equation.
In order to find the values of a, b and c we need to formulate three equations using the three given points.
Since for the three unknowns a, b, and c, we will require three equations.
For that we have to take the Point (0,1) i.e. x = 0 and y = 1
Substituting the values of x and y in the standard parabola equation, then we get,
1 = a(0)² + b(0) + c
1 = 0 + 0 + c
c = 1 -------------------(1)
Next, we have to take the Point (1, 5) i.e. x = 1 and y = 5
Substituting the values of x and y in the standard parabola equation, then we get,
5 = a(1)² + b(1) + c
5 = a + b + c
It can be written as,
a + b + c = 5 -----------------------------(2)
Finally, we have to take the Point (2, 3) i.e. x = 2 and y = 3
Substituting the values of x and y in the standard parabola equation, then we get,
3 = a(2)² + b(2) + c
3 = 4a + 2b + c
It can be written as,
4a + 2b + c = 3 -----------------------------(2)
Apply the value of c as 1 in equation (2), then we get,
a + b + 1 = 5
a + b = 4 ---------------------(4)
Similarly, apply the value of c on the equation (3), then we get,
4a + 2b + 1 = 3
4a + 2b = 2
Divide the equation by 2 on both sides, then we get,
2a + b = 1 --------------------(5)
Subtract equation (5) from equation (4),
(2a - a) +(b - b) = 1 - 4
a = -3
Apply the value of a in the equation (4) to get the value of b,
(-3) + b = 4
b = 7
Therefore, the equation of the parabola is
y = -3x² + 7x + 1
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Growing linearly, the balance owed on your credit card doubles from $600 to $1200 in 6 months. If the balance were growing according to the exponential function f(x)=600(1+0.1220)^x where x represents the number of months, what would the balance be after 6 months? Round your answer to the nearest cent.
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Evaluate the given expression at x=6. This is, replace every x in the equation for 6 and solve:
[tex]\begin{gathered} f(6)=600(1+0.1220)^6 \\ f(6)=600(1.1220)^6 \\ f(6)=600\cdot(1.99506) \\ f(6)=1197.04 \end{gathered}[/tex]The balance after 6 months is 1197.04.
Maleri Designs sells cartons of cloth face masks ($10) and cartons of hand-sanitizer ($4) on eBay. One of their
customers, Mod World, purchased 24 cartons for $210. How many of cartons of each did Mod World purchase?
Check your answer. Hint: Let F = Face masks.
Answers
Number of cartons of cloth face masks purchased will be 19 and number of cartons of hand-sanitizer purchased will be 5.
We had given that Maleri Designs sells cartons of cloth face masks ($10) and cartons of hand-sanitizer ($4) on eBay.
Also given that Mod World, purchased 24 cartons.
Let number of cartons of cloth face masks be x and let number of cartons of hand-sanitizer be y.
As total carton purchased is 24.
∴ x + y = 24 --(1)
also Mod World, purchased 24 cartons for $210.
∴ Also price of cartons of cloth face masks is $10 and cartons of hand-sanitizer is $4 which is buyed at $210.
∴ 10x + 4y = 210 --(2)
Now multiplying equation (1) by 10
∴ 10x + 10y = 240 --(3)
Now subtracting (2) from (3) by simplification
∴ y = 5
∴ x = 19
Number of cartons of cloth face masks purchased will be 19 and number of cartons of hand-sanitizer purchased will be 5.
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H-4/j=k for help
Please
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Given:
The expression is 2p +5r = q.
The objective is to solve for p.
Explanation:
For the value of p, the expression can be solved as,
[tex]\begin{gathered} 2p+5r=q \\ 2p=q-5r \\ p=\frac{q-5r}{2} \end{gathered}[/tex]Hence, the expression for p is, (q-5r)/2.
Find the x - and y-intercepts of the graph of the linear equation 3x - y = 2. The x-intercept is The y-interceptis
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• x-intercept can be found by letting y equal to 0.
,• y-intercept can be found by letting x equal to 0.
X intercept is the x-axis cutting point of the graph.
Y intercept is the y-axis cutting point of the graph.
The equation given is:
[tex]3x-y=2[/tex]First, finding x intercept (let y = 0):
[tex]\begin{gathered} 3x-y=2 \\ 3x-0=2 \\ 3x=2 \\ x=\frac{2}{3} \end{gathered}[/tex]Second, find y intercept (let x = 0):
[tex]\begin{gathered} 3x-y=2 \\ 3(0)-y=2 \\ 0-y=2 \\ y=-2 \end{gathered}[/tex]Hence,
x-intercept: x = 2/3y-intercept: y = -2Is my answer correct?
Answers
Answer:
Of course it is
Step-by-step explanation:
In the expression: 9 + 3y + 6 + y
Combining like terms, the expression becomes: 3y + y + 9 + 6
Final answer: 4y + 15 which is option B
So you're correct
The weights of four puppies are shown in pounds. 9.5, 9 3/8, 9.125, 9 3/4 Which list shows these weights in order from greatest to least?
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The data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.
What is Descending order?Any data, including numbers, alphabets, amounts, lengths, etc., are arranged in descending order from highest to lowest.
In other terms, anything is considered to be in descending order when it is arranged from a higher value to a lower value. It is possible to arrange numbers in descending order, including whole numbers, natural numbers, integers, fractions, and decimals.
For example 7, 3, 9, 2 in decreasing order, for instance. Starting with the biggest number, we'll work our way down to the lesser ones one at a time. When these numbers are listed in descending sequence, they are written as 9, 7, 3, and then 2.
Given data:
9.5, 9 3/8, 9.125, 9 3/4
Now, simplifying the mixed fraction as
9 3/8
=75/8
= 9.375
9 3/4
=39/4
= 9.75
Thus, we have the data in decimal form
9.5, 9.375, 9.125, 9.75
Hence, the data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.
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Rosa uses 1/2 of a cup of vinegar in her salad dressing recipe. How
much vinegar would Rosa use to make 1/3 of a recipe?
Answers
Answer:
1/6
Step-by-step explanation:
1/2 1/3
lcd(least common denomitator)=6
there fore it is 1/6
A map has a scale of 1:2500. On the map a reservoir has an area of 2cm2.
what is the area of the reservoir? give your answer in m2
Answers
The actual area of the reservoir in m² as required in the task content is; 0.5m².
Conversions using scale factors.It follows from the task content that the actual area of the reservoir is to be determined.
Hence, since it is given that the area of the reservoir on the map is 2cm² and the map has a scale of 1: 2500.
Hence, it follows from proportions that the area of the reservoir is; 2cm² × 2500 = 5000cm².
However, when expressed in m²; the actual area of the reservoir is; 5,000/10000 = 0.5m².
Ultimately, the area of the reservoir in m² is; 0.5m².
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Where is the result of combining the terms represented by the titles below?A. x^2+x-5B. x^2+2x+1C. x+1D. x+5
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if we take the black boxes as representation of negative numbers, and the white boxes as a representation of positive numbers, then we get:
[tex]-x^2+x-x-x+1+1+1+1-1+x^2-1-1+x+x[/tex]after combining the similar terms we get:
[tex](-x^2+x^2)+(x-x-x+x+x)+(1+1+1+1-1-1-1)=x+1[/tex]therefore, the final expression is x + 1
PLEASE HELP The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 17 HCF of water is $32.13 and the cost for using 35 HCF IS 61.83. . What is the cost for using 19 HCF of water?
Answers
Based on the system of equations, the cost of using 19 HCF of water is $35.43
What is an equation?An equation is a mathematical statement that two or more values are equivalent.
Equations are stated to show that two mathematical expressions are equal using the equation sign (=).
Cost of using 17 HCF of water = $32.13
Cost of using 35 HCF of water = $61.83
Total cost of 17 HCF water = 17x + a
17x + a = 32.13 ... equation 1
Total cost of 35 HCF water = 35x + a
35x + a = 61.83 ... equation 2
Subtract equation 1 from equation 2:35x + a = 61.83
-17x + a = 32.13
18x = 29.70
18x = 29.7
x = 29.7/18
x = 1.65
Find a:17x + a = 32.13 ... equation 1
17(1.65) + a = 32.13
28.05 + a = 32.13
a = 4.08 (32.13 - 28.05)
The cost of 19 HCF of water:= 19(1.65) + 4.08
= $35.43
Thus, using the equations above, we can conclude that 19 HCF of water costs $35.43.
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12 and 3/8 simplified
Answers
Answer:
(99/8)
Step-by-step explanation:
3
12 -------
8
8 × 12 = 96
96 + 3 = 99
99
-------
8
I hope this helps!
because 12x8=96 and 96+3=99 and it’s over 8
P (0.3 < Z < 1.4) =0.30130.14030.91921.4014
Answers
Answer
P (0.3 < Z < 1.4) = 0.3013
Explanation
P (0.3 < Z < 1.4) = P (0 < Z < 1.4) - P (0 < Z < 0.3)
P (0.3 < Z < 1.4) = 0.4192 - 0.1179
P (0.3 < Z < 1.4) = 0.3013
3 sailboats to 5 fan boatsHow many fan boats if therewere 54 sailboats?
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we can use cross multiplication
[tex]\begin{gathered} 3\text{sail}\longrightarrow5\text{fan} \\ 54\text{sail}\longrightarrow\text{xfan} \end{gathered}[/tex]where x is the number of fan boats
[tex]\begin{gathered} x=\frac{54\times5}{3} \\ \\ x=90 \end{gathered}[/tex]the number of fan boats to 54 sailboats is 90
Select the table that represents a linear function. (Graph them if necessary.)
Answers
Step-by-step explanation:
any linear function represents a straight line (hence the name) and is therefore of the structure
y = f(x) = ax + b
"a" is the slope of the line, and it is represented by the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another point.
"b" is the y-intercept (the y-value when x = 0).
so, let's look at the answer options :
A.
x = 0 gives us b (the y value) : 2
so, then for x = 1, y = 3 ?
3 = a×1 + 2
a = 1
now, the next point must be also on the same line for the whole function to be linear (and that means the equation has to be true for all numbers involved) :
x = 2, y = 6
6 = 1×2 + 2 = 4
6 is for sure NOT 4, so this is not a linear function.
it is actually y = x² + 2
B.
x = 0 gives us b : 1
for x = 1, y = 3 ?
3 = a×1 + 1
a = 2
again, the next point must be on the same line :
x = 2, y = 9
9 = 2×2 + 1 = 5
9 is for sure NOT 5, so this is not a linear function.
it is actuality y = 3^x.
C.
x = 0 gives us b : 0
for x = 1, y = 1 ?
1 = a×1 + 0 = a
a = 1
the next point :
x = 2, y = 4
4 = 1×2 = 2
4 is for sure NOT 2, so this is not a linear function.
it is actually y = x².
D.
x = 0 gives us b : 3
for x = 1, y = 9
9 = a×1 + 3
a = 6
the next point(s) must fit :
x = 2, y = 15
15 = 6×2 + 3 = 12 + 3 = 15
correct
x = 3, y = 21
21 = 6×3 + 3 = 18 + 3 = 21
correct
yes, this is a linear function.
it is y = 6x + 3
If theta is in quadrant II and cos theta= -3/5, what is sin 2 theta + cos 2 theta?
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ANSWER
sin(2θ) + cos(2θ) = -31/25 = -1.24
EXPLANATION
If we do the inverse of the cosine to -3/5 we would get the angle θ. Then we can know the value of the sine:
[tex]\sin \theta=\sin (\cos ^{-1}(-\frac{3}{5}))=\frac{4}{5}[/tex]So we have:
• sin(θ) = 4/5
,• cos(θ) = -3/5
To find sin(2θ) + cos(2θ) we'll have to use the trigonometric identities:
[tex]\begin{gathered} \sin 2\theta=2\sin \theta\cos \theta \\ \cos 2\theta=1-2\sin ^2\theta \end{gathered}[/tex]Since we have the sine and cosine of theta, we can solve this:
[tex]\sin 2\theta=2\cdot\frac{4}{5}\cdot(-\frac{3}{5})=-\frac{24}{25}[/tex][tex]\cos 2\theta=1-2(\frac{4}{5})^2=1-2\cdot\frac{16}{25}=1-\frac{32}{25}=-\frac{7}{25}[/tex]The sum is:
[tex]\sin 2\theta+\cos 2\theta=-\frac{24}{25}-\frac{7}{25}=-\frac{31}{25}=-1.24[/tex]a child is covering a square board with mosaic tiles the board is 40×40cn each tile is 2 cm ×2 cm how many mosaic tiles are needed for one complete now
Answers
Answer:
Step-by-step explanation:
The area of the floor is 4×3=12 sqare meters
=12×100×100= 120000 square centimetres.
Area of each tile is 20×20=400 square centimetres.
Therefore number of tiles required will be
120000÷400 =300.
300 tiles will be required to cover the floor.
A family budget estimator shows that the Richardson family would need 990272a year to live within their budget in Athens, Texas. If Mrs. Richardson works a 22-hour week and Mr. Richardson works a 40-hour week, how much hourly incomecould they both eam to live within their budget in Athens?
Answers
Mrs. Richardson and Mr. Richardson have to make their hourly income 306.314 to live within their budget in Athens.
What is income?
Income is the amount of money that an individual or an organization gets in return for their services or goods offered. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.
Given in the question,
The Richardson family needs 990272 per year to in their budget.
Mrs. Richardson works 22 hours a week.
Mr. Richardson works 40hours a week.
We need to calculate their hourly income.
Lets first calculate total weeks in a year.
We know that, a year has 365 days and a week has 7
So, total no. of weeks in a year = 365/7 = 52.143 weeks.
no. of weeks in a year = 52.143 weeks
Their weekly income = yearly income/no. of weeks in a year
So, weekly income = 990272/52.143
weekly income = 18991.466
Their hourly income = weekly income/working hours per week
Their weekly income is 18991.466 and,
working hours = 22 + 40 = 62 hours.
Their hourly income = 18991.466/62
Hourly income = 306.314
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how do you write 4.501795324E^-6 in simpler form
Answers
Answer: you cant but here are some ways to practice:)
Find the greatest common divisor of both the numerator and the denominator. This can be done either with prime factor trees or another method.
Divide both the numerator and the denominator with the greatest common divisor.
The result is a simplified fraction. hope this helps and sorry.
Amy wants to save $500 to buy a TV. She saves $17 each week. The amount, A (in dollars), that she still needs after w weeks is given by the following function.
A (w) = 500 - 17w
(a). How much money does Amy still need after 7 weeks?
(b). If Amy still needs $211, how many weeks has she been saving?
Answers
After 7 weeks she would have the total of 119$
A. $381
B. 17 weeks
500-211=289/17=17
in a class of 34 students 19 of them are girls what percentage of the class are girls give you answer to one decimal place
Answers
In class of 34 students, 19 of them are girls, then the percentage of girls in the class is 55.9%
The total number of students in the class = 34
Number of girls in the class = 19
The percentage is defined as the ratio that can be expressed as the fraction of 100. The percentage is often represented using the percentage sign "%"
The percentage of girls in the class = (Number of girls in the class/The total number of students in the class) ×100
Substitute the values in the equation
The percentage of girls in the class = (19/34)×100
= 0.559×100
= 55.9%
Hence, in class of 34 students, 19 of them are girls, then the percentage of girls in the class is 55.9%
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Solve the compound inequality -8≤x+4<5
Answers
Answer:
-12≤x<1
Step-by-step explanation:minus both side by 4
Please help me. I know I’m solving for the principal but need help with the steps
Answers
Given: The information below
[tex]\begin{gathered} time(t)=5\text{years} \\ rate(r)=4\%=0.04 \\ Interest(I)=40 \end{gathered}[/tex]To Determine: How much Austine invested
Solution
Please note that the amount invested is the Principal
The formula combining principal, rate, time and interest for simple interest is
[tex]I=\text{Prt}[/tex]Make P the subject of the formula
[tex]P=\frac{I}{rt}[/tex]Substitute for I, r and t given into the formula as shown below
[tex]\begin{gathered} P=\frac{40}{0.04\times5} \\ P=\frac{40}{0.2} \\ P=200 \end{gathered}[/tex]Hence, the amount invested by Austine is $200
1.Which expression is equivalent to (92)8?A. -81321B.9161C.9 10D.818
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Given the standard form:
[tex]\begin{gathered} 5\times10^{-4} \\ \end{gathered}[/tex]This can be expressef as a decimal by shifting the decimal point to the back 4 times (since the power is a negative 4) as shown:
[tex]\begin{gathered} 0.0005 \\ \end{gathered}[/tex]Hence the equivalent value for the standard form is 0.0005. Option B is correct
find n(A) for the following set A:{x : x is a letter in the word "nonintervention"} n(A) = _________
Answers
Given,
{x : x is a letter in the word "nonintervention"}
A={x : x is a letter in the word "nonintervention"}
The roster form of the set is,
A={e, i, n, o, v, t, r}
The number of elements in the set A is,
n(A)=7
Hence, the number of elements in the set A is 7.
simplify 5/7 x + 2/7 y − 2 − 1/7 x + 7
Answers
The simplification of the given expression would be; 4x/7 + 2y /7 + 5.
What is a simplification of an expression?Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
We have been given an expression as 5/7 x + 2/7 y − 2 − 1/7 x + 7
Thus,
5/7 x + 2/7 y − 2 − 1/7 x + 7
Combine the like terms first;
5/7 x − 1/7 x + 2/7 y − 2+ 7
Then solve the like terms;
(5 -1)x/7 + 2y /7 + 5
4x/7 + 2y /7 + 5
Therefore, the simplification of the given expression would be; 4x/7 + 2y /7 + 5.
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Expand (x-3)^5 using the vi al theorem and Pascal’s triangle. Show all the steps
Answers
Given:
[tex](x\text{ - 3\rparen}^5[/tex]To find:
To expand the expression using binomial's theorem
To expand, we will apply the binomial theorem formula:
[tex](x\text{ + y\rparen}^n=\text{ }^nC_0x^n\text{ + }^nC_1x^{n-1}y\text{ + }^nC_2x^{n-2}y^2+.\text{ . . + }^nC_ny^n[/tex][tex]\begin{gathered} (x\text{ - 3\rparen}^5\text{ = }^5C_0x^5\text{ + }^5C_1x^{5-1}y\text{ + }^5C_2x^{5-2}y^2+\text{ }^5C_3x^{5-3}y^3\text{ + }^5C_4x^{5-4}y^4\text{ + }^5C_5y^5 \\ \\ We\text{ will use pascal's triangle to get the coefficient of the terms.} \\ The\text{ coefficients represents the value of the combinations} \\ \\ The\text{ pascals triangle coefficients for power of 5 = 1 5 10 10 5 1} \end{gathered}[/tex][tex]\begin{gathered} (x\text{ - 3\rparen}^5\text{ = \lparen1\rparen}x^5\text{ + \lparen5\rparen}x^{5-1}y\text{ + \lparen10\rparen}x^{5-2}y^2+\text{ \lparen10\rparen}x^{5-3}y^3\text{ + \lparen5\rparen}x^{5-4}y^4\text{ + \lparen1\rparen}y^5 \\ \\ y\text{ = -3} \\ (x\text{ - 3\rparen}^5\text{ = \lparen1\rparen}x^5\text{ + \lparen5\rparen}\times x^4\times(-3)\text{ + \lparen10\rparen}\times x^3\times(-3)^2+\text{ \lparen10\rparen}\times x^2\times(-3)^3\text{ + \lparen5\rparen}\times x^1\times(-3)^4\text{ + \lparen1\rparen\lparen-3\rparen}^5 \\ \\ (x\text{ - 3\rparen}^5\text{ = }x^5\text{ -15}x^4\text{ + 90}x^3-27\text{0}x^2\text{ + 405}x^1\text{ -243} \end{gathered}[/tex]The expansion becomes:
[tex](x\text{ - 3\rparen}^5\text{ = }x^5\text{ - 15}x^4\text{ + 90}x^3-27\text{0}x^2\text{ + 405x - 243}[/tex]help me I'm practicing
Answers
we calculate the area of one trangle and multiply by 2
we apply formula of the triangle area
[tex]A=\frac{b\times h}{2}[/tex]where b is the base and h the height of the triangle
then replacing
[tex]\begin{gathered} A=\frac{6\times5.2}{2} \\ \\ A=15.6 \end{gathered}[/tex]area of one triangle is 15.6square centimeters
Area of both triangles
[tex]\begin{gathered} 15.6\times2 \\ =31.2 \end{gathered}[/tex]Area of the two triangle bases is 31.2 square centimeters
Yea I do it all right I just got the one
Answers
Answer:
[tex]v_0=20.7\frac{m}{s}[/tex]
Explanation:
We are given the equation for the height:
[tex]h(t)=10+v_0t-4.9t^2[/tex]If we differentiate this equation, we get the equation of the velocity:
[tex]h^{\prime}(t)=v(t)=v_0-9.8t[/tex]The problem tells us that the object hits the ground at a velocity of -25m/s. We can write this:
[tex]-25=v_0-9.8t_0[/tex]Where t0 is the time when the object hits the ground, and the velocity is -25m/s
Now, we can solve for v0:
[tex]v_0=9.8t_0-25[/tex]And if we use this in the height h(t) equation, we can find the value of t0. At t0, the height is 0. Thus:
[tex]0=10+(9.8t_0-25)t_0-4.9t_0^2[/tex]And solve:
[tex]\begin{gathered} 0=10+9.8t_o^2-4.9t_0^2-25t_0 \\ 0=10-25t_0+4.9t_0^2 \end{gathered}[/tex]Next, we can use the quadratic formula to solve this:
[tex]\begin{gathered} t_{\pm}=\frac{-(-25)\pm\sqrt{(-25)^2-4\cdot4.9\cdot10}}{2\cdot4.9}=\frac{25\pm\sqrt{625-196}}{9.8}=\frac{25\pm\sqrt{429}}{9.8}=\frac{25\pm20.71231}{9.8} \\ . \\ t_+=\frac{25+20.71231}{9.8}=4.664521seconds \\ . \\ t_-=\frac{25-20.71231}{9.8}=0.43751seconds \end{gathered}[/tex]Let's see which of the two solutions is the time we are looking for.
Let's go back to our solution for v0:
[tex]v_0=9.8t_0-25[/tex]If we use t0 = 0.43751 s:
[tex]v_0=9.8\cdot0.46751-25=-20.7123m/s[/tex]This means that the initial velocity is negative, thus the object goes downwards. But, the problem tells us that initially the object is thrown upwards.
The correct value of t0 = 4.66 seconds
Now we can find v0:
[tex]v_0=9.8\cdot4.664521-25=20.712[/tex]Thus, v0 = 20.7 m/s
Algebra 14.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! GotWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanksThe administrative assistant at a software company often provides breakfast when there is amorning meeting. For last week's sales meeting, she purchased 6 dozen doughnuts and 2dozen croissants, spending a total of $42. In preparation for yesterday's safety meeting, shespent $40 on 2 dozen doughnuts and 5 dozen croissants. Assuming she purchased the itemsat the same bakery both times, how much does a dozen of each cost?A dozen doughnuts costs $and a dozen croissants costs $Submit
Answers
SOLUTION
Define a variable for the unkwons
[tex]\begin{gathered} \text{Let } \\ A\text{ dozen of doughnuts cost=\$x} \\ A\text{ dozen of Croissant cost=\$y} \end{gathered}[/tex]Then
6 dozen of doughnuts and 2 dozen of croissant cost $42, is written as
[tex]6x+2y=42\ldots\text{equation 1}[/tex]Similarly
$40 for 2 dozen of doughnuts and 5 dozen of croissant is witten as
[tex]2x+5y=40\ldots\text{equation 2}[/tex]Applying Elimination to solve the two system of equation, we have
[tex]\begin{gathered} 6x+2y=42\ldots\text{equation 1} \\ 2x+5y=40\ldots\text{equation 2} \\ To\text{ eliminate x multiply equation 2 by 3 and equation 1 by 1} \\ 1\times(6x+2y=42)\rightarrow6x+2y=42 \\ 3\times(2x+5y=40)\rightarrow6x+15y=120 \end{gathered}[/tex]Then, subtract the equation obtained above
[tex]\begin{gathered} 6x+2y=42 \\ 6x+15y=120 \\ -13y=-78 \\ \text{Divide both sides by -13} \\ -\frac{13y}{-13}=-\frac{78}{-13} \\ \\ y=6 \end{gathered}[/tex]Hence Y=6
Then you Eliminate Y from eqaution 1 an d 2 by
Multiplying equation 1 by 5 and equation 2 by 2
[tex]\begin{gathered} 5\times(6x+2y=42)\rightarrow30x+10y=210 \\ 2\times(2x+5y=40)\rightarrow4x+10y=80 \end{gathered}[/tex]The sunbtract the equation obtained
[tex]\begin{gathered} 30x+10y=210 \\ 4x+10y=80 \\ 26x=130 \\ \text{Divide both sides by 26} \\ \frac{26x}{26}=\frac{130}{26} \\ \\ x=5 \end{gathered}[/tex]Hence X=5
Therefore
A Dozen of doughnuts cost $5
A Dozen of Croisant cost $6