SOLUTION:
Step 1:
We are given the following:
Find the side length of a cube with a volume of 941 cubic meters.
If necessary, round your answer to the nearest tenth.
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Volume\text{ of a cube = length x length x length} \\ Now,\text{ we have that: Volume = 941 m}^3 \end{gathered}[/tex][tex]\begin{gathered} 941\text{ = l x l x l} \\ 941\text{ = l}^3 \\ cube\text{ - root both sides, we have that:} \end{gathered}[/tex][tex]\begin{gathered} l\text{ =}\sqrt[3]{941} \\ l\text{ = 9.799333566} \\ l\approx\text{ 9.8 meters \lparen to the nearest tenth\rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]l\approx\text{ 9.8 meters \lparen to the nearest tenth\rparen}[/tex]The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 132° arc?Give the exact answer in simplest form. ____ square kilometers. (pi, fraction,)
To find the area of the sector we will use
[tex]A=\frac{L\cdot r}{2}[/tex]Where L is
[tex]\begin{gathered} L=\frac{2\cdot\pi\cdot6\text{ km}}{360^{\circ}}\cdot132^{\circ} \\ L=\frac{132\pi\text{ km}}{30}=\frac{66\pi\text{ km}}{15}=\frac{22\pi\text{ km}}{5} \end{gathered}[/tex]Finally, we must replace L and r in the intial equation
[tex]A=\frac{\frac{22\pi\text{ km}}{5}\cdot6\operatorname{km}}{2}=\frac{\frac{132\pi\text{ km2}}{5}}{2}=\frac{132\pi\text{ km2}}{10}=\frac{66\pi}{5}km^2[/tex]list the sides in order from largest to shortest JKL
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
∠ J = 71
∠ K = 41
∠ L = 68
sides from largest to shortest = ?
Step 02:
We must apply relationship between sides and angles.
The sides from largest to shortest :
1 . ∠ J = 71 ===> side KL
2. ∠ L = 68 ===> side JK
3. ∠ K = 41 ===> side JL
This is the solution.
KL , JK , JL
I need help understanding how to convert the expressions so they can cancel out in order to achieve the answer
Recall the equivalent expression of each term.
[tex]cos\beta=\frac{x}{r}[/tex][tex]tan\beta=\frac{y}{x}[/tex][tex]csc\beta=\frac{r}{y}[/tex][tex]cot\beta=\frac{x}{y}[/tex]Using their equivalents, we can rewrite the expression as:
[tex](\frac{x}{r})(\frac{y}{x})(\frac{r}{y})(\frac{x}{y})[/tex]Then, multiply the variables.
[tex]\frac{x^2yr}{xy^2r}[/tex]Then, simplify by subtracting the exponents of each respective variable. The result is:
[tex]\frac{x}{y}[/tex]Since x/y is equivalent to cot β, then the given trigonometric expression is just equal to cot (β).
Can I Plss get some help on this can I get help on 48
To find the area of a kite, the formula is:
[tex]A=\frac{d_1d_2}{2}[/tex]This means that we need to find the lengths of the diagonals. We can use the Pythagorean Theorem for this.
Let's first solve for the length of d1.
[tex]\begin{gathered} x^2+x^2=11^2 \\ 2x^2=121 \\ x^2=\frac{121}{2} \\ x=\frac{11\sqrt{2}}{2} \end{gathered}[/tex]Because the d1 is twice the length of x, then
[tex]d_1=2(\frac{11\sqrt{2}}{2})=11\sqrt{2}\approx15.6[/tex]Now we solve for d2.
Again, we use the Pythagorean Theorem.
[tex](\frac{11\sqrt{2}}{2})^2+y^2=61^2[/tex][tex]\begin{gathered} y^2=61^2-(\frac{11\sqrt{2}}{2})^2 \\ \\ y^2=\frac{7,321}{2} \\ \\ y\approx60.5 \end{gathered}[/tex]So d2 = 2y = 121.
To find the area, we multiply the diagonals then divide by 2.
[tex]A=\frac{15.6(121)}{2}=943.8[/tex]The area is approximately 943.8 square units.
The perimeter is much easier to find. We simply add all of the sides.
We know that a kite has 2 pairs of consecutive sides that are congruent.
So the perimeter is 11 + 11 + 61 + 61 or 144 units.
Find the real or imaginary solutions solutions of the following equation by factoring. y^3-512=0Choose the correct answer below.
B
1) The best way to tackle this question is to think of the difference between two cubes:
[tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex]2) So now, let's apply to the binomial we have:
[tex]\begin{gathered} \sqrt[3]{512}=8 \\ y^3-512=(y-8)(y^2+8y+64) \end{gathered}[/tex]So now, let's make use of the factor zero property for the first factor and solve the quadratic using the quadratic formula:
[tex]\begin{gathered} y-8=0,y=8 \\ \\ y_=\frac{-8\pm\sqrt{8^2-4\cdot\:1\cdot\:64}}{2} \\ y_1=\frac{-8+8\sqrt{3}i}{2}=\quad4+4\sqrt{3}i \\ y_2=\frac{-8-8\sqrt{3}i}{2}=\quad-4-4\sqrt{3}i \end{gathered}[/tex]3) Thus, the answer is:
B
In the right triangle shown, m angle Y=30^ and XY = 6 . Z х 6 30 Y How long is Y Z
to find the value of XZ, we will use the trigonometric ratio
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenus} \\ \theta=30^0 \\ \text{adjacent}=x \\ \text{hypotenus}=6 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \cos 30^0=\frac{x}{6} \\ x=6\times\cos 30^0 \\ x=6\times0.8660 \\ x=5.196 \end{gathered}[/tex]Hence,
The value of YZ= 5.196
Describe the effect of the transformation on (x,y) and describe the transformation in words: (x, y) → ( )
The effect of the transformation on (x,y) , it will make a similar images but at different coordinates of x and y , as shown in the image, two similar figures but at different places
To describe the given transformation, at first, we need to find the rule of transformation
Take the point as a reference and find its image
Let the point is the vertex of the image which is (1 , 2 )
the image of the point is ( 3 , 1 )
So, x coordinates changed from 1 to 3, which mean the image moved 2 units to the right
And, y- coordinates changed from 2 to 1, which mean the image moved 1 units down
So, the desciption of the transformation is:
The total image moved 2 units right and 1 unit down
The area of Seth's bedroom is 1/2 of the area of his mom's living room. Seth also has a closet with an area of 12 square feet. If the total area Seth has at his disposal is 132 square feet, what is the area of the living room?
Let S be the area of Seth's bedroom and let M be the area of his mom's living room.
Let's first set-up the e
From the question, "The area of Seth's bedroom is 1/2 of the area of his mom's living room" can be written mathematically as;
S = 1/2 M ---------------------------------------------(1)
Also, "the total area Seth has at his disposal is 132 square feet" implies;
S + 12 = 132 -----------------------------------------------------(2)
The length of a photograph of Mr. Lemley playing golf is 1 4/5 inches. If the area of the photo is 33/20 square inches, what is the width of the photograph? * Your answer
Take into account that the area of a rectangular shape, is given by the following formula:
A = l·w
w: width = ?
l: length = 1 4/5 in
A: area = 33/20 in²
In order to determine the width of the photo, solve the previous formula for w:
w = A/l
convert 1 4/5 to a normal fraction:
1 4/5 = (5 + 4)/5 = 9/5
replace the values of A and l into the expression for w:
w = (33/20)/(9/5)
w = 165/180
simplify the previos fraction:
w = 165/180 = 33/36 = 11/12
Hence, the width of the photograp is 11/12 in
On a number line, 6.49 would be locatedChoose all answers O A. between 6 and 7B. between 6.48 and 6.50O C. to the right of 6.59D. between 6.4 and 6.5
6.49 is greater than 6 but less than 7, which means the first answer is correct.
It is also greater than 6.48 but less than 6.50, which means that the second answer is also correct.
It is not greater than 6.59, which means it would be to the left of 6.59, the third option is not correct.
It is greater than 6.4 and less than 6.5, the last option is correct too.
All answers are correct, except for the third option.
graph the equation y equals 4x - 5 by plotting points
Given the equation:
y = 4x - 5
Use the slope intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
To plot the points, first make a point on the y-intercept, y = -5
At y-intercept, x = 0.
Thus, we have the point (0, -5)
Let's find the value of y, when x = 1.
y = 4(-1) -5
y = 4 - 5 =
y = -1
When x = 1, y = -1
We have the point (1, -1)
When x = 2
y = 4(2) - 5
y = 8 - 5
y = 3
When x = 2, y = 3
We have the point (2, 3)
Thus, mark the following points:
(0, -5)
(1, -1)
(2, 3)
Then connect the plotted points with a straight line.
We have the graph attached below:
Refer to the figure below. Then find the indicated values:A) f(7)B) g(0) + f(3)C) f(g(7))D) g(f(8))E) x if f(x) =2
Given the graph in the image question, it can be seen that:
[tex]\begin{gathered} y=f(x) \\ y=g(x) \end{gathered}[/tex]To answer the questions, we have:
a. f(7)
[tex]f(7)=1[/tex]b. g(0)+f(3)
[tex]\begin{gathered} g(0)=6 \\ f(3)=-1 \\ g(0)+f(3)=6+(-1)_{} \\ =6-1 \\ =5 \end{gathered}[/tex]c. f(g(7))
[tex]\begin{gathered} We\text{ do }g(7)\text{ first and then do the f(x) of the result:} \\ g(7)=6 \\ f(g(7))=f(6) \\ =1 \end{gathered}[/tex]d. g(f(8))
[tex]\begin{gathered} We\text{ do f}(8)\text{ first and then do the f(x) of the result:} \\ f(8)=1 \\ g(f(8))=g(1) \\ =6 \end{gathered}[/tex]e. x if f(x)=2
[tex]\begin{gathered} f(x)=2 \\ \text{ To get }f(x),\text{ we look at the point 2 on the y axis and trace it to x} \\ f(x)=2\text{ at point }-7\text{ on the x axis} \\ \text{Hence, x=-7} \end{gathered}[/tex]Sean started with 15.5 points during a trivia game. Then, he lost 15.25 points on one turn and also lost 12.75 points on his final turn. What is Sean's final score?
When Sean started with 15.5 points during a trivia game. If he lost 15.25 points on one turn and also lost 12.75 points on his final turn, Sean's final score is -12.5 points
The point that he has at starting = 15.5 points
The point that he lost on one turn = 15.25 points
The point that he lost on final turn = 12.75 points
The final score = The point that he has at starting - The point that he lost on one turn - The point that he lost on final turn
Substitute the values in the equation
= 15.5 - 15.25 - 12.75
Subtract the terms
= -12.5
Hence, when Sean started with 15.5 points during a trivia game. If he lost 15.25 points on one turn and also lost 12.75 points on his final turn, Sean's final score is -12.5 points
Learn more about subtraction here
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Find an ordered pair(X, Y) that is a solution to the equationX minus 5Y equals five
To solve this problem, the first step is to find the slope intercept form of the equation:
[tex]\begin{gathered} x-5y=5 \\ 5y+5=x \\ 5y=x-5 \\ y=\frac{1}{5}x-1 \end{gathered}[/tex]Now, use a random value of x and find y, for example in this case we can use x=5 :
[tex]\begin{gathered} y=\frac{1}{5}(5)-1 \\ y=1-1 \\ y=0 \end{gathered}[/tex]The ordered pair that is a solution for the given equation is (5,0).
2 tablets, 3x per day14 days neededtablets per bottle: 15How many full bottles and additional tablets are needed?
Since the dosage is 2 tables, 3 times a day, so the number of tablets needed per day is 3 * 2 = 6 tablets.
The number of days required is 14, so the total number of tablets needed is 14 * 6 = 84.
If each bottle has 15 tablets, so the number of bottles required is:
[tex]\frac{84}{15}=5.6[/tex]So we will need 5 full bottles.
These 5 bottles can hold 5 * 15 = 75 tablets. To reach 84 tablets, we also need 84 - 75 = 9 additional tablets.
If the length and width of a rectangle each change by a factor of nine, what happens to the area of the rectangle?
The area of the rectangle changes by the factor of
[tex]9^2[/tex]Explanation:Let l and w represent the length and width of the rectangle respectively.
The area is
A = lw
If these change by a factor of nine, then we have:
9l and 9w
The area, which is the product of the length and width becomes:
[tex]\begin{gathered} A=9l\times9w \\ =9^2lw \\ =9^2A \end{gathered}[/tex]Find a translation that has the same effect as the composition of translations below. T(5.1) (x,y) followed by T-3,7) (x,y) T Choose the correct answer below. O A. (x,y) → (X + 8.y-6) O B. (x,y)(x+2.y-6) O C. (x,y)-(x + 2.y + 8) O D. (x,y)--(X + 8.y + 8)
Answer
Option C is correct.
Explanation
The translation T (a, b) changes the coordinates A (x, y) into A (x + a, y + b).
So, a translation of T (5, 1) followed by T (-3, 7) becomes a single translation of
T (5 - 3, 1 + 7) = T (2, 8)
And this would turn A (x, y) into A' (x + 2, y + 8).
Hope this Helps!!!
Write fractions for points A and B on the number line
Given: The line from 0 to 1 is divided in 6 parts and has two points. A and B marked on it.
To find:The fraction for point A and B.
Explanation: The length from 0 to 1 is divided into 6 parts.
Therefore, the length of one part will be 1/6.
The point A is markes at the second division.
Since, 1 division= 1/6
therefore, 2 divisions will be = 2x(1/6)
Therefore, the point A will correspond to the fraction
[tex]\begin{gathered} A=2\times\frac{1}{6} \\ =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}[/tex]Now the next pint B lets count its division.
It is marked at the fifth division.
Therefore, the fraction representing B can be written as:
[tex]\begin{gathered} B=5\times(1\text{ division\rparen} \\ =5\times\frac{1}{6} \\ =\frac{5}{6} \end{gathered}[/tex]Therefore, the point B can be represented as 5/6.
Final answer : Point A = 1/3
and point B = 5/6.
=-=Solve this system of equations by usingthe elimination method.+x+ 5y = 29 Combine the equationsto eliminate the xx - 2y = -8variable.0 + [?]y =Hint: Add together 5ý and (-2y).Enter the new coefficient of y.=
Explanation
[tex]\begin{gathered} -x+5y=29 \\ x-2y=-8 \end{gathered}[/tex]Step 1
a) add the equations to eliminate the x variable
[tex]\begin{gathered} -x+5y=29 \\ x-2y=-8 \\ _{\text{ + \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \\ \lparen x-x)+\left(5-2\right)y=\left(29-8\right) \\ 0+3y=21\Rightarrow blanks \\ \end{gathered}[/tex]Step 2
[tex]0+3y=21[/tex]divide both sides by 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{21}{3} \\ y=7 \end{gathered}[/tex]so
y=7
Step 3
finally, replace the y value in equation (1) and solve for x
[tex]\begin{gathered} -x+5y=29 \\ replace \\ -x-5*7=29 \\ -x+35=29 \\ subtract\text{ 35 in both sides} \\ -x+35-35=29-35 \\ -x=-6 \\ x=6 \end{gathered}[/tex]so,
x=6
therefore, the solution to the system of equations is
[tex]\begin{gathered} x=6 \\ y=7 \end{gathered}[/tex]I hope this helps you
Calculate the percent discount on an item that is regularly priced at $400 andcosts $339 after 13% tax.
Percentages
It's known the current price of an item is $339 after 13% tax and some discount to be determined.
Let's get this done from end to beginning.
The final price is $339 and it has already been charged 13% tax.
If the price before tax was x, then the price after tax is:
x + 13% of x
Calculating:
x + 13/100*x
x + 0.13 x
1.13x
The final price is 113% (100% plus 13% tax) of the previous price.
We can now calculate the value of x:
x = $339 / 1.13
x = $300
This price was already discounted by a certain percent with respect to the original price. The discount was $400 - $300 = $100
The percent discount is $100 / $400 * 100 = 25%
The percent discount is 25%
what is the answer?
If anything is written unclearly, just say so and I will type it out. Thank you!
Given:
[tex]g(x)\text{ = -2x}^2\text{+4x+16}[/tex]To find:
the answers to the multiple questions applicable to the function
a) The sign of the leading coefficient (coefficient of highest power) is negative, As a result, the graph will open down
b) The higher the quadratic leading coefficient, the narrower the graph
A value of like 0.5 gives a wider graph, so 2 will be seen as narrow
It is narrow
c) To get the factored form, we will factorised the given expression
[tex]\begin{gathered} g(x)\text{ = -2x}^2\text{ + 4x + 16} \\ a\text{ = -2, b = 4, c = 16} \\ We\text{ need to find }factors\text{ of ac whose sum gives b} \\ ac\text{ = -2\lparen16\rparen= -32} \\ factors\text{ of -32 whose sum gives 4 = 8 and -4} \\ \\ g(x)\text{ = -2x}^2\text{ + 8x - 4x + 16} \end{gathered}[/tex][tex]\begin{gathered} g(x)\text{ = -2x\lparen x - 4\rparen - 4\lparen x - 4\rparen} \\ g(x)\text{ = \lparen-2x - 4\rparen\lparen x - 4\rparen \lparen factored form\rparen} \end{gathered}[/tex]d) the vertex form of a quadratic equation is given as:
[tex]\begin{gathered} y\text{ = a\lparen x - h\rparen}^2\text{ + k} \\ where\text{ \lparen h, k\rparen = vertex} \end{gathered}[/tex][tex]\begin{gathered} We\text{ need to get h and k to complete the vertex form} \\ h\text{ = }\frac{-b}{2a} \\ k\text{ = g\lparen}\frac{-b}{2a}) \\ \\ a\text{ = -2, b = 4, c = 16} \\ h\text{ = }\frac{-4}{2(-2)} \\ h\text{ = }\frac{-4}{-4}\text{ = 1} \\ \\ k\text{ = g\lparen}\frac{-b}{2a})\text{ = g\lparen value of h\rparen} \\ k\text{ = g\lparen1\rparen} \\ g(1)\text{ = -2\lparen1\rparen}^2\text{ + 4\lparen1\rparen + 16} \\ g(1)\text{ = -2 + 4 + 16 = 18} \\ k\text{ = 18} \end{gathered}[/tex][tex]\begin{gathered} h\text{ = 1, k = 18} \\ substitute\text{ in to the vertex form formula:} \\ y\text{ = a\lparen x - 1\rparen}^2\text{ + 18} \\ \\ leading\text{ coefficient = -2} \\ a\text{ = leading coefficient = -2} \\ y\text{ = -2\lparen x - 1\rparen}^2+\text{ 18} \end{gathered}[/tex]Vertex: (h, k)
[tex]Vertex\text{ = \lparen1, 18\rparen}[/tex]Axis of symmetry: The value of x which gives a mirror image when the parabola is split into two
The axis of symmetry is the value of h in the vertex. h = 1
Since it is an x coordinate, the axis of symmetry is x = 1
Roots are the values of x which makes the function equal to zero
We will use the factored form to get x
[tex]\begin{gathered} g(x)\text{ = }(-2x\text{ - 4\rparen\lparen x - 4\rparen} \\ g(x)\text{ = 0 to get root} \\ 0\text{ = \lparen-2x - 4\rparen\lparen x - 4\rparen} \\ -2x\text{ - 4 = 0 ; x - 4 = 0} \\ -2x\text{ = 4} \\ x\text{ = 4/-2} \\ x\text{ = -2} \\ \\ x\text{ - 4 = 0} \\ \text{x = 4} \\ zeros\text{ are x = -2 and 4} \end{gathered}[/tex]Let f(x) represent the linear parent function.Which descriptions match the given transformations?Drag and drop the answers into the boxes.13 f (x)f(x-13)f(x) is translated 13 units up.11f(x) is translated 13 units left.f(z) is vertically stretched by a factor of 13.1f (x) is vertically compressed by a factor of 13.f(x) translated 13 units right.23 456 7 8 9 10Next88°F Clear
Given
Linear parent function f(x)
Find
Which descriptions match the given transformations?
13f(x)
f(x-13)
Explanation
13f(x) = it represents the vertically stretched by a factor of 13
f(x-13) = it represents the translated 13 units to the right
Final Answer
Therefore, the correct match is
13f(x) = f(x) is vertically stretched by a factor of 13.
f(x-13) =f (x) translated 13 units right.
what is the quotient of 789 and 34?
EXPLANATION:
The quotient is the result of the division.
[tex]\begin{gathered} \frac{789}{34}=23 \\ \text{the answer is 23} \end{gathered}[/tex]IMPORTANT NOTE:
The quotient indicates the number of times that the divisor is contained in the dividend.
Answer:
Step-by-step explanation:
The answer is 23.
Runner #1's distance (in miles) with time (in minutes) is d= 1/15t.What is the Pace of the runner?Runner 1 is going 1 mile per ____ min.
The given equation is
[tex]d=\frac{1}{15}t[/tex]Remember that the coefficient of the variable represents the range of change.
hence, the pace of the runner is 1 miler per 15 minutes.I got it wrong on my quiz, my exam is tomorrow and id like help understanding it.
The perimeter of the sandwich is the sum of all its sides, then we have:
[tex]2x^2+8+2x^2+8+2x^2+9+2x^2+9=8x^2+34[/tex]Therefore the perimeter is:
[tex]8x^2+34[/tex]The length of the crust is the same as the perimeter of the sandwich; if x=1.2 we have that:
[tex]8(1.2)^2+34=45.52[/tex]Therefore the length of the crust is 45.52
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (suchas printing). The one-time fixed costs will total $39.160. The variable costs will be $11 per book. The publisher will sell the finished product to bookstores at aprice of $24.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Given:
The one-time fixed costs = $39.160.
The variable costs = $11 per book.
The price of the book = $24.75 per book.
Let x be the number of books.
The production cost of the x number of books is
[tex]=39.160+11x[/tex]The sales price of the x number of books is
[tex]=24.75x[/tex]Given that the production cost = the sales cost.
[tex]=39.160+11x[/tex]Boris rented a truck for one day. There was a base fee of $16.95, and there was an additional charge of 72 cents for each mile driven. Boris had to pay $232.23when he returned the truck. For how many miles did he drive the truck?
Given:-
The base fee of rented truck is $16.95.
The additional charge of 72 cents for each mile driven.
Boris payed $232.23 when he rerturned the vechile.
we know that 1 dollar = 100 cents. Therefore 72 cents is,
[tex]72cents=0.72dollars[/tex]So the value if 72 cents is 0.72 dollars.
Let m be the miles. so to find the required miles are,
[tex]\begin{gathered} m=\frac{232.23-16.95}{0.72} \\ m=\frac{215.28}{0.72} \\ m=299 \end{gathered}[/tex]Therefore Boris covered 299 miles.
Question 7-8 Work doesn’t have to be shown just an short explanation.
Step 1
Given;
[tex]\begin{gathered} \text{Two points;} \\ (1,2) \\ (-3,-4) \\ \text{where } \\ x_1=1 \\ x_2=-3 \\ y_1=2 \\ y_2=-4 \end{gathered}[/tex]Required; To find the slope
Step 2
State the formula for the slope of a line and find the slope on the line in question 7
[tex]\begin{gathered} m=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-4-2}{-3-1}=\frac{-6}{-4}=\frac{3}{2} \end{gathered}[/tex]Hence, the slope of the line = 3/2
x=3y+12x+4y=12Solve each system by Substitution
Answer:
[tex]\text{ The solution of the system is }(4,1)[/tex]Step-by-step explanation:
The substitution method consists in isolating one of the variables and plugging it into the other equation. Given the following system of equations, solve for substitution:
[tex]\begin{gathered} x=3y+1\text{ }(1) \\ 2x+4y=12\text{ }(2) \end{gathered}[/tex]Since ''x'' is already isolated in (1), plug it into equation (2):
[tex]\begin{gathered} 2(3y+1)+4y=12 \\ \text{ Using distributive property:} \\ 6y+2+4y=12 \\ 10y+2=12 \end{gathered}[/tex]Solve for y.
[tex]\begin{gathered} 10y=10 \\ y=\frac{10}{10} \\ y=1 \end{gathered}[/tex]Now, knowing the y-value for the solution of the system. Substitute y=1 into equation (1):
[tex]\begin{gathered} x=3y+1 \\ x=3(1)+1 \\ x=4 \end{gathered}[/tex][tex]\text{ The solution of the system is }(4,1)[/tex]