Given data:
The given numbers are 309+23143240-59234881.
The simplification of the given numbers is,
-36091332.
Which of the following is the exact value of cot(pi/4)
We have to select the correct value of cot (pi/4).
It is known that the value of cot (pi/4) is 1.
Thus, the correct option is B.
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
True.
area of green square + area of purple square = area of red square
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
what is the measure in radians of central angle 0 in the circle below
For this exercise you need to use the following formula:
[tex]\theta=\frac{S}{r}[/tex]Where θ is the Central angle in radians, "S" is the arc length and "r" is the radius of the circle.
In this case, you can identify that:
[tex]\begin{gathered} S=8\pi cm \\ r=8\operatorname{cm} \end{gathered}[/tex]Knowing these values, you can substitute them into the formula and then evaluate, in order to find the measure of the Central angle in radians. This is:
[tex]\begin{gathered} \theta=\frac{8\pi cm}{8\operatorname{cm}} \\ \\ \theta\approx\pi radians \end{gathered}[/tex]The answer is:
[tex]\pi radians[/tex]Which graph represents the table below?
Answer:
The answer will be D because you have to look very close and make sure the 1 is on the x-intercept and not the y-intercept.
Find the areas of the figure. Area of Parallelogram, Trapezoid and Composite figure. Round to the nearest hundredth where necessary.
Let
A₁ be the area of the parallelogram
A₂ be the area of the trapezoid
Solving for the area of the parallelogram
Given the following dimensions
b = 23 cm
h = 14 cm
The area is solved using
[tex]\begin{gathered} A_1=bh \\ A_1=(23\text{ cm})(14\text{ cm}) \\ A_1=322\text{ cm}^2 \end{gathered}[/tex]The area of the parallelogram therefore is 322 square centimeters.
Solving for the area of the trapezoid.
Given the following dimensions
b₁ = 15 cm
b₂ = 34 cm
h = 19 cm
The area is solved using
[tex]\begin{gathered} A_2=\frac{b_1+b_2}{2}\cdot h \\ A_2=\frac{15\text{ cm}+34\text{ cm}}{2}(19\text{ cm}) \\ A_2=\frac{49\text{ cm}}{2}(19\text{ cm\rparen} \\ A_2=(24.5\text{ cm})(19\text{ cm}) \\ A_2=465.5\text{ cm}^2 \end{gathered}[/tex]The area of the trapezoid is 465.5 square centimeters.
Solving for the area of the composite figure.
Get the sum of the two areas to get the area of the composite figure, we have
[tex]\begin{gathered} A_{\text{total}}=A_1+A_2 \\ A_{\text{total}}=322\text{ cm}^2+465.5\text{ cm}^2 \\ A_{\text{total}}=787.5\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the composite figure is 787.5 square centimeters.
Find the area of the yellow region. Round to the nearest tenth. 7.53cm
The figure shows a square inscribed in a circle of radius r = 7.53 cm.
The yellow region corresponds to the area of the circle minus the area of the square.
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]Calculating:
[tex]A_c=\pi(7.53\text{ cm})^2=178.13\text{ }cm^2[/tex]The radius of the circle is half the diagonal of the square. The diagonal of the square is:
d = 2 x 7.53 cm = 15.06 cm
The area of a square, given the diagonal d, is calculated as follows:
[tex]A_s=\frac{d^2}{2}[/tex]Calculating:
[tex]\begin{gathered} A_s=\frac{(15.06\text{ cm})^2}{2} \\ \\ A_s=113.40\text{ }cm^2 \end{gathered}[/tex]The required area is:
A = 178.13 - 113.40 = 64.73 square cm
I need help simplify each expression look for the terms first
8k + 3 +4k
________________
First, add the k
8k + 4k = (8+4) k = 12 k
________________
you add if there are other variables or numbers
3
________________
12k + 3
Do you have any questions regarding the solution?
Two cars are driving on the same road, in the same
direction. They start driving from the same place and are
traveling at a constant speed. The second car started
driving 1.5 hours after the first car started driving. If the
second car drives 60 miles per hour and the first drives 40
miles per hour, how many miles will each car have
traveled when the second car catches up to the first?
Answer:
180 miles
Step-by-step explanation:
distance = rate x time
t = time
1st car:
distance = 40t
2nd car:
distance = 60(t - 1,5)
When the car catch up to each other the distances will be the same, so set the equation equal to each other. Calculate the time and then put the time back into either equation and solve for the distance.
40t = 60(t-1.5) Distribute the 60
40t = 60t -(60)1.5
40t = 60t - 90 Subtract 60t from both sides of the equation
-20t = -90 Divide both sides by -20
t = 4.5
Now that we know the time, substitue that back into either equaiton and solve for the time
distance = 40 (4.5)
180 miles
I need help with my pre-calculus homework, the image of the problem is attached. Please show me how to solve this problem, thank you!
Given the following equation:
[tex]\text{ }\frac{\text{ 2}}{5x}\text{ + 4 = }\frac{2}{x}[/tex]Let's find x,
[tex]\text{ }\frac{\text{ 2}}{5x}\text{ + 4 = }\frac{2}{x}[/tex][tex]\text{ 5x( }\frac{\text{ 2}}{5x}\text{ + 4) = (}\frac{2}{x})5x[/tex][tex]\text{ 5x(}\frac{\text{ 2}}{5x})\text{ + 5x(4) = (}\frac{2}{x})5x[/tex][tex]\text{ 2 + 20x = 10}[/tex][tex]\text{ 2 + 20x - 2 = 10 - 2}[/tex][tex]\text{ 20x = 8}[/tex][tex]\text{ }\frac{\text{20x}}{20}\text{ = }\frac{\text{8}}{20}[/tex][tex]\text{ x = }\frac{8}{20}[/tex][tex]\text{ x = }\frac{\frac{8}{4}}{\frac{20}{4}}\text{ = }\frac{2}{5}[/tex]Therefore, the answer is letter A: 2/5
helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. y = -250x + 3750
B. $2125
Step-by-step explanation:
A.
(5, 2500), (7, 2000)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2000 - 2500 -500
m = ----------------- = ---------------------- = ---------- = -250
x₂ - x₁ 7 - 5 2
y - y₁ = m(x - x₁)
y - 2500 = -250(x - 5)
y - 2500 = -250x + 1250
+2500 +2500
-------------------------------------
y = -250x + 3750
B.
y = -250x + 3750
y = -250(6.50) + 3750
y = -1625 + 3750
y = 2125
(6.50, 2125)
I hope this helps!
The probability that John recieves junk mail is 11 percent. If he receives 94 pieces of mail in a week, about how many of them can he expect to be junk mail.a. 5 b. 15 c. 10 d.20
10 (option C)
Explanation:The probability of getting a junk mail = 11%
Number of mails received = 94
Amount that will be junk mail = The probability of getting a junk mail × Number of mails received
Amount that will be junk mail = 11% × 94
= 0.11 × 94 = 10.34
Since we can't have decimal number of mails, we would approximate to the nearest whole number
10.34 to the nearest whole number is 10
Hence, 10 junk mails are expected
need help with this question please help
Let:
[tex]k\cdot RT=TU[/tex]Where:
k = Constant of proportionality
[tex]\begin{gathered} k\cdot4=6 \\ solve_{\text{ }}for_{\text{ }}k \\ k=\frac{6}{4} \\ k=\frac{3}{2} \end{gathered}[/tex]So:
[tex]\begin{gathered} k\cdot RS=UV \\ \frac{3}{2}(6)=UV \\ \frac{18}{2}=UV \\ UV=9 \end{gathered}[/tex]Which value of x makes the equation true 3x-6/3= 7x-3/6
The value of x that makes the equation true is - 3 / 8.
How to solve equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Therefore, the value of x that makes the equation true is the value that makes the two sides of the equation equal.
Hence,
3x - 6 / 3 = 7x - 3 / 6
3x - 2 = 7x - 1 / 2
add 2 to both sides of the equation
3x - 2 = 7x - 1 / 2
3x - 2 + 2 = 7x - 1 / 2 + 2
3x = 7x - 1 / 2 + 2
3x = 7x + 3 / 2
subtract 7x from both side of the equation
3x - 7x = 7x - 7x + 3 / 2
- 4x = 3 / 2
cross multiply
- 8x = 3
x = - 3 / 8
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The value of x which makes the equation true is - 3 / 8.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 3x-6/3= 7x-3/6
Three x minus six divided by three equal to seven times of x minus three divided by six
3x-6/3= 7x-3/6
(9x-6)/3=(42x-3)/6
Apply cross multiplication
6(9x-6)=3(42x-3)
Apply distributive property
54x-36=126x-9
add 36 on both sides
54x=126x-9+36
54x=126x+27
-27=126x-54x
-27=72x
x=-27/72
x=-9/24=-3/8
Hence value of x is -3/8 for equation 3x-6/3= 7x-3/6.
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I inserted a picture of the question Please don’t ask tons of questions. & please state whether it’s a b c or d
As given by the question
There are given that the graph of the triangle.
Now,
According to the properties,
If the point (x, y) or (-x, y) rotated about the origin by the angle of 360 degrees.
That means,
There is no difference between rotating 360 degrees clockwise or anti-clockwise around the origin.
Then,
From the vertices of the triangle ABC is:
[tex]\text{A is (-6, 3), B is (-5, 7) and C is (-4, 3).}[/tex]Since the triangle map onto itself
[tex]\begin{gathered} A=A^{\prime} \\ B=B^{\prime} \\ C=C^{\prime} \end{gathered}[/tex]So, the triangle is rotated 360 degrees about the origin
Hence, the correct option is D.
A glacier in Republica was observed to advance 22inches in a 15 minute period. At that rate, how many feet will the glacier advance in one year?
To fins the rate in feet/year we must change first the measurements to the units required
inches to feat
minutes to years
[tex]22in\cdot\frac{1ft}{12in}=\frac{11}{6}ft[/tex][tex]15\min \cdot\frac{1h}{60\min}\cdot\frac{1day}{24h}\cdot\frac{1year}{365\text{days}}=\frac{1}{35040}\text{years}[/tex]to find the rate divide the distance over the time
[tex]\frac{\frac{11}{6}ft}{\frac{1}{35040}\text{year}}=\frac{11\cdot35040ft}{6\text{year}}=\frac{385440}{6}=\frac{64240ft}{\text{year}}[/tex]the table shows a proportional relationship between the weight on a spring scale and the distance the spring has stretched. describe the scale you can use on X and Y axes of a coordinate grid that would show all of the distances and weights in the table
Here the values are proportional to each other.
Proportionality ratio is,
[tex]\frac{20}{28}=\frac{5}{7}[/tex]Then scale on X-axis representing weight in Newton is 1 unit is equal to 7 Newton
And on the the Y axis representing distance in cm is 1 unit is equal to 5 cm.
Solve for the dimensions of the rectangle. Area= length•widthThe length of a rectangle is 2cm greater than the width. The area is 80cm2. Find the length and width.
The length of a rectangle is 2cm greater than the width. The area is 80cm2. Find the length and width.
L=W+2
W=W
[tex]\begin{gathered} A=L\cdot W \\ A=(W+2)\cdot W \\ A=W^2+2W \\ A=80\operatorname{cm} \\ Then, \\ 80=W^2+2W \\ W^2+2W-80=0 \end{gathered}[/tex][tex]\Delta=4+320=324[/tex][tex]\begin{gathered} W=\frac{-2\pm\sqrt[]{324}}{2}=\frac{-2\pm18}{2} \\ W_1=\frac{-20}{2}=-10 \\ W_2=\frac{16}{2}=8 \end{gathered}[/tex]The width should be positive, therefore W=8
L=W+2
L=8+2=10
The length is L=10
Please help me on #1 Please show your work so I can follow and understand
Answer:
Between markers 3 and 4.
Explanation:
We know that each student runs 2 / 11 miles. Given this, how many miles do the first two students run?
The answer is
[tex]\frac{2}{11}\cdot2=\frac{4}{11}\text{miles}[/tex]Now, we know that the course has markers every 0.1 miles. How many markers are ther in 4 /11 miles?
The answer is
[tex]\frac{2}{11}\text{miles}\times\frac{1\text{marker}}{0.1\; miles}[/tex][tex]=3.6\text{ markers}[/tex]This is between markers 3 and 4. Meaning that the second student finishes between markers 3 and 4.
K
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in
the table.
Drive-thru Restaurant D
B C
D
280
245
122
60
32
12
A
Order Accurate
331
Order Not Accurate 38
If one order is selected, find the probability of getting an order that is not accurate or is from Restaurant C. Are the events of selecting an order that is not accurate and
selecting an order from Restaurant C disjoint events?
The probability of getting an order from Restaurant C or an order that is not accurate is
(Round to three decimal places as needed.)
Are the events of selecting an order from Restaurant C and selecting an inaccurate order disjoint events?
disjoint because it
possible to
The events
The probability is 0.236 and the events are not disjoint events
Given,
The data;
A B C D
Order accurate ; 280 245 122 331
Order not accurate; 60 32 12 38
The probability of getting an order that is not accurate or is from Restaurant C
This is illustrative of
P(Not accurate or Restaurant C) (Not accurate or Restaurant C)
The calculation is
P(Not accurate or Restaurant C) is equal to [n(Not accurate) + (Not accurate and Restaurant C) - n(Restaurant C)] /Total
Thus, we have
P(Not accurate or Restaurant C) is calculated as follows: (60 + 32 + 12 + 38 + 122 + 12 - 12)/(280 + 245 + 122 + 331 + 60 + 32 + 12 + 38).
Analyze the difference and the total.
Restaurant C or P(Not accurate) = 264/1120
Assess the quotient.
P(Not accurate or Restaurant C) = 0.236
Last but not least, choosing an incorrect order and choosing an order from Restaurant C are not separate events.
This is because choosing an inaccurate order from restaurant C is a possibility.
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For each ordered pair, determine whether it is a solution to the system of equations. 7x - 4y=8 -2x+3y=7 Is it a solution? (x, y) Yes No (0, -2) a (-9,-6) (4,5) (7.7)
7x - 4y = 8 (eq. 1)
-2x + 3y = 7 (eq. 2)
Isolating y from equation 1:
-4y = 8 - 7x
y = 8/(-4) - 7/(-4)x
y = -2 + 7/4x
Isolating y from equation 2:
3y = 7 + 2x
y = 7/3 + 2/3x
Given that the slopes of the equations are different, then there is a solution, which can be found as follows,
[tex]\begin{gathered} -2+\frac{7}{4}x=\frac{7}{3}+\frac{2}{3}x \\ \frac{7}{4}x-\frac{2}{3}x=\frac{7}{3}+2 \\ \frac{^{}_{}7\cdot3-2\cdot4}{4\cdot3}x=\frac{7+3\cdot2}{3} \\ \frac{13}{12}x=\frac{13}{3} \\ x=\frac{13}{3}\cdot\frac{12}{13} \\ x=4 \end{gathered}[/tex]Replacing x = 4 into one of the equations, we get:
[tex]\begin{gathered} y=-2+\frac{7}{4}x \\ y=-2+\frac{7}{4}\cdot4 \\ y=-2+7 \\ y=5 \end{gathered}[/tex]The solution is (4,5)
To check if an ordered pair is a solution, we have to replace the x-coordinate and the y-coordinate of the pair into the equation, as follows:
(0, -2)
7(0) - 4(-2) = 8
8 = 8
-2(0) + 3(-2) = 7
-6 ≠ 7
Given that the second equation is not satisfied, then (0, -2) is not a solution
(-9, -6)
7(-9) - 4(-6) = 8
-81 + 24 ≠ 8
-2(-9) + 3(-6) = 7
18 - 18 ≠ 7
Given that the equations are not satisfied, then (-9, -6) is not a solution
(7,7)
7(7) - 4(7) = 8
49 - 28 ≠ 8
-2(7) + 3(7) = 7
-14 + 21 = 7
Given that the first equation is not satisfied, then (7, 7) is not a solution
for #5 solve for x. then find the missing piece(s) of parallelogram.
Answer:
Given that,
From the parallelogram, the opposite sides of the parallelogram are -2+4x and 3x+3
Explanation:
From the properties of parallelogram, we have that
Opposite sides of a parallelogram are equal
We get,
[tex]-2+4x=3x+3[/tex]Solving we get,
[tex]4x-3x=3+2[/tex][tex]x=5[/tex]Answer is :x=5
13. A 640 kg of a radioactive substance decays to 544 kg in 13 hours. A. Find the half-life of the substance. Be sure to show your work including the formulas you used. Round to the nearest tenth of an hour. Only solutions using formulas from the 4.6 lecture notes will receive credit.B. How much of the substance is present after 3 days? Be sure to show the model you used.C. How long does it take the substance to reach 185 kg? Be sure to show your work.
EXPLANATION
The equation for half-life is given by the following formula:
[tex]H=\frac{t\cdot\ln(2)}{\ln(\frac{A_0}{A_t})}[/tex]Replacing terms:
[tex]H=\frac{t\cdot\ln(2)}{\ln(\frac{A_0}{A_t})}=\frac{13\cdot\ln(2)}{\ln(\frac{640}{544})}=\frac{9.0109}{0.1625}=55.45[/tex]The half-life time is H =55.4 hours.
B) After three days, that is, 72 hours, the amount of substance will be given by the following relationship:
[tex]A=A_o\cdot e^{-(\frac{\ln2}{H})t}=640\cdot e^{-(\frac{\ln2}{55.4})\cdot72}=640\cdot e^{-0.90084}[/tex]Multiplying terms:
[tex]A=640\cdot0.4062=259.96\text{ Kg}[/tex]There will be 259.96 Kg after 3 days.
C) In order to compute the number of days that will take to the substance to reach a concentration equal to 185 Kg, we need to apply the following formula:
[tex]t=\frac{\ln (\frac{A}{A_o})}{-\frac{\ln (2)}{t\frac{1}{2}}}[/tex]Replacing terms:
[tex]t=\frac{\ln (\frac{185}{544})}{-\frac{\ln (2)}{55.45}}=\frac{-1.0785}{-0.0125}=\frac{1.0785}{0.0125}=86.28\text{ hours}[/tex]It will take 86.28 hours to the substance to reach 185 Kg.
A farm raises cows and chickens. The farm has total of 43 animals. One day he counts the legs of all his animals and realizes he has a total of 122. How many cows and chickens does he have?
Assume that there are x cows and y chickens in the form
Since there are 43 animals, then
Add x and y, then equate the sum by 43
[tex]x+y=43\rightarrow(1)[/tex]Since a cow has 4 legs and a chicken has 2 legs
Since there are 122 legs, then
Multiply x by 4 and y by 3, then add the products and equate the sum by 122
[tex]4x+2y=122\rightarrow(2)[/tex]Now, we have a system of equations to solve it
Multiply equation (1) by -2 to make the coefficients of y equal in values and opposite in signs
[tex]\begin{gathered} -2(x)+-2(y)=-2(43) \\ -2x-2y=-86\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3) to eliminate y
[tex]\begin{gathered} (4x-2x)+(2y-2y)=(122-86) \\ 2x+0=36 \\ 2x=36 \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{36}{2} \\ x=18 \end{gathered}[/tex]Substitute x by 18 in equation (1)
[tex]18+y=43[/tex]Subtract 18 from each side
[tex]\begin{gathered} 18-18+y=43-18 \\ y=25 \end{gathered}[/tex]The answer is
There are 18 cows and 25 chickens on the farm
Write a numerical expression for the word expression.The product of 2 groups of 7
The given statement is the product of 2 groups of 7.
This statement can be expressed as
[tex]7\cdot7[/tex]Where each seven represent one group.
Find conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k should be equal or not equal to specific values, then enter a value or a list of values separated by commas.
To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible.
What is a matrix?matrix, a collection of numbers lined up in rows and columns to produce a rectangular array.
In computer graphics, where they have been used to describe picture transformations and other alterations.
The elements of the matrix, also known as the entry, are the numerals.
A matrix will be invertible only and only if the determinant is non-zero.
Given the matrix A.
The determinant of A is that |A| will be,
|A| = -3(8 - 8) - 0(-k + 2) - 3(-4k + 8) ≠ 0
0 + 0 + -3(-4k + 8) |A| ≠ 0
-4k + 8 ≠ 0
-4k ≠ -8
k ≠ 2
Hence "To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible".
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Question Evaluate. 7⋅5+42−23÷4 Responses 49 49 41 41 34 34 9 9
Answer: 71.25
This is not of of the options, but is the right answer.
Step-by-step explanation:
7 x 5 + 42 - 23 / 4 =
Step 1: Make parentheses
(( 7 x 5 ) + 42) - ( 23 / 4) =
Step 2: Solve parentheses ( Multiplication and division first )
(35 + 42) - 5.75 =
Step 3: Solve parentheses ( Addition )
77 - 5.75 =
Step 4: Subtract
= 71.25
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I
Three relationships are described below:
I. The amount of time needed to mow a yard increases as the size of the yard increases.
II. The amount of timeneeded to drive from city A to city B decreases as the speed you are driving increases.
III. The income of a worker who gets paid an hourly wage increases as the number of hours worked increases and
increases as the salary rate increases.
What type of variation describes each relationship?
The type of variation that describes each relationship include the following:
Direct variation: the amount of time needed to mow a yard increases as the size of the yard increases.Indirect variation: the amount of time needed to drive from city A to city B decreases as the speed you are driving increases.Joint variation: the income of a worker who gets paid an hourly wage increases as the number of hours worked increases and increases as the salary rate increases.What is an indirect variation?An indirect variation simply refers to a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other, which means as one variable increases, the other variable decreases and vice-versa.
What is direct variation?Direct variation refers to a type of proportional relationship in which a variable is directly proportional to another variable. This ultimately implies that, a direct variation represents two variables that are directly proportional to each other, which means as one variable increases, the other variable also increases and vice-versa.
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Question 2(Multiple Choice Worth 2 points)
(01.06 MC)
Simplify 31.
1
0-1
-1
Answer:
[tex]-i[/tex]
Step-by-step explanation:
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].
Given expression:
[tex]i^{31}[/tex]
Rewrite 31 as 30 + 1:
[tex]\implies i^{30+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies i^{30} \cdot i^1[/tex]
[tex]\implies i^{30}i[/tex]
Rewrite 30 as 2 · 15:
[tex]\implies i^{(2 \cdot 15)}i[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left(i^2\right)^{15}i[/tex]
[tex]\textsf{Apply\:imaginary\:number\:rule}\quad \:i^2=-1:[/tex]
[tex]\implies \left(-1\right)^{15}i[/tex]
As -1 to the power of an odd number is -1:
[tex]\implies -1 \cdot i[/tex]
[tex]\implies -i[/tex]
N8) solve the system using substitution method and then graph the equations.2x - 4y = -23x + 2y = 3-
Solution
Given:
2x - 4y = -2
3x + 2y = 3
Substitution method
[tex]\begin{gathered} From\text{ 3x+2y=3} \\ 3x=3-2y \\ x=\frac{3-2y}{3} \end{gathered}[/tex][tex]\begin{gathered} Substitute\text{ }x=\frac{3-2y}{3}\text{ into the first equation} \\ 2x-4y=-2 \\ 2(\frac{3-2y}{3})-4y=-2 \\ \frac{6-4y}{3}-4y=-2 \\ Multiply\text{ }trough\text{ by 3} \\ 6-4y-12y=-6 \\ 6-16y=-6 \\ -16y=-6-6 \\ -16y=-12 \\ y=\frac{-12}{-16} \\ y=\frac{3}{4} \end{gathered}[/tex][tex]\begin{gathered} Substitute\text{ y=}\frac{3}{4}\text{ into }x=\frac{3-2y}{3} \\ x=\frac{3-2(\frac{3}{4})}{3}=\frac{3-\frac{3}{2}}{3}=\frac{\frac{6-3}{2}}{3}=\frac{\frac{3}{2}}{3} \\ x=\frac{3}{6} \\ x=\frac{1}{2} \end{gathered}[/tex][tex]Thus,\text{ x=}\frac{1}{2},y=\frac{3}{4}[/tex]Graphical method:
Plot the graph of the two equations on the same graph
The point of intersection of the two graphs gives the solution to the system of equations
The point of intersection is (0.5, 0.75)
Which in fraction gives (1/2, 3/4)
Thus. x = 1/2, y= 3/4
Question 1 4 pts Match each quadratic expression that is written as a product with an equivalent expression that is expanded. A. (x + 2)(x + 6) [Choose ] [Choose ] B. (2x + 3)(x + 2) 2x^2 + 10x + 12 X^2 + 12x + 32 C. (X + 8)(x + 4) x^2 + 8x + 12 2x^2 + 12x + 16 D. (x + + 2)(2x + 6) [Choose ]
(x +2) (x +6) ------> x^2 +8X + 12
(2x + 8) (x +2) -------> 2x^2 +12x + 16
(x +8) (x+4) ------------> x^2 +12x +32
(x + 2) (2x+6) ----------> 2x^2 +10x +12
