47. in the parabola, = 3^2 + 12 + 11, the vertex isA.(2,1) b(-2,-1) c (2,-1) d (-2,1)e (3,11)
Answers
The Solution.
The given parabola is
\(y=3x^2+12x+11\)Let the vertex of the given parabola be (h,k).
So,
\(\begin{gathered} h=-\frac{b}{2a} \\ \text{Where a=3,b=12,c=11} \end{gathered}\)Substituting these values, we get
\(h=-\frac{12}{2\times3}=-\frac{12}{6}=-2\)Now, substituting -2 for x in the given parabola, we get
\(\begin{gathered} k=3(-2)^2+12(-2)+11 \\ k=3(4)-24+11 \\ k=12-24+11 \\ k=-12+11=-1 \end{gathered}\)So, the vertex of the given parabola is (-2,-1)
Thus, the correct answer is option B.
Related Questions
in the US, 1 in 16 (6.25%) will be diagnosed with lung cancer in their lifetime.
(A) in a random sample of 100 americans what is the probability that less than 5% will be diagnosed with lung cancer?
(B) suppose that a random sample of 100 americans who smoke cigarettes results in 20 or more being diagnosed with lung cancer. what might you conclude ( is 20 or more normal and if it's rare, what do you think this means)?
Answers
A) The prοbability that less than 5% οf Americans in a sample οf 100 will be diagnοsed with lung cancer is very small, οnly 0.02%.
B) As there is still variability in the number οf cases that may arise due tο chance.
What is the Prοbability?Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.
(A) We can use the binοmial distributiοn tο mοdel the number οf Americans in a sample οf 100 whο are diagnοsed with lung cancer. Let X be the number οf Americans in the sample whο are diagnοsed with lung cancer. Then X ~ Bin(100, 0.0625).
We want tο find P(X < 5). We can use the nοrmal apprοximatiοn tο the binοmial distributiοn, since n is large and p is nοt tοο clοse tο 0 οr 1. Using the cοntinuity cοrrectiοn, we have:
P(X < 5) = P(X < 5.5)
\(= P((X - np) \sqrt{(np(1-p))} < (5.5 - np)\sqrt{(np(1-p))})\)
\(= P(Z < (5.5 - 6.25100)\sqrt{(6.25100*(1-0.0625)))\)
= P(Z < -3.52)
= 0.0002 (frοm standard nοrmal table)
Therefοre, the prοbability that less than 5% οf Americans in a sample οf 100 will be diagnοsed with lung cancer is very small, οnly 0.02%.
(B) If 20 οr mοre Americans whο smοke cigarettes are diagnοsed with lung cancer in a sample οf 100, this is quite rare based οn the expected rate οf 6.25% in the general pοpulatiοn. This suggests that smοking is a significant risk factοr fοr develοping lung cancer, as the οbserved rate is much higher than the expected rate.
Hοwever, we cannοt cοnclude that all smοkers will develοp lung cancer, as there is still variability in the number οf cases that may arise due tο chance.
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Within six (6) weeks, four (4) colleagues in your department will make an important project. After the project, they were given Php100,000.00 as prize. Give the following amount of contribution each of their member exerted in making the project. How should the prize be divided to the members?
• Member A has made 25% of the total project.
• Member B has made 40% of the total project.
• Member C has made 25% of the total project.
• Member D has made 10% of the total project.
and why did you come up with your decision?
Answers
Answer:
The prize is p100,000.00, and we can define this as the 100%.
Now, we could say:
"Each member receives the same percentage of the price as the total percentage of the project that he/she did"
Then:
Member A did 25% of the total project.
Then he gets an amount X.
X = 25%
p100,000.00 = 100%
We can solve this system for X as:
X = (25%/100%)*p100,000.00 = p25,000.00
Now we can use the samme aproach for the other members:
Member B did 40% of the total project:
Then he gets an amount X.
X = 40%
p100,000.00 = 100%
X = (40%/100%)*p100,000.00 = p40,000.00
Member C did 25% of the total project.
Then he gets an amount X.
X = 25%
p100,000.00 = 100%
X = (25%/100%)*p100,000.00 = p25,000.00
Member D did 10% of the total project.
Then he gets an amount X.
X = 10%
p100,000.00 = 100%
X = (10%/100%)*p100,000.00 = p10,000.00
Now, we also could divide the price evenly between the four members:
p100,000.00/4 = p25,000.00
So they all get the same amount, but i think that the actual solution to this problem is the other one.
Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R). a. Construct frequency and percent frequency distributions to summarize the data. Position Frequency Percent Frequency (to one decimal) Pitcher % Catcher % 1st base % 2nd base % 3rd base % Shortstop % Left field % Center field % Right field % b. What position provides the most Hall of Famers
Answers
Answer:
a. See below for the Frequency and Relative frequency Table.
b. Pitcher (P) is the position provides the most Hall of Famers.
c. 3rd base (3) is the position that provides the fewest Hall of Famers.
d. R is the outfield position that provides the most Hall of Famers.
e. Th number of Hall of Famers of Infielders which is 16 is less than the 18 Hall of Famers of those of outfielders.
Step-by-step explanation:
Note: This question not complete. The complete question is therefore provided before answering the question as follows:
Data for a sample of 55 members of the Baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R).
L P C H 2 P R 1 S S 1 L P R P
P P P R C S L R P C C P P R P
2 3 P H L P 1 C P P P S 1 L R
R 1 2 H S 3 H 2 L P
a. Use frequency and relative frequency distributions to summarize the data.
b. What position provides the most Hall of Famers?
c. What position provides the fewest Hall of Famers?
d. What outfield position (L, C, or R) provides the most Hall of Famers?
e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).
The explanation of the answers is now provided as follows:
a. Use frequency and relative frequency distributions to summarize the data.
The frequency is the number of times a position occurs in the sample, while the relative frequency is calculated as the frequency of each position divided by the sample size multiplied by 100.
Therefore, we have:
Frequency and Relative frequency Table
Position Frequency Relative frequency (%)
P 17 30.91%
H 4 7.27%
1 5 9.09%
2 4 7.27%
3 2 3.64%
S 5 9.09%
L 6 10.91%
C 5 9.09%
R 7 12.73%
Total 55 100%
b. What position provides the most Hall of Famers?
As it can be seen from the frequency table in part a, Pitcher (P) has the highest frequency which is 17. Therefore, Pitcher (P) is the position provides the most Hall of Famers.
c. What position provides the fewest Hall of Famers?
As it can be seen from the frequency table in part a, 3rd base (3) has the lowest frequency which is 2. Therefore, 3rd base (3) is the position that provides the fewest Hall of Famers.
d. What outfield position (L, C, or R) provides the most Hall of Famers?
As it can be seen from the frequency table in part a, we have:
Frequency of L = 6
Frequency of C = 5
Frequency of R = 7
Since R has the highest frequency which is 7 among the outfield position (L, C, or R), it implies that R is the outfield position that provides the most Hall of Famers.
e. Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R).
Total frequency of infielders = Frequency of 1 + Frequency of 2 + Frequency of 3 + Frequency of S = 5 + 4 + 2 + 5 = 16
Total frequency of outfielders = Frequency of L + Frequency of C + Frequency of R = 6 + 5 + 7 = 18
The calculated total frequencies above imply that number of Hall of Famers of Infielders which is 16 is less than the 18 Hall of Famers of those of outfielders.
can somone help with this
Answers
If the cylindrical-barrel has volume of 785.4 ft³, then the radius of the barrel is 5 ft, option(c) is correct.
We know that volume of cylindrical barrel is given by formula : V = πr²h
where V denotes volume, r denotes radius, and h denotes height of the cylinder.
In this case, we are given that the volume of the barrel is 785.4 ft³ and the height is 10 ft.
Substituting these values and taking π ≈ 3.14, into the Volume-formula,
We get,
785.4 = 3.14 × r² × (10);
Simplifying this equation,
We get,
785.4/31.4 = r²,
r = √(785.4/31.4),
r ≈ 5 ft
Therefore, the radius of the barrel is approximately 5 feet, correct option is (c).
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if point c, shown on the coordinate plane below is reflected over both axes to create c what will be the coordinate of c
Answers
Explanation:
The coordinate of c in the plane looks like x= 3 while y = 2
This we assumed because there is no grid line to determine the numbers. The location shows it is within that coordinate
c (3, 2):
Reflecting acrossboth axes means reflecting across the y and reflection across the x axis
Reflection across y axis: (x, y) to (-x, y)
The coordinate of becomes: (-3, 2)
determine the solutions to the following systems of linear equations
Answers
Answer: 5: (-2, -1) 6: (0,2)
Step-by-step explanation:
This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Answers
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =\($36.34 + $26.03\)
= \($62.37\)
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = \($36.34 + $26.03\)
= \($62.37\)
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
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what is the answer to this simplify
2(3 + 5y)
Answers
Answer:
6 + 10y
Step-by-step explanation:
Hi,
To begin, you need to distribute the 2 to 3 and 5y (same thing as multiplying it).
2(3 + 5y)
6 + 10y
(Multiply the 2 by 3 and then the 2 by 5y)
Since 6 doesn't have a variable and 10y does, you can't combine them and, therefore, 6 + 10y is your answer.
I hope this helps :)
find the slope of the line that passes through the points (20,8) and (9,16)
Answers
Answer:
slope: \(-\frac{8}{11}\)
slope-intercept form: y= \(-\frac{8}{11}\)x+\(\frac{248}{11}\)
Step-by-step explanation:
Hope this helps!
The ______ sum of squares measures the variability of the observed values around their respective
treatment means
error
Answers
The variability of a observed values all around respective treatment means is measured by the "error" sum of squares.
Explain the term error sum of squares?SSE, also referred to as residual sum of squares, stands for sum of squares error. It is the discrepancy between the actual value and the value projected.
The product of a score's deviation from the mean and this same difference. The amount of variance in the dependent variable which can be affected by the independent is reflected with in denominator of a F ratio in a variance analysis. Additionally known as residual sum of squares and sum of squared errors (SSE).Thus, the variance of the observed values surrounding the means of the corresponding treatments is measured by the "error" sum of squares.
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The correct question is-
The ______ sum of squares measures the variability of the observed values around their respective treatment means.
Review the graph.
On a coordinate plane, a circle has center (4, 0) and radius 4. Another circle has center (2, negative 3) and radius 6. The area inside of the first circle and outside of the second circle between the 2 circles is shaded.
Which system of inequalities is shown in the graph?
36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
36 < (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
Answers
Answer:
36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²
Step-by-step explanation:
This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.
what is the value of x ?
Answers
Answer:
x = 19
Step-by-step explanation:
The two angles form a right angle
A right angle has a measure of 90 degrees
Thus, x + 14 + 3x = 90
^This is the equation we will use to solve for x
x + 14 + 3x = 90
step 1 combine like terms
x + 3x = 4x
we now have 4x + 14 = 90
step 2 subtract 14 from each side
90 - 14 = 76
14 - 14 cancels out
we now have 76 = 4x
step 3 divide each side by 4
4x / 4 = x
76 / 4 = 19
we're left with x = 19
find the indicated side of the right triangle. 45 degrees, 45 degrees, 6, y, x, x = ?
Answers
3√2 and 3 are the values of x and y respectively from the figure.
Trigonometry identitiesThe given diagram is a right triangle with an acute angle of 45 degrees
We need to determine the values of variables x and y.
Applying the trigonometry identity, we will have:
sin 45 = opposite/hypotenuse
sin45 = 3/x
x = 3/sin45
x = 3/(1/√2)
x = 3√2
Similarly:
tan 45 = opposite/adjacent
tan 45 = 3/y
1 = 3/y
y = 3
Hence the values of x and y from the figure is 3√2 and 3 respectively
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What is (3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)?
Answers
Answer:
Hope this helps ;) don't forget to rate this answer !
Step-by-step explanation:
To solve this problem, we need to perform the indicated operations in order. The first step is to simplify the expressions inside the parentheses.
(3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)
= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)
The next step is to combine like terms within each parentheses:
= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)
= (56x - 3x² + 7) + (-8x + 2x³ + 3)
Finally, we can add the two expressions:
= (56x - 3x² + 7) + (-8x + 2x³ + 3)
= 56x - 3x² - 8x + 2x³ + 3 + 7
= 56x - 3x² - 8x + 2x³ + 10
The final answer is 56x - 3x² - 8x + 2x³ + 10.
need help with both of these please. give 20 points
Answers
The following gives the variations:
m= -4p -----------> direct variation
r=9/t----------->indirect variation
n=(1/2)f----------->direct variation
u=2/z----------->indirect variation
The value of y when x=2 is -14
What are direct and indirect variations ?
One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.
When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.
m= -4p -----------> direct variation
r=9/t----------->indirect variation
n=(1/2)f----------->direct variation
u=2/z----------->indirect variation
General equation for an indirect variation:
y = k/x
substitute y=7 and x= -4
7=k/-4
k=7*-4 = -28
To find y when x=2:
Substitute x=2 and k=-28 into the equation
y=-28/2 = -14
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HELP ASAP! HELP ASAP!
Answers
Answer:
The answer is b because if you move it to the right you don't go to the other side
You buy 10 vegetarian pizzas and pay with $100. How much change do you receive?
3 Vegetarian Pizzas for
$25.50
You receive $ in change.
Answers
Answer:
$15
Step-by-step explanation:
3÷25.50 to get $8.50 per pizza then you would time that by 10 to get $85 as the total cost
HELP PLEASEEEEEEEEEEE
Answers
Answer:
Which one is at the bottom? if the one at the bottom is 0 then the answer is 0. If its not then its related to pemdas or something else
Step-by-step explanation:
Answer:
? = 4
4 is the answer
Step-by-step explanation:
heart = 21
rainbow = 7
unicorn horn = 9
so, we have
heart + rainbow + rainbow = 35
21 + 7 + 7 = 35
heart + unicorn horn + rainbow = 37
21 + 9 + 7 = 37
rainbow + unicorn horn + unicorn horn =25
7 + 9 + 9 = 25
unicorn horn + unicorn horn + rainbow - heart = ?
9 + 9 + 7 - 21 = 4
I need help I needa pass this test all 9 questions
Answers
Answer: The answer is b
Step-by-step explanation: Check the image! It matches. Hope this helps!
What is the M.A.D. (mean absolute deviation) of the following data set?
8 9 9 7 8 6 9 8
Answers
The mean absolute deviation is 0.75
How to determine the mean absolute deviationTo calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set
From the information given, we have that the data set is;
8 9 9 7 8 6 9 8
Let's calculate the mean, we get;
Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8
Mean = 64 / 8
Divide the values
Mean = 8
Let's determine the absolute difference, we get;
Absolute differences=
|8 - 8| = 0
|9 - 8| = 1
|9 - 8| = 1
|7 - 8| = 1
|8 - 8| = 0
|6 - 8| = 2
|9 - 8| = 1
|8 - 8| = 0
Find the mean of the absolute differences:
Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8
Absolute difference = 6 / 8 = 0.75
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McDonald's offers 2 free bottles of water or juices for ever 20 purchases . whataburger offers 3 free bottled waters or juices for ever 25 purchases
what is wataburger's ratio of free drinks to purchased drinks? simplify if possible
Answers
Answer:
3:25
Step-by-step explanation:
You can't simplify it
Given the cost function, C(x), and the revenue function, R(x), more than how many units must be produced and sold for the business to make money?
C(x)= 2,000x + 60,000
R(x)= 8,000x
Answers
Answer:
x= 10
Step-by-step explanation:
C(x) = 2,000x + 60,000
R(x) = 8,000x
Set the solution to zero.
R(x) - C(x) = 0
8,000x - (2,000x + 60,000) = 0
6,000x - 60,000 = 0
x=10
Please help. Systems of equations. Solve using elimination.
12X + 16y = 96
12X + 48y = 192
Answers
Answer:
x=4
y=3
Step-by-step explanation:
12X + 16y = 96--(1)
12X + 48y = 192---(2)
(2)-(1),
12x + 48y - (12x+ 16y)= 192- 96
12x + 48y - 12x - 16y = 96
32y = 96
y= 96÷32
y =3
substituting y=3 in (1),
12x +(16×3) = 96
12x + 48 = 96
12x = 96-48
12x = 48
x= 48÷12
x= 4
Hope this helps!
Unit Activity: Volume
Modern Art
an artist has been commissioned to install a large sculpture in a park. she is planning an abstract geometric sculpture and has created the scaled design.
Part A: what three basic solids is the sculpture composed of?
- cone
- triangular prism
- triangular pyramid
- hemisphere
- square prism
- square pyramid
Part B: the artist will use concrete to create the form of the sculpture. how much concrete will the artist need to make up each of the three parts that make up the sculpture? use the text tool to write the volume of each of the three parts on the diagram. round each volume to the nearest whole cubic meter.
(the diagram is just a blank (without the numbers) version of the picture provided)
Part C: the artist will be tiling the sculpture with mosaic squares that are 2 centimeters long on each edge. how can she calculate how many tiles to buy? write a strategy to explain how to find the number of tiles.
Part D: at least how many mosaic squares does the artist need to cover the sculpture? select the correct answer from the drop down menu. “she will need at least ___ tiles.”
Answers
The answer should be chosen from the given drop-down menu options based on the calculated number of tiles in Part C.
1. Triangular prism
2. Square pyramid
3. Hemisphere
Part A: The sculpture is composed of the following three basic solids:
Part B: To determine the amount of concrete needed for each part of the sculpture, we need to calculate the volume of each solid.
To find the volume of a triangular prism, you would multiply the area of the triangular base by the height of the prism.
To find the volume of a square pyramid, you would multiply the area of the square base by the height of the pyramid and divide it by 3.
To find the volume of a hemisphere, you would use the formula (4/3)πr³, where "r" represents the radius of the hemisphere.
Once you have the dimensions for each part, you can apply these formulas to find their respective volumes. Remember to round each volume to the nearest whole cubic meter.
Part C: To calculate the number of mosaic tiles needed, the artist can follow these steps:
1. Determine the surface area of each part of the sculpture that will be covered with tiles. This involves calculating the area of each face or surface that will be tiled.
2. Divide the surface area of each part by the area of a single mosaic tile.
This will give you the number of tiles needed to cover that specific part.
3. Sum up the number of tiles needed for each part to get the total number of tiles required for the entire sculpture.
Part D: Since the question doesn't provide the dimensions of the sculpture or its parts.
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Answer: A
Step-by-step explanation: why A because if you in the word said
-cone
-triangular prism
-square prism
only those are the answer if i am incorrect please forgive me
Find the area someone please help
Answers
Answer:
33.3cm²
Step-by-step explanation:
9 multiplied by 3.7 is equal to 33.3cm²
Answer:
the answer is 33.3
Step-by-step explanation:
the formula is
Area= base × height
A =9×3.7
=33.3
What are the new coordinates if the figure were rotated 90 degrees counterclockwise
Answers
Answer:
third option
Step-by-step explanation:
under a counterclockwise rotation of 90° about the origin
a point (x, y ) → (y, - x )
Then
A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )
B (2, - 2 ) → (- 2, - 2 )
C (1, - 4 ) → (- 4, - 1 )
The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)
How to determine the new coordinates rotating by 90 degrees counterclockwiseFrom the question, we have the following parameters that can be used in our computation:
The figure,
Where, we have
A = (-1, -2)
B = (2, -2)
C = (1, -4)
The rule of 90 degrees counterclockwise is
(x, y) = (-y, x)
Using the above as a guide, we have the following:
A = (2, -1)
B = (2, 2)
C = (4, 1)
Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)
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tyler orders a meal thats 15$ if the tax rate is 6.6% how much will the sales tax be on tylers meal?
Answers
Answer : 0.99
Explanation : 15 * 6.6/100 For The Tax.
Total : 15.99
Work out the area of this circle.
Give your answer in terms of r and state its units.
TT
6 mm
Answers
=Pi6 to the power of 2
Answer is 113.0 (rounded to the 1 decimal place)
pls solve this questions 4and 5
Answers
Answer:
86km/h
80km/h
Step-by-step explanation:
weighted average
bus took 5hrs so van took 3.75 hrs
300/3.75
Match each determinant value to the correct matrix - partially solved, see photo
Answers
We would find the determinant of each matrix and match them with the given values.
\(\begin{gathered} \begin{bmatrix}{1} & {5} & {-\text{ 2}} \\ {7} & {4} & {1} \\ {-\text{ 3}} & {1} & {6}\end{bmatrix} \\ Determinant\text{ = 1\lparen4}\times6\text{ - 1}\times1)\text{ - 5\lparen7 }\times6-1\times-3)-2(7\times1-4\times-3) \\ =\text{ \lparen24-1\rparen-5\lparen42+3\rparen-2\lparen7+12\rparen} \\ =\text{ 23-225-38} \\ =\text{ - 240} \end{gathered}\)\(\begin{gathered} \begin{bmatrix}{7} & {2} & {5} \\ {2} & {-2} & {5} \\ {1} & {11} & {4}\end{bmatrix} \\ Determinant\text{ = 7\lparen-2}\times4\text{ -5}\times11)-2(2\times4-5\times1)+5(2\times11-1\times-2) \\ =7(-8-55)-2(8-5)+5(22+2) \\ =-441-6+120 \\ =\text{ - 327} \end{gathered}\)\(\begin{gathered} \begin{bmatrix}{3} & {6} & {4} \\ {3} & {6} & {7} \\ {2} & {4} & {-2}\end{bmatrix} \\ Determinant\text{ = 3\lparen6}\times-2\text{ - 7}\times4)-6(3\times-2-7\times2)+4(3\times4-6\times2) \\ =3(-12-28)-6(-6-14)+4(12-12) \\ =-120+120+0 \\ =\text{ 0} \end{gathered}\)\(\begin{gathered} \begin{bmatrix}{1} & {8} & {-4} \\ {2} & {3} & {3} \\ {-1} & {1} & {-4}\end{bmatrix} \\ Determinant\text{ = 1\lparen3}\times-4-1\times3)-8(2\times-4-3\times-1)-4(2\times1-3\times-1) \\ =\text{ 1\lparen-12-3\rparen-8\lparen-8+3\rparen-4\lparen2+3\rparen} \\ =-15+40-20 \\ =\text{ 5} \end{gathered}\)