Evaluate the determinant for the following matrix:
-4 -4 -3
3 3 -5
-5 2 -5
A. –203 B. 75 C. –152 D. –263
Answers
Answer:
The determinant of matrix is -203
Step-by-step explanation:
Given the matrix of order 3 i.e
[tex]A=\begin{bmatrix}-4&-4&-3\\ 3&3&-5\\ -5&2&-5 \end{bmatrix}[/tex]
we have to find the determinant of matrix A
[tex]|A|=-4(-5(3)-(-5)(2))-3((-4)(-5)-(-3)(2))+(-5)((-5)(-4)-(-3)(3))\\\\|A|=-4(-15+10)-3(20+6)-5(20+9)\\\\|A|=-4(-5)-3(26)-5(29)\\\\|A|=20-78-145\\\\|A|=-203[/tex]
Hence, the determinant of matrix is -203
Option A is correct.
Related Questions
show or describe two different ways to complete the comparison using < , > ,or =: 0.26 () 0.4
Answers
Reason: 0.26 is less than 0.4 which also can be written as 0.40.
The "mouth" points to the bigger number.
f √6 is the geometric mean between 6 and another number, then the number is
Answers
What you have here is a geometric series beginning with x ⇒ √6 ⇒ 6
x = √6 / 6 It is the smallest number in the series.
Each number is multiplied by √6 to get to the next number in the series.
√6/6 <<<< answer
HELLO!!! ^-^
The answer is 1.
If √6 is the geometric mean between 6 and another number, then the number is 1.
(I had the same question and got it right using this answer so yeah) ^-^
Have an amazing day!!! ^-^
Historical Fact:
Back in the older days, the word awful was a word used to praise someone! That is because aw in awful comes from the origin awe which is used when someone is in awe of you!!! For example: You are AWESOME!!!
Norma has an A-frame cabin.The back is shown below. How many square feet of paint will she need to cover the back of the cabin?
Answers
PLEASE SEE ATTACHED IMAGE.
For this case what you should do is find the area of the triangle which will be given by:
A = (1/2) * (b) * (h)
Where
b: base
h: height
Substituting the values we have:
A = (1/2) * (25 1/2) * (15)
A = 191.25 feet ^ 2
Answer:
she will need 191.25 feet ^ 2 to cover the back of the cabin
Two number cubes are rolled. What is the probability that the sum of the numbers rolled is either 3 or 9?
A.1/6
B.1/13
C.1/18
D.1/162
Answers
[tex] |\Omega|=6^2=36\\
|A|=\underbrace{2}_{\text{the sum is 3}}+\underbrace{4}_{\text{the sum is 9}}=6\\\\
P(A)=\dfrac{6}{36}=\dfrac{1}{6}\approx17\% [/tex]
Math help.... Please....
This doesn't make any sense to me. Pls help me. I'm not begging, but this problem has been stumping me and I don't understand how to do it.... I'm using 99 points to give to a person who maybe can help me. I will give Brainliest if you are correct.
Thank you so very kindly.
When Julia dumped out the big jar of dimes and nickles she found 287 coins. If there was $20.50 in the jar, how many of each kind of coin was there??
Don't answer this unless you actually are answering the question!!! If you have any questions, or it doesn't make sense, please say something in the "Ask for Details" section.
Thanxs again!!!
Answers
0.05N + 0.10D = 20.50
While N = The amount of nickels, and D = The amount of dimes.
Since N = 164, and D = 123. It would add up to 287 coins. 164 + 123 = 287.
Now that you have the number for those two variables, solve the equation for when N = 164, and D = 123.
0.05N + 0.10D = 20.50
0.05(164) + 0.10(123) = 20.50
8.2 + 12.3 = 20.50
20.50 = 20.50
So, there is 164 nickels, and 123 dimes for your answer.
I hope this helps!
~ Notorious Sovereign
Answer:First, you want to solve for the equation for this problem, would be:
0.05N + 0.10D = 20.50
While N = The amount of nickels, and D = The amount of dimes.
Since N = 164, and D = 123. It would add up to 287 coins. 164 + 123 = 287.
Now that you have the number for those two variables, solve the equation for when N = 164, and D = 123.
0.05N + 0.10D = 20.50
0.05(164) + 0.10(123) = 20.50
8.2 + 12.3 = 20.50
20.50 = 20.50
So, there is 164 nickels, and 123 dimes for your answer.
I hope this helps you
32 deanna bought a shirt that was on sale for 40% off the original price. she also used a coupon that gave her an additional 20% off the sale price of the shirt. the original price of the shirt was $54. what is the new price of the shirt before tax?
Answers
60% = 0.60
54 x 0.60 = 32.40
54 - 32.40 = 21.60
the price was $21.60
PLEASE ANY HELPFUL PERSON HELP!!!!!!
Answers
4.5x < 175 - 94
4.5x < 81
x < 81/4.5
x < 18
A rocket is launched from atop a 55-foot cliff with an initial velocity of 138 ft/s. a. Substitute the values into the vertical motion formula h = −16t2 + vt + c. Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
Answers
Substituting the values into the equation, we have:
0 = -16t² + 138t + 55
The quadratic formula is:
[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Inserting our information we have:
[tex]t=\frac{-138\pm \sqrt{138^2-4(-16)(55)}}{2(-16)} \\ \\=\frac{-138\pm \sqrt{19044--3520}}{-32} \\ \\=\frac{-138\pm \sqrt{19044+3520}}{-32} \\ \\=\frac{-138\pm \sqrt{22564}}{-32} \\ \\=\frac{-138\pm 150}{-32}=\frac{-138+150}{-32}\text{ or } \frac{-138-150}{-32} \\ \\=\frac{12}{-32}\text { or } \frac{288}{32}=-0.375 \text{ or } 9[/tex]
Jessica is designing a large, circular garden for a neighborhood park. A part of the garden will be occupied by a fountain. If the diameter of the garden is 82 meters and the measure of the angle formed by the fountain is 126°, what will be the approximate length of the garden cover by the fountain?
Answers
S = R * theta
Where
S: length of the garden covered by the fountain.
R: Garden radio
theta: angle formed by the source.
Substituting values we have:
S = (82/2) * ((126) * (pi / 180))
S = 90.16 m
Answer:
The approximate length of the garden cover by the fountain will be:
S = 90.16 m
Use the Venn diagram to calculate probabilities.
Which probability is correct?
P(A|B)=1/2
P(B|A)=7/20
P(A|C)=6/23
P(C|A)=13/17
Answers
Answer: The correct probability is (D) [tex]P(C/A)=\dfrac{13}{17}.[/tex]
Step-by-step explanation: We are given to select the option that gives the correct probability statements using the Venn-diagram in the figure.
From the figure, we can see that there are three events, A, B and C.
And,
[tex]n(A)=1+6+7+3=17,\\\\n(B)=1+6+4+9=20,\\\\n(C)=6+4+6+7=23,\\\\n(A\cap B)=1+6=7,\\\\n(A\cap C)=6+7=13,\\\\n(B\cap C)=6+4=10,\\\\n(A\cap B\cap C)=6.[/tex]
By the law of SET THEORY, we have
[tex]n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\\\\\Rightarrow n(A\cup B\cup C)=17+20+23-7-13-10+6\\\\\Rightarrow n(A\cup B\cup C)=36.[/tex]
So, the total number of elements in the sample space 'S' will be
n(S) = 36 + 8 = 44.
Therefore,
[tex]P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{\dfrac{n(A\cap B)}{n(S)}}{\dfrac{n(B)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{20}=\dfrac{7}{20},\\\\\\\\P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\dfrac{n(B\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{17}=\dfrac{7}{17},\\\\\\\\P(A/C)=\dfrac{P(A\cap C)}{P(C)}=\dfrac{\dfrac{n(A\cap C)}{n(S)}}{\dfrac{n(C)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{23}=\dfrac{13}{23},\\\\\\\\P(C/A)=\dfrac{P(C\cap A)}{P(A)}=\dfrac{\dfrac{n(C\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{17}=\dfrac{13}{17}.[/tex]
Thus, the correct probability is [tex]P(C/A)=\dfrac{13}{17}.[/tex]
Option (D) is correct.
The probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
For the value of probability P(A|B):
We know that:
[tex]\rm P(A/B)=\frac{P(A\cap B)}{P(B)} \Rightarrow \frac{\frac{n(A\cap B)}{n(T)} }{\frac{n(B)}{n(T)} }[/tex]
From the Venn diagram:
n(A∩B) = 7, n(B) = 20, n(T) = 44
P(A/B) = (7/44)×44/20)
P(A/B) = 7/20
For P(B|A):
[tex]\rm P(B/A)=\frac{P(B\cap A)}{P(A)} \Rightarrow \frac{\frac{n(B\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]
The values of n(B∩A) = 7, n(A) =17
P(B/A) = (7/44)×(44/17)
P(B/A) = 7/17
For P(A|C):
[tex]\rm P(A/C)=\frac{P(A\cap C)}{P(C)} \Rightarrow \frac{\frac{n(A\cap C)}{n(T)} }{\frac{n(C)}{n(T)} }[/tex]
The value of n(A∩C) = 13, n(C) = 23
P(A/C) = (13/44)×(44/23)
P(A/C) = 13/23
For P(C|A):
[tex]\rm P(C/A)=\frac{P(C\cap A)}{P(A)} \Rightarrow \frac{\frac{n(C\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]
The values of n(C∩A) = 13, n(A) = 17
P(C|A) = (13/44)×(44/17)
P(C|A) =13/17
Thus, the probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.
Learn more about the Venn diagram here:
brainly.com/question/1024798
#SPJ3
The center of a circle is at (−2, −7) and its radius is 6.
What is the equation of the circle?
(x−2)2+(y−7)2=36
(x−2)2+(y−7)2=3
(x+2)2+(y+7)2=3
(x+2)2+(y+7)2=36
The equation of a circle is (x+4)2+(y−5)2=121.
What is the center and radius of the circle?
center: (4, −5); radius: 11
center: (−4, 5); radius: 121
center: (−4, 5); radius: 11
center: (−4, −5); radius: 121
Answers
2.) center: (-4, 5) radius 11
Answer:
1. option D is correct; [tex](x+2)^2+(y+7)^2=36[/tex]
2. option C is correct; center: (-4, 5) and radius = 11 unit
Step-by-step explanation:
The general equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex] .....[1]
where,
(h, k) is the center of the circle and r is the radius of the circle.
1.
As per the statement:
The center of a circle is at (−2, −7) and its radius is 6.
⇒(h, k) = (-2, -7) and r = 6 units
Substitute these in [1] we have;
[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]
⇒[tex](x+2)^2+(y+7)^2=36[/tex]
Therefore, the equation of circle is, [tex](x+2)^2+(y+7)^2=36[/tex]
2.
As per the statement:
The equation of a circle is:
[tex](x+4)^2+(y-5)^2 = 121[/tex]
We can write this as:
[tex](x-(-4))^2+(y-5)^2 = 11^2[/tex]
On comparing with equation [1] we have;
(h, k) = (-4, 5) and r = 11 units
Therefore, the center and radius of the circle is,
center: (-4, 5) and radius = 11 unit
1 question pleasee i need this asap!! thank you :D
Answers
________________________________________________________
Explanation:
________________________________________________________
Given the following equation:
________________________________________________________
" x² + 3x – 54 = 0 " ; Solve for "x" ;
_____________________________________________________
Check if the part of the equation on the "left-hand side" can be "factored":
" x² + 3x – 54 " ;
→ We see the " + 3x " and the " – 54 "
Factors of " -54 " that add up to " +3" ;
Let us try: " -9, 6" ; → " -9 + 6 = -3 " ; → " -3 ≠ +3 ;
Let us try: " 9, -6" ; → " 9 + (-6) = 9 – 6 = 3 " ; YES!
→ {that is: " +9 , -6 "} ;
So, we can rewrite the entire equation:
→ " (x + 9)(x – 6) = 0 " ;
→ " x = -9 " ; or, " x = 6 " ; which is:
→ Answer choice: [A]: " x = 6 " or " x = - 9 " .
______________________________________________________
Multiply. −5m(−2m6+4m4+m−9) Express the answer in standard form. Enter your answer in the box.
Answers
10m^6-20m^4-5m^-9
im sorry if its not right, just know if its wrong i sacrificed 3 points off my unit test. lol
What is 6 divided by 1/3
Answers
to find the answer, you must flip the second fraction, and change the division into a multiplication
6 x 3
6 x 3 = 18
18 is your answer
hope this helps
Which of the following best describes the solutions to the inequality shown below?
4c + 5 < 4c + 3
A. All real numbers
B. c < 1/2
C. c > 1/4
D. No solution
Answers
Help plz!!
Graph of y equals negative 2 times x squared plus 40 x plus 600
Which of the following coordinates is not an intercept for the function?
A. (−10, 0)
B. (0, 600)
C. (0, 800)
D. (30, 0)
Answers
Since you can determine the intercept through the equation y=mx+b and b in this equation is 600 so the answer is C
Answer:
0,800
Step-by-step, explanation: took test and got correct
How do you write 230% as a fraction or mixed number in simplest form?
Answers
a doctor is using a treadmill to assess the strength of a patients heart. he sets the 48 inch long treadmill at an incline of 10 degrees. how high is the treadmill raised
Answers
x = 48* .1736
x = 8.3335
rounds to 8.3"
sin 1o^0 = h/48
h = 48 sin 10^0
so; h = 8.3 inches; or
8.3 in.
say you have a triangle:
outside = 48
outside = h
inside = 10^0
In this exercise we have to use the knowledge of sine to be able to calculate the triangle values, in this way we can say that:
[tex]h= 8.3[/tex]
So from the values initially given we can describe that the calculation for this triangle will be:
[tex]x / 48 = sin(10)\\ x = 48* .1736\\ x = 8.3335\\ sin 10^0 = h/48\\ h = 48 sin 10^0\\ h = 8.3 inches[/tex]
See more about triangles at brainly.com/question/25813512
What is the exact value of sin 30° ?
Enter your answer, as a simplified fraction, in the box.
Answers
1. By defnition, sine is one of the trigonometric functions. The sine of an angle can be written as below: "sin(α)".
2. The sine of 30 degrees, is:
sin(30°)=1/2
3. Therefore, the answer for the exercise shown above: sin(30°)=1/2
A quadrilateral has angle measures of 52°, 94°, and 97°.
What is the measure of the fourth angle?
Enter your answer in the box.
Answers
A quadrilateral has angle measures of 52°, 94°, and 97°.
What is the measure of the fourth angle?
Enter your answer in the box.
Answer: 117
Step-by-step explanation:
The birdwatching club has 27 members, 18 girls and 9 boys. What is the ratio of the girls to boys in the birdwatching club?
Answers
answer
2/1
HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answers
[tex]\sqrt{a}=b\iff b^2=a\\\\a\geq0\ \wedge\ b\geq0\\\\\text{therefore your answer is}\\\\\text{(A) The equation has no solutions.}[/tex]
What perfect squares divide into 337? I only need two!
Answers
[tex]337 \cdot 337 = 113569[/tex]
A second perfect square that divides into 337 is
[tex]337 \cdot 337 \cdot 2 \cdot 2 = 674\cdot 674 = 454276
[/tex]
PLEASE HELP ME QUICKLY!!
Answers
Keep in mind unfortunately I am not 100% sure, but this is what I think. Hope this helps a little!
How are experimental and theoretical probability alike?
Answers
If a fair coin is tossed 5 times what is the probability of getting 3 heads in a row
Answers
Just a short answer please help :( the top
Answers
26/100 = x/82
A hiker is lost in the woods. A search team has created a coordinate grid to represent the woods. Each unit on the grid is one square mile. The hiker was last seen at (4, -9) and could have walked 10 miles in any direction since then. Which equation represents the area the hiker could be in?
A) (x - 4)2 + (y + 9)2 = 102
B) (x + 4)2 + (y - 9)2 = 102
C) (x + 4)2 + (y + 9)2 = 1002
D) (x - 4)2 + (y - 9)2 = 1002
Answers
.. (x -h)^2 +(y -k)^2 = r^2
Selection A is appropriate.
_____
It would be helpful if you would use appropriate math symbols. 102 is very different from 10^2. (Copying and pasting does not work--editing is needed.)
Can anyone please help
Answers
9)
∠DBC=90-54=36°
∠CAD=∠DBC=36°
10)
∠BOC=1/2(360-2*100)=1/2*160=80°
∠l=1/2∠AOD=1/2∠BOC=40°
11)
JL=10
JA=7==>AL=10-7=3
LC=AL=3
LK=11
CK=11-3=8
KB=KC=8
BJ=JA=7
perimeter=10+11+15=36
Perform the indicated operation. then estimate to see whether the proposed results is reasonable. 11.58 + 11.9 + 9.2
32.68
22.68
33.68
31.68 Preform the indicated operation. Then estimate to see whether the proposed result is reasonable.
93.8 - 6.48
87.32
97.44
87.42
94.34
Preform the indicated operation. Then choose the best answer. 27.7 x 1.9 5.363
52.63
53.62
5.263 Choose the best estimate. 64.1 ÷ 97
641
6.41
0.641
6410 Use estimation to determine whether the result is reasonable or not. 108.93 x 32.6 Result: 355.112 Is it reasonable or not?
Answers
2) 87.32
3) 52.63
4) 0.641
5) Unreasonable, the decimal point should be moved 1 space to the right.