Answer:
First, we write the augmented matrix.
⎡
⎢
⎣
1
−
1
1
2
3
−
1
3
−
2
−
9
|
8
−
2
9
⎤
⎥
⎦
[1−1123−13−2−9 | 8−29]
Next, we perform row operations to obtain row-echelon form.
−
2
R
1
+
R
2
=
R
2
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
3
−
2
−
9
|
8
−
18
9
⎤
⎥
⎦
−
3
R
1
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
0
1
−
12
|
8
−
18
−
15
⎤
⎥
⎦
−2R1+R2=R2→[1−1105−33−2−9|8−189]−3R1+R3=R3→[1−1105−301−12|8−18−15]
The easiest way to obtain a 1 in row 2 of column 1 is to interchange
\displaystyle {R}_{2}
R 2
and
\displaystyle {R}_{3}
R 3
.
Interchange
R
2
and
R
3
→
⎡
⎢
⎣
1
−
1
1
8
0
1
−
12
−
15
0
5
−
3
−
18
⎤
⎥
⎦
InterchangeR2andR3→[1−11801−12−1505−3−18]
Then
−
5
R
2
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
57
|
8
−
15
57
⎤
⎥
⎦
−
1
57
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
1
|
8
−
15
1
⎤
⎥
⎦
−5R2+R3=R3→[1−1101−120057|8−1557]−157R3=R3→[1−1101−12001|8−151]
The last matrix represents the equivalent system.
x
−
y
+
z
=
8
y
−
12
z
=
−
15
z
=
1
x−y+z=8 y−12z=−15 z=1
Using back-substitution, we obtain the solution as
\displaystyle \left(4,-3,1\right)
(4,−3,1)
PLEASE HELP: Click on the graph to choose the correct answer to the equation.
y > 2
(Choose one of the graphs from the image as the answer)
Answer:
The 8th graph.
Step-by-step explanation:
It has a horizontal line over two which indicates that the y axis is known and over 2.
The required graph of the given inequality y > 2 is shown in the attached file, which is the correct answer that would be an option (H).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have been the given inequality y > 2
Plot the "y=" line (a solid line for y or y, and a dashed line for y or y>). The shade above the line for a "greater than" (y> or y), or below the line for a "less than" (y or y).
It has a horizontal line over two which represents that the y-axis is known and over 2 in the attached graph.
Therefore, the required graph of the given inequality y > 2 is shown in the attached file.
Hence, the correct answer would be option (H).
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What is the next term in the sequence below?
0.25, 0.75, 2.25, 6.75, …
A. 6.25
B. 10.25
C. 20.25
D. 60.75
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {C. \:20.25}}}}}}[/tex]
[tex]0.25, 0.75, 2.25, 6.75,20.25,..[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]0.25, 0.75, 2.25, 6.75,20.25 \\ \\ ➺ \: 0.25 \times 3 = 0.75 \\ \\ ➺ \: 0.75 \times 3 = 2.25 \\ \\ ➺ \: 2.25 \times 3 = 6.75 \\ \\ ➺ \: 6.75 \times 3 = 20.25[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
pls help me !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9.89 m
Step-by-step explanation:
AC is the hypotenuse (H)
x is the opposite (O)
O and H are in sine
sin=O/H
H=O/sin
H=7.9/sin(53)
=9.89187169943418
3 SF
9.89 m
Answer:
AC= 13.144
Step-by-step explanation:
cos ∅ = Adjacent/ Hypotenuse
cos (53°) = x/AC
cos (53°) = 7.9/AC
(0.601).(AC)=7.9
AC=(7.9)/(0.601)
AC= 13.144 (3 S.F)
If the inverse of a function is also a function, then
The function is said to be ….?
Answer: Invertible
Step-by-step explanation:
If inverse of a function exists, then the function is said to be invertible. A unique value exits for each given input.
Inverse of a function can be obtained by expressing the given function in terms of y and then replace y by x.
Who wants to help me
Answer:
Step-by-step explanation:
Please answer quickly
Answer:
10
Step-by-step explanation:
given :
length WX ≅ (congruent means equal) length XY
therefore , WX = 3
WZ = WX + XZ
WZ = 3 + 7
WX = 10
-y-22-13
6< X/2-2
I need help solving both
Answer: The first one is y≤11 and the second question is x>16 Hope that helps Goodbye!
Step-by-step explanation: 1. Add 22 to both sides.
-13+2
−y≥−13+2
2 Simplify -13+2−13+2 to -11−11.
-y\ge -11
−y≥−11
3 Multiply both sides by -1−1.
y\le 11
y≤11
1 Add 22 to both sides.
6+2<\frac{x}{2}
6+2<
2
x
2 Simplify 6+26+2 to 88.
8<\frac{x}{2}
8<
2
x
3 Multiply both sides by 22.
8\times 2<x
8×2<x
4 Simplify 8\times 28×2 to 1616.
16<x
16<x
5 Switch sides.
x>16
x>16
Determine the value of c that makes the function f(x y) = c/x-y/ a joint discrete probability density function for x=2,0,2 and y=-2,3
Given: The given function is
[tex]f(x,y)=c(x-y)[/tex]
To find: Here we need to find the value of c for which f(x,y) will be a joint
discrete probability density function.
Solution:
Now, to find c we have,
[tex]\int\limits^3_{-2} \,\int\limits^2_0 {f(x,y)} \, dx dy\\=\int\limits^3_{-2} \,\int\limits^2_0 {c(x-y)} \, dx dy\\\\=\int\limits^3_{-2} \,[2c-2cy]dy\\=10c-5c\\=5c\\The integral should be1.\\So, 5c=1\\[/tex]
∴[tex]c=\frac{1}{5}[/tex]
Therefore, the required value of c is 1/5.
the gravitational acceleration on Earth is 9.8m/s^2 what is the weight of a car on earth if the mass is 1360
Answer:
13328 N
Step-by-step explanation:
9.8 m/s^2 • 1360 = X
13328 N = X
How do I fill this out I need to pass this class to move up a grade
Answer: x = 8,-2
Step-by-step explanation:
x^2-6x-16=0
x =[ -(-6)+-sqrt(-6)^2 - 4x1x(-16)/2x1
x = [6+-sqrt 36+64]/2
x = 6+-sqrt 100/2
x = 6 +-10/2
x = 6+10/2, 6-10,2
x = 8, -2
Answer:
Step-by-step explanation:
This is the quadratic equation formula for the roots.
x^2 - 6x - 16 = 0
x = [- (-6) +/- √( (-6)^2 - 4*1*-16) / 2*1
x = (6 +/- √(36 + 64) / 2
x = (6 +/- √(100) / 2
x = (6 +/- 10) / 2
x = 16/2 = 8
x = -4/2 = -2
Is [tex]18x^6+5y^6[/tex] prime polynomial why or why not
No files
Answer:
yes
Step-by-step explanation:
[tex]18x^6 + 5y^6 \ cannot\ be \ factorized \ further. \\\\So \ it \ is \ a \ prime\ polynomial.[/tex]
What is m angle A? Enter your answer in the box.
Answer:
ANSWER: 22
Step-by-step explanation:
hope it helps thankks
Answer:
I agree with the person above
Mrs. Jeffers bought 3 ¼kg of caramels and 2½ of chocolate. How many kilograms of candy did she buy altogether?
Which of the following equations is of a parabola with a vertex at (0, 6)?
y = ( x + 6) 2
y = ( x - 6) 2
y = x2 + 6
y = x2 - 6
Answer:
y = x² + 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (0, 6) , let a = 1 , then
y = (x - 0)² + 6 , that is
y = x² + 6
Need help with this ASAP! THANKS
What is the factorization of 49b2 − 81?
(7b – 9)(7b – 9)
(7b – 9)(7b + 9)
(7b2 – 9)(7b2 – 9)
(7b2 – 9)(7b2 + 9)
Answer:
B. (7b – 9)(7b + 9)
Step-by-step explanation:
got 100% on my quiz
Which expression is equivalent to 2^-3/2^-5
Answer:
2^2
Step-by-step explanation:
2^-3/2^-5
We know that a^b / a^c = a^(b-c)
2^-3/2^-5 = 2^( -3 - -5) = 2^(-3+5) = 2^2
You want to nail your 4 championship plaques onto a wooden
plank. The plaques are each 5 inches wide, and the plank
measures 33 inches in length. If you have 2 inches of space on
both ends of the plank and want to space out your plaques
evenly, how much space should there be between each
plaque?
=============================================================
Explanation:
The overall plank is 33 inches long. Subtract 2 copies of 2 inches off to represent those left and right 2 inches of space at each end.
33 - 2*2 = 33 - 4 = 29
So we have 29 inches to work with.
There are 4 plaques to hang up, and each is 5 inches wide. So that accounts for 4*5 = 20 inches of space just for the plaques themselves. We have 29-20 = 9 inches left for the gaps between plaques.
Since we have 4 plaques, there are 4-1 = 3 gaps between the adjacent plaques. The gap width is 9/3 = 3 inches.
See the diagram below. The values in black are the widths of each championship (5 inches each). The values in red are the gaps either between the plaques or between the plaque and the edge of the plank.
As a check, the values in that diagram should add to 33.
2+5+3+5+3+5+3+5+2 = 33
So the answer is confirmed.
In a community of 9,400 people the number of women exceeds the number of men by 1,500.Find the ratio of men to women in the community
Answer:
Step-by-step explanation:
x +(x+1500) = 9400
2x + 1500 = 9400
2x = 7900
x=3950 (men)
y = 5450 (woman)
5450 :3950
109:79
if a triangle has one angle that measure 81 degrees and another that measures 47 degrees, what is the measure of the third angle?
Answer: 52
Step-by-step explanation:
81 + 47 is 128.
180 - 128 =52 degrees.
:)
What is the slope for these 2
equations: y=-8x-5/4 and y=1/8 + 4/5
Answer:
y = -8x-5/4: -8
y = 1/8x + 4/5: 1/8
Step-by-step explanation:
The slope is the first number after the y =
In the circle shown below, The length of chord AB is 24 and the length of OC is 5. What is the radius of the circle with center O
Answer:
radius = 13
Step-by-step explanation:
OC is a perpendicular bisector of AB , then AC = 12
OA is the radius of the circle
Using Pythagoras' identity in right triangle OAC
OA² = OC² + AC²
OA² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )
OA = [tex]\sqrt{169}[/tex] = 13
The radius = 13 units
Answer:
13
Step-by-step explanation:
AB is bisected by perpendicular OC so AB is divided into intwo two equal halves.
if AB = 24
AC =[tex]\frac{1}{2} *AB[/tex]
=[tex]\frac{1}{2} *24[/tex]
=12
no join OA and name its length as x
OA = X
OC = 5
AC = 12
when u join O and A it forms a triangle . SO to find OA lets find pythagoras theorem
OC^2 + AC^2 = OA^2
5^2 + 12^2 = OA^2
25 + 144 = OA^2
169 = OA^2
[tex]\sqrt{169}[/tex] = OA
13 = OA
radius is the line joining the centre and any point on the circumference.So here since O is the centre and A is the points on the circumference and they are joined so the line can be named as radius of a circle.
Therefore radius of a circle is 13
what’s 818*426 (multiplication)
Answer:
348468
Step-by-step explanation:
Answer:
348,468
Step-by-step explanation:
Hope it's help you !!!!:)
can you help answer these:
1) (-3 ) * ( + 3 ) = ___
2) ( - 3) * ( - 3)= ______
3) ( + 20 ) ( + 5) = ____
4) ( + 21 ) ( - 3 ) )= ___
5) (-2) * (+3) * (- 4) = ___
Answer:
1) -3 x 3=-9
2) -3x-3=9
3)20x5=100
4) 21x-3=-63
5) -2x3x-4=24
note: negative x positive= negative
negative x negative=positive
positive x positive= positive
Step-by-step explanation:
hope this is helpful
Step-by-step explanation:
(-3)*(1+3) = -9 (-3)*(-3) = 9(+20)(+5) =100(+21)(-3) = -63(-2)*(+3)*(-4) = 24
Please help me with this question please!!!
A = x * x = x^2
B = 6 * x = 6x
C = 8 * x = 8x
D = 6 * 8 = 48
So the area of the whole shape is each side added up then multiplied to give (x+6)(x+8) =
x^2 + 14x + 48
find the outer perimeter of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate π.
Answer:
19.42 ft.
Step-by-step explanation:
The diameter of the semicircle is 6, so 3.14 x 6 = 18.84. Since it is a semicircle, we divide that by 2 to get 9.42.
The hypotenuse of the right triangles only matter for the perimeter. 5 + 5 = 10, and 9.42 + 10 = 19.42 ft.
The outer perimeter is 19.42 ft.
What is perimeter?Perimeter is the distance around the edge of a shape.
Given:
radius= 3 ft
height= 4 ft
slant height= 5 ft
diameter of the semicircle is 6 feet.
So,
= 3.14 x 6 = 18.84.
Since it is a semicircle,
=18.84/2
=9.42 feet
Now, the perimeter.
= 5 + 5 +9.42
= 19.42 ft.
Hence, the perimeter is 19.42 feet.
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please answer fast pls .................
Answer:
A
Step-by-step explanation:
Kunal Sagar
12 10 -6 years before is 6:5
18 16 -Now
22 20 - 4 years in the future at 11:10
So it all works out :)
what are the steps to this problem?
i’ll give you brainliest
Answer:
the answer you want is number 2
Can someone help me with this.
Answer:
A' (-1, 1), B' (-2,1), C'(-2, 2), D'(-1, 3)
Step-by-step explanation:
Rotate all of the points 90 degrees clockwise and move them to the second quadrant.