Let A be an m x n matrix and let b be a vector in RM. Three of the following four statements are all equivalent to each other. Choose the one statement that is not equivalent to the other three.
(a) The reduced row echelon form of Ab] has no zero row.
(b) The system Ax = b has a solution.
(c) b can be expressed as a linear combination of the columns of A.
(d) b is in the span of the columns of A.
Answer:
A.
Step-by-step explanation:
From the given information:
If A = m × n matrix
where;
b is a vector in [tex]R^m[/tex]
Then; the statement that doesn't fit and is not related to the other three from the given options is Option A.
This is because the statement in Option A appears to be inconsistent. For the model Ax=b to have a solution, A must be non-singular and b must be in A's column space.
Option c and d are equivalent, also option b and c are equivalent.
What would you do to solve the system?
System of equations
Click on the correct answer.
12x = 48 - 8y
10x + 8y = 38
?
Add the equations.
12x = 48 - 8y
10x = 38 - By
Subtract the equations.
3. To decide whether to add or subtract,
determine if the values of the
coefficients are the same or opposites:
. If the values are the same, subtract the
equations.
• If the values are opposites or additive
inverses, add the equations.
Remember, you're trying to remove one
variable.
Answer:
To decide whether to add or subtract, determine if the values of the coefficients are the same or opposites:
. If the values are the same, subtract the equations.
• If the values are opposites or additive inverses, add the equations.
Step-by-step explanation:
Given
[tex]12x = 48 - 8y[/tex]
[tex]10x + 8y = 38[/tex]
Required
How to solve
Options (1) and (2) are incorrect because none of the options eliminate x or y.
For option (3),
- Check for the coefficients of x and y
- If they are the same (sign and value), then subtract; otherwise add
For instance:
[tex]12x = 48 - 8y[/tex]
[tex]10x + 8y = 38[/tex]
Rewrite the second equation
[tex]12x = 48 - 8y[/tex]
[tex]10x = 38 - 8y[/tex]
The coefficient of y are the same, so we subtract;
[tex]12x - 10x = 48 - 38 -8y -(-8y)[/tex]
[tex]12x - 10x = 48 - 38 -8y +8y[/tex]
[tex]2x = 10[/tex]
[tex]x= 5[/tex]
See that y has been eliminated
A woman has eight keys on a key ring, one of which fits the door she wants to unlock. Sherandomly selects a key and tries it. If it does not unlock the door, she randomly selects anotherkey from those remaining and tries to unlock the door with it. She continues in this manner untilthe door is unlocked. Let X be the number of keys she tries before unlocking the door, countingthe key that actually worked.
Required:
Find the expected number of keys she will try before she opens the door.
Answer:
The expected number of keys she will try before she opens the door is 4.5.
Step-by-step explanation:
A woman has eight keys on a key ring, one of which fits the door she wants to unlock.
Each of them is equally as likely to be the one to work, which means that this situation is represented by an uniform distribution with lower bound [tex]a = 1[/tex] and upper bound [tex]b = 8[/tex].
Find the expected number of keys she will try before she opens the door.
The expected value of the uniform distribution is given by:
[tex]E = \frac{a + b}{2}[/tex]
Considering [tex]a = 1, b = 8[/tex], as is the case in this exercise:
[tex]E = \frac{1 + 8}{2} = 4.5[/tex]
The expected number of keys she will try before she opens the door is 4.5.
The area of a right triangle is 49 square inches. The base is
twice as long as the height. The formula for the area of a
triangle is A = 1/2 bh, where b is the base and h is the height.
How long is the base and how tall is the height?
Answer:
height: 7 in
base: 14 in
Step-by-step explanation:
Let the height of the triangle equal x. This means that the base can be represented by the expression 2x. Now we plug these values into the area formula for a triangle:
A = bh / 2
49 = x * 2x / 2
And simplify
49 = x^2
We can find the square root of both sides to get x = 7, so the height is 7 inches. Since the base is twice the height, it is 14 inches.
Answer:
[tex]h=7,\\b=14[/tex]
Step-by-step explanation:
Since the base is twice as long as the height, set up the following proportion:
[tex]b=2h[/tex].
The area of the a right triangle is equal to [tex]A=\frac{1}{2}bh[/tex], where [tex]b[/tex] is a base of the triangle and [tex]h[/tex] is the respective height.
To solve for height, set up the equation (substituing [tex]b=2h[/tex]:
[tex]\frac{1}{2}\cdot2h\cdot h=49,\\2h^2=98,\\h^2=49,\\h=\boxed{7}[/tex]
To solve for base, substitute [tex]h=7[/tex] in the proportion [tex]b=2h[/tex]:
[tex]b=2(7),\\b=\boxed{14}[/tex]
NO LINKS, NO OTHER SITES, 100 POINTS
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this? because the system of equations actually has only one solution because the system of equations actually has no solution because the graphs of the two equations overlap each other because the graph of one of the equations does not exist
Answer:
because the graphs of the two equations overlap each other
Step-by-step explanation:
Equations that have an infinite amount of solutions overlap each other when graphed.
This is because equations with an infinite amount of solutions have a similar equation so when graphed you only see one line
What is the volume, in cubic m, of a rectangular prism with a height of 17m, a width of 14m, and a length of 11m?
Answer:
The answer is 2618m
Answer:
2618
Step-by-step explanation:
The mean temperature for the first 4 days in January was 1°C.
The mean temperature for the first 5 days in January was 3°C.
What was the temperature on the 5th day?
Answer:
Step-by-step explanation:
mean is average, so if we label the first through fifth days of january a-e we can solve it.
So average of the first four is (a+b+c+d)/4 = 1 and the first five is (a+b+c+d+e)/5 = 2. Since it's easy, let's get rid of the fraction in both.
(a+b+c+d)/4 = 1 and (a+b+c+d+e)/5 = 2
a+b+c+d = 4 and a+b+c+d+e = 10
Now, we know a+b+c+d is 4, so we can replace that in the second equation
a+b+c+d+e = 10
4 + e = 10
e = 6
ad since e is the fifth day, we know the temperature of it. Let me know if something here didn't make sense
Which is most likely the correlation coefficient for the
set of data shown?
Answer:
0.872
Step-by-step explanation:
The regression fits the data well leavubgbiut just one of the points, this shows there is a strong relationship between the plotted variables. Also, we have to look at the direction of the regression line which will give us an idea of the slope, hence the type of correlation between the two variables (either positive or negative relationship). In this case the slope is positive and hence the correlation Coefficient will be positive as well. Hence we can say there is a strong positive relationship between the variable. The only option which depicts this association is 0.872
Write the equation of the circle that is centered at (- 13, - 2) and has a diameter of 24^ *
Step-by-step explanation:
Given :-
Centre = (-13,-2) Diameter = 24And we need to find out the equation of the circle. Since the diameter is 24 u therefore it's radius will be 12 u . Now we can use the Standard equation of circle to find out the equation .
Standard equation of circle :-
[tex]\implies (x-h)^2+(y-k)^2 = r^2 [/tex]
Where (h,k) is centre and r is radius.[tex]\implies (x-(-13))^2+(y-(-2))^2 = 12^2 \\\\\implies ( x+13)^2+(y+2)^2=144 \\\\\implies x^2+169+26x+y^2+4+4y=144\\\\\implies x^2+y^2+26x+4y+ 29 =0[/tex]
solve this inequality 2(4x+1)<3(2x-3)
Answer:
x<-11/2
Step-by-step explanation:
but don't trust me too much bestie
help lol -30=5(x+1) x= ?
1.Distribute
-30=5(x+1). x
[tex]-30=5x^{2}+5x[/tex]
2. Move terms to the left side
[tex]-30=5x^{2} +5x[/tex]
[tex]-30-(5x^{2} +5x)=0[/tex]
3. Rearrange terms
[tex]-30-5x^{2} -5x=0[/tex]
[tex]-5x^{2} -5x-30=0[/tex]
Hope this helps! Sorry if I'm wrong
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{ORIGINAL EQUATION}\downarrow[/tex]
[tex]\large\textsf{ -30 = 5(x + 1)}[/tex]
[tex]\large\text{TURN the EQUATION}[/tex]
[tex]\large\textsf{5(x + 1) = -30}[/tex]
[tex]\large\text{DISTRIBUTE \textsf{5} WITHIN the PARENTHESES}[/tex]
[tex]\large\textsf{5(x) + 5(1) = -30}[/tex]
[tex]\large\textsf{5(x) = \bf 5x}\\\large\textsf{5(1) = 5}[/tex]
[tex]\rightarrow\large\textsf{5x + 5 = -30}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{5x + 5 = -30}}[/tex]
[tex]\large\text{SUBTRACT \textsf{5} to BOTH SIDES}[/tex]
[tex]\large\textsf{5x + 5 - 5 = -30 - 5}[/tex]
[tex]\large\text{CANCEL out: \textsf{5 - 5} because that gives you \textsf{0}}[/tex]
[tex]\large\text{KEEP: \textsf{-30 - 5} because that helps you solve for your \textsf{x-value}}[/tex]
[tex]\large\textsf{-30 - 5 = \bf -35}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{5x = -35}}[/tex]
[tex]\large\text{DIVIDE \textsf{5} to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{5x}{5}= \dfrac{-35}{5}}[/tex]
[tex]\large\text{CANCEL out: }\mathsf{\dfrac{5x}{5}}\large\text{ because that gives you the value of \textsf{1}}[/tex]
[tex]\large\text{KEEP: }\mathsf{\dfrac{-35}{5}}\large\text{ gives you the \textsf{x-value}}[/tex]
[tex]\large\textsf{x = }\mathsf{\dfrac{-35}{5}}[/tex]
[tex]\large\text{SIMPLIFY ABOVE \& YOU HAVE YOUR x-value}[/tex]
[tex]\boxed{\boxed{\large\textsf{ANSWER: \huge \bf x = -7}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A triangular prism. The rectangular sides are 2 centimeters by 13 centimeters, 12 centimeters by 2 centimeters, and 5 centimeters by 2 centimeters. The 2 triangular sides have a base of 5 centimeters and height of 12 centimeters. Which equation could be used to find the surface area of the net of the triangular prism shown? SA = (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2) SA = (1/2) (5)(13) + (1/2) (5)(13) + (5)(2) + (13)(2) + (12)(2) SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2) SA = (2)(5)(13) + (5)(2) + (13)(2) + (12)(2)
Answer:
(C)SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)
Step-by-step explanation:
egde
Answer:
C
Step-by-step explanation:
Explain your steps
(I hated this math haha)
Answer:
x=10
Step-by-step explanation:
180-170 as 180 is the whole sttaight line
66,66,70,88.........?,236
Answer:
I am so confused I don't know how to answer this.
−3.5+2.5+(−0.25)+(−3.25)
Answer:
-4.5
Step-by-step explanation:
WILL
GIVE BRAINLIST
C
C
C
C
C
Answer: September
Step-by-step explanation:
The bar for September is the highest above the horizontal axis.
How many gallons of pure water should be added to 10 gallons of a solution containing 15% juice so that
the remaining solution contains 5% juice?
Fill in the table:
What is the amount of juice in the original solution? a =
What is the original amount of solution in gallons? b =
How much juice is added? c=
How much total solution is added? d =
Original
Added
New
Amount of juice
a
c
Total solution
b ь
d
DONE
Answer:
1.5 gallons of juice
a. 10 gallons
b. none
c. 10 gallons (all water)
hope its right!!! good luck
Step-by-step explanation:
At which approximate x-value are these two equations equal
y = √1 - x^2
y = 2x - 1
9514 1404 393
Answer:
x = 0.8
Step-by-step explanation:
If you mean y = √(1 -x²), then the curves cross at x=0.8.
__
If you equate the y-expressions, then square both sides, you have ...
√(1-x²) = 2x-1
1 - x² = (2x -1)² = 4x² -4x +1
0 = 5x² -4x . . . . . subtract the left-side expression
x(5x -4) = 0 ⇒ x = 0, or x = 4/5
The x=0 solution is extraneous.
The two equations are equal at x = 4/5.
Which is an expression in square units that represents the area of the shaded segment of center ofOC
A: 1/4 r^2(3.14-4)
B: 1/4pier^2
C: 1/4pier^2-2r^2
D: 1/2r^2(1/2pie-1)
9514 1404 393
Answer:
D
Step-by-step explanation:
The formula for the area of a segment is ...
A = 1/2r²(θ -sin(θ))
for radius r and central angle θ.
Here, we have θ = π/2, so this becomes ...
A = 1/2r²(π/2 -1) . . . . . matches choice D
WHAT IS 22 DIVIDED BY TAN 75?? please help me!!!! i’m taking a math test i need a good grade! (question in picture)
Answer: -52.2936778905
Step-by-step explanation:
Need help !! Plz!!!??!
Answer:
here, diameter is 4 cm
radius=diameter/2
=4/2 cm
=2 cm
now use formula pie (r)^2 where pie is 3.14
=pie *(r)^2
=3.14*(2cm)^2
=12.56 cm^2
Step-by-step explanation:
Find the measure of angle QZT.
========================================================
Explanation:
Minor arc QV is 80 degrees because it adds to minor arc VU = 100 to get 80+100 = 180. Note how angle QPU = 180, since it's a straight line and QU is a diameter of the circle.
Add up the minor arcs
TUUVVQto get: 44+100+80 = 224
This means arc TUQ is 224 degrees. Inscribed angle QZT subtends arc TUQ. Use the inscribed angle theorem to say that the inscribed angle is half of the arc it cuts off.
angle QZT = (arc TUQ)/2
angle QZT = 224/2
angle QZT = 112 degrees
URGENT HELPP!!!NO LINKS
Answer:
25 I believe
Step-by-step explanation:
think has 5 letters
only using it once ofc
5×5= 25
Please hel p me. !!!!!!! I need the median.
In ascending order,
36, 43, 50, 51, 58, 59, 60, 69, 73
N=9
median (Q2)= N+1/2
or, Q2= 9+1/2
or, Q2= 10/2
= 5th item
Therefore, the median is 58.
I don't know if this is correct or not.
Help find the volume of this equation
Always know the formula for volume prism because that shape is a prism.
Formula For PRISM: BH/2 x Height.
So then we are going to solve the triangle first... 7 x 22= 154/2= 77
Then multiply by the height which is 25.
77 x 25= 1,925.
So your answer should be 1,925 meters cubed. *Don't forget to write the measurement
*hope this helps
Answer:1925
Step-by-step explanation:
HELP! Will give branliest!!
Answer:
10y + 29 ≤ -23
Step-by-step explanation:
subtract 29 from each side to get:
10y ≤ -52
y ≤ -5.2
The volume of the rectangular prism is 240 cubic meters. What is the width of the prism?
5 meters would be the answer I believe.
12 x 4 = 48
240/48 = 5
Answer:
5
Step-by-step explanation:
hope this helps :)
measure of the angle labeled?
Given:
The figure of a circle.
The measure of arc SR = 75 degrees.
Measure of angle RSQ = 95 degrees.
To find:
The measure of SQ.
Solution:
Let us consider, O be the center of the circle.
According to the central angle theorem, the measure central angle on an arc is twice of inscribed angle on the corresponding angle.
Using the central angle theorem, we get
[tex]m\angle QOR=2\times m\angle RSQ[/tex]
[tex]m\angle QOR=2\times (95^\circ)[/tex]
[tex]m\angle QOR=190^\circ[/tex]
It is the central angle on major arc QR.
We know that the measure of complete central angle is 360 degrees.
The central angle on minor arc QR is:
[tex]360^\circ -190^\circ =170^\circ[/tex]
It means the measure of arc RSQ is 170 degrees.
[tex]m(arc RS)+m(arc SQ)=m(arcRSQ)[/tex]
[tex]75^\circ+m(arc SQ)=170^\circ[/tex]
[tex]m(arc SQ)=170^\circ -75^\circ[/tex]
[tex]m(arc SQ)=95^\circ[/tex]
Therefore, the measure of arc SQ is 95 degrees.
Help please I’m confusion
easy math question good luck
Answer:
c/d
Step-by-step explanation:
pretty sure it's just circumfrence over diameter
c/d
Answer:
The value of pi is the ratio of the circumference of a circle to its diameter. So then, you can determine the value of pi by drawing a perfect circle
Step-by-step explanation: