Rewrite the system of equations in matrix form.
[tex]\begin{bmatrix}1&2&-2\\3&7&-1\\2&4&m\end{bmatrix} \mathbf x = \mathbf b[/tex]
This system has a unique solution [tex]\mathbf x = \mathbf A^{-1}\mathbf b[/tex] so long as the inverse of the coefficient matrix [tex]\mathbf A[/tex] exists. This is the case if the determinant is not zero.
We have
[tex]\det(\mathbf A) = m+4[/tex]
so the inverse, and hence a unique solution to the system of equations, exists as long as m ≠ -4.
g^x+1 =27 solve for x
Answer:x=-3.5
Step-by-step explanation:
If it takes you 2 1/2 hours to assemble one unit, how many units will you complete in 15 hours? (Change 2 1/2 to improper fraction first)
Answer:37.5
Step-by-step explanation:
2 1/2 as an improper fraction is 5/2
If i'm wrong tell me please i hope this helped you
The sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second. What are the numbers?
The numbers are 30, 22, and 66 if the sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the number are x, y and z
Then,
x + y + z = 118 ...(1)
y = x - 8 ...(2)
z = 3y ....(3)
After solving the above three equation by plugging the value of z in the equation (1) then solve this equation with (2) we will get:
x = 30
y = 22
Then z from the equation (3):
z = 3(22) = 66
Thus, the numbers are 30, 22, and 66 if the sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second.
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Scientific notation question in mathematics please answer
A newly discovered planet has a mass of 4.8743 · 10 22 kilograms. It's estimated that there is water on the surface and that, the water's mass is only 4 · 10 -2 percent of the planet's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.
Answer:
1.94972 × 10¹⁹ kgStep-by-step explanation:
Mass of the planet:
4.8743 × 10²² kgThe water's mass:
4×10⁺²%Mass of the planet's water:
4.8743 × 10²² * 4×10⁺² / 100 = 19.4972 × 10²²⁺²⁺² = 19.4972 × 10¹⁸ = 1.94972 × 10¹⁹Myra ordered 648 roses for her flower shop. Her helpers made boquets for every 8 roses.How many bouquet of roses were made for sale?What is the solution
bouquet of roses were made for sale : 648/8 = 81
ok done. Thank to me :>
A rectangle has length 72 cm and width 56 cm. The other rectangle has the same area as this one, but its width is 21 cm. What is the length of the second rectangle?
Answer:
Step-by-step explanation:
As given, the other rectangle has the same area as this one, but its width is 21 cm. Hence, length is 192 cm.
helppppppppppppppppppppppppppp
A machine cuts a strip of carpet into two pieces. The length of the smaller piece is 5 meters greater than 1/4 the length of the larger piece. If the length of the smaller piece is 12 meters, the length of the bigger piece is _____________ meters
and the total length of the carpet is _____________ meters.
Answer:
longer = 28 meters
Total = 40 meters
Step-by-step explanation:
Let the smaller piece be s,
and the longer piece be b
s = ¼b + 5
s = 12
¼b + 5 = 12
¼b = 7
b = 28 m
Total length = 28+12 = 40 meters
which statement is true about the points located in quadrant IV on the coordinate plane
Answer:
B. The x-coordinate is positive, and the y-coordinate is negative
Step-by-step explanation:
Counting for the quadrants starts and the positive x-axis and then moves counterclockwise. This means that the IV quadrant will be the bottom right quadrant. The right axis is the positive x-axis and the bottom axis is the negative y-axis. This means that the coordinate for the IV quadrant must look like (x,-y).
What is the inequality graphed below?
Answer:
y>=5/3x+5
Step-by-step explanation:
line is y=5/3x+5
shading is above the line
line is shaded
y>=5/3x+5
patrick is thinking of a number. his number is twice as large as the smallest number that rounds to 30 when rounding to the nearest ten. what is patrick’s number?
What equation represents this sentence?
7 less than a number is 16.
7=16−n
7=n−16
7−n=16
n−7=16 100 ponits
Answer:
n - 7 = 16
Step-by-step explanation:
as it says "7 less than a number". If it was "a number less than 7" then it would be the 3rd one.
Answer: n - 7 = 16
Step-by-step explanation: i did quiz
If ACD and BAC are alternate interior angles and mACD=101°
Answer is A. 101°
Step-by-step explanation:
Solve for g.
16g–11g+g=6
g=
Which one is the correct answer ? Find the amplitude , period. Phase shift asymptotes domain range Use the fact that cos(x)=0 will be an asymptote
Answer:
3. is your correct answer ok
Help me ASAP now like really fast
Answer: I think the answer is C.. It looks like an 180 angle from my perspective.
I hope that is correct
Answer:
C
Step-by-step explanation:
Well, we know all the angles must sum up to 180º. From this, we can write the equation ' 3xº + 80º + 2xº = 180º ', which is answer choice C
domain and range of y = x/(x+4)
Answer:
Step-by-step explanation:
[tex]y=\frac{x}{x+4}[/tex]
for domain x+4≠0
x≠-4
domain={R-{-4}}
R=all real numbers.
y(x+4)=x
yx+4y=x
yx-x=-4y
x(y-1)=-4y
[tex]x=-\frac{4y}{y+1} \\y+1\neq 0\\y\neq -1\\[/tex]
so Range ={R-{-1}}
Lines r and s are perpendicular and intersect at point k ray kt is drawn forming angles 1 and 2 if angle 1 is 4x-12 and angle 2 equals 3x -8 what is angle 1 to nearest 10th
The measure of angle 1 to the nearest tenth is 50.9 degrees
Since the line r and s are perpendicular, hence the sum of the angle m<RKT and m<SKT is 90 degrees.
Given the following parameters
m<RKT = m<1 = 4x - 12
m<SKT = m<2 = 3x - 8
Taking the sum of the angle and equating it to 90degrees, hence;
m<RKT +m<SKT = 90
4x - 12 + 3x - 8 = 90
7x = 90 + 20
7x = 110
x = 110/7
x = 15.71
Get the measure of angle 1
m<1 = 4x - 12
m<1 = 4(15.71) - 12
m<1 = 50.9 degrees
Hence the measure of angle 1 to the nearest tenth is 50.9 degrees
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The following statement is from the contract Peter signed with his Homeowner's Association (HOA).
"Overnight parking on community streets is prohibited. For the purpose of this contract, 'overnight' will be defined as the hours between 11:00 p.m. and 4:00 a.m. The HOA will monitor overnight parking not less than once every calendar week with nightly patrols by community security.
"In the event a car is found parked on community streets overnight and that ownership of the offending car can accurately be verified as a community homeowner, the homeowner will receive one (1) written warning asking him or her to correct the situation. A second and third infraction by the same homeowner, whether or not it is with the same car, will result in a monetary fine as permitted by CC&R guidelines and HOA bylaws. Further infractions (past 3) will result in monetary fines in addition to the towing of the car at the homeowner's expense."
Because of the extremely low ground effects and body profile on his racing car, Peter is unable to drive his car off of the street and onto the driveway. He has parked on the street overnight for the past five weeks. He has received one written warning and one monetary fine from the HOA. What consequences should Peter expect after this week's security check?
a.
His car will be towed.
b.
He will receive another monetary fine.
c.
He will receive a monetary fine and his car will be towed.
d.
A "boot" will be place on his car to prevent him from driving it.
Have a good day and remember to smile!
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Help me with questions please
Three classes at a junior high school raised money to buy a new computers.
Answer:
what's the question...?
Step-by-step explanation:
Leave a comment?
Explain how you can multiply to find equivalent fractions
Answer:
One example for an equivalent fraction would be 2/5 = 4/10
Step-by-step explanation:
It is equivalent because in both the denominator and the numerator you multiply by 2 which means that if you would divide 4/10 by 2 top and bottom, you would get 2/5. If you were to but these fractions on a number line; one on top of the other; they would equally have one under the other.
*** I hope this helps (brainly if possible)
Work out Simplify if possible.
Answer:
a.1×9/1=9
b.3×5/1=15 i think this would be the answer
Answer:
a) 9
b) 15
you
can
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to help you with your math :)
Hope this helps you......
PLEASE ANSWER ASAP (no links please)
Solve for the indicated variable
g/h = e - 10 for g
Answer:
g = he - 10h
Step-by-step explanation:
Hey whats 2+2? i need to know ASAP! IM IN PRESCHOOL-
Answer:
lol Its 4
Step-by-step explanation:
Dont worry you got this
Answer:
=4
Step-by-step explanation:
2 + 2 = 4
1 + 1 = 2
1 + 3= 4
Hope this helps, have a nice day/night! :D
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What is 7.83 x10^6 in decimal form
Answer:
7830000.00
Step-By-Step Explanation:
78 - 783 - 7830 - 78300 - 783000 - 7830000
Answer: 7830000
Step-by-step explanation:
7.83*10^6=
------------->
7.83*10^6=7.83
since the exponent equals 6, lets move the decimal sign 6 places to the right.
7.83*10^6=7.8.3.0.0.0.0.
Result is 7 8 3 0 0 0 0
7.83*10^6=7830000
It is impossible to solve this mixture problem: How many gallons of a 10% solution would need to be
added to a 20% solution to obtain a 30% solution.
True or False?
Answer:
false
Step-by-step explanation:
How many gallons of a 10% solution. Would need to be added to a 20% solution to obtain 50 gallons of a 30% solution?
2.How many gallons of milk containing 4% fat is mixed with milk containg 1% fat to obtain a 15 gallon mixture containing 2% fat?
trevin puts 8 gallons of
Answer:
24.75 is answer
Step-by-step explanation:
Answer:
That was a good start, but we need the rest of the question.
Step-by-step explanation:
find the amount of money Khairul had initially
Answer
Find the amount of money Khairul had initially
money with Khairul initially = 6x = 6(60) = 360
Step-by-step explanation:
which function is represented by the graph?
Answer:
[tex]y=-\sqrt{x+2}-1[/tex]
Step-by-step explanation:
Hi there!
Please take a look at the attached image. This is the parent function of the radical function.
[tex]y=\sqrt{x}[/tex]
This equation represents the transformations of the parent function:
[tex]y=a\sqrt{b(x-h)}+k[/tex]
a dictates vertical stretch.
b dictates horizontal stretch.
h dictates horizontal translation.
k dictates vertical translation.
If we take a look at the given graph, we can tell that the following transformations have been applied:
- reflection across x-axis (a = -1)
- translation 2 units to the left (h = -2)
- translation 1 unit down (k = -1)
Therefore, the function that represents the graph is:
[tex]y=-\sqrt{x+2}-1[/tex]
I hope this helps!