The matrix representation of the system looks:
| -650 0 |
| -1 120 |
To clarify, it seems you have provided a system of equations:
y = 650x + 175
y = 25,080 - 120x
Now, you want to create a matrix representation of this system by filling in the values in the columns and rows.
Column 1: The coefficient of x in the first equation is 650, so we put -650 in Column 1.
Column 2: The coefficient of x in the second equation is -120, so we put -120 in Column 2.
Column 3: There are no constants in front of x in the given system, so we put 0 in Column 3.
Row 1: Since the first equation has a positive coefficient of x, we put -1 in Row 1.
Row 2: The second equation has a negative coefficient of x, so we put 120 in Row 2.
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Helpppppp meeee plzzzz
Answer:
its rather B or C
Step-by-step explanation:
c(c)=y
so the slope is Y=2x+2
the reason why its rather B or C is because of the axis
i dont know what belongs where
the image of the circle x2+y2-2x+3y=8 after being reflected by the line y=2x-3 is----------------.pls anyone
Answer:
The image of the circle is 9·x² + 9·y² - 42·x + 33·y = 22
Step-by-step explanation:
We convert the equation to the form (x - h)² + (y - k)² = r²
Where:
(h, k) = Coordinates of the center of the circle
We therefore have;
x² + y² - 2·x + 3·y = 8 which gives;
x² - 2·x + 1 - 1 + y² + 3·y + (3/2)² - (3/2)² = 8
(x - 1)² + (y + 3/2)² - 1 - (3/2)² = 8
(x - 1)² + (y + 3/2)² = 8 + 1 + (3/2)² = 45/4
Therefore, the center = (1, -3/2) and the radius = √5 × 3/2
The line joining the centers of the actual (1, -3/2) and reflected circle (h, k) is bisected by the line of reflection, therefore the midpoint of the line is on the line of reflection with coordinates;
Midpoint between (1, -3/2) and (h, k) = [tex]\left (\dfrac{{h - 1}}{2}, \, \dfrac{k - 3/2}{2} \right )[/tex]
Which gives;
y = 2·x - 3 being equivalent to [tex]\dfrac{k - 3/2}{2} = 2\times\dfrac{{h - 1}}{2} - 3[/tex]
Which gives;
4·h -2·k -13 = 0.......(1)
Similarly the slope of the reflecting line is perpendicular to the line joining the centers of the actual and reflected circles
Therefore;
The slope of the line, y = 2·x - 3 = 2, hence we have;
[tex]\dfrac{\left ( \dfrac{k - 3/2}{2} \right ) + 3/2}{\left (\dfrac{{h - 1}}{2}-1 \right )} = \dfrac{1}{2}[/tex]
Which gives;
2·h -4·k -12 = 0.......(2)
Multiplying equation (2) and subtracting from equation (1) gives
4·h -2·k -13 - 2×(2·h -4·k -12) = 0
6·k + 11 = 0
k = -11/6
From which we have;
2·h -4×(-11/6) -12 = 0
Hence;
h = 7/3
Therefore, the center of the reflected circle = (7/3, -11/6)
The equation of the reflected circle is therefore;
(x - 7/3)² + (y + 11/6)² = 45/4
Which gives;
9·x² + 9·y² - 42·x + 33·y - 22 = 0
or x² + y² - 42/9·x + 33/9·y = 22/9.
What is the volume of the rectangular prism? one cube is 1/3
Pleaser answer fastt
Answer:
A
Step-by-step explanation:
15 boxes multiplied by 2 is 30, 1/3 times 30 is 10
calculate 16% of £50
What is the solution of 3square root x+8 = -4?
• x=-72
• x=-66
• x=58
• no solution
Answer:
No solution
Step-by-step explanation:
I'd suggest you try to solve this first: 3√(x + 8) = 4. First, square both sides; this results in 9(x + 8) = 16, or x + 72 = 16/9, or x = -632/9. We cannot let x = -632/9 in √(x + 8) because -632/9 is not in the domain of the square root function. No solution.
If we now write 3√(x + 8) = -4 (note the negative sign), similar efforts at solution result in 9(x + 8) = -4, or x + 8 = -4/9, or x = -8 - 4/9. If we now substitute this result for (x + 8) in 3√(x + 8) = -4 (above), we get 3√(-8 + 8 - 4/9), which has no solution; -4/9 is not in the domain of the square root function.
The solution for the given equation is 16.
The given equation is 3√x+8=-4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The solution for the given equation can be determined as follows:
Now, 3√x+8=-4
⇒ 3√x=-4-8
⇒ 3√x=-12
⇒ √x=-12/3
⇒ √x=-4
Squaring both the sides, we get
x=16
Therefore, the solution for the given equation is 16.
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When the transformation T, -, is performed on
point A, its image is point A'(-3,4). What are the
coordinates of A?
1) (5,-5)
2) (-5,5)
3) (-1,3)
4) (-6,-4)
Which choice shows the image of triangle ABC after a reflection over the y-axis followed by a rotation of 180° around the origin?
Answer: the second one
Step-by-step explanation:
The first one is reflection over the x-axis, rotated, and translated. The third one is rotated 90 degrees
The triangle A'B'C' with the coordinates A'(4, -5), B'(4, -2) and C'(1, -1). Therefore, option A is the correct answer.
What is the reflection on y-axis?When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
From the graph coordinates of triangle ABC are A(-5, 4), B(-2, 4) and C(-1, 1).
(x, y) becomes (-y, x) in 180° clockwise rotation
A(-5, 4)→(-4, -5)
B(-2, 4)→(-4, -2)
C(-1, 1)→(-1, -1)
Now,
The reflection of point (x, y) across the y-axis is (-x, y).
Then, coordinates become
(-4, -5)→A'(4, -5)
(-4, -2)→B'(4, -2)
(-1, -1)→C'(1, -1)
The triangle A'B'C' with the coordinates A'(4, -5), B'(4, -2) and C'(1, -1). Therefore, option A is the correct answer.
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4. Alistair has an infinite number of bags numbered 1, 2, 3, 4... Each bag
contains an infinite number of marbles numbered 1, 2, 3, 4... Is the set of
all marbles that Alistair possesses larger than the set of marbles he has in
just the first bag?
Answer:
No
Step-by-step explanation:
One infinity cannot be larger than another
How many edges and vertices does a prism with a 50 sided end face have
plzzz help me
I will mark as brainliest
expand the following 3(5n + 6)
Answer:
15n+18
Step-by-step explanation:
you have to multiply both integers(5n + 6) from inside the bracket with the number outside the bracket *3*
equation working below
3×5n=15n
3×6=18
final answer:
15n+18
help me please i need this done ASAP
Answer:
20 miles
Step-by-step explanation:
1 : just use the line to trace how long it would be
What is the radius of a circle whose equation is (x + 5)2 + (y - 3)2 = 42?
2 units
4 units
8 units
16 units
Answer:
the answer is b, 4 units
Answer:
4
Step-by-step explanation:
quatro
What are the next three numbers in this pattern?
11, 22, 12, 23,...
A 13, 24, 15
B 13, 24, 14
C 13, 23, 14
D 32, 43, 33
Answer:
B
Step-by-step explanation:
because first it is 11, 12, after it is 13, and 14
: for 22, 23 and after 24
Answer:
B
Step-by-step explanation:
Pure gold is often mixed with other metals to produce jewelry. Pure gold is 24 carat. 12 carat gold is 12/24 or 50% gold, 6 carat gold is 6/24 or 25% gold, etc. A jeweler has some 12 carat gold and some 21 carat gold and wants to produce 90 g of 75% gold.
a. What percentage of gold is 21 carat?
b. How many grams of 12 carat gold and 21 carat gold are needed to produce the mixture?
Answer:
a. 87.5%
b. 30 g of 12 carat and 60 g of 21 carat.
Step-by-step explanation:
a. The percentage of gold in 21 carat is given by:
[tex]gold_{21} = \frac{21}{24}*100 = 87.5 \%[/tex]
b. Since the mass he wants to produce is 90 g, then the added mass of the 12 carat, "x", and the mass of the 21 carat "y", must be equal to that:
[tex]x + y = 90[/tex]
The sum of gold on each carat type must be equal to the amount of gold on the final mixture, since a 12 carat has 50% gold and a 21 carat has 87.5% gold, then we have:
[tex]0.5*x + 0.875*y = 0.75*90\\\\0.5*x + 0.875*y = 67.5\\[/tex]
We now have a system of equations which we can solve to find the necessary mass of each type.
[tex]x + y = 90 \text{ } *-0.5\\0.5*x + 0.875*y = 67.5\\\\-0.5*x - 0.5*y = -45\\0.5*x + 0.875*y = 67.5\\\\0.375*y = 22.5\\\\y = 60[/tex]
[tex]x = 90 - y = 90 - 60\\\\x = 30[/tex]
He needs 30 g of 12 carat gold and 60 g of 21 carat gold.
Answer:
a. 87.5%
b. 30 g of 12 carat and 60 g of 21 carat.
Step-by-step explanation:
a. The percentage of gold in 21 carat is given by:
b. Since the mass he wants to produce is 90 g, then the added mass of the 12 carat, "x", and the mass of the 21 carat "y", must be equal to that:
The sum of gold on each carat type must be equal to the amount of gold on the final mixture, since a 12 carat has 50% gold and a 21 carat has 87.5% gold, then we have:
We now have a system of equations which we can solve to find the necessary mass of each type.
He needs 30 g of 12 carat gold and 60 g of 21 carat gold.
Step-by-step explanation:
How to check if a binomial is a difference of squares ?
What would the football player's weight be on the moon where acceleration due to gravity is
1.60 m/s??
Answer:
Step-by-step explanation:
Around 0
The graph of y= -2x + 10 is:
O A. a point that shows the y-intercept.
O'B. a point that shows one solution to the equation.
O c. a line that shows the set of all solutions to the equation.
O D. a line that shows only one solution to the equation.
SUBMIT
Helppp me plzzzz
Answer:
A. a point that shows the y-intercept
Step-by-step explanation:
What is the range of the data
represented in the dot plot below?
2
3
0
Answer:
Range = 3
Step-by-step explanation:
First, start off by ordering the list from least to greatest. Then, subtract the least number (0) from the greatest number (3), which will get you the range of 3.
Hope this helps! :D
dino has 14 coins and 2 one dollar bills which describes the relationships between the coins and the dollar bills
Answer:
they are both money
Step-by-step explanation:
that's why they relate, they're both currency
Answer:
B
Step-by-step explanation:
I took the quiz
Sean drinks 350mL of milk every day. How many liters of milk does he drink in a week?
Answer:
2.45 L in a week
Step-by-step explanation:
First find out how many ml he drinks in a week
350 mL * 7 days
2450 mL in a week
We know that 1000 mL = 1 L
2450 mL * 1 L /1000 mL = 2.45 L in a week
Answer:
2.450 litres.
Step-by-step explanation:
The answer is converting into Litres as we know 7 x 35 = 350-105 = 245++0 = 2450 ml
What is the problem with this statement?
If you taking geometry, then you are in the 9th grade
A. It does not assume that all students take geometry
B. It does not assume that all students are in the 9th grade
C. It assumes that no students taking geometry are in the 9th grade
D. It assumes that all students taking geometry are in the 9th grade
Please I need help with this
Answer:
D. It assumes that all students taking geometry are in the 9th grade
Step-by-step explanation:
Since it is a ratio of two integers,
6/4 is irrational
Answer:
is this a question? also, 6/4 is not irrational, it is rational, and an irrational number is a number that cannot be expressed as a ratio of two integers, aka a simple fraction
Find the first five terms of the geometric sequence a1=0.3,an=10an-1
Answer:
{0.3, 3, 30, 300, 3000}
Step-by-step explanation:
Here a(1) = 0.3, and
a(2) = 3, and
a(3) = 30, and
a(4) = 300, and
a(5) = 3000
The first term (given) is 0.3, and the common ratio is 10.
What is the solution to this equation?
2x + 3 = x − 4
Answer:
-7
Step-by-step explanation:
2x+3=x-4
Let's start by subtracting 3 from both sides
2x=x-7
Now, subtract x from both sides
x=-7
Let's plug it in to make sure!
2(-7) +3= (-7)-4
-11=-11
Answer:
x= -7
Step-by-step explanation:
You subtract both sides by x meaning the x on the right side will turn to zero and then you subtract both sides by 3
Mrs. Linda has 17.16 cups of brownie mix. If each
brownie uses 0.33 cups of mix, how many
brownies can Mrs. Linda make?
Answer:
52 brownies
Step-by-step explanation:
If you divide 17.16 by 0.33, you get 52
Solve the system of equations.
y= 3x
y= x2-10
Answer:
(-5, 2) and (2, 6)
Step-by-step explanation:
Use the substitution method. We know that y = 3x and y = x^2 - 10, so we can set them equal to one another.
3x = x^2 - 10
x^2 - 3x - 10 = 0
Use the quadratic equation to solve for x.
x = - 5, 2
Now solve for y using these two values of x by substituting it back into the equations.
y = - 15, 6
In coordinate form, (-5, 2) and (2, 6)
The value of x in 5(8+x)=20
Answer:
x = -4
Step-by-step explanation:
5(8+x)=20
Divide each side by 5
5/5(8+x)=20/5
8+x = 4
Subtract 8 from each side
8+x-8 = 4-8
x = -4
The right answer is -4.
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
A premier credit card has an initiation fee that provides you with the privilege to use it and a monthly fee after the first two months. The initiation fee is $62 and the monthly fee is $30 per month after the first two months. If C represents the cost and g represents the total number of months, which equation could represent this plan when you have this card for more than two months?
A. C = 30 + 62(g-2)
B. C = 30 + 62(2-g)
C. C = 62 + 30(g-2)
D. C = 62 + 30(2-g)
Answer:
The correct option is C.
Step-by-step explanation:
To have this credit card there is two fees, one that is fixed payed upfront and other that is payed after the second month. The fixed fee costs $62, and doesn't escalate with time, while the other one is $30 and starts to be charged after the second month. Therefore, the total cost of the card is the fixed fee plus the monthly fee multiplied by the number of months the user had the card subtracted by two, or as shown below:
[tex]C(g) = 62 + 30*(g-2)[/tex]
The correct option is C.
A frustum is made by removing a small cone from a similar large cone. Work out the volume of the frustum, below. Give your answer in terms of pie
Answer:
Step-by-step explanation:
volume of cone=1/3 πr²h
volume of frustum=vol of larger cone-vol of smaller cone=1/3πR²H-1/3πr²h
=1/3π(R²H-r²h)
=1/3π(4.5²×9-3²×6)
=1/3π×9×3(4.5×1.5-2)
=9π(6.75-2)
=9π×4.75
=42.75π cm³
The volume of frustum of cone is [tex]42.75\pi[/tex]
What is frustum of cone?Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum. To get this part of the right circular cone we have to slice it horizontally or parallel to the base.
Volume of frustum of cone = [tex]\frac{\pi H}{3} [ R^{2} + r^{2} + rR][/tex]
Where,
R = Radius of the bigger circular end
r = radius of the smaller circular end
H = height of frustum
According to the question
Original height of cone = 9 cm
Radius of the bigger circular end = 4.5 cm
Radius of the smaller circular end = 3 cm
Height of frustum = 3 cm
Volume of frustum of cone = [tex]\frac{\pi H}{3} [ R^{2} + r^{2} + rR][/tex]
= [tex]\frac{\pi 3}{3} [ 4.5^{2} + 3^{2} + 4.5*3][/tex]
= [tex]\pi [ 20.25 + 9 + 13.5][/tex]
= [tex]42.75\pi[/tex]
Hence, The volume of frustum of cone is [tex]42.75\pi[/tex] .
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solve this proportion x/14 6/21
Answer:
X=4
Step-by-step explanation:
Solution: x equals 4
x/14-(6/21)=0
1. Simplify 2/7
x/14- 2/7 is 0
It’s too much steps
