In matrix form, the given system is written as
[tex]\begin{bmatrix}1&1&0\\6&2&-3\\k&0&-1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3-k\\1\\-3\end{bmatrix}[/tex]
and the system has no solution is the coefficient matrix is singular. The determinant is
[tex]\begin{vmatrix}1&1&0\\6&2&-3\\k&0&-1\end{vmatrix} = -3k+4[/tex]
and this is zero when k = 4/3.
On the other hand, in case you are missing a factor of z in the first equation, so that the system should read
x + y + (k - 1) z = 2
6x + 2y - 3z = 1
kx - z = -3
reframing it as a matrix equation gives
[tex]\begin{bmatrix}1&1&k-1\\6&2&-3\\k&0&-1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}2\\1\\-3\end{bmatrix}[/tex]
Then the determinant of the coefficient matrix is
[tex]\begin{vmatrix}1&1&k-1\\6&2&-3\\k&0&-1\end{vmatrix} = -2k^2-k+4[/tex]
and the determinant is zero at two values, k = (-1 ± √33)/4.
9. Choose the equation that represents the graph below:
Answer:
y= -4/3 x + 4
Step-by-step explanation:
i guess
draw the Venn diagram of b union b
A=(2 4 6 8 10 12)
B=(1 3 5 7 9 11)
Step-by-step explanation:
Explanation is in the attachment
hope it is helpful to you ☺️
The midpoint of AB is M(1,1). If the coordinates of A are (3, 3), what are the coordinates of B?
Answer:
The answer in (-1,-1) because it goes down by x-2 and y-2
8. A juice container shaped like a cylinder has a base area of 100 cm2 and can hold 1500 cm3 of juice. The height of the juice container is
The height of a juice cylinder container with base area of 100 cm² and volume of 1500 cm³ is 15 cm
Base area of a cylinderBase area = πr²
base area = 100 cm²
100 = π × r²
r² = 100 / π
r = √100 / π
Volume of a cylindervolume = πr²h
1500 = π (√100 / π)² × h
1500 = π(100 / π) × h
1500 = 100h
divide both sides by 100
h = 1500 / 100
h = 15 cm
learn more on cylinder here: https://brainly.com/question/27342403
There are 25 rows of seats in the high school auditorium with 20 seats in the first row, 21 seats in the second
row, 22 seats in the third row, and so on. How many total seats are in the auditorium?
OA) 800 seats
OB) 860 seats
Answer:
A) 800 seats
Step-by-step explanation:
Notice that an arithmetic sequence is formed with the number of seats. Since we're adding one seat each row, the last (25th) row will have 44 seats since the first row has 20 seats.
The sum of an arithmetic sequence is given by:
[tex]S_n=n\left(\frac{a_1+a_n}{2}\right)[/tex], where [tex]n[/tex] is the number of terms, [tex]a_1[/tex] is the first term, and [tex]a_n[/tex] is the last term
Therefore, substituting [tex]a_1=20[/tex], [tex]a_n=44[/tex], and [tex]n=25[/tex], we get:
[tex]S_n=25(\frac{20+44}{2}),\\s_n=25\cdot 32=\boxed{800}[/tex]
x-(x-(x-y³)) use x=9, and y=1
Answer:
The answer: 8
Step-by-step explanation:
x-(x-(x-y³))
x=9 , y=1 —> 9 - (9-(9-1³)) —> 9 - (9-(8))—> 9 - ( 1) —> =8
Been on this math problem for almost an hour will mark most brainly(just the bottom part)
Answer:
5. (8,33) (-1, -21) (5, 15)
6. (-5, 29) (2, 1) (4, -7)
7. (-4, -9) (0, -1) (7, 13)
8. (-9, 0) (1, 8) (5, 4)
Step-by-step explanation:
Since X is given, you plug it into the equations.
Then put the answers into the Y. hope it helps!!
Factor the following polynomial 9x2 + 21x – 18
Answer:
factors are
21 and x
Step-by-step explanation:
equation 9 × 2 + 21x - 18
terms 9 , 2, 21x, -18
factors 21x = 21 and x
Answer:
3(x + 3)(3x - 2)
Step-by-step explanation:
Given
9x² + 21x - 18 ← factor out 3 from each term
= 3(3x² + 7x - 6) ← factor the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 6 = - 18 and sum = + 7
The factors are + 9 and - 2
Use these factors to split the x- term
3x² + 9x - 2x - 6 ( factor first/second and third/fourth terms )
3x(x + 3) - 2(x + 3) ← factor out (x + 3) from each term
(x + 3)(3x - 2)
Then
9x² + 21x - 18 = 3(x + 3)(3x - 2) ← in factored form
Solve for the triangle: ABC
A: 90 degrees
B: 6 feet
C: 10 feet
How much less is 17km than 24.6km?
Answer:
[tex]7.4km[/tex]
Step-by-step explanation:
[tex]24.6km - 17km \\ = 7.4km[/tex]
hope this helps you.
What is the slope of a line that is perpendicular to the line: -4x + 6y = -1 ?
A. -3/2
B. -2/3
C. 1/4
D. 3/2
What are the steps to this problem (and the answer?)
Answer:
[tex](25 {x}^{2} + 20xy + 16 {x}^{2} )(5x - 4y) = \\ 125 {x}^{3} + 100 {x}^{2} y + 80x {y}^{2} - 100 {x}^{2} y \\ - 80x {y}^{2} - 64 {y}^{3} = \\ 125 {x}^{3} - 64 {y}^{3} \\ please \: give \: brainliest[/tex]
HELP QUICK ILL GIVE BRAINLIEST
Answer:
A=35 degrees, B=55 degrees, C=110 degrees
Step-by-step explanation:
The 35 degree given angle is vertical angles with A, so they are congruent
The sum of angles in a triangle is 180, and we already have 2 angles (35 and 90) so subtract those and you get 55
angle c and the other given angle (70 degrees) are supplementary so subract 70 from 180
The wind is blowing opposite to leg AB. Given the fact that you’re traveling in a wind-powered boat, which leg of the course will take you the longest? Why? (4 points)
Answer:
The leg of the course that will take longest is from A to B
The reason is that the leg of the course, A to B is slowed by the wind
Step-by-step explanation:
The direction of the wind is opposite to leg AB
The starting and finishing point is point A, and the course is from A to B to C and back to point A
The leg of the course that will take the longest is course in which th motion is against the wind which is from B to A
The motion from B to C and from C to A are partly in the wind ward direction, because the wind would be behind the sales and will therefore be aided by the wind, leading to rapid motion
However, the starting motion on the leg from A to B is opposite the wind and will be slowed down by the wind, and would therefore, take the longest.
2. The parameter "b": Compare the graphs of several different exponential growth functions in
Mathematica to discover the significance of the parameter "b". Explain in detail what the
parameter "b" tells you about the graph of an exponential growth function.
Answer:
See explanation
Step-by-step explanation:
Required
The significance of "b" in exponential function
An exponential function is represented as:
[tex]y = ab^x[/tex]
In the above equation, parameter "b" is the rate of the function
In other words, the constant multiplier of the function.
Take for instance;
[tex]y = 2*4^x[/tex]
By comparison:
[tex]b = 4[/tex]
Another instance is:
[tex]y = 2(-4)^x[/tex]
By comparison
[tex]b = -4[/tex]
Other significance of parameter b are:
If [tex]b > 0[/tex] then b represents a growth factor
If [tex]b < 0[/tex] the b represents the factor of decay
[tex]b \ne 0[/tex] i.e. b is never 0
Patricia has $34,000 to invest. She invests some at 17% and the balance at 20%. Her total annual interest income is $6245. Find the amount invested at each rate
Answer:
she invest $18,500 at the 17% rate and $15,500 at the 20% rate.
Step-by-step explanation:
Suppose that you invest some quantity A to an invest rate of x%
At the end, the amount you will have is given by:
Amount = A + A*(x%/100%)
Where:
A*(x%/100%) is the interest income
So, here she initially has $34,000
And she invest some quantity X to a 17% and a quantity Y to 20%
Then we have:
X + Y = $34,000
And we know that her total anual income is $6245
X*(17%/100%) + Y*(20%/100%) = $6245
Then we have a system of two equations:
X + Y = $34,000
X*(17%/100%) + Y*(20%/100%) = $6245
First we can rewrite the second one to a more simpler form:
X*(0.17) + Y*(0.20) = $6245
Now we can isolate one of the variables in the first equation to get:
X = $34,000 - Y
Now we can replace that in the other equation to get:
( $34,000 - Y)*0.17 + Y*0.20 = $6245
Now we can solve this for Y:
$34,000*0.17 + Y*(0.20 - 0.17) = $6245
$5,780+ Y*0.03 = $6245
Y*0.03 = $6245 - $5,780 = $465
Y = $465/0.03 = $15,500
And X = $34,000 - Y = $34,000 - $15,500 = $18,500
So she invest $18,500 at the 17% rate and $15,500 at the 20% rate.
Mr. Serpe started with $200. He has a hole in his pocket and he lost $2 every day for a week. He then found $150. How much money does he have?
Answer:
336
Step-by-step explanation:
2x7=14, so 200-14=186, then 186+150=336
What should be done first to evaluate the expression?
4 + 8 ÷ 4 - 2 × 5
Add 4 and 8.
Divide 8 by 4.
Subtract 2 from 4.
Multiply 2 by 5.
Divide 8 by 4
Because is PEDMAS, division comes first.
Answer:
divide 8 by 4
Step-by-step explanation:
PEMDAS or BODMAS
which expression is equivalent to (4 square root 5 to the power of 3) to the power of 1/2?
the answer is on the photo
50 POINTS!!!! If you were on a rocket ship for a month that sat in between the moon and earth, how might moon phases be different? (need quickly!!!) also at least 2-4 sentences
Answer:I would sayif the planet earth was making a shadown on it. when u on other side
Step-by-step explanation:
That is the best i got
Answer:
Different times
Step-by-step explanation:
The closer you could get to the moon, the faster the phases will move. If you are about half way it should cut the time it takes to get through a season. Since you get closer to the object.
For each function, state whether it is linear, quadratic, or exponential.
Answer:
Step-by-step explanation:
Table for function 1,
x y Difference 1 Difference 2
2 10 - -
3 1 1 - 10 = -9 -
4 10 10 - 1 = 9 9 - (-9) = 18
5 37 37 - 10 = 27 27 - 9 = 18
6 82 82 - 37 = 45 45 - 27 = 18
Since, difference 2 is common as 18,
Table will represent a quadratic function.
Table for function 2,
x y Difference 1 Difference 2
5 16 - -
6 19 19 - 16 = 3 -
7 28 28 - 19 = 9 9 - 3 = 6
8 43 43 - 28 = 15 15 - 9 = 6
9 64 64 - 43 = 21 21 - 15 = 6
Since, difference 2 is common as 6,
Table will represent a quadratic function.
Table for function 3,
x y Ratio
1 112 -
2 56 56 ÷ 112 = [tex]\frac{1}{2}[/tex]
3 28 28 ÷ 56 = [tex]\frac{1}{2}[/tex]
4 14 14 ÷ 28 = [tex]\frac{1}{2}[/tex]
5 7 7 ÷ 14 = [tex]\frac{1}{2}[/tex]
Since, ratio is common as [tex]\frac{1}{2}[/tex].
Table will represent an exponential function.
Which r-value represents the weakest correlation?
–0.75
–0.27
0.11
0.54
Answer:
0.11
Step-by-step explanation:
Strongest correlation:
The strongest correlations happen for [tex]r = -1[/tex] and [tex]r = 1[/tex], that is, when r has the higher absolute value.
In this question:
The value of r with the lowest correlation is the one with the lowest absolute value(absolute value of -0.75 is 0.75 for example), so it is 0.11, which is the answer.
Answer:
it's C on edg
Step-by-step explanation:
.11
Complete the equations below. 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals \text{ hundredths}\div 2 hundredths÷2start text, space, h, u, n, d, r, e, d, t, h, s, end text, divided by, 2 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals \text{ hundredths} hundredths start text, space, h, u, n, d, r, e, d, t, h, s, end text 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals
Answer:
[tex]1.86 \div 2 = 0.93[/tex]
Step-by-step explanation:
The correct form of the question is:
Complete the equations below.
[tex]1.86 \div 2 =[/tex]
Required
Solve
Start from left to right
[tex]1 \div 2 = ??[/tex] --- this will give a fraction.
So, we append the next digit
[tex]1.8 \div 2 = 0.9[/tex]
Next:
[tex]0.06 \div 2 = 0.03[/tex]
Bring the results together:
[tex]1.86 \div 2 = 0.9+ 0.03[/tex]
[tex]1.86 \div 2 = 0.93[/tex]
what is (2x9)- (15 divided by 3)
Answer:
13
Step-by-step explanation:
We can simplify it:
(2x9)-(15/3)
(18)-(5)
18-5
13
Find the missing side length
Answer:
35
Step-by-step explanation:
Since the triangles are similar, we can write a ratio
25 ?
---- = -----
5 7
Using cross products
25*7 = 5 ?
Divide each side by 5
25*7/5 = 5?/5
35 = ?
please help. i need this done today
Answer:
herlojffhgdxvjdxhyeb olis the tim view on the euros 2020 final
Can someone help me with this math homework please!
Write an equation of the line that passes through the point (6, -9) with the given slope m = 3.
Answer:
y = 3x - 27
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 3 , then
y = 3x + c ← is the partial equation
To find c substitute (6, - 9) into the partial equation
- 9 = 18 + c ⇒ c = - 9 - 18 = - 27
y = 3x - 27 ← equation of line
16:32:12
Which linear inequality is represented by the graph?
O x < 2 x + 3
Oy> x+3
O y>x+3
O y<{x+3
-3 -2 -1
The linear inequality that represents the graph is y > (2/3)x + 3.
Option C is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
y < (2/3)x + 3
y > (3/2)x + 3
y > (2/3)x + 3
y < (3/2)x + 3
The graph is on the positive side of the y-coordinate so,
We can consider:
y > (3/2)x + 3
y > (2/3)x + 3
Now,
Plotting in a graph we see that,
We need to have the y-intercept at y = 3 and the x-intercept at x = 4.5.
So,
y > (2/3)x + 3 satisfied.
Thus,
y > (2/3)x + 3 represents the graph.
Learn more about inequalities here:
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Today only, a desk is being sold at a 33% discount. The sale price is $268. What was the price yesterday?
Discount percent = 33%
Sale price = $268
Let the original price be $x.
So,
[tex]x - (33\% \: of \: x) = 268 \\ = > x - ( \frac{33}{100} \times x) = 268 \\ = > x - ( \frac{33x}{100}) = 268 \\ = > \frac{100x}{100} - \frac{33x}{100} = 268 \\ = > \frac{(100x - 33x)}{100} = 268 \\ = > \frac{67x}{100} = 268 \\ = > 67x = 268 \times 100 \\ = > 67x = 26800 \\ = > x = \frac{26800}{67} \\ = > x = 400[/tex]
So, yesterday the price was $400.
