The sοlutiοn tο the equatiοn is: x = 1/2 and y = 0.
What is absοlute value?The absοlute value is the distance frοm zerο. It is the nοn-negative quantity.
|A| = B --> det(A) = |B|
Using the definitiοn οf absοlute value οf a matrix, we can write:
det( | 1 1+2j 0 | ) = det(2j)
| 1-j -1 -1 |
| x 0 yj |
Expanding the determinant οf the left-hand side, we get:
det( | 1 1+2j 0 | ) = 1(-1)(yj) + (1+2j)(-1-j)(x) + (1-j)(-1)(0)
| 1-j -1 -1 |
| x 0 yj |
Simplifying this expressiοn, we get:
det( | 1 1+2j 0 | ) = (2x + 2yj + 2j) + (2jx - 2xy - 2jx - 2j²) + 0
| 1-j -1 -1 |
det( | 1 1+2j 0 | ) = 2x + 2yj + 2j - 4xy
| 1-j -1 -1 |
Setting this equal tο the determinant οf 2j, we get:
2x + 2yj + 2j - 4xy = 2j
Simplifying and dividing by 2, we get:
x + yj - 2xy = 1
Substituting y = 0 intο the real part οf the equatiοn, we get:
x = 1/2
Therefοre, the sοlutiοn tο the equatiοn is: x = 1/2 and y = 0.
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Solve equation step by step...
6x+13y=15
QUESTION 4
.
1 POINT
The sum of eight times a number and four is ninety-two. Find the number.
Provide your answer below:
Answer:
The missing number is 11
Step-by-step explanation:
Step-by-step explanation:
x is the number
8x + 4 = 92 (8 times the number plus 4 is 92).
8x = 88
x = 11
the number is 11.
Cam anyone answer these 4 questions?
Answer:
The first one is correct
Step-by-step explanation:
ITs all good
solve the following question
The decay constant for the plutonium is - [ln (0.5 ) / 6300].
option C.
What is the decay constant?The decay constant for the plutonium is calculated by applying the following formula.
The given function for the radioactive decay;
\(Q(t) = Q_0e^{-kt}\)
where;
Q(t) is the quantity remaining after a given timeQ₀ is the initial quantityk is the decay constantt is the timeThe decay constant for the plutonium is calculated as;
k = ln(2) / T½
k = ln(2) / 6300
k = ln(0.5⁻¹) / 6300
k = - [ln (0.5 ) / 6300]
Thus, the decay constant for the plutonium is - [ln (0.5 ) / 6300].
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Evaluate the following expression.
53
Enter the answer
Answer:
125
Step-by-step explanation:
5^3 = 5 ✕ 5 ✕ 5, and 5 ✕ 5 ✕ 5 = 125
Hope this helps :)
Answer:
125
Step-by-step explanation:
all you have to do is 5*5*5. so multiply the number that many times it tells you on the exponent.
Solve (t-3)^2=6
The arrow is at a height of 48 ft after approx. ___ s and after ___ s.
The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.
To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:
s = v0t - 16t^2
Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.
Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:
48 = 96t - 16t^2
Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.
Rearranging the equation:
16t^2 - 96t + 48 = 0
Dividing the equation by 16 to simplify:
t^2 - 6*t + 3 = 0
We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.
Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
t = (6 ± √((-6)^2 - 413)) / (2*1)
t = (6 ± √(36 - 12)) / 2
t = (6 ± √24) / 2
Simplifying the square root:
t = (6 ± 2√6) / 2
t = 3 ± √6
Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.
In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.
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Note the complete question is
The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?
Solve (t-3)^2=6
The arrow is at a height of 48 ft after approx. ___ s and after ___ s.
1. Suppose that a die is rolled twice. What are the possible values that the following random variables can take on: (a) the maximum value to appear in the two rolls: (b) the minimum value to appear in the two rolls; (c) the sum of the two rolls; (d) the value of the first roll minus the value of the second roll? 2. If the die in Problem 1 is assumed fair, calculate the probabilities associated with the random variables in parts (a) through (d).
Answer:
hat mather chosen to be mather
15) Amy is playing a video game. She
scores 8 points, then loses 10, then
scores 5 more points, then scores 7
more points, then loses 20. What is her
final score? Show your work.
If a = 17, what is 18a - 89 ?
Answer: 18(a)-89=217
Step-by-step explanation:
If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.
Hope this helped.
Answer:217
Step-by-step explanation:
putting the value of a in the equation.
18×17-89= 217
What is the value of the expression
In the equation 11 - 4(x +4) = 6x, the first step is to simplify 11 - 4.
True
False
Answer:
False
Step-by-step explanation:
You first need to distribute the -4 to (x+4).
Question 1 of 10 Solve - 5 < 4x + 3 <= 7 x > - 2orx <= 1 B. x < - 2orx < 4 O C.-2 and x <= 1 D. x > 2 and x < 4
For the inequality -5 < 4x + 3 ≤ 7 the combined solution are x < -2 and x ≤ 1.
To solve the inequality -5 < 4x + 3 ≤ 7, we need to consider two separate inequalities:
Solve the inequality -5 < 4x + 3:
-5 < 4x + 3
Subtract 3 from both sides:
-5 - 3 < 4x
-8 < 4x
Divide both sides by 4
-8/4 > x
-2 > x
x < -2.
Now let's solve the inequality 4x + 3 ≤ 7:
4x + 3 ≤ 7
Subtract 3 from both sides:
4x ≤ 7 - 3
4x ≤ 4
Divide both sides by 4:
x ≤ 1
Therefore, the combined solution is x < -2 and x ≤ 1.
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Jimmy needs to save at least $30 to buy a new video game. Write an inequality that represents
this situation.
Answer:
About $10
Step-by-step explanation:
We know that Jimmy equally needs enough money to buy a new video game, which is $30.
Since more than 1 number equals 30, there might be multiple answers for this.
He might have about 10 dollars, hence 10 times 3 is 30.
Please help quickly
Answer:
Figure J does not show y as a function of x ⇒ D
Step-by-step explanation:
y is a function of x if and only if every x has only one value of y
Let us check each given figure if it shows a function or not
#Figure F
∵ Every value of x has an arrow is pointed to one value of y
∴ Every x has only one value of y
∴ The figure shows y as a function of x
#Figure G
∵ The ordered pairs have different values of x-coordinates
∴ Every x-coordinate has only one value of y-coordinate
∴ The figure shows y as a function of x
#Figure H
∵ Every x in the table appears once
∴ Every x has only one value of y
∴ The figure shows y as a function of x
#Figure J
∵ The ordered pairs were drawn in the figure are (-3, -2), (-3, -3), (-2, 0),
(-2, -1), (-1, 1), (-1, 2), (0, 3), (0, 4)
∵ x = -3 has two values of y, y = -2 and -3
∵ x = -2 has two values of y, y = 0 and -1
∵ x = -1 has two values of y, y = 1 and 2
∵ x = 0 has two values of y, y = 3 and 4
∴ Every x-coordinate has more than one value of y-coordinate
∴ Figure J does not show y as a function of x
please help :((
show that 2x+1 /3 + 5x-2 /2 simplifies to 19x-4 /6
Hello!
(2x+1)/3 + (5x-2)/2
= (4x+2)/6 + (15x-6)/6
= (4x+2+15x-6)/6
= (19x-4)/6
Answer:
see explanation
Step-by-step explanation:
\(\frac{2x+1}{3}\) + \(\frac{5x-2}{2}\)
we require the denominators of both fractions to be the same value
the LCM of 2 and 3 is 6, so convert both denominators to 6
multiply the numerator/ denominator of the first fraction by 2
multiply the numerator/denominator of second fraction by 3
= \(\frac{2(2x+1)}{3(2)}\) + \(\frac{3(5x-2)}{2(3)}\)
= \(\frac{4x+2}{6}\) + \(\frac{15x-6}{6}\)
now add the numerators, with a common denominator of 6
= \(\frac{4x+2+15x-6}{6}\)
= \(\frac{19x-4}{6}\)
PLEASE HELP ME The cost of gasoline is $2.35 per gallon. The price per gallon increased an average of 4% per day over the period of a week. This can be modeled by the function G(t) = 2.35(1.04)t, where t is the number of days since Sunday. What would be the most appropriate domain of G(t)? (1 point)
Group of answer choices
0 ≤ t ≤ 1
0 ≤ t ≤ 7
2.35 ≤ t ≤ 2.45
2.35 ≤ t ≤ 3.09
9514 1404 393
Answer:
(b) 0 ≤ t ≤ 7
Step-by-step explanation:
The appropriate domain is the set of values of the independent variable (t) for which the function reasonably makes sense. We are told the model is of prices over a week, and that t represents the number of days since the beginning of the week.
It seems reasonable that the model is intended to apply to a period between t=0 (the beginning of the week) and t=7 (the end of the week). Thus the appropriate domain is ...
0 ≤ t ≤ 7
In 924,130, the 2 is in the what place
Answer:
The hundredth thousands place.I hope this helps. Can you give me brainlest
Step-by-step explanation:
The table represents a linear relationship
X—2 0 4
Y-4 3 1
Which equation represents the table
Y=1/2x+5
y=-1/2x+3
Y=2x-3
Y=-4x+2
The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.
To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.
Given the table:
X: 2 0 4
Y: -4 3 1
We can plot these points on a graph and see that they form a straight line.
Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.
Based on the given options, we can now evaluate each equation to see which one represents the line:
Y = 1/2x + 5
When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.
Y = -1/2x + 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.
Y = 2x - 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.
Y = -4x + 2
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.
In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.
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Use the information to answer the question. The table shows the amount of lemon juice and water that 4 students mix. Student Luca Kal Jenna Micah Lemon Juice Water (fluid ounces) (fluid ounces) 2 6 4 6 10 8 9 B Which two students mix the same ratio of lemon juice to water? Choose two students to show the answer.
The two students that mix the same ratio of juice to water is given as follows:
A. Luca.
D. Micah.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is given as follows:
a to b.
Which is also the division of the two amounts.
Hence the ratio of juice to water for each person is given as follows:
Luca: 2/6 = 1/3.Kal: 6/10 = 3/5.Jenna: 4/8 = 1/2.Micah: 3/9 = 1/3.Hence Luca and Micah used the same ratio, meaning that options A and D are correct.
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Can some one help me?
Answer:
x=3
Step-by-step explanation:
can someone hep me with this
Answer:
What do you need help with?
Step-by-step explanation:
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
B, C, E
Step-by-step explanation:
For a rectangle,
area = length × width
Let length = y.
Then the width is y - 5.
A = LW
750 = y(y - 5)
y(y - 5) = 750
y² - 5y - 750 = 0
All equations that can be put in the form above are correct.
A) y(y + 5) = 750
y² + 5y - 750 = 0
No
B) y² – 5y = 750
y² - 5y - 750 = 0
Yes
C) 750 – y(y – 5) = 0
750 - y² + 5y = 0
y²- 5y - 750 = 0
Yes
D) y(y – 5) + 750 = 0
y² - 5y + 750 = 0
No
E) (y + 25)(y – 30) = 0
y² + 25y - 30y - 750 = 0
y² - 5y - 750 = 0
Yes
You want to restrict the domain of the function shown in the graph below to make it one-to-one so that it will have an inverse. What are the largest domains, in interval notation you could use
Answer:
(-∞, -3] or [-3, ∞)
Step-by-step explanation:
You want the largest domain interval(s) on which the function shown in the graph could be one-to-one.
One-to-oneA one-to-one function must pass the horizontal line test. That is, no horizontal line can intersect its graph in more than one place.
ApplicationFor that to be true of the given function, the interval on which it is defined cannot include values on both sides of x=-3, where the graph has a minimum. That is, the domain must be either x ≤ -3, or x ≥ -3, (or some subset of either of these).
The largest intervals on which the function has an inverse are ...
(-∞, -3] or [-3, ∞)
<95141404393>
To make the given function one-to-one and have an inverse, we can restrict its domain to (-∞, a) or (a, ∞), where 'a' is the x-coordinate of the highest or lowest point on the graph.
Explanation:To make the given function one-to-one and have an inverse, we need to restrict its domain. The largest domains, in interval notation, that can be used are: (-∞, a) or (a, ∞) where 'a' is the x-coordinate of the highest or the lowest point on the graph, depending on the function type.
If the graph has a highest point, the domain is restricted to (a, ∞), where 'a' is the x-coordinate of the highest point. If the graph has a lowest point, the domain is restricted to (-∞, a), where 'a' is the x-coordinate of the lowest point.
For example, if the graph has a highest point at (3, 5), the domain would be restricted to (3, ∞) to make the function one-to-one and have an inverse.
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Need help ASAP
the value of each variable. If your answer is not
teger, express it in simplest radical form.
The length of a is
The length of b is
(Simplify your answer.)
Answer:
me too (help)
Step-by-step explanation:
Solve for length of segment c.
11 cm
10 cm
8.8 cm
c = [?] cm
If two segments intersect inside
or outside a circle: ab = cd
Answer:
c = 8
Step-by-step explanation:
Using the Intersecting Chords Theorem, we can form the following equation and solve for c:
\(ab=cd\\(10)(8.8)=11c\\88=11c\\c=8\)
length in the boundary of any figure is called
Answer:
perimeter
Step-by-step explanation:
Perimeter is the distance around a two dimensional shape, a measurement of the distance around something; the length of the boundary.
-6y-3x=-18 for x and y
The answer fam is..... X = 6 - 2y, Y = 3 - x/2
Rey started out with $149 in her bank account. She spends $2 per
week for snacks at the school cafeteria.
1. What is the slope (m) for this situation?
2. What is the y-intercept (b) for this situation?
3. Write an equation for the amount of money,(y), in her bank account after x weeks, in slope-intercept form
Draw a model to represent each expression.
Answer:
OK
Step-by-step explanation:
The first screenshot is for #7 and the second screenshot is for #8
Math Homework: Unit 3 Assignment