The values of a and b are dependent on the equation. For example, in the equation a = 2y and b = 3, then a = 6 and b = 3. However, in the equation a = 2y and b = -3, then a = -6 and b = -3.
In the given options, the values of a and b are stated as a = 2y and b = –3. This means that the value of a is equal to twice the value of y (a = 2y), and the value of b is equal to -3. The other options do not match these conditions. It is important to note that without further context or information about the variable y, we cannot determine a specific value for a or b. The values provided only establish the relationship between a, b, and y as described in the option a = 2y and b = –3.
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Carole used 3 3/4cups of butter for baking. The
amount of sugar she used was 1/3 of the amount of
butter she used. How much sugar, in cups, did
she use?
1 1/4cups
1 1/3cups
2 1/2 cups
3 5/12cups
Answer:
1 1/4 cups
Step-by-step explanation:
3 3/4 cups = 3.75
1/3 = .33333
3.75 x .33333 = 1.25
1.25 = 1 1/4 cups
The rectangle has an area of x^2 - 9 square meters and a width of x - 3 meters.
What expression represents the length of the rectangle?
Answer:
Length = x + 3 meters
Step-by-step explanation:
Expression for the area of the rectangle = [tex]x^2 - 9 = (x + 3)(x - 3) m[/tex]
Expression for width of rectangle = ([tex]x - 3[/tex]) m
Area of a rectangle = [tex]Length \times Width[/tex]
⇒ Expression for length of rectangle = [tex]\frac{Area}{Width} = \frac{(x + 3)(x - 3)}{(x - 3)} = (x + 3) m[/tex]
Let x be an even integer. What is the product of the next two consecutive even integers?
O x^2+2x+4
O x^2+6x+8
O x(x+1)(x+2)
O x^2+3x+2
Answer:
The desired product is (x + 2)(x + 4).
Step-by-step explanation:
If x is an even integer, x + 2 is the next consecutive even integer and x + 4 the next.
The desired product is (x + 2)(x + 4).
Let f(3) = 1/(z^2+1) Determine whether f has an antiderivative on the given domain
(a) G=C\{i, –i}.
(b) G = {z Rez >0}.
To determine whether the function f(z) = 1/(z^2 + 1) has an antiderivative on a given domain, we need to check if the function is analytic on that domain.
(a) For the domain G = C\{i, -i}, the function f(z) = 1/(z^2 + 1) is analytic on G. This is because it is a rational function and does not have any singularities (poles) within the domain. Hence, it has an antiderivative on G.
(b) For the domain G = {z Re(z) > 0}, the function f(z) = 1/(z^2 + 1) does not have an antiderivative on G. This is because the function has singularities at z = i and z = -i, which lie on the imaginary axis. Since the domain excludes these points, f(z) is not analytic on G and does not have an antiderivative on G.In summary, the function f(z) = 1/(z^2 + 1) has an antiderivative on the domain G = C\{i, -i} but does not have an antiderivative on the domain G = {z Re(z) > 0}.
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Consider the following system of differential equations:
dx/dt +y=0
dt/dy + 4x = 0.
Write the system in matrix form and find the eigenvalues
If A is equal to [0, 4] and I is equal to [1, 0], [0, 1], then [0 - 4][1 0] equals 0 and [0 - 4] equals 0 and [2 - 4] equals 0. Accordingly, the eigenvalues of the matrix
[dt/dy] + [0, 4] [x] = [0] can be written as the differential equation above in a matrix. Here, [0, 4] is the coefficient network and [x] is the variable grid. Given, arrangement of differential conditions, dt/dy + 4x = 0. Let [0, 4] be the framework's eigenvalue, and then [0, 4] [x] = [x] => (A-I) [x] = 0, where An represents the coefficient grid, I represents the character lattice, and x represents the variable network.
The determinant of [A-I] is 0 if for a non-trivial solution, [A-I] [x] = 0. On the off chance that An is equivalent to [0, 4] and I is equivalent to [1, 0], [0, 1], then [0 - 4][1 0] equivalents 0 and [0 - 4] equivalents 0 and [2 - 4] equivalents 0. As a result, the matrix's eigenvalues
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Find the value of y. Will give out a brainly for help
Answer:
3
Step-by-step explanation:
the scale is 2 so you need to figure out 3y + 5 = 14
La relación del aspecto de una pantalla o la relación entre el ancho y alto de una televisión es de 16:9. El tamaño de una TV está dado por la distancia diagonal de la TV, si se sabe que una HDTV tiene 41 pulgadas de ancho, determina el tamaño de la pantalla.
Answer:
[tex]23\frac{1}{16}[/tex] pulgada
Step-by-step explanation:
[tex]\frac{16}{9} =\frac{41}{y}[/tex]
16 × y = 9 × 41
16y = 369
16y ÷ 16 = 369 ÷ 16
[tex]y=23\frac{1}{16}[/tex]
- 100 points -
Use synthetic division to completely factor:
y= x^3 + 3x^2 - 13x - 15 by x + 5
A - y = (x+5)(x+3)(x-1)
B - y = (x+5)(x+3)(x+1)
C - y = (x+5)(x-3)(x-1)
D - y = (x+5)(x-3)(x+1)
Answer:
B
Step-by-step explanation:
D) - y = (x + 5)(x - 3)(x + 1).
EXPLANATION:Table in this case would look like this:
Write coefficients of x³, x² ,x and the constant in a row and divisor would be the x value obtained by equation x + 5 = 0.
The sequence of multiplications would be as shown in picture.
x² - 2x - 3
x² - 3x + x - 3
x(x - 3) + 1(x - 3)
(x + 1)(x - 3)(x + 5).
please help me! I'd be filled with so much gratitude
Answer:
0
Step-by-step explanation:
-9 x (0/-3)
-9 x 0
0
Help me please it’s due today
H⊃I
J⊃K
~K
H∨J
. Show that each of the following arguments is valid by
constructing a proof
I
The proof shows that if we assume the premises are true and the conclusion is false, it leads to a contradiction. Therefore, the argument is valid. The modus ponens and conjunction are used.
To construct a proof for the given argument, we'll use a proof by contradiction. We'll assume the premises are true and the conclusion is false, then we'll derive a contradiction. If a contradiction is reached, it means the original assumption was false, and thus the argument is valid.
Argument:
H ⊃ I
J ⊃ K
~K
H ∨ J
Conclusion: I
Proof by contradiction:
H ⊃ I (Premise)
J ⊃ K (Premise)
~K (Premise)
H ∨ J (Premise)
~I (Assumption for proof by contradiction)
H (Disjunction elimination from 4)
I (Modus ponens using 1 and 6)
~J (Assumption for proof by contradiction)
K (Modus ponens using 2 and 8)
~K ∧ K (Conjunction introduction of 3 and 9)
Contradiction: ~I ∧ I (Conjunction introduction of 5 and 7)
Conclusion: I (Proof by contradiction)
The proof shows that if we assume the premises are true and the conclusion is false, it leads to a contradiction. Therefore, the argument is valid.
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What is the difference between a monomial and a polynomial?
Answer:
Is that your answer
Plz help last one thanks
Answer:
110.45 inches cubed
Step-by-step explanation:
5in x 4.7in x 4.7in
What is the theoretical probability of rolling a 3 on a die?
Answer:
1/6 or 16.67% chance
Step-by-step explanation:
Assuming its a normal six sided dice. You would have a 16.67% chance of getting a 3.
Given a △ PQR with vertices P (2, 3), Q (-3, 7) and R(-1, -3): The equation of median PM is __________.
The equation of the median PM in triangle PQR with vertices P(2, 3), Q(-3, 7), and R(-1, -3) is y = (1/3)x + 7/3.
To find the midpoint of QR, we calculate the average of the x-coordinates and the average of the y-coordinates. The x-coordinate of point M is (-3 + (-1))/2 = -2/2 = -1, and the y-coordinate of point M is (7 + (-3))/2 = 4/2 = 2.
Therefore, the coordinates of point M are (-1, 2). Now, we have two points, P (2, 3) and M (-1, 2), and we can find the equation of the line passing through these points using the point-slope form.
The slope of the line passing through P and M is (2 - 3)/(-1 - 2) = -1/-3 = 1/3. Using the point-slope form, we have:
y - 3 = (1/3)(x - 2)
Expanding and rearranging the equation, we get:
y = (1/3)x + 7/3
Therefore, the equation of the median PM in triangle PQR is y = (1/3)x + 7/3.
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Let Y~ N(μ, 2). Find the MGF of Y using the fact that Y = μ+oZ where Z~ N(0, 1). You don't have to derive the MGF of Z since it was done in lecture 1.
The MGF of Y using the fact that Y = μ + oZ where Z ~ N(0, 1) is e^(tμ + t²/2).
The MGF of Y is given by,
E[exp(tY)] = E[exp(t(μ+Z))]
We know that if X is a normal random variable, X~N(μ, σ²) with μ as the mean and σ² as the variance.
The MGF of X is given by,
MGF_X(t) = E[e^(tx)] = e^(μt + (σ²t²)/2)
Here, Y ~ N(μ, 2) we have Y = μ + oZ where Z ~ N(0, 1)
MGF_Y(t) = E[exp(tY)] = E[exp(t(μ+Z))]MGF_
Y(t) = E[e^(tμ+tZ)]MGF_
Y(t) = e^(tμ) E[e^(tZ)]
We know that the MGF of Z is already derived in the lecture 1,
It is MGF_Z(t) = e^(t²/2)MGF_
Y(t) = e^(tμ) e^(t²/2)MGF_
Y(t) = e^(tμ + t²/2)
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Given information is that Y~ N(μ, 2), let's find the MGF of Y using the fact that Y = μ + oZ where Z~ N(0, 1).
The MGF of Y becomes:
MGF of [tex]Y = e^{t} \mu+ MGF\ of\ o \times e^{((t^2)/2)}[/tex]
Hence, the MGF of Y is [tex]e^{t}\mu + MGF\ of\ o \times e^{((t^2)/2)}[/tex].
The MGF of Y is as follows:
MGF of Y = MGF of μ + MGF of oZ
The MGF of Y = MGF of μ + MGF of oMGF of Z
Since the mean of Y is μ, we can substitute the above equation with the following:
[tex]MGF\ of\ Y = e^{t}\mu + MGF\ of\ oMGF\ of\ Z[/tex]
Now let's find the MGF of Z: We know that the MGF of Z is given by;
MGF of [tex]Z = e^{((t^2)/2)}[/tex]
Therefore, the MGF of Y becomes: MGF of [tex]Y = e^{t}\mu + MGF\ of\ o \times e^{((t^2)/2)}[/tex]
Hence, the MGF of Y is [tex]e^{t}\mu + MGF\ of\ o \times e^{((t^2)/2)}[/tex].
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Can someone help me please
pllssss help I put B, but I got it wrong the first time. NO LINKS
Answer:
D.1767.1 in³
Step-by-step explanation:
volume of a sphere=4/3πr³
where r=radius of the sphere
Given diemeter= 15in
so radius=15/2=7.5in
volume=4/3×π×(7.5)³
=4/3×22/7×(7.5)³
=1767.1in³
hope it helps...
have a great day!!
Suppose [v]B2 is as follows. 11 14 mo [v]B2 = 13 14 7 6 10 If ordered bases B1 = ={[?][*}a and B2 = find [v]B {[i][ 13}} 4 [v]B, = 1
The value of [v]B1 is [[1][0]][[0][0]]
Suppose [v]B2 is as follows:
[v]B2 = [[11][14]]
[13][14]]
[7][6]]
[10]]
If the ordered bases are B1 = {a, b} and B2 = {c, d}, we want to find [v]B1.
To find [v]B1, we need to express the columns of [v]B2 in terms of the basis vectors of B1.
The first column of [v]B2 is [11, 13, 7, 10]. We want to express this column in terms of the basis vectors of B1: [a, b].
To do this, we set up the following equation:
[11][13][7][10] = [a][b]
Solving this equation, we find that:
11a + 13b = 11
13a + 14b = 13
7a + 6b = 7
10a = 10
From the last equation, we can see that a = 1.
Substituting this value of a into the first three equations, we can solve for b:
11 + 13b = 11
13 + 14b = 13
7 + 6b = 7
Simplifying these equations, we find that b = 0.
Therefore, [v]B1 is as follows:
[v]B1 = [[1][0]]
[0][0]]
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Express the following complex number in polar form: Z = (20 + 120)6
The complex number Z = (20 + 120i) can be expressed in polar form as Z = 2√370(cos(1.405) + isin(1.405)).
To express the complex number Z = (20 + 120i) in polar form, we need to find its magnitude (r) and argument (θ).
The magnitude of a complex number Z = a + bi is given by the formula:
|r| = √(a^2 + b^2)
In this case, a = 20 and b = 120.
Therefore, the magnitude of Z is:
|r| = √(20^2 + 120^2) = √(400 + 14400) = √14800 = 2√370.
The argument (θ) of a complex number Z = a + bi is given by the formula:
θ = arctan(b/a)
In this case, a = 20 and b = 120. Therefore, the argument of Z is:
θ = arctan(120/20) = arctan(6) ≈ 1.405 radians.
Now we can express Z in polar form as Z = r(cosθ + isinθ), where r is the magnitude and θ is the argument:
Z = 2√370(cos(1.405) + isin(1.405)).
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Please help!!
Brainlest to best answer.
Answer:
D. 42
2X3X7=42
Step-by-step explanation:
It's just volume baseXwidthXhight. Hope this helps.
Students set a goal for the
number of cans to collect
for the canned food drive.
They reached 120% of
their goal. What is 120%
expressed as a fraction
and as a decimal?
Answer:
Fraction = 120/100 | Decimal = 1.2
Step-by-step explanation:
Fraction:
100% is 100/100 but 120% is 20% over so the fraction is now 120/100 (20% = 20/100)
Decimal:
100% is 1 but as I said earlier, 120% is 20% over so the decimal is now 1.2 (20% = 0.2)
write the equations of these parabolas in vertex form: • focus at (-5,-3), and directrix y = -6 • focus at (10,-4), and directrix y = 6
Answer:
y=0.12/1(x-5)^2 -3
y=1/10(x-10)^2 -4
Step-by-step explanation:
Given the directrix and focus of the parabolas, the equation of the parabolas are [tex]y=\frac{1}{6}(x^{2} +10x - 2)[/tex] and [tex]y=\frac{1}{20}(-x^{2} +20x - 80)[/tex].
What is equation of a parabola?Equation of a parabola is given by-
Distance of a point (x, y) on parabola from directrix = Distance of a point (x, y) on parabola from focus
focus = (-5, -3)
directrix = y = -6
[tex]\sqrt{(x+5)^{2}+(y+3)^{2} } = (y+6)\\\\ (x+5)^{2}+(y+3)^{2} = (y+6)^{2}\\\\x^{2} +25+5x = 6y+27\\\\y=\frac{1}{6}(x^{2} +10x - 2)[/tex]
focus = (10,-4)
directrix = y = 6
[tex]\sqrt{(x-10)^{2}+(y+4)^{2} } = (y-6)\\\\ (x-10)^{2}+(y+4)^{2} = (y-6)^{2}\\\\x^{2} +100-20x = -20y+20\\\\y=\frac{1}{20}(-x^{2} +20x - 80)[/tex]
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A tank contains 120 liters of oil initially. Oil is being pumped out of the tank at a rate R(t), where R(t) is measured in gallons per hour, and t is measured in hours. The table below shows selected values for R(t). Using a trapezoidal approximation with three subintervals and the data from the table, find an estimate of the number of gallons of oil that are in the tank at time t = 14 hours. t (hours) 2 5 10 14 R(t) gallons per hour 8.2 7.8 8.6 9.3 A. 220.8 В. 19.2 C. 100.8 D. 18.75
The estimate of the number of gallons of oil in the tank at t = 14 hours is 100.8 gallons. The correct answer is option C.
To estimate the number of gallons of oil in the tank at t = 14 hours using a trapezoidal approximation,
we need to calculate the total change in oil volume over the given time period.
The trapezoidal approximation involves dividing the time interval into subintervals and approximating the change in volume as the sum of trapezoidal areas.
Let's calculate the approximate volume of oil at t = 14 hours using the given data and the trapezoidal approximation: Interval 1 (2 to 5 hours):
Average rate = (R(2) + R(5)) / 2 = (8.2 + 7.8) / 2 = 16 / 2 = 8 gallons per hour.
Volume change =
[tex]Average rate \times time = 8 \times (5 - 2)[/tex]
= 24 gallons.
Interval 2 (5 to 10 hours):
Average rate = (R(5) + R(10)) / 2 = (7.8 + 8.6) / 2 = 16.4 / 2 = 8.2 gallons per hour
Volume change =
[tex]Average rate \times time = 8.2 \times (10 - 5) [/tex]
= 41 gallons
Interval 3 (10 to 14 hours):
Average rate = (R(10) + R(14)) / 2 = (8.6 + 9.3) / 2 = 17.9 / 2 = 8.95 gallons per hour
Volume change =
[tex]Average rate \times time = 8.95 \times (14 - 10)[/tex]
= 35.8 gallons.
Total volume change = Interval 1 + Interval 2 + Interval 3 = 24 + 41 + 35.8 = 100.8 gallons.
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Jamar to the local snack shop near his school He bought 3 hotdogs and 2 bags of chips for $Kenny went to the same snack shop and bought 5 hotdogs and 6 bags of chips for $9.55 ordered 2 hotdogs and 3 bags of chips, then how much did she pay her order?
Answer:
Marcy paid $4.15
Step-by-step explanation:
Given
Represent hotdogs with x and chips with y.
So, we have:
Jamal
[tex]3x + 2y = 4.85[/tex]
Kenny
[tex]5x + 6y = 9.55[/tex]
See attachment for complete question
Required
Determine the amount for 2x and 3y
From Jamal's and Kenny's orders we have:
[tex]3x + 2y = 4.85[/tex] --- (1)
[tex]5x + 6y = 9.55[/tex] --- (2)
Multiply (1) by 3
[tex]3 * [3x + 2y = 4.85][/tex]
[tex]9x + 6y = 14.55[/tex] --- (3)
Subtract (2) and (3)
[tex]9x - 5x + 6y - 6y = 14.55 - 9.55[/tex]
[tex]9x - 5x = 5[/tex]
[tex]4x = 5[/tex]
Solve for x
[tex]x = \frac{5}{4}[/tex]
[tex]x = 1.25[/tex]
Substitute [tex]x = 1.25[/tex] in [tex]3x + 2y = 4.85[/tex]
[tex]3 * 1.25 + 2y = 4.85[/tex]
[tex]3.75 + 2y = 4.85[/tex]
Solve for y
[tex]y = \frac{4.85 - 3.75}{2}[/tex]
[tex]y = \frac{1.10}{2}[/tex]
[tex]y = 0.55[/tex]
So, the cost of 2x and 3y is:
[tex]Cost = 2x + 3y[/tex]
[tex]Cost = 2*1.25 + 3*0.55[/tex]
[tex]Cost = \$4.15[/tex]
Approximately how long does it take a sample of francium-223 to decay by 50%?
A. 80 minutes
B. 100 minutes
C. 20 minutes
D. 40 minutes
By reading off the graph as shown in the question, we can see that the time that is required is 20 minutes.
What is the half life?The half life is the time that it taken for only half or 50% of the isotopes that were originally present in the sample to remain. We know that the half life does differ by the kind of sample that is used.
In this case, we want to determine how long does it take a sample of francium-223 to decay by 50%. This could easily be done from the graph of the decay as shown in the question.
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If a 2ft stick in the ground casts a shadow of 0.8ft, what is the height of a tree that casts a shadow that is 14.24ft?
Answer:
35.6 feets
Step-by-step explanation:
To obtain tree height :
(Height of stick / shadow of stick = height of tree / shadow of tree)
Height of stick = 2 feets
Shadow of stick = 0.8 feets
Shadow of tree = 14.24 feets
Height of tree = h
(2 / 0.8 = h /14.24)
Cross multiply
0.8h = 14.24 * 2
0.8h = 28.48
h = 28.48 / 0.8
h = 35.6 feets
Show that x=0 is a regular singular point of the given differential equation
b. Find the exponents at the singular point x=0.
c. Find the first three nonzero terms in each of two solutions(not multiples of each other) about x=0.
xy'' + y = 0
The first three nonzero terms of two linearly independent solutions about x = 0 can be obtained by Taylor expanding the solutions in terms of the exponent r and truncating the series to the desired order.
To determine if x = 0 is a regular singular point of the differential equation xy'' + y = 0, we substitute y = x^r into the equation and solve for the exponent r. Differentiating y twice with respect to x, we have y'' = r(r - 1)x^(r - 2). Substituting these expressions into the differential equation, we get [tex]x(x^r)(r(r - 1)x^(r - 2)) + x^r = 0[/tex]. Simplifying, we obtain r(r - 1) + 1 = 0, which yields r^2 - r + 1 = 0. Solving this quadratic equation, we find that the exponents at the singular point x = 0 are complex and given by r = (1 ± i√3)/2.
To find the first three nonzero terms of two linearly independent solutions about x = 0, we can use the Taylor series expansion. Let's consider the solution y1(x) corresponding to the exponent r = (1 + i√3)/2. Expanding y1(x) as a series around x = 0, we have y1(x) =[tex]x^r = x^((1 +[/tex]i√3)/2) = x^(1/2) *[tex]x^(i√3/2[/tex]). Using the binomial series expansion and Euler's formula, we can write [tex]x^(1/2) and x^(i√3/2)[/tex] as infinite series.
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Math question: Solve for y: 2x-y=3
Answer:
[tex]y=2x-3[/tex]
Step-by-step explanation:
This is just algebraic manipulation. In order to solve for y, you need to isolate it. Start this by moving the 2x from the left side of the equation. You can do this by subtracting 2x from both sides and you should end up with:
[tex]-y=-2x+3[/tex]
After this, you still have a negative y, which means you just need to divide both sides of the equation by -1 to get rid of the negative. That should reverse the signs of all the variables in the equation, making it look like:
[tex]y=2x-3[/tex]
Which set of ordered pairs does not represent a function?
Answer:
Hi! The answer to your question is D. {(0,0),(0,1),(1,2)(1,3)}
Step-by-step explanation:
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