Answer:
Below
Step-by-step explanation:
Question 1:
The quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants. If one solution of the equation is 7-13i, the other solution must be the complex conjugate of 7-13i, which is 7+13i. To find the complex conjugate of a complex number, you simply need to change the sign of the imaginary part of the number. In this case, the complex conjugate of 7-13i is 7+13i.
Question 2:
1. (4-3i) (-7+21)
To add two complex numbers, we need to add their real parts and imaginary parts separately. In this case, we have:
(4-3i) (-7+21)
= (4 - 7) + (-3i + 21)
= -3 + 18i
2. (-7+6i)+(2-3i)+(4+5i)
To add multiple complex numbers, we can add them one at a time using the same procedure as before. In this case, we have:
(-7+6i)+(2-3i)+(4+5i)
= (-7+2) + (6i - 3i) + (4 + 5i)
= -5 + 3i + 4 + 5i
= -1 + 8i
3. (-6-i)/4-2i
To divide two complex numbers, we need to multiply the numerator and denominator by the complex conjugate of the denominator. In this case, we have:
4. (-6-i)/4-2i
= (-6-i)(4+2i)/(4-2i)(4+2i)
= (-24 - 2i + 6i - i^2)/20
= (-24 + 4 -1)/20
= (-21)/20
= -1.05 - 0.05i
5. (-2-7i)(-2+7i)
To multiply two complex numbers, we use the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms separately and then adding the results. In this case, we have:
(-2-7i)(-2+7i)
= (-2 * -2) + (-2 * 7i) + (-7i * -2) + (-7i * 7i)
= 4 + (-14i) + 14i + 49
= 4 + 49
= 53
6. (5-3i)-(-2-6i)
To subtract two complex numbers, we need to add the first number to the opposite of the second number. In this case, we have:
(5-3i)-(-2-6i)
= (5-3i) + (2 + 6i)
= 7 + 3i
This is the final answer for each of the problems.
What is the quotient of 2 1/4 and 5/8?
Answer:42/5.
21*8=168
4*5=20
168 divided by 20 is 8.4 which is 42/5
How does the closure property relate to the addition of polynomials?
For the Polynomials to be closed under closure property for the operation of addition if the addition operation produces another polynomial.
Closure property states that when a set of numbers is closed beneath any arithmetic operation such as subtraction, addition, division, and multiplication and is performed on any two numbers of the set with the reply being another number from the set itself. When including polynomials, the factors and their exponents don't alter. As it were their coefficients will possibly alter. This ensures that the sum has factors and exponents which are as of now classified as having a place in polynomials. Polynomials are closed beneath the addition.
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solve the system of equations using elimination: 3x-2y=2 and 2x-5y=27
Answer:
(-4,-7)
Step-by-step explanation:
Multiply both sides of the first equation by-5 or 2 (I'll use 5) and both sides of the second equation by - 2 or 3 (I'll use -2).
3x - 2y = 2
5(3x-2y)= 5(2)
-15x - 10y = 10
2x - 5y = 27
-2(2x - 5y) = -2(27)
-4x + 10y = -54
Now you see that the absolute values of the y-values of the 2 equations match up . They are still the same equations but scaled up.
-15x + 10y = 10
-4x - 10y = -54
Add to eliminate y.
-11x = 44
Divide both sides by -11.
[tex]\frac{-11x}{-11} = \frac{44}{-11}[/tex]
x = -4
Plug back in to either equation to solve. I'll use the first equation.
3x - 2y = 2
x = - 4
3(-4) - 2y = 2
-12 - 2y = 2
Add 12 on both sides.
-12 + 12 - 2y = 2 + 12
- 2y = 14
Divide -2y on both sides.
[tex]\frac{-2y}{-2} = \frac{14}{-2}[/tex]
y = -7
(-4,-7)
find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 5xy.
The equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 5xy is [tex]e^{\frac{5x^2}{2} }[/tex] .
The slope of the curve is 5xy.
Therefore:
dy/dx = 5xy
dy/y = (5x)dx
Then,
The integrate both sides giving us
ln(y) = (15x²)/2 + C
Since, the curve passes through (0,1) .
Therefore, x=0 and y=1 for solving 2
ln(1) = 0/2 + C
0 = 0 + C
⇒ C = 0
We now,
substitute C back in and isolate y
ln(y) = (15x²)/2
⇒ y = e(15x²) / 2
Therefore, The answer is y = [tex]e^{\frac{5x^2}{2} }[/tex]
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Ava can swim 70 yards in 2 minutes. At this rate, how many yards would you expect her to swim in 5 minutes?
Answer:
175 yards
Step-by-step explanation:
70/2 = 35
35 x 5 = 175
ethan buys a video game on sale . if the video game useully costs $39.99 and it was on sale for 20% off how much did ethan pay?
Answer:
31.992 dollars
Step-by-step explanation:
39.99 times 80%
=31.992
Use the divergence theorem to compute the net outward flux of the vector field f across the boundary of the region d. F= 32-x,x - 5y,7y +9z
Using the divergence theorem we can compute that the outward flux of the vector field is 16π .
The outward flux of F over the solid cylinder and z = 0 is
∫∫F·ds = ∫∫∫ DivF dv
F = 2xy² i + 2x²y j + 2xy k
Div F = D/dx (2xy²) + D/dy (2x²y )
Div F = 2y² + 2x²
In cylindrical coordinates dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ
Using the parametric form of the surface equation
x = rcosθ y = r sinθ and z = z
Div F = 2r² sin²θ + 2r²cos²θ
∫∫∫ DivF dv = ∫∫ [2r²sin²θ + 2r²cos²θ] × rdrdθ
∫∫ 2r² [sin²θ + cos²θ] × rdrdθdz ⇒ ∫∫ 2r³ drdθ
Integration limits
0 < r < 2 0 < θ < 2π
2∫₀² r³ ∫dθ
(2/4) × (2)⁴ × 2π
The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.
In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.
Therefore the flux is 16π .
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A certain tar i 3. 6 x 10^2 light year from the earth. One light year i about 5. 9 x 10^12 mile how far from the earth in mile i the tar
Answer:
Could you please explain your question with proper English?
Step-by-step explanation:
Thank you.
How do you solve 4 linear equations?
The easiest way to solve 4 linear equations is to use the substitution method. This involves substituting the values of one equation into the other equations until you are left with a single equation that can be solved for the remaining variable.
if you have the following four linear equations:
A + B = 10
A - B = 2
A + C = 12
A - C = 3
You can substitute A = 10 - B into the third and fourth equations to get:
10 - B + C = 12
10 - B - C = 3
Then you can add the two equations together and solve for C:
2B + 2C = 15
2C = 15 - 2B
C = (15 - 2B) / 2
Once you have C, you can substitute it into one of the other equations to solve for B:
A + B = 10
A = 10 - C
B = 10 - (15 - 2B) / 2
B = 5 - (15 - 2B) / 2
2B = 10 - 15
2B = -5
B = -2.5
Now you have both B
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The radius of the base of a cone is decreasing at a rate of 222 centimeters per minute. The height of the cone is fixed at 999 centimeters. At a certain instant, the radius is 131313 centimeters. What is the rate of change of the volume of the cone at that instant (in cubic centimeters per minute)?.
If the radius of the base of a cone is decreasing at rate of 2 cm/minute and the height is kept constant at 9 cm, the rate of change of the volume at radius 13 cm is 489.4 cm³/minute
To calculate the rate of change, we need to take the derivative of the variables with respect to time.
The volume of a cone is given by:
V = 1/3 . πr²h
Where:
r = radius of the base
h = height
Since the height of the cone is held constant, then the derivative with respect to time is:
dV/dt = 1/3 h. 2πr dr/dt
Parameters given:
dr/dt = 2 cm/minute
h = 9 cm
r = 13 cm
Hence,
dV/dt = 1/3 x 9 x 2π x 13 x 2
dV/dt = 489.4 cm³/minute
Hence, at radius 13 cm, the rate of change of the volume is 489.4 cm³/minute
It looks like there was typos in your question, most probably your question was:
The radius of the base of a cone is decreasing at a rate of 2 centimeters per minute. The height of the cone is fixed at 9 centimeters. At a certain instant, the radius is 13 centimeters. What is the rate of change of the volume of the cone at that instant (in cubic centimeters per minute)?
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20 List the steps of the perpendicular bisector construction in order from 1 to 4
The steps of the perpendicular bisector construction in order from 1 to 4 are;
1) Open the compass
2) Draw arcs above and below the segment to be bisected
3) Draw arcs from the other endpoint of the segment to be bisected
4) Join the intersection of the arcs with a line
What is a perpendicular bisector?A perpendicular bisector is a line, that is perpendicular to another line, and which divides the other line into two congruent segments.
The steps of a perpendicular bisector construction includes;
1) Opening the compass to a radius that is more than half the length of the segment to be bisected
2) With the radius of the compass opening in step 1, place the compass at one endpoint of the segment to be bisected and draw arcs above and below the the segment to be bisected
3) With the same radius of the compass from step 1, place the compass at the other endpoint and draw arcs above and below the segment to be bisected to intersect the arcs drawn in step 2
4) With a straightedge, draw a straight line joining the point of intersection of the arcs in step 3. The line is the perpendicular bisector of the segment.
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What are examples of functions in real life situation?
The examples of functions in real life situation is given below .
In the question,
we have to give few examples for functions in real life .
the term Function is defined as as a relationship between two variables where for every input variable there is one output variable.
the examples are :
Example 1 :
Suppose that a car is driving at a constant speed of 30 mph.
the total distance "d" is equal to the rate, 30 times the time "t" ,that we drive for . the function for the relationship between our distance, d, and the time for driving is
d = f(t) =30 × t .
Example 2:
Suppose that the cost for 1 bag is $9 , then the function for the cost of "x" bags can be written as
Cost = f(x) = 9x .
Therefore , the real life situations examples are shown above.
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The points (1,2) and (-4,6) are rotated 90 degrees and translated right 4 units and down 2 units
Calculate the equation of a line that goes through both transformed points. (if needed use fractions with no spaces)
y=-3/4x-9/2 is the equation of a line that goes through both transformed points.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
we must translate the given point (x,y) into the translation given. We begin with the 90 degree clockwise rotation such that
90 degree clockwise rotation = (x, y) => (y, -x)
we translate the coordinate (y, -x)
2 units to the right such that
(y-4, -x - 2)
So the coordinate of points changed (1,2) and (-4,6) from (-2, -3) and (2, -6)
m=-6-(-3)/2-(-2)
m=-3/4
Now let us find the y intercept.
-3=-3/4(-2)+b
-3=3/2+b
-3-3/2=b
-9/2=b
Hence, y=-3/4x-9/2 is the equation of a line that goes through both transformed points.
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A bag contains five snicker bars, nine moly
Answer:
31%
Step-by-step explanation:
total number of candy bars in the beginning = 28
number of milkyway bars in the beginning = 9
probability = 9/28 x 100 = 32% (rounded)
number of candy bars after = 27
number of milkway bars after = 8
probablity = 8/27 x 100 = 30 (rounded)
total probablity = (30+32)/200 x 100 = 31
Express the area of the entire rectangle. Your answer should be a polynomial in standard form.
The standard size of the rectangle's area is x² + 12x + 35
Given:
a diagram that depicts the polynomial that denotes a rectangle's length and width.
The rectangle's area is equal to its length x width.
Given that length is equal to x + 7 and width is equal to x + 5, the area is equal to length plus width.
Add the numbers in brackets: Area = x2 + 5x + 7x + 35
Area = x2 + 12x + 35
A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. We are surrounded by numerous rectangular objects. The length and width of a rectangular shape are the two dimensions that define it. The rectangle's length and width are its longer and shorter sides, respectively. We will learn about the properties of the rectangle shape in this chapter.
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Full Question = Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
x+7 x+5
What is the formula of equation?
The formula of an equation is a mathematical expression that is used to represent the relationship between two or more variables
It is written in the form of a mathematical statement that expresses the relations between the variables. The equation is written using symbols such as +, -, =, and other mathematical operators to denote the relationships between the variables. The equation can be used to solve problems and to find unknown values. By using the equation, it is possible to determine the values of the unknowns given the values of the knowns. for an example such as x+2=4.
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Please help me with this
Complete the following statement
Answer: B they are parallel
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Lines that are both perpendicular to a given line are parallel.
What’s the multiplicity for number 5
The zeros of the function, along with their multiplicities and effects, are given as follows:
Zero of -4, multiplicity 2, turning effect.Zero of -5/2, multiplicity of 5, crossing effect.Zero of 1, multiplicity of 1, turning effect.What are the zeros of the function, along with their multiplicities and effects?The zeros of the function are given by the zeros of the linear factors.
The linear factors are given as follows:
2x + 5.x + 4.x - 1.Then the zeros are given as follows:
x = -5/2, as 2x + 5 = 0 -> x = -5/2.x = -4, as x + 4 = 0 -> x = -4.x = 1, as x - 1 = 0 -> x = 1.Then the multiplicities are given by the exponents, and the effects are defined according to the multiplicities, as follows:
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. syrup is draining from a conical tank into a snow cone machine at the rate of 8 cubic feet per minute. the height of the conical tank is 6 feet and the radius of the tank's top is 2 feet. how fast, in feet per minute, is the level in the tank falling when the height of the syrup level is 3 feet? express answer in terms of pi.
The rate the level in the tank falling when the height of the syrup level is 3 feet is 8/π feet per minute. The result is obtained by using the rate of change concept.
How to count the rate of change?A conical tank containing syrup is draining.
The rate of water volume decreasing, dV/dt = 8 ft³/min.Height of conical tank = 6 ft.Radius of conical tank = 2 ft.Find the rate of syrup level falling (dh/dt) when h = 3 ft!
See the picture in the attachment!
By the similar triangles, we get
r/h = 2/6
r/h = 1/3
r = 1/3 h
Find the volume of the syrup left at a certain height.
V = 1/3 πr²h
V = 1/3 π(1/3 h)²h
V = 1/3 π(1/9) h² h
V = 1/27 πh³
The rate of syrup level falling is
dV/dt = dV/dh . dh/dt
dV/dt = d/dt [1/27 πh³] . dh/dt
dV/dt = 1/27 π 3h² dh/dt
8 = 1/27 π 3(3)² dh/dt
8 = π dh/dt
dh/dt = 8/π ft/min
Hence, the rate of syrup level falling is 8/π feet per minute.
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A major automobile company claims that its new electric powered car has an average range of more that 300 miles. A random sample of 40 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test. A) what would be the consequences of making a type ii error in this problem? b) compute the probability of making a type ii error if the true population mean is 305 miles. C) what is the maximum probability of making a type i error in this problem?
Answer:
Step-by-step explanation:
urmom
2. The coordinates of the vertices of ADEF are D(-8, 5), E(-5, 8), and F(-1, 4).
Which set of coordinates describes a triangle that is similar to ADEF? (TEKS G.7.A)
FA(-24, 15), B(−15, 24), and C(−3, 8) +
G J(16,-10), K(10, −16), and L(2, -8)
HP(-8, 10), Q(-5, 16), and R(-1,8)
U(-10, 5), V(−7, −2), and W(−2, −7)
Just number 2 pls
Answer:
it is 9
Step-by-step explanation:
What is the constant of proportionality in this proportional relationship?
x 2 4 6 8
y 5/6 1 2/3 2 1/2 3 1/3
Responses
12
5
12/5
5/12
The constant of proportionality in this proportional relationship is (D) 5/12.
What is the constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.
Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
So, the constant of proportionality formula:
y = kx ⇒ k = y/x
Now, calculate as follows:
(A)
k = y/x
k = 5/6 / 2
k = 5/6 * 1/5
k = 5/12
(B)
k = y/x
k = 5/3 / 4
k = 5/3 * 1/4
k = 5/12
Similarly, we can say that (C) and (D) will also be k = 5/12.
Therefore, the constant of proportionality in this proportional relationship is (D) 5/12.
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Complete question:
What is the constant of proportionality in this proportional relationship?
x 2 4 6 8
y 5/6 1 2/3 2 1/2 3 1/3
Responses
a. 12
b. 5
c. 12/5
d.5/12
Can the triangles be proven congruent if so how?
Triangles can be proven congruent by using the congruency theorems - SSS, SAS, ASA, and AAS.
Congruency is shown by the sign (≅). It is when the given figures have the same shape and size.
To prove that the given triangles are congruent there are some rules, one of which it must satisfy in order to prove its congruency. The theorems are stated below-
SSS rule: if 3 sides of the given triangles are equal, then the triangles are congruent.
SAS rule: if 2 sides and an angle of the given triangles are equal, then the triangles are congruent.
ASA rule: if 2 angles and a side (in the middle of the angles)of the given triangles are equal, then the triangles are congruent.
AAS rule: if 2 angles and a side(adjacent to the angles) of the given triangles are equal, then the triangles are congruent.
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What is the range of the function?
all real numbers
O. all real numbers greater than or equal to 0
all real numbers greater than or equal to 11
all integers greater than or equal to 11
Answer:
all integers greater than or equal to 11
A carnival game has a circular target on a coordinate plane. The target has the equation (x
+ 5)2 + (y + 5)² = 16. Sylvie throws a dart at point (-1,-6). Where is the point located in
relation to the target?
The point is located (d) outside the target in relation to the target
How to determine the location of the point?From the question, we have the following parameters that can be used in our computation:
Circle equation: (x + 5)² + (y + 5)² = 16. Sylvie throws a dart at point (-1,-6)This means that we substitute (-1,-6) for x and y in the circle equation = (x + 5)² + (y + 5)² = 16.
So, we have the following representation
(x + 5)² + (y + 5)² = 16.
Substitute the known values in the above equation, so, we have the following representation
(-1 + 5)² + (-6 + 5)² = 16.
Evaluate the sum
(4)² + (-1)² = 16.
Evaluate the exponent
16 + 1 = 16.
Evaluate the sum
17 = 16
17 is greater than 16
Hence, the point is not in the target
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The following are the dimensions of each room in a house:
Living room = 20 ft x 15 ft Kitchen = 12 ft x 10 ft
Bedroom 1 = 12 ft x 12 ft Bedroom 2 = 12 ft x 10 ft
Bathroom = 8ft x 12 ft
What is the total square footage of the house?
The Total Square Footage of the House is 780 sq. ft.
What is Area?
The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Solution:
Area of Living Room = 20*15 = 300 sq. ft.
Area of Kitchen = 12*10 = 120 sq. ft.
Area of Bedroom 1 = 12*12 = 144 sq. ft.
Area of Bedroom 2 = 12*10 = 120 sq. ft.
Area of Bathroom = 8*12 = 96 sq. ft.
Total Area is 300 + 120 + 144 + 120 + 96 = 780 sq. ft.
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Emma has 3 1/8 slices of pizza in her lunch box. Ryan has 1/4 the amount of pizza that Emma does. How much pizza do they have together?
Please Help!
Emma and Ryan both have 125/32 pizzas.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given, Emma has [tex]3\frac{1}{8}[/tex] slices of pizza.
Simplifying to improper fraction;
Emma has 25/8 slices of pizza.
And Ryan has 1/4 x The amount of pizza Emma has, slices of pizza.
That means, Ryan has 1/4 x (25/8) slices of pizza.
Applying multiplication of fraction.
That is, 25/32 slices of pizza.
To find the total amount of pizza;
add the number of pizza,
25/8 + 25/32
To add the number:
First, we take LCM,
25/8 + 25/32
= (100+ 25) / 32
= 125/32
Therefore, they both have 125/32 pizzas.
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Which graph represents y as a function of x?
I will give 100 points for help because I feel that's a good trade
Answer:
The last graph that is a straight line represents y as a function of x
Step-by-step explanation:
In order for a graph to be considered a function, it can't intercept the same value twice. To test this, use the vertical line test to see if the graph hits the line twice. If it does, then it is not a function. But if the line hits the graph only once, then it is a function.
The profit, P(x), that Rivka's Delivery Service makes from delivering packages between local businesses is P(x), where x is the number of $0.10 price increases for each delivery. Use the graph below to answer the question.
Graph with x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 50), increases to (2.5, 81.25), and then decreases through (6.531, 0).
What is the approximate number of price increases needed to maximize profit?
0
2.5
50
81
The approximate number of price increases needed to maximize profit is 2.5
How to determine the number of price?From the question, we have the following parameters that can be used in our computation:
x = number of price increases
y = Profit
Also from the question, we have
Begins at (0, 50)
Increases to (2.5, 81.25)
Decrease through (6.531, 0)
This means that
Maximum = (2.5, 81.25)
Recall that
x = number of price increases
So, we have
x = 2.5
Hence, the number of price increases is 2.5
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