Answer:
\(\textsf{Apply the Perfect Square Formula}\quad (a + b)^2 = a^2 + 2ab + b^2:\)
\(\implies (a+bi)^2=a^2+2abi+(bi)^2\)
\(\textsf{Apply exponent rule} \quad (a\cdot b)^c=a^cb^c:\)
\(\implies a^2+2abi+b^2i^2\)
\(i=\sqrt{-1} \implies i^2=-1\)
\(\textsf{Apply imaginary number rule} \quad i^2=-1:\)
\(\implies a^2+2abi+b^2(-1)\)
\(\implies a^2+2abi-b^2\)
\(\textsf{Collect the real parts:}\)
\(\implies a^2-b^2+2abi\)
\(\textsf{Factor the real parts by applying the Difference of Two Squares Formula}\\x^2-y^2=(x+y)(x-y) :\)
\(\implies (a+b)(a-b)+2abi\)
LHS
(a+bi)²(a+bi)(a+bi)a²+b²i²+2abia²-b²+2abiRHS
(a+b)(a-b)+2abia²-b²+2abiHence verified
TOPIC=Rearranging
Task:Make x the subject of these equations
6x + v = 4x + w
ax + 9 = 2x + b
7x - w = vx+4
6 - wx = vx + 4
3(wx-v) = 4(x+v)
All the solutions are,
⇒ x = 1/2 (w- v)
⇒ x = (b - 9)/(a - 2)
⇒ x = (4 + w) / (7 - v)
⇒ x = 2 / (v + w)
⇒ x = 7v/(3w - 4)
Given that;
Expressions are,
⇒ 6x + v = 4x + w
⇒ ax + 9 = 2x + b
⇒ 7x - w = vx+4
⇒ 6 - wx = vx + 4
⇒ 3(wx - v) = 4(x + v)
We can simplify as;
⇒ 6x + v = 4x + w
⇒ 6x - 4x = w - v
⇒ 2x = w - v
⇒ x = 1/2 (w- v)
⇒ ax + 9 = 2x + b
⇒ ax - 2x = b - 9
⇒ (a - 2)x = b - 9
⇒ x = (b - 9)/(a - 2)
⇒ 7x - w = vx+4
⇒ 7x - vx = 4 + w
⇒ (7 - v) x = 4 + w
⇒ x = (4 + w) / (7 - v)
⇒ 6 - wx = vx + 4
⇒ vx + wx = 6 - 4
⇒ (v + w)x = 2
⇒ x = 2 / (v + w)
⇒ 3(wx - v) = 4(x + v)
⇒ 3wx - 3v = 4x + 4v
⇒ 3wx - 4x = 7v
⇒ (3w - 4)x = 7v
⇒ x = 7v/(3w - 4)
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Please help asap!! im stumped
graph the inequality below on the number line
explanation would be appreciated
Answer:
O----->
Step-by-step explanation:
open circle= bigger that or smaller than according to the direction this symbol is facing <
Closed circle= bigger or smaller that and equals to the number according to the direction this symbol is facing ≤
In here we have this symbol < facing the y which means Y is bigger than -10 so the arrow will be going to the right from -10 to 11 and the open circle will be on the -10
Can 7/30 be reduced?
Answer:
no
Step-by-step explanation:
as 7 is a prime numbers and prime numbers cannot be reduced .
Could someone please help me?
You have 3 spreads, 4 meats, and 3 kinds of bread. How many different sandwiches can you make using one of each ingredient?
36
24
10
15
The total number of different sandwiches that can be made is 36.
What is multiplication principle?There are m x n methods to execute both tasks separately if there are m ways to perform one job and n ways to complete another, according to the multiplication principle of counting, a key counting principle in combinatorics. When we need to count the number of outcomes in a scenario where the outcomes are influenced by a number of separate decisions, we utilise this approach. When there are only a limited number of options available for each activity, as there are in the sandwich-making dilemma, it is very helpful. We may calculate the total number of outcomes by multiplying the number of options for each assignment.
For the given number of toppings we can use the counting principle.
3 x 4 x 3 = 36
Hence, the total number of different sandwiches that can be made is 36.
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the number of pumps in use at both a six-pump station and a four-pump station will be determined. give the possible values for each of the following random variables. (enter your answers in set notation.) (a) t
For each variable, the possible values are:
a) T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
b) X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
c) U = {0, 1, 2, 3, 4, 5, 6}
d) Z = {0, 1, 2}
Item a:
In total, there are 10 pumps, hence the possible values are all integers from 0 to 10, that is:
T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Item b:
In the first, there are 6 pumps, and in the second 4, hence, the difference ranges from -4 to 6, that is:
X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
Item c:
The maximum number in a station is 6 pumps, hence this variable ranges from 0 to 6.
U = {0, 1, 2, 3, 4, 5, 6}
Item d:
Either none of the stations has exactly two pumps in use, or one has or both, hence the variable ranges from 0 to 2.
Z = {0, 1, 2}
The question is incomplete. The complete question is:
"The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.)
a. T = the total number of pumps in use
b. X = the difference between the numbers in use at stations 1 and 2.
c. U = the maximum number of pumps in use at either station
d. Z = the number of stations having exactly two pumps in use"
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what is the standard form for graphs of y-5=4/5(x-30)
Answer:
y=0.8*x -19
Step-by-step explanation:
y-5=4/5(x-30)
5*(y-5)=5*(4/5(x-30))
5y-25=4x-120
5y=4x-120+25
5y=4x-95
y=(4/5)*x -19
y=0.8*x -19
(2/5)^3=
anybody help???
Answer:
8/ 125
Step-by-step explanation:
8/ 125
Answer:
8/125
Step-by-step explanation:
I think. you can use the app photo math
last year megan had 63 books in her collection now she has 112 books what is the percentage increase
Answer:
56.25%
Step-by-step explanation:
Divide
63/112 = .5625
Convert to a percentage
56.25%
What is the inverse of f(x) = 2x2 -4?
By altering the x and y values, one can algebraically determine a function's inverse.
What does inverse mean example?In mathematics, the word inverse refers to the opposite of another operation. Let us look at some examples to understand the meaning of inverse. The addition means to find the sum, and subtraction means taking away. So, subtraction is the opposite of addition.
Because they enable the reversal of mathematical operations, inverse procedures are crucial for solving equations (e.g. logarithms, the inverses of exponential functions, are used to solve exponential equations).
y= (x= 2)² - 4 → x = (y+2)²-4
x+ 4 = (y+2)²
≠√x=4 =y+2
≠√x=4-2=y
f-1 (x)=≠√x+4-2
y= √12+4-2
or
y=- √12+4-2
→y=-6
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Simplify these expressions:
1) 8y + 5 - 10y - 2
Answer:
here I think
Step-by-step explanation:
8y + 5 - 10y - 2 = (8y-10y)+(5-2)=-2y+3
PLZ HELP ME ITS DUE TODAY!!!!!
Answer:
the last one makes more sense compared to all the other choices.
need help asapppop!!!!!
Answer:
√ 17 , 4.23 , 9/2
Step-by-step explanation:
√ 17 = 4.12310562 ... (about 4.1)
9/2 = 4.5
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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The volume of the prism is 900 cubic centimeters. The
height of the prism is 15 centimeters and the height of
the triangular base is 10 centimeters. What is the
length of edge FC?
Answer:
?
Step-by-step explanation:
i dont now how to arrange
Answer:
12
Step-by-step explanation:
trust me bro
An airplane is preparing to land at an airport. It is 59,400 feet above the ground and is descending at the rate of 3,000 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,400 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.
Product: Your report needs to include the following:
a. Define the variables that you will be using.
b. Create a system of equations.
c. Solve the system using graphing. Be sure to include the graph in your report.
d. Solve the system using either substitution or elimination to check your graphing work.
Explain what your solution means in the context of the problem.
Answer:
a. Variables:
Let's define the variables for the problem:
t: time in minutes (the variable we are solving for)
h1: altitude of the descending airplane in feet
h2: altitude of the ascending airplane in feet
b. System of Equations:
Based on the given information, we can create a system of equations:
Equation 1: h1 = 59,400 - 3,000t (altitude of descending airplane)
Equation 2: h2 = 0 + 2,400t (altitude of ascending airplane)
c. Solving the System using Graphing:
To solve the system using graphing, we need to plot the two equations on a graph and find the point of intersection. Here's the graph:
[Graph]
From the graph, we can see that the two lines intersect at a point. The x-coordinate of the point of intersection represents the time (t), and the y-coordinate represents the altitude (h) where the two airplanes are at the same altitude.
d. Solving the System using Substitution or Elimination:
To check our graphing work, we can solve the system using either substitution or elimination. Let's use substitution:
From Equation 1: h1 = 59,400 - 3,000t
Substitute h1 into Equation 2:
59,400 - 3,000t = 2,400t
Add 3,000t to both sides:
59,400 = 5,400t
Divide both sides by 5,400:
t = 11
Now, substitute the value of t back into either Equation 1 or Equation 2 to find the altitude (h) at that time:
h1 = 59,400 - 3,000 * 11
h1 = 59,400 - 33,000
h1 = 26,400 feet
Therefore, the two airplanes will be at the same altitude of 26,400 feet after approximately 11 minutes.
Explanation of Methods:
Graphing: Graphing the equations provides a visual representation of the problem and helps identify the point of intersection. However, it may not provide an exact value, and the precision depends on the accuracy of the graph.
Substitution or Elimination: These algebraic methods allow for precise calculations and the exact determination of the time and altitude at which the airplanes meet. They require more steps and calculations but offer a more accurate solution.
In the context of the problem, the solution means that after approximately 11 minutes, both airplanes will be at the altitude of 26,400 feet. At this moment, the descending airplane will have descended to the same altitude as the ascending airplane is ascending, resulting in the two airplanes being at the same height above the ground.
Step-by-step explanation:
Х
Area of a circle
You might need: Calculator
What is the area of the following circle?
Either enter an exact answer in terms of " or use 3.14 for # and enter your answer as a decimal.
d=14
units?
Answer:
153.86 units^2
Step-by-step explanation:
the area of a circle = pi * r^2
To find r, divide the diameter in half.
14/2 = 7
Now, area = pi * 7^2
= pi * 49
= 153.86
hope this helps!
Answer:
153.94 square units
Step-by-step explanation:
d=14 units
r=d/2
=14/2
=7 units
Area of a circle=math.pi x r^2
=3.14 x (7)^2
Summary statistics are given for independent simple random samples from two populations. Use the nonpooled t-test to conduct the required hypothesis test. 1 = 75.1, s 1 = 4.5, n 1 = 11, 2 = 66.2, s 2 = 5.1, n 2 = 9 Perform a two-tailed hypothesis test using a significance level of α = 0.01.
Answer:
The decision rule is
Reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The first sample mean is \(\= x_1 = 75.1\)
The first sample standard deviation is \(s_1 = 4.5\)
The first sample size \(n_1 = 11\)
The second sample mean is \(\= x_2 = 66.2\)
The second sample standard deviation is \(s_2 = 5.1\)
The second sample size is \(n_2 = 9\)
The significance level is \(\alpha = 0.01\)
The null hypothesis is \(H_o : \mu_1 = \mu_2\)
The alternative hypothesis is \(H_a : \mu_1 \ne \mu_2\)
Generally the pooled standard deviation is mathematically represented as
\(s = \sqrt{ \frac{(n_ 1 - 1) s_1^2 + (n_2 - 1) s_2^2}{n_1 + n_2 -2 } }\)
=> \(s = \sqrt{ \frac{(11 - 1) 4.5^2 + (9 - 1) 5.1^2}{11 + 9 -2 } }\)
=> \(s = 4.78\)
Generally the degree of freedom for the is mathematically represented as
\(df = [ \frac{[\frac{s_1^2 }{n_1} + \frac{s_2^2}{ n_2} ]^2}{[\frac{[\frac{s_1^2}{n_1} ]^2}{n_1 - 1 } ] + [\frac{[\frac{s_2^2}{n_2} ]^2}{n_2 -1} ]} ]\)
=> \(df = [ \frac{[\frac{4.5^2 }{11} + \frac{5.1^2}{9} ]^2}{[\frac{[\frac{4.5^2}{11} ]^2}{ 11 - 1 } ] + [\frac{[\frac{5.1^2}{9} ]^2}{9 -1} ]} ]\)
=> \(df = 16 \)
Generally the test statistics is mathematically represented as
\(t = \frac{\= x_1 - \= x_2}{ \sqrt{\frac{s_1^2 }{n_1} + \frac{s_2^2}{n_2} } }\)
=> \(t = \frac{ 75.1 - 66.2 }{ \sqrt{\frac{ 4.5^2 }{ 11} + \frac{5.1^2}{ 9} } }\)
=> \(t = 4.092\)
Generally the student distribution table the probability of \(t = 4.092\) to the right at a degree of freedom of \(df = 16 \) is
\(P( T > 4.092 ) = 0.00042536\)
Generally the p-value is mathematically represented as
\(p-value = 2 * P(T > 4.092)\)
=> \(p-value = 2 * 0.00042536\)
=> \(p-value = 0.001\)
From the value obtained we see that \(p-value < \alpha\) hence we
The decision rule is
Reject the null hypothesis
Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
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Hello everyone-SOLVING nonlinear system of equations- ALGEBRA 1
The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.
To solve the nonlinear system of equations:
Equation 1: \(y = -x^2 + 7\)
Equation 2: y = 2x + 4
We can equate the right sides of both equations since they both represent y.
\(-x^2 + 7 = 2x + 4\)
To simplify the equation, we can rearrange it to be in the standard quadratic form:
\(x^2 + 2x - 3 = 0\)
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
(x + 3)(x - 1) = 0
From this equation, we get two possible solutions:
x + 3 = 0 => x = -3
x - 1 = 0 => x = 1
Now, we substitute these x-values back into either equation to find the corresponding y-values.
For x = -3:
y = 2(-3) + 4
y = -6 + 4
y = -2
For x = 1:
y = 2(1) + 4
y = 2 + 4
y = 6
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Question 1-1
Which expression is equivalent to the measure of <4 in the image below?
\( \quad\rule{300pt}{1.5pt}\)
Ⲋⲟⳑⳙⲧⳕⲟⲛ :Using the property of alternate angles , let's first make the pair of equal angles :
ㅤㅤㅤ➙ m∠1 = m∠ 5
ㅤㅤㅤ➙ m∠2 = m∠ 6
ㅤㅤㅤ➙ m∠4 = m∠3 + m∠ 5
ㅤㅤㅤ➙ Since , m∠ 5 = m∠1
ㅤㅤㅤ➙ m∠ 4 = m∠ 3 + m∠1
Alternate Angles :
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.
\( \rule{350pt}{2pt}\)
Simplify the expression 21p + 9q2 + 10p + q2 by combining like terms.
Answer:
31p + 10q2
Step-by-step explanation:
Answer:
10q^2+31p
Step-by-step explanation:
How many 20kobo make up #20
Answer:
100
Step-by-step explanation:
#20 naira - 20 * 100
= 2000kobo
2000/20
100
QED✅✅
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A mountain lodge charges a weekly cabin rental fee of $450 for a single guest, plus $125
for each additional guest.
Which of these equations models the relationship between the number of guests, x, and
the total charge, y?
A. y = 450 + 125x
B. y = 450+ 125(x - 1)
C. y = 450+ (125 - 1)x
D. y = (450-x) + 125
The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.
Figure 1 and Figure 2 below are congruent. Which point corresponds to point C'?
The point in Figure 2 that corresponds to point L in Figure 1 is the midpoint of line segment NP.
When two figures are congruent, it means that they have the same shape and size. This implies that corresponding points in the two figures have the same position and distance from each other.
In Figure 1, the points I, J, L, K, N, P, and Q are labeled. To find the point in Figure 2 that corresponds to point L, we need to look for a point that has the same relative position and distance as point L in Figure 1.
From Figure 1, we can see that point L is the midpoint of the line segment JK. Therefore, to find the corresponding point in Figure 2, we need to look for a point that is the midpoint of the line segment that corresponds to JK. In Figure 2, the line segment that corresponds to JK is NP, and the midpoint of NP corresponds to the point that is equivalent to point L. Therefore, the point that corresponds to point L in Figure 2 is the midpoint of line segment NP.
It is important to note that identifying corresponding points in congruent figures is a fundamental concept in geometry and is often used to solve problems involving congruence and similarity.
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A helicopter flies 1,500 feet over the ocean. A whale swims 150 feet below the ocean. How far apart are the helicopter and the whale?
Answer:
1000
Step-by-step explanation:
Answer: they are 1450 feet apart since all your doing is just subtracting the ammount of space between them (hope this helps) :)
The graph of g(x) is the result of translating the graph of f(x) = (one-half) Superscript x three units to the left. What is the equation of g(x)?
Answer:
\(g(x) = 0.5^{(x+3)}\)
Step-by-step explanation:
Assuming f(x) = \(0.5^{x}\) is a correct interpretation of f(x),
the way to translate three units to the left is to change x to x+3. This gives our answer: \(g(x) = 0.5^{(x+3)}\)
Answer:
B. g(x) = (1/2)⁽ˣ⁺³⁾
Hope this helps!
Step-by-step explanation:
The amount of a same le remaining after T days is giving by the equation p(f)=a(1/2) T/h
Answer:
6
Step-by-step explanation:
Choose the best description for the real number 2.33663336663333666689...
Irrational, because it is a terminating decimal
O Rational, because it is a repeating decimal
Irrational, because it is non-terminating decimal
O Rational, because it is a terminating decimal
Answer:
Irrational, non-terminating
Step-by-step explanation:
This number is irrational because it is a non-terminating decimal. Notice how it continues with the '...'. <3
What was the golfers total score for the tournament ?
Answer:
-11
Step-by-step explanation:
-3+(-1)+(-5)+(-2)
-3+(-1)=(-4)
-4+(-5)=(-9)
-9+(-2)=(-11)
(-11)
HOPE THIS HELPS!!