Answer:
1 if u cut all of them in half
Step-by-step explanation:
We know for a fact that the equation:
[tex]|z+z'| \leqslant |z|+|z'|[/tex]
holds for any 2 complex numbers
I came up with the conclusion that:
[tex]|z+z'|=|z|+|z'|[/tex]only holds when z and z' are pure imaginary or pure real numbers of the SAME sign.
How can i prove this algebraically/geometrically?
Note: Irrelevant answers will be reported
They don't need to be pure real or imaginary. Any "mixed" complex number works so long as [tex]z=z'[/tex].
Let [tex]z=z'=a+bi[/tex]. Then
[tex]|z+z'| = |2a+2bi| = 2 \sqrt{a^2+b^2}[/tex]
[tex]|z| + |z'| = 2|a+bi| = 2 \sqrt{a^2+b^2}[/tex]
so [tex]|z+z'|=|z|+|z'|[/tex].
The geometric interpretation is essentially identical. [tex]|z+z'|=2|z|[/tex] is a complex number twice the distance away from the origin in the complex plane as [tex]z[/tex], which is exactly [tex]|z|+|z|[/tex].
Write the recursive rule for the 5th term of the sequence: -7, -3, 1, 5, 9
Answer:
Step-by-step explanation:
Let [tex]x_{n}[/tex] represent the nth term in the sequence. Then [tex]x_{n-1}[/tex] represents the previous term
The first term, [tex]x_{1}[/tex] = -7
Each consecutive term is obtained by adding 4 to the previous term.
So the recursive relation is
[tex]\left \{ {{x_{1}= -7} \atop {x_{n}= x_{n-1} + 4}} \right.[/tex]
Which equation could possibly represent the graphed function?
Answer: A
Step-by-step explanation:
The polynomial has roots at [tex]x=-4, -2, 4[/tex].
So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].
This eliminates everything except for A.
Question 7 (1 point) The two tables below show the amount of tip, y, included on a bill charging x dollars. A 2-column table with 3 rows titled Restaurant A. Column 1 is labeled x with entries 10, 20, 30. Column 2 is labeled y with entries 1, 2, 3. A 2-column table with 3 rows titled Restaurant B. Column 1 is labeled x with entries 25, 50, 75. Column 2 is labeled y with entries 5, 10, 15. Which compares the slopes of the lines created by the tables?
The slope of restaurant B is twice that of restaurant A
How to compare the slopes?The tables of values are given as
X(Bill) Y(Tip) X(Bill) Y(Tip)
Rest A 10 1 Rest B 25 5
Rest A 20 2 Rest B 50 10
Rest A 30 3 Rest B 75 15
The slopes are calculated using
Slope = (y2 - y1)/(x2 - x1)
Using the table of values, we have:
Rest A = (2 - 1)/(20 - 10)
Rest A = 0.1
Rest B = (10 - 5)/(50 - 25)
Rest B = 0.2
By comparing the slopes, we have:
Rest B = 2 * Rest A
This implies that the slope of restaurant B is twice that of restaurant A
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What is the product?
2
12 64
78 30
6
32
78 30
(050
69
78 30
899
32
39 15
66 8
64
38 30
Answer:
the product is 1.32057606543E32
A number is negative if and only if it is less than 0.
p. A number is negative.
q. A number is less than 0.
Which represents the inverse of this statement? Is the inverse true or false?
~p4~9
The inverse of the statement is sometimes true and sometimes false.
Oq+p
The inverse of the statement is true.
q→P
~q→ ~p
The inverse of the statement is false.
The inverse statement is:
¬q ⇒ ¬p
Which is true.
How to get the inverse statement?
Here we have the biconditional statement:
A number is negative if and only if it is less than zero.
Where:
p = a number is negative.q = a number is less than 0.So we can write the statement as:
p ⇔ q
The inverse statement is:
if not q, then not p.
or
¬q ⇒ ¬p
Replacing p and q, we have:
"if a number is not less than zero, then the number is not negative".
This is true, if the number is not less than zero, then the number is 0 or larger, so that number is not negative.
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Answer:
D.
∼p↔∼q
and
G.
The inverse of the statement is true.
Step-by-step explanation:
Express the formula in terms of the height, Use that formula to find the height when the volume is and the radius is
The formula to find the height of the Cylinder is; h = V/(πr²) and at V = 45π and r = 3, we have; h = 5
How to change the subject of the formula?We are given the formula for volume of a cylinder as;
V = πr²h
where;
h is height
r is radius
To make h the subject, let us divide both sides by πr² to get;
V/(πr²) = h
At V = 45π and r = 3, we have;
h = 45π/(πr²)
h = 45/3²
h = 5
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DATE PAGE No. Demand 10 a) A ratio of two number is equal to 3:8. If the smaller number is 12, find the greater number:
From ratio concept, the greater number number is 32 .
What is the greater number from concept of ratio ?A ratio exists as an ordered pair of numbers a and b, written a / b where b does not equivalent to 0. A proportion exists in an equation in which two ratios stand set equal to each other. For example, if there exists 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there exist 3 girls)
Let the greater number be x .
The ratio given is 3:8 .
Thus, by the concept of ratio -
⇒ 3/8 = 12/x
⇒ x = (8/3 * 12)
∴ x = 32
Therefore, from ratio concept, the greater number number is 32 .
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Simplify
18÷[7+2{7+2(7-6)}+2
Answer is
[tex] \frac{2}{3} [/tex]
Show me the steps by steps
Answer:
[tex] \frac{2}{3} [/tex]
Step-by-step explanation:
=18÷[7+2{7+2(7-6)}+2]
=18÷[7+2{7+2×1}+2]
=18÷[7+2×9+2]
=18÷[7+18+2]
=18÷27
=[tex] \frac{18}{27} [/tex]
=9 two is 18 and 9 three is 27
So,
=[tex] \frac{2}{3} [/tex]
Craig decides to purchase a property that has been valued at $475,000. He has $80,000 available as a deposit and will require a mortgage for the remaining amount. The bank offers him a 25 year mortgage at 2% interest. Calculate the total interest he will pay over the life of the loan, assuming he makes monthly payments. Give your answer in dollars to the nearest ten dollars. Do not include commas or the dollar sign in your answer.
THE REAL ANSWER IS $107, 270
First, we note that Craig requires a mortgage on $475,000−$80,000=$395,000. To calculate the monthly repayments we must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk)(rk).
We have P0=$395,000,r=0.02,k=12,N=25, so substituting in the numbers into the formula gives
$395,000=d(1−(1+0.0212)−25⋅12)(0.0212),
that is,
$395,000=235.9301d⟹d=$1,674.22.
Therefore the total interest payable is
I=$1,674.22×25×12−$395,000=$107,266
which is $107,270 to the nearest $1
The total interest is $107,270
What is monthly payment formula?
The formula for monthly payment is:
[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]
We can find total interest as shown below:
Value of property = $475,000
Money available as a deposit = $80,000
P = 475,000-80,000
= 395000
t = 25 year
r = 2% = 0.02
n = 25*12 = 300
[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]
Putting the value of P, t, r, and n in the above formula
[tex]=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}[/tex]
after solving the above expression
M = $1674.22
Interest = M*n-P
Putting the value of P, n and M
= 1674.22*300-395000
= 502266-395000
= 107,266
Rounding to nearest ten dollar
= $107,270
Hence, the total interest is $107,270.
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Answer:
Step-by-step explanation:
In the triangle below M, Z, and P are the midpoints of the sides. Name a segment that is parallel to the one given. Pay attention to the order of the points used in the given side.
Based on the triangle midsegment theorem, the midsegments and the sides they are parallel to are:
MP is parallel to XY
PZ is parallel to WX
MZ is parallel to WY
What is the Triangle Midsegment Theorem?The segment that connects the midpoints of two sides of a triangle is referred to as the midsegment of the triangle. All triangles possess three midsegments. According to the triangle midsegment theorem, the third side of the triangle that is directly opposite the midsegment is twice the size of the midsegment and it is parallel to it.
In the diagram showing triangle WXY with midpoints at points M, Z, and P, the midsegments are:
MP which is parallel to XY, also, MP = 1/2(XY)
PZ which is parallel to WX, also, PZ = 1/2(WX)
MZ which is parallel to WY. also, MZ = 1/2(WY)
Thus, the midsegments and the sides they are parallel to are:
MP is parallel to XY
PZ is parallel to WX
MZ is parallel to WY
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I need some help please
The values of x and y that can represent the equation is illustrated.
How to illustrate the information?The equation given us 32 = xy + 16
The table will be:
x. y
4. 4
16. 1
2. 8
32. 0.5
For example, when x and y are 4. This will be:
= xy + 16
= (4 × 4) + 16
= 32
Other values of x and y will also give 32.
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The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 57.5% of their carbon-14. How old were the bones at the time they were discovered?
Therefore, the bones were 6612.5 years old at the time they were discovered.
Half lifeGiven that the radioactive element carbon-14 has a half-life of 5750 years, and a scientist determined that the bones from a mastodon had lost 57.5% of their carbon-14, to determine how old were the bones at the time they were discovered, the following calculation must be made:
50 = 5750100 = 1150057.5 = X57.5 x 11500 / 100 = X6612.5 = XTherefore, the bones were 6612.5 years old at the time they were discovered.
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Answer:Therefore, the bones were 6612.5 years old at the time they were discovered.
Step-by-step explanation:
which quantity is scalary
Step-by-step explanation:
find the greatest number which divides 225 and 1029 leaving remainder of 5 in each case
Luther High School's basketball coach won a record 33 out of 42 games how many games must the team win in the next 28 games for the coach to maintain to the ratio of wins to losses?
Using proportions, they must win 22 games to maintain to the ratio of wins to losses.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the next 28 games, we have that:
The team will have won 33 + x games.The team will have played 42 + 28 = 70 games.To keep the same proportion, we have that:
[tex]\frac{33}{42} = \frac{33 + x}{70}[/tex]
Applying cross multiplication:
42(33 + x) = 33 x 70
Simplifying by 14:
3(33 + x) = 33 x 5
3x = 33 x 5 - 33 x 3
3x = 33 x 2
3x = 66
x = 66/3
x = 22.
They must win 22 games to maintain to the ratio of wins to losses.
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The functions f(x) and g(x) are described using the following equation and table: f(x) = −6(1.05)x x g(x) −4 −9 −2 −6 0 −3 2 2 Which equation best compares the y-intercepts of f(x) and g(x)? The y-intercept of f(x) is equal to the y-intercept of g(x). The y-intercept of f(x) is equal to 2 times the y-intercept of g(x). The y-intercept of g(x) is equal to 2 times the y-intercept of f(x). The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x). Question 12(Multiple Choice Worth 1 points) (01.04 MC) A store manager can spend at most $1,000 a day for operating costs and payroll. It costs $100 each day to operate the store and $30 dollars a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at most: 30x + 100 ≤ 1000 x ≥ 30 x ≥ 33 x ≤ 33 x ≤ 30 Question 13(Multiple Choice Worth 1 points) (02.01 LC) Which of the following tables represents a function? x 1 −1 4 −4 y 8 8 10 10 x 2 2 3 3 y 6 −6 7 7 x 5 −5 5 −5 y 10 11 12 13 x 2 2 7 7 y 2 3 4 5 Question 14(Multiple Choice Worth 1 points) (01.06 LC) Joy needs 8 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.15. How much will the fabric cost? [1 ft = 0.305m] $9.20 $2.12 $2.81 $30.16 Question 15(Multiple Choice Worth 1 points) (04.02 LC) What is the solution to the following system of equations? x − 3y = 5 2x + y = 10 (5, 0) (0, 5) (7, 0) (0, 7) You must check the box below prior to submitting your exam! Check this box to indicate you are ready to submit your exam Instructors monitor ALL areas of a student's account Student e-mail accounts are to be used for FLVS course-related email only and not for general introductions or spamming of people in your address book. Please remember to click the Logoff link when you have completed your work in the course. FDK191.12
Based on our examination of the y-intercepts, we can deduce that the y-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)
What is the examination of the y-intercept?The value of the function at the point where the value of x is equal to zero is known as the y-intercept.
f(x)=-6(1.05)^x
Considering x
x=0
f(0)=-6(1.05)^0
f(0)=-6(1)
f(0)=-6
Therefore, the y-intercept is point (0,-6)
Generally, the equation for the function of the y-intercept of g(x) is mathematically given as
From table
at x=0
The y-intercept is the point (0,-3)
Based on our examination of the y-intercepts, we can deduce that the ty-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)
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what is the measure of this
Answer:
60
Step-by-step explanation:
140-80=60
The length of two sides of the right triangle ABC shown in the illustration are given. Find the length of the third side in centimeters. a=12cm and c=37cm
By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.
How to find the missing side of a right triangle
In this question we know the lengths of two sides of the right triangle. By Pythagorean theorem we get the length of the missing side:
a² + b² = c²
b² = c² - a²
b = √(c² - a²)
b = √(37² - 12²)
b = 35
By using Pythagoran theorem, the length of the third side of the triangle ABC is 35 centimeters.
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To graph the inequality y < 2x - 1, you would draw a solid line. A true B false
True
Personally, when I see the line underneath the equality sign, I know I've got to draw a dotted line. That's how I remember the difference between drawing a solid / dotted line.
Hope this helps!
According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?
f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48
Option A, The option that has the same potential roots according to the rational root theorem is 3x5 – 2x4 – 9x3 + x2 – 12.
How to solve for the rootsWe have p, this is the factors of the number 12.
The factors are ±(1, 2, 3, 4, 6, 12)
We have factors of q = 3
= ±(1, 3)
The rational roots are the roots that have the same factors that are contained in the question.
Hence the answer is A.
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Answer:
The Answer is A
Step-by-step explanation:
Did it on edge :)
Tell whether the equation 3x - 6y = 0 is a direct variation. Explain. If the equation is a direct variation, identify the constant of variation.
The equation is in direct variation and have constant of variation is 2.
According to the statement
we have given equation is 3x - 6y = 0 and find that the equation is direct variation of not.
Direct variation is the mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.
So, to find the direct variation equate the given equation equal to zero and solve it.
So, 3x - 6y = 0
3x=6y
or
x/ y=2 or x=2⋅y
here x is directly proportional to the y by 2 times.
∴x∝y
So, this equation in direct variations and constant of variation is 2.
From above this is clear that the equation is in direct variation and have constant of variation is 2.
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PLEASE HELP!!
From the triangle below, if AD=2 and CD=8. Find the Length of side AB
solve for x the triangles are similar
Answer:
x = 10
Step-by-step explanation:
∆RSE ~ ∆FGE
SE/ GE = RE/ FE
45/ 12x-3 = 55/ 143
3/ 3(4x - 1) = 11/ 143
11(4x-1) = 429
44x-11 = 429
44x = 440
x =10
On a recent trip to the convenience store, you picked up 2 gallons of milk, 6 bottles of water, and 7 snack-size bags of chips. Your total bill (before tax) was $25.65. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.90 more than a bottle of water, how much does each item cost?
Answer:
The water costs $1.90, the chips are $.95 and the milk is $3.80.
Step-by-step explanation:
Let m = milk
Let w = water
Let c = chips
2m+6w+7c =25.65 w = 2c m = w + 1.90
For the first equation, substitute w for 2C and m for w + 1.90 to get:
2(w+1.90) +6(2c) + 7c = 25.65
2w+3.8+12c+7c=25.65
2w+19c = 21.85
Now substitute 2c for w:
2(2c)+19c =21.85
4c + 19c = 21.85
23c = 21.85
c = .95 Now that we know the cost of the chips we can use that to find the water and the milk for the original equations that we wrote at the top.
w = 2c
w=2(.95) = 1.90
m = w + 1.90 = 1.90+1.90 = 3.80
This is worth 33 POInTS PLEASE HELP
The maximum amount of water that can be used by each house on a daily basis is 100 liters.
EquationCommon utilities in the community = 500 litersNumber of houses = 40 housesCapacity of water tank = 4,500 litersWater used per house = x4,500 = 500 + 40x
4,500 - 500 = 40x
4,000 = 40x
x = 4,000 / 40
x = 100 liters
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PLEASE NEED HELP
A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has an approximately Normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. Boxes are often weighed before shipping, and any box with a weight of at most 27.5 ounces is considered underweight and is rejected for distribution. What percentage of filled boxes of rice are rejected for distribution?
Find the z-table here.
4.0%
24.2%
75.8%
96.0%
Answer:
D) 96%
Step-by-step explanation:
If you take 96% of 28.6 you get 27.6 so it fits
How do u solve for X?
Answer:
x = 70
Step-by-step explanation:
x and 2x - 30 are supplementary angles , sum to 180° , then
x + 2x - 30 = 180 ( add 30 to both sides )
3x = 210 ( divide both sides by 3 )
x = 70
Answer:
2x - 30 and x degrees should add up to 180 degrees
2x - 30 + x = 180
3x = 210
x = 70 degrees
The correct answer would be D
Ivy is running errands for her mother. She bikes along straight paths to the supermarket, the bank, and then back home.Find the distance between Ivy's house and the supermarket and the distance between the supermarket and the bank. Each distance is rounded to the nearest meter.
The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.
Notice that the Angles of a Triangle add up to 180° That is
∠A + ∠B + ∠C = 180°
Thus,
∠C = 180° - 32° - 109°
= 39°
Recall the Sine Theorem which indicates;
a/SinA = b/SinB = c/SinC
thus given that
AC = 1,523m
We have
AC/SinB = BC/SinA
BC = AC/SinB * SinA
= 1523/Sin109° * Sin32°
BC =854m
Therefore
AC/SinB = AB/SinC
Thus,
AB = AC/SinB * SinC
= 1523/Sin109° * Sin39°
AB ≈ 1,014m
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Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.
What is the value of y?
3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units
The value of y in the triangle is B. 6✓3.
How to calculate the value?From the information given,
NU = 9
UM = 3
MN = 3 + 9 = 12
NT² = 9 × 12 = 108
NT = ✓108
NT = 6✓3
Therefore, y is 6✓3.
The value of y in the triangle is 6✓3.
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Answer:
B
Step-by-step explanation:
Question 9(Multiple Choice Worth 5 points)
(04.06A LC)
What is the slope of the line segment?
15
12
9
6
63
0123
0-3
0-13/1
O
O
1/3
3
5
Answer: 3
Step-by-step explanation:
[tex]\frac{3-0}{1-0}=3[/tex]