real number can be a complex number but a complex number can not be a real number, verified.
the lengths of the complex number and its conjugate are equal but the converse is not necessarily true., verified.
Not all complex numbers are real numbers, despite the fact that every complex number is a real number.
In fact, determining whether the complex number z = a + bi is real is one of the complex conjugate's most useful applications. If and only if z = a + 0i, a complex number is real. In other words, a complex number is real if it contains an imaginary part.
Mathematical proof:
Let z = a+bi, where a and b = real numbers.
Let z* =complex conjugate of z.
Then the magnitude (absolute value) of z is:
|z| = √(a²+b²).
And the value of z* is:
|z*| = √[a²+(-b)²] = √(a²+b²).
So |z| = |z*|.
This Completes the Proof.
what are real numbers?
its a quantity whose decimal expansion has an endless range. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilised in measurements of continuously altering quantities such as size and time.
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What real-world knowledge did you use to understand the STEM Task?
The real world knowledge we use to understand the STEM task are :
A) STEM integrates it's concepts and applications to real life.
B) STEM helps in finding solution to the practical issues.
C) Focuses on building models and replicating scenarios.
What is STEM ?
STEM education refers to the integrated teaching and learning of the subjects such as science, technology, engineering, and mathematics.
We know that STEM teaches critical thinking skills and instills a passion for innovation. Beyond the advantages of learning STEM subjects, STEM supports the problem-solving and inquisitive learning that are essential for success in a range of tasks and professions. Colleges are now incorporating all of these helpful ideas into their normal study courses, and the results are clearly very favorable.
The real world knowledge we use to understand the STEM task is as follows :
STEM education stresses the application of knowledge to real-life situations while integrating concepts that are often taught as separate courses in various classrooms.Finding a solution to a practical issue is often the focus of a STEM lesson or unit, which frequently emphasizes project-based learning.Building models and replicating scenarios are common STEM instructional activities. Students' understanding of the relationship to the real world is ensured by a competent STEM lesson.Therefore , the real world knowledge we use to understand the STEM task are :
A) STEM integrates it's concepts and applications to real life.
B) STEM helps in finding solution to the practical issues.
C) Focuses on building models and replicating scenarios.
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Samir and Elizabeth deposit $600.00 into a savings account which earns 1% interestcompounded quarterly. They want to use the money in the account to go on a trip in 2 years.How much will they be able to spend?nt)"Use the formula A = P 1 + , where A is the balance (final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times peryear that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.$
To determine a compound Interest
The above formular is for solving compound interest
[tex]\begin{gathered} P\text{ = Principal = \$600, A = Amount , r = rate = 1 \% = 0.01 } \\ n\text{ = number of times quartely = }\frac{12}{4}=3\text{ , t = time in years = 2} \end{gathered}[/tex][tex]\begin{gathered} A\text{ = P ( 1 + }\frac{r}{n})^{nt} \\ A\text{ = \$ 600 ( 1 + }\frac{0.01}{3})^{3x2} \\ A=600(1+0.003)^6 \end{gathered}[/tex][tex]\begin{gathered} A=600(1.003)^6 \\ A\text{ = 600(1.020167)} \\ A\text{ = 612.1}002 \\ A\text{ = 612.10 (nearest cent)} \end{gathered}[/tex]Hence the compound interest = 612.10 (nearest cent)
Help I don’t understand what’s happening
Solution of Square root, x² = 30: x = √30 = √30² = 30, x = -√30 = -√30² = 30
Solution of Cube root, x³ = 30: x = ∛30 = ∛30³ = 30, x = -∛30 = -∛30³ = -30
Given,
Square root x² = 30
Then, the value of:
x = √30 = √30² = 30
x = -√30 = -√30² = 30
x = ∛30 = ∛30² = 3.107
x = -∛30 = -∛30² = -3.107
Now,
Cube root, x³ = 30
x = √30 = √30³ = 164.317
x = -√30 = -√30³ = -164.317
x = ∛30 = ∛30³ = 30
x = -∛30 = -∛30³ = -30
Therefore,
Solution of Square root, x² = 30:
x = √30 = √30² = 30
x = -√30 = -√30² = 30
Solution of Cube root, x³ = 30:
x = ∛30 = ∛30³ = 30
x = -∛30 = -∛30³ = -30
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HELPP Determine which integer will make the inequality 5x + 12 > 2x + 6 false.
S:{−3}
S:{3}
S:{−1}
S:{1}
Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.
The equation y = 2/3x + 1 has a solution of (6, 5) and not (9, 8)
How to determine if the ordered pairs are part of the solutions?From the question, the equation is given as
y = 2/3x + 1
Also, we have the ordered pairs to be
(6, 5) and (9, 8)
For (6, 5), we have
x = 6 and y = 5
So, the equation becomes
5 = 2/3 x 6 + 1
Evaluate
5 = 5 --- true
For (9, 8), we have
x = 9 and y = 8
So, the equation becomes
8 = 2/3 x 9 + 1
Evaluate
8 = 7 --- false
Hence, (6, 5) is part of the solution and (9, 8) is not
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The total surface area of this cuboid is 112 cm². Find the value of x. 10 cm length 2 cm width x height
Answer:
3 cm
Step-by-step explanation:
Given dimensions of the cuboid:
Length (l) = 10 cmWidth (w) = 2 cmHeight (h) = x cmIf the total surface area of the cuboid is 112 cm²:
[tex]\begin{aligned}\textsf{Total SA of cuboid}&= 2 (\sf lh +wh + lw)\\\implies 112&=2(10x+2x+10 \cdot 2)\\112&=2(12x+20)\\112&=24x+40\\24x&=72\\x&=3\end{aligned}[/tex]
Therefore, the height of the cuboid is 3 cm.
Circle O has a circumference of 88π cm.
Circle O has a radius length of r.
What is the length of the radius of the circle?
The length of the radius of the circle is 44cm.
This problem bothers on the mensuration of flat shapes, a circular shape.
Given data
Circumference of circle C= 88πcm
Radius of circle r=?
To find the length of the radius of the circle.
To solve for the radius let us apply the formula for the circumference of a circle
C=2πr
Substituting our given data
88π=2πr
Making r subject of formula we have
r= 88π/2π
r= 44cm
Hence, The length of the radius of the circle is 44cm.
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write and simplify a division expression to find the number of cups of flour max needs to use if he has just 1 egg
The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.
1 egg = M/N cups of flour.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Let M cups of flour be needed for N eggs.
This can be written as:
N eggs = M cups of flour
Divide both sides by N.
1 egg = M/N cups of flour
Thus,
The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.
1 egg = M/N cups of flour.
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Please help super confused ASAP.
Find f(-9) if f(x) = -2x + 5.
Enter DNE if the value does not exist.
f(-9)=
Work Shown:
f(x) = -2x+5
f(-9) = -2(-9)+5
f(-9) = 18+5
f(-9) = 23
Please help the Asap the question is in the picture
The length is 16.6ft and the width is 8.9ft
Area of the rectangular area = Length × width
A = LW … 1
What is the explanation?If he wants to have a rectangular area of turf with length one foot less than 3 times the width, then
L = 3W - 1 … 2
Substitute 2 into 1
A = (2W-1)W
A = 2W^2 - W
Since area = 150sq.ft
150 = 2W^2 - W
2W^2 - W - 150 = 0
Factorize
2W^2 - W - 150 = 0
W = 1±√1+4(300)/2(2)
W = 1±√1201/2(2)
W = 1±34.655/4
W = 35.655/4
W = 8.91375
W = 8.9 (to nearest tenth)
Get the length
L = A/W
L = 150/8.9
L = 16.85
L = 16.6ft
Hence the length is 16.6ft and the width is 8.9ft
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donuts are sold in bags and cartons. a bag holds four donuts and a carton holds 10 donuts. tom buys b bags of donuts and c cartons of donuts. he buys a total of t donuts. write down a formula for t in terms of b and c
Answer:
t = b+ c
total = bags + cartons
Write an equation of the parabola in vertex form.
(-2, 6)
(-1,3)
The equation of parabola in vertex form is y=-3(x+2)^2+6
What is parabola and equation of parabola in vertex form?
Parabola is equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The equation of parabola in vertex form is
y=a(x-h)^2+k
Given the vertex (-2,6) and (-1,3)
h=-2 and k=6
y=a〖(x+2)〗^2+6
To find the value of a at vertex (-1,3)
Put y = 3 and x = -1
3=a(-1+2)^2+6
3=a+6
a=-3
The equation of parabola is given by y=-3(x+2)^2+6
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[Isosceles and Equilateral Triangles] Solve for x.
The required value of x is 34° in figure 4, x is 57° in figure 5, x is 81° in figure 6, x is 122° in figure 7, x is 65° in figure 8, x is 54° in figure 9, x is 90° in figure 10, x is 60° in figure 11, and x is 62° in figure 12.
What are the Equilateral Triangles?
In any equilateral triangle, the three angles are of equal measure and they equal 60 degrees.
As per figure 4,
x° + 56° + 90° = 180
x = 180 - 146
x = 34°
As per figure 5,
x = 57°
As per figure 6,
36 + 90/2 + 180-x = 180
36 + 45 - x = 180 - 180
x = 36 + 45
x = 81°
As per figure 7,
By the property of Equilateral Triangles
⇒ x = 180 - 58
⇒ x = 122°
As per figure 8,
By the property of Isosceles Triangles
x + 115 = 180
x = 180 - 115
x = 65°
As per figure 9,
6 + x + 60 + 60 = 180
x = 180 - 60 - 60 - 6
x = 54°
As per figure 10,
By the property of Equilateral Triangles
60/2 + 60 + x = 180
x = 180 - 60 - 30
x = 90°
As per figure 11,
By the property of Equilateral Triangles
2(30) + 60 + x = 180
x = 180 - 60 - 60
x = 60°
As per figure 12,
28 + 90 + x = 180
x = 180 - 118
x = 62°
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What do the Zero Exporient and Negative Exponent Properties mean?
Answer:
Step-by-step explanation:
Zero exponent numbers = 1
When you try to multiply an exponent by zero, it equals one.
Negative exponents is just a 1/x
Negative just flips over the equation.
For example, 9^-1
1/9^1
1/9
Answer:
Step-by-step explanation:
Zero Exponent Property: The zero exponent rule states that when a nonzero number is raised to the power of zero, it equals 1.
Example: x^0 = 1
Negative Exponent Properties: the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice verse. It also describes how many times we have to multiply the reciprocal of the base.
An example of negative exponents is [tex]3^{-2}[/tex].
9. Find the area of the shaded region.
22 cm
10 cm
7 cm
Solve for x. Leave your answer in simplest radical form
Answer:
x = √213
I would appreciate this being marked as brainliest...
Step-by-step explanation:
This is a Pythagoras question because we are given two right-angled triangles and no internal angles other than the right angles.
That 7 is annoying because it won't form a Pythagorean triplet with 10. It means that the answer will probably be in radical form.
We can use radicals to represent the common side.
Introduce Pythagoras. The equation below forms a circle on a graph by the way where r is the radius of the circle.
a² + b² = c²;
Substitute the first triangle.
10² + 7² = c²;
100 + 49 = c²;
149 = c²;
c = √149;
Substitute the second triangle.
(√149)² + 8² = x²;
149 + 64 = x²;
213 = x²;
x = √213;
ANSWER QUICK FOR BRAINLIEST!!! THREE MATH QUESTIONS!!!
Question 10 (Multiple Choice Worth 2 points)
(One-Step Inequalities MC)
Write the inequality for the statement:
the difference between a number and seven eighths exceeds negative two thirds
f plus 7 over 8 is greater than 2 over 3
f minus 7 over 8 is less than or equal to negative 2 over 3
f minus 7 over 8 is greater than negative 2 over 3
f minus 7 over 8 is less than negative 2 over 3
Question 11 (Multiple Choice Worth 2 points)
(Adding and Subtracting Linear Expressions MC)
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Question 13 (Multiple Choice Worth 2 points)
(Solving Two-Step Equations MC)
Solve the equation for x.
−0.28x − 15.3 = 1.92
x = 61.5
x = −61.5
x = 47.8
x = −47.8
1. The inequality for the statement is C. f minus 7 over 8 is greater than negative 2 over 3
2. The value of the expression is C. 43 over 24 times j plus 1 over 12.
3. −0.28x − 15.3 = 1.92 will be B. -61.5.
What is the inequality?1. The difference between a number and seven eighths exceeds negative two thirds is:
Let the number be f.
This will be:
f - 7/8 > -2/3
2. The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths will be:
= -1/8j + 2/3 - 5/3j + 9/12
= -1/8j - 5/3j + 9/12 - 8/12
= -3/24j - 40/24j + 1/12
= -43/24j + 1/12
3. −0.28x − 15.3 = 1.92
Collect like term
−0.28x = 1.92 + 15.3
-0.28x = 17.22
x = 17.22 /- 0.28
x = -61.5
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A $1,000 deposit is made at a bank that pays 12% compounded
How much will you have in your account at the end of 10
monthly.
years?
Answer- 3,315.53007332
Step-by-step explanation:
In this example the compounded is weekly, so the interest rate has to be converted to a weekly interest rate of tex2html_wrap_inline224 .
At the end of the first week, you will have the $1,000 you had at the beginning of the week plus the interest on the $1,000 or tex2html_wrap_inline226 . At the end of the week you will have
displaymath228
∠1 and ∠2 are vetical angles. If m∠1 =(5x+12)° and m∠2 =(6x−11)°. m∠1=
⇒Vertical angles are equal .
This means that ∠1=∠2
⇒The trick is to first find the value of the unknown variable x then substitute it in the expression of ∠1 to get the exact magnitude of the angle.
[tex]5x+12=6x-11\\5x-6x=-11-12\\-x=-23\\\frac{-x}{-1} =\frac{-23}{-1} \\x=23[/tex]
x=23°
To get the exact value of ∠1 Plug in 23° in the place of x in the expression of ∠1:
[tex]< 1=5x+12\\=5(23)+12\\=127[/tex]
∠1=127°
What is the value of x in the equation −x = 6 − 3x + 8?−14−7147
S={7}
1) Let's solve for x, for the given equation :
-x = 6 -3x +8 Add 3x to both sides
3x-x=-3x+3x +6 +8
2x =14 Divide both sides by 2
x= 7
S={7}
And that is the answer
2b+3=7
2z+2=8
6b+2=14
7d−3=18
Answer:
b=2
z=3
again b=2
d=3
Step-by-step explanation:
don't know what to explain
a design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. he knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. on three recent production batches, he tested service life on random samples of four headlamps, with these results: sample service life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 what is the mean of the sampling distribution of sample means when the service life is in control? multiple choice 500 hours 515 hours 495 hours 250 hours 470 hours
The mean of the sampling distribution of sample means is 495 hours.
What is the mean of the samples?
The mean of samples is the average of a set of samples or data.
This can be calculated using the formula:
Mean= (Sum of terms)/(Number of terms)
Find the mean of each sample as shown below:
Mean service life of sample 1 = [tex]\frac{495+500+505+500}{4} = \frac{2000}{4}[/tex]
= 500 hours
Mean service life of sample 2 =[tex]\frac{525 +515 +505 +515 }{4}=\frac{2060}{4}[/tex]
= 515 hours
Mean service life of sample 3 = [tex]\frac{470 +480 +460+ 470}{4}=\frac{1880}{4}[/tex]
= 470 hours
Find the mean of the sampling distribution of sample means using the formula:
Mean of the sampling distribution (M)
=(Sum of mean of given samples )÷( Number of samples)
M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]
M=495 hours
So, the mean of the sampling distribution of sample means is 495 hours.
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The mean of the sampling distribution of sample means is 495 hours.
What is the mean of the samples?
The mean of samples is the average of a set of samples or data.
This can be calculated using the formula:
Mean= (Sum of terms)/(Number of terms)
Find the mean of each sample as shown below:
Mean service life of sample 1 = [tex]\frac{495+ 500+ 505+ 500}{4}=\frac{2000}{4}[/tex]
= 500 hours
Mean service life of sample 2 = [tex]\frac{525+ 515+ 505+ 515 }{4}=\frac{2060}{4}[/tex]
= 515 hours
Mean service life of sample 3 = [tex]\frac{ 470+ 480 +460 +470}{4}=\frac{1880}{4}[/tex]
= 470 hours
Find the mean of the sampling distribution of sample means using the formula:
Mean of the sampling distribution (M)
=(Sum of mean of given samples )÷( Number of samples)
M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]
M=495 hours
So, the mean of the sampling distribution of sample means is 495 hours.
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ABCD is a rectangle that represents a park. The lines show all the paths in the park. The circular path is in the centre of the rectangle and has a diameter of 10 m. Calculate the shortest distance from A to C across the park, using only the lines shown. B 40 m A 70 m C D
solve for v: -28 = v +-12
Answer:
v = -16
Step-by-step explanation:
Move the variable to the left-hand side and change its sign, so it would then be -28 - v = -12
Then move the constant to the right-hand side and change its sign, so it would become - v = -12 + 28
Then you would calculate the sum: - v = 16
After doing so, change the sides on both sides of the equation, v = -16
So, your answer should be v = -16
What is the equation of the line below?
Answer: Y = -2x + 1
Step-by-step explanation:
The line has a Y-Intercept of 1, shown as that's where the line passes the Y-Axis. The slope is negative 2, you can find such information by finding one point on a line, then making a triangle to the next point. In this case you would start at (0,1) and go right once (x axis) and down twice (y axis). The slope formula is y2-y1/x2-x1 or change in y/change in x, so if you put 2 (y axis) over 1 (x axis) you would have a slope of 2.
Ming had 59 birthday cupcakes. He gave 30 cupcakes to his classmates at school. Ming's family ate another 11 cupcakes at home.
How many cupcakes does Ming have left?
Answer:18
Step-by-step explanation:
59 - 30 - 11 = 18
in the united states, the mean birth weight for boys is kg, with a standard deviation of kg. assuming that the distribution of birth weight is approximately normal, complete parts a through e.
The proportion of baby boys in the United States that are born with low birth weight is 0.0495
In a set with mean u and standard deviation σ , the z score of a measure X is given by:
Z= X - u / σ
Z = 2.5- 3.41/ 0.55
Z= -1.6545
Z= -1.65 has a p value of 0.0495
The proportion of baby boys in the United States that are born with low birth weight is 0.0495.
the complete question is
In the United States, the mean birth weight for boys is 3.41 kg with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. A baby is considered of low birth weight if it weighs less than 2.5 kg. What proportion of baby boys in the United States are born with low birth weight
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Find (a) f(-8) and (b) f(3).
(a) f(-8)=
(b) f(3) =
Answer:
[a] 15
[b] 13
Step-by-step explanation:
We can use the visual diagram given to solve. We can see that when you input -8 (on the left side) the arrow leads to the output 15, our answer.
We use the same method for part b. When you input 3 (on the left side) the arrow points to 13 (on the right side) giving us an answer of 13.
Please answer all 3 questions in the photo for easy point! ( 30 points + Brainliest )
Answer:
6. a because a rectangle with sides 8 and 2 has a perimeter of 20 but its area is 16.
7. d because 4 is an even number and it is a perfect square.
8. b because a pen can be used to write but is not a utensil.
Step-by-step explanation:
Kaylie is 6 years old. Her sister, Amanda is 2x younger. Kaylie is now 36. How old is Amanda?
In a case whereby Kaylie is 6 years old and Her sister, Amanda is 2x younger. Kaylie is now 36 the, Amanda age will now be expressed as 33 years.
How can the age of Amanda be calculated?This implies that when Kaylie is 6 years old then her Her sister, Amanda will be 6/2 = 3 years old.
Then we were told again that Kaylie is now 36, then the age of Amanda will now be (36-3)= 33 years
This is because when Kaylie was 6 years old , she was older by her sisiter by just just 3 years, which is still the same when she grown in age again, the 3 years interval is maintained.
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