Answer:
4 -i
Step-by-step explanation:
For your condition to be met, neither the real part nor the imaginary part can exceed √17 in magnitude. That excludes the first three answer choices.
The magnitude of 4-i is ...
√(4^2 +(-1)^2) = √17.
Answer:
4 – iStep-by-step explanation:
First, we need to know that a complex number, which has a real part and an imaginary part, it's like a vector, where the horizontal coordinate is the real part, and the vertical coordinate is the imaginary part.
So, to find the distances we applied the conventional definition:
[tex]d=\sqrt{r^{2}+i^{2} }[/tex]
Where [tex]r[/tex] refers to the real part and [tex]i[/tex] refers to the imaginary part.
So, we test each answer and see which one gives us the root of 17.
Option 1.[tex]d=\sqrt{2^{2}+15^{2} }=\sqrt{4+225}=\sqrt{229}[/tex]
Option 2.[tex]d=\sqrt{17^{2}+1^{2} }=\sqrt{290}[/tex]
Option 3.[tex]d=\sqrt{20^{2}+(-3)^{2} }=\sqrt{409}[/tex]
Option 4.[tex]d=\sqrt{4^{2}+(-1)^{2} }=\sqrt{17}[/tex]
Therefore, the right answer is the last one, because the distance is the squared root of 17.
what is the product of (3 squared 8)(4 squared 3)? Simplify your answer.
Answer:
3456
Step-by-step explanation:
the given equation is: [tex](3^{2} 8) (4^{2} 3)[/tex]
= (9 × 8) (16 × 3)
= (72) (48)
= 3456
Find the median, first quartile, third quartile, interquartile range, and any outliers for each set of data.
14.6, 28.1, 3.9, 7.1, 5.3, 30.9, 2.8, 6.5, 20.8, 16.4, 16.4, 27.1, 53.5, 12.5, 6.1
Here is what i figured out.
Answer:
First, to find the median, we have to order all numbers, from least to highest:
2.8; 3.9; 5.3; 6.1; 6.5; 7.1; 12.5; 14.6; 16.4; 16.4; 20.8; 27.1; 28.1; 30.9; 53.5Now, we calculate the position of each quartile:
[tex]Q_{k}=\frac{k(n+1)}{4}\\Q_{1}=\frac{1(15+1)}{4}=4\\Q_{2}=\frac{2(15+1)}{4}=8\\Q_{3}=\frac{3(15+1)}{4}=12[/tex]
So, the first quartile is in the fourth position, the thirds quartile is in the twelfth position:
So, first quartile is 6.1. Second quartile is 14.6, and the third quartile is 27.1.
It's important to remember that the second quartile is the median. So the median is 14.6
Lastly, the interquartile range is the difference between the third and first quartile. So:
[tex]Q_{3}-Q_{1}=27.1-6.1=21[/tex]
Therefore, the interquartile range is 21.
Which graph represents the absolute value of -3?
Answer:
The third graphStep-by-step explanation:
|a| = a for a ≥ 0
|a| = -a for a < 0
therefore
|3| = 3 and |-3| = -(-3) = 3
Answer:
Graph 1 is the correct representation of absolute value of -3.
Step-by-step explanation:
Absolute value of a number is the measure of positive distance on a number line from zero to that number.
It is denoted by:
[tex]\mid c \mid = c, \text{if c} > 0\\ ~~~~~ = -c, \text{if c} < 0[/tex]
So, the absolute value of -3 =
[tex]\mid -3 \mid = 3[/tex]
The correct representation of the absolute value option 1.
As the graph in option 1 represents the positive distance between zero and -3.
For questions 2 and 3, simplify each polynomial.
3x2 + 6 - 2x + 5x - 4x2 +9
A. -x^2 + 3x + 15
B. 7x^2 + 3x + 3
C. x^2-3x+15
D. -x^2 + 7x + 15
Answer:
A
Step-by-step explanation:
3x² + 6 - 2x + 5x - 4x² + 9
Combine like terms:
3x² - 4x² - 2x + 5x + 6 + 9
-x² + 3x + 15
Final answer:
To simplify the polynomial, combine like terms by adding or subtracting coefficients of terms with the same variable and exponent. The terms simplify to -x^2 + 3x + 15, matching option A.
Explanation:
The subject of the student's question involves simplifying a polynomial. To simplify the given polynomial 3x2 + 6 - 2x + 5x - 4x2 + 9, we need to combine like terms. This process involves adding or subtracting the coefficients of terms with the same variable and exponent. Let's go through the steps:
Combine the terms with x2: 3x2 - 4x2 = -1x2
Combine the terms with x: -2x + 5x = 3x
Add the constant terms: 6 + 9 = 15
Putting it all together, the simplified form of the polynomial is -x2 + 3x + 15, which matches option A.
Remember, when simplifying polynomials, always look for like terms that can be combined and ensure the final expression is written in standard form, with terms ordered from highest to lowest degree.
Please help me with the process to find the answer for #15, #16, #17 and #18
Thank you it’s very much appreciated! :)
Well I wanna do you want us to pick you guys up tomorrow at night to
Can you show how you did it?
8.31 - 3.43 =
Answer:
4.68
Step-by-step explanation:
Remember to line up the decimal point. Subtract as ordinarily.
8.31
-3.43
--------
4.68
4.68 is your answer
~
The surface area of sphere T is 452.16 units squared. The surface area of sphere X is 1808.64 units squared. how many times larger is the radius of sphere X than the radius of sphere T?
Answer:
the radius of sphere X is 2 times larger than the radius of sphere T
Step-by-step explanation:
Given
Surface area of sphere, T =452.16
Surface area of sphere, X= 1808.64
how many times larger is the radius of sphere X than the radius of sphere T?
Finding radius of both spheres:
Surface area of sphere is given as
A=4πr^2
Now putting value of Ta=452.16 in above formula
452.16=4πrt^2
rt^2=452.16/4π
rt^2=35.98
Taking square root on both sides
rt=5.99
Now putting value of Xa=1808.64 in above formula
1808.64=4πrx^2
rx^2=1808.64/4π
rx^2=143.92
Taking square root on both sides
rx=11.99
Comparing radius of sphere X and the radius of sphere T
rx/rt=11.99/5.99
= 2.00
rx=2(rt)
Hence the radius of sphere X is 2 times larger than the radius of sphere T!
The answer is:
The radius of the sphere X is 2 times larger than the radius of the sphere T
Why?To solve the problem, we need to find the radius of both spheres using the following formula:
[tex]Area=\pi *radius^{2}\\\\radius=\sqrt{ \frac{Area}{\pi }}[/tex]
Where,
Area, is the area of the circle.
r, is the radius of the circle.
So,
We are given:
[tex]T_{area}=452.16units^{2}\\X_{area}=1808.64units^{2}[/tex]
Now, calculating we have:
For the sphere X,
[tex]X_{radius}=\sqrt{ \frac{X_{area}}{\pi }}=\sqrt{\frac{1808.64units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{1808.64units^{2} }{\pi }}=\sqrt{575.71units^{2} }=23.99units[/tex]
For the sphere T,
[tex]T_{radius}=\sqrt{ \frac{T_{area}}{\pi }}=\sqrt{\frac{452.16units^{2} }{\pi } }\\\\X_{radius}=\sqrt{\frac{452.16units^{2} }{\pi }}=\sqrt{143.93units^{2} }=11.99units[/tex]
Then, dividing the radius of the X sphere by the T sphere to know the ratio (between their radius), we have:
[tex]ratio=\frac{23.99units}{11.99units}=2[/tex]
Hence, we have the radius of the sphere X is 2 times larger than the radius of the sphere T.
Have a nice day!
a storage container has a shape of a rectangular prism. it’s height is 8 feet. it’s length is two times it’s width. the volume is 400 cubic feet. find the length and width of the container.
please help
Given that the volume of a rectangular prism is length x width x height, this problem can be solved by setting up the equation 2w * w * 8 = 400, where w is the width and 2w is the length. Solving this equation, we find that the width is 5 feet and the length is 10 feet.
Explanation:In mathematics, the volume of a rectangular prism is given by the formula length x width x height. We are given that the volume of the storage container is 400 cubic feet, its height is 8 feet, and the length is twice the width. Let us denote the width as w, then the length is 2w.
From the given volume formula, we have:
Length x Width x Height = Volume
Substituting the values, we get:
2w * w * 8 = 400
Solving this equation, we find:
w^2 = 25
Taking the square root of both sides, we get:
w = 5
Substituting w=5 into 2w, we find the length:
Length = 2*5 = 10
So the width of the container is 5 feet and the length is 10 feet.
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Please someone hurry.
Answer:
b
Step-by-step explanation:
Describe the end behavior of the function below f(x)=4(2)^(-x)-3
Final answer:
The function f(x) = 4(2)^(-x) - 3 approaches -3 as x approaches infinity and decreases without bound as x approaches negative infinity, with a horizontal asymptote at y = -3.
Explanation:
The end behavior of a function describes what happens to the function's values as x approaches infinity or negative infinity. For the function f(x) = 4(2)^(-x) - 3, as x approaches infinity, the term 2^(-x) approaches zero, because any non-zero base raised to the power of negative infinity is zero. Thus, the function approaches -3. Conversely, as x approaches negative infinity, the term 2^(-x) grows exponentially, and the function's values decrease without bound, heading towards negative infinity. However, since f(x) involves a negative exponential function, the graph ultimately will approach the horizontal asymptote y = -3.
A survey found that 4 out of 100 people have red hair. On the basis of this survey, how many people in a group of 12,000 people are likely to have red hair
Answer:
480
Step-by-step explanation:
Answer:
480
Step-by-step explanation:
4/100 is 4% so find 4% of 12,000
12,000(.04) = 480
PLEASE HELP I AM DESPERATELY LOOKING FOR GOOD ANSWERS
Which question ? Are you looking for?
4. Point A=-1.5 Point B =-.2. Point c= 1.2
5.8x 4=32. 32+21=53
Megan drove from her house to work at an average speed of 45 miles per hour. The drive took her
20 minutes. If the drive home took her 30 minutes and she used the same route in reverse, what was her average speed going home?
Question 10 options:
30 miles per hour
13.33 miles per hour
26.6 miles per hour
3 miles per hour
Answer:
30 mph
Step-by-step explanation:
The average speed = Total distance / Total Time
Distance at 45 m/hr.
t = 20 minutes = 20/60 = 1/3 hour.
r = rate = 45 miles / hour
d = r * t
d = 45 * 1/3 = 15 miles.
Average Speed going home.
t = 30 minutes
t = 30 min / 60 min // hour = 1/2 hours
r = 15 miles / 1/2 = 15 * 2 = 30 miles / hr.
Point O is the center of the circle. What is the value of x?
Hello!
I want to help you but where is the image or answer choices? Thanks for asking— I’ll help if a I have the answer options or a photo because the question can’t be answered as there would be an infinite possible choices. It’d be great help! Thanks!
Have a great day!
~ Destiny ^_^
Answer:
24
Step-by-step explanation:
If its the figure shown, the answer is 24.
Problem: A fair coin is flipped nine times and the numbers of heads are counted. Question: What is the variance for this distribution?
5 points
2.25
0.5
4.5
9
Answer: Option A
[tex]\sigma ^ 2 = 2.25[/tex]
Step-by-step explanation:
The number of faces obtained by flipping the coin 9 times is a discrete random variable.
If we call this variable x, then, the probability of obtaining a face in each test is p.
Where [tex]p = 0.5[/tex]
If we call n the number of trials then:
[tex]n = 9[/tex]
The distribution of this variable is binomial with parameters
[tex]p = 0.5\\\\n = 9[/tex]
For a binomial distribution, the variance "[tex]\sigma^2[/tex]" is defined as
[tex]\sigma ^ 2 = np(1-p)[/tex]
[tex]\sigma ^ 2 = 9(0.5)(1-0.5)[/tex]
[tex]\sigma ^ 2 = 9(0.5)(0.5)[/tex]
[tex]\sigma ^ 2 = 2.25[/tex]
20 POINTS What are the x-intercepts of the graph? A) x = -5 B) x = 1 and 5 C) x = 0 and 4 D) x = -1 and 5
Answer:
B) x = 1 and 5Step-by-step explanation:
x-intercept: the intersection point of the graph with the x axis.
Therefore, the x-intercepts are x = 1 and x = 5 (look at the picture).
Max walks 6 laps around the track in 30 minutes. How many laps around the track does Max walk in 1 minute
Answer:5
Step-by-step explanation:
6:30 is the ration
6/30 reduced is 1/5
1:5
so its 5
Max walks 0.2 laps per minute around the track. This conclusion was reached by dividing the total number of laps (6) by the total number of minutes (30).
Explanation:The Mathematics problem posed is one concerning rates. It is given that Max walks 6 laps in 30 minutes. We need to find out how many laps would Max be able to walk in 1 minute.
To do this, we divide the total number of laps walked by the total number of minutes. In this case, we would divide 6 laps by 30 minutes.
6 laps ÷ 30 minutes = 0.2 laps per minute
Therefore, Max walks 0.2 laps around the track in 1 minute.
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The result of subtracting (4x2-x) from -3x2 is
Answer:
Step-by-step explanation:
-3x²-(4x²-x)
=-3x²-4x²+x
=-7x²+x
Answer:
[tex]-7x^2+x[/tex]
Step-by-step explanation:
(4x2-x) from -3x2 is
Subtract [tex]4x^2-x from -3x^2[/tex]
[tex]-3x^2 - (4x^2-x)[/tex]
Remove the parenthesis by multiplying negative sign inside the parenthesis
[tex]-3x^2 - 4x^2+x[/tex]
Now combine like terms, add -3 and -4 and it becomes -7
[tex]-7x^2+x[/tex]
*Help* Whats The Answer To This Graph?
Answer:
C. The growth factor of g is twice the growth factor of f.
Step-by-step explanation:
Let's find the growth factor of g(x) by getting its equation. To do it, we are using the standard exponential equation:
[tex]y=a(b+1)^x[/tex]
where
[tex]a[/tex] is the initial value
[tex]b[/tex] is the growth factor
We know form our graph that g(x) passes throughout (0, 3), so [tex]x=0[/tex] and [tex]y=3[/tex].
Replacing values
[tex]3=a(b+1)^0[/tex]
[tex]3=a(1)[/tex]
[tex]a=3[/tex]
We also know from our graph the g(x) passes throughout (1, 12), so [tex]x=1[/tex] and [tex]y=12[/tex].
Replacing values
[tex]y=a(b+1)^x[/tex]
[tex]12=3(b+1)^1[/tex]
[tex]12=3(b+1)[/tex]
[tex]b+1=\frac{12}{3}[/tex]
[tex]b+1=4[/tex]
[tex]b=4-1[/tex]
[tex]b=3[/tex]
The growth factor of g(x) is 4.
Now, to find the growth factor of f(x), we just need to equate 1+b with [tex]\frac{5}{2}[/tex] and solve for b:
[tex]1+b=\frac{5}{2}[/tex]
[tex]b=\frac{5}{2} -1[/tex]
[tex]b=\frac{3}{2}[/tex]
[tex]b=1.5[/tex]
Finally, we can divide the growth factor of g(x) by the growth factor of f(x) to find how many times bigger is the growth factor of g(x):
[tex]\frac{3}{1.5} =2[/tex]
We can conclude that the growth factor of g is twice the growth factor of f.
Answer:
C
Step-by-step explanation:
A copy machine at your school can print 80 sheets per minute. How long will it take your teacher to print 6,000 pages?
1 hour
1.25 hours
1.5 hours
1.75 hours
Answer: it will take 1.25 hours
Step-by-step explanation:
It
It will take the teacher 1.25 hours to print 6,000 pages.
To calculate how long it will take to print 6,000 pages with a copy machine that can print 80 sheets per minute, we need to divide the total number of pages by the rate of printing per minute to find out the time in minutes, and then convert that time into hours if necessary.
Step 1: Divide the total number of pages by the printing speed to find the time in minutes.
Total pages: 6,000
Printing speed: 80 pages/minute
Time calculation: 6,000 pages divided by 80 pages/minute = 75 minutes
Step 2: Convert minutes into hours by dividing by 60 since there are 60 minutes in an hour.
Conversion to hours: 75 minutes divided by 60 minutes/hour = 1.25 hours
Therefore, it will take the teacher 1.25 hours to print 6,000 pages.
Ac is tangent to circle O at A. The diagram is not drawn to scale. If m by=52 degrees what is m yac?
A. 38°
B.64°
C.78°
D.104°
ANSWER
A. 38°
EXPLANATION
The tangent, AC to the circle meets the diameter AB to the circle at right angle.
This implies that,
[tex]m \angle BAY + m \angle YAC = 90 \degree[/tex]
Substitute the given angle:
[tex]52 \degree + m \angle YAC = 90 \degree[/tex]
[tex]m \angle YAC = 90 \degree - 52 \degree[/tex]
[tex]m \angle YAC = 38 \degree[/tex]
Using the tangent theorem and the inscribed angle theorem, m∠YAC is: A. 38°
What is the Tangent Theorem?According to the tangent theorem, a right angle (90°) is formed at the point of intersection between the radius and the tangent of a circle.
m∠BAY = m(BY) = 52° (inscribed angle theorem)
m∠BAC = 90° (tangent theorem)
m∠YAC = m∠BAC - m∠BAY
Substitute
m∠YAC = 90 - 52 = 38°
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find x
13+6+2x-18=4x-29
Answer:
x = 15
Step-by-step explanation:
Answer:
x = 15
Step-by-step explanation:
13+6+2x-18=4x-29
Combine like terms
2x + 1 = 4x - 29
Subtract 4x from both sides
-2x + 1 = - 29
Subtract 1 from both sides
-2x = -30
Divide both sides by -2
x = 15
What is the geometric mean of the pair of numbers? 245 and 5
Answer:
35
Step-by-step explanation:
The geometric mean of n numbers is the n-th root of their product.
The geometric mean of these two numbers is ...
√(245·5) = √1225 = 35
Answer:
35
Step-by-step explanation:
Take the product of the two numbers, then get the square root of the product.
[tex]245*5=1225\\\sqrt{1225} = 35[/tex]
At the football game, 4 hamburgers and 5 soft drinks cost $27, and 3 hamburgers and 3 soft drinks cost 18$. Which system of equations below can be used to determine the price of a hamburger and the price of the soft drink
The system of equations that can be used to determine the price of the hamburger and the soft drink is 4H + 5S = $27 (H = hamburger cost, S = soft drink cost) and 3H + 3S = $18.
Explanation:The question you're asking involves setting up a system of equations to solve for the cost of a hamburger and a soft drink based on the given information. Since two different meals with different quantities of hamburgers and soft drinks have specific costs, we can make the following two equations where H represents the cost of a hamburger and S represents the cost of a soft drink: 4H + 5S = $27 and 3H + 3S = $18. This system of equations can be solved using various methods like substitution or elimination to determine the individual costs of a hamburger and a soft drink.
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7x+4+x=20 what is x? plz help
7x+4+x=20
8x+4=20
8x+4-4=20-4
8x=16
Divide by 8 for 8x and 16
8x/8=16/8
x=2
Check answer by using substitution method
7(2)+4+2=20
14+6=20
20=20
Answer is x=2
Answer:
x=2
Step-by-step explanation:
7x+4+x=20
Combine like terms
8x +4 = 20
Subtract 4 from each side
8x+4-4 =20-4
8x = 16
Divide each side by 8
8x/8 = 16/8
x = 2
Un rombo tiene un ángulo de 22 grados. Cuanto vale la suma de sus ángulos que no midan 22 grados?
Answer:
The sum of the angles that do not measure 22 degrees is equal to 316°
Step-by-step explanation:
The question in English is
A rhombus has a 22-degree angle. How much is the sum of its angles that do not measure 22 degrees worth?
we know that
The opposite internal angles of a rhombus are equal and the adjacent internal angles are supplementary
so
Let
x -----> the measure of an adjacent angle to 22 degrees in the rhombus
x+22°=180°
x=180°-22°=158°
therefore
The sum of the angles that do not measure 22 degrees is equal to
158°+158°=316°
Find the reciprocal of 5/7
Answer:
7/5
Step-by-step explanation:
reciprocal means flip the equation
The answer is 7/5.
Hope this helps!
Annette has a credit card that uses the previous balance method. The
opening balance of one of her 30-day billing cycles was $2990, but that was
her balance for only the first 7 days of the billing cycle, because she then paid
off her entire balance and didn't make any new purchases. If her credit card's
APR is 31%, which of these expressions could be used to calculate the
amount Annette was charged in interest for the billing cycle?
Answer:
Option D is correct.
Step-by-step explanation:
Previous Balance Method uses the "previous" balance, that is, the balance from the month before.
Here, it is given that the opening balance of one of her 30-day billing cycles was $2990. This means this was previous month amount or previous balance.
So, Annette will be charged the interest on $2990.
Hence, option D is correct.
Answer:
D.
Step-by-step explanation:
A cube with side lengths measuring 4 inches. The cube was sliced parallel to the base. Identify the cross-section and calculate its area.
Answer:
The resulting cross section is a square an the area is [tex]A=16\ in^{2}[/tex]
Step-by-step explanation:
we know that
All the faces of the cube are square with side lengths measuring 4 inches
If the cube was sliced parallel to the base
then
the cross section is a square with side lengths measuring 4 inches
so
The area of a square is
[tex]A=b^{2}[/tex]
we have
[tex]b=4\ in[/tex]
substitute
[tex]A=4^{2}[/tex]
[tex]A=16\ in^{2}[/tex]
write the quadratic equation whose roots are -4 and 6 and whose leading coefficient is 3
Answer:
y = 3x² - 6x - 72
Step-by-step explanation:
Since the roots are x = - 4 and x = 6 then the factors are
(x + 4) and (x - 6) and the quadratic function is
y = a(x + 4)(x - 6) ← a is a multiplier, in this case 3, so
y = 3(x + 4)(x - 6) ← expand factors and distribute by 3
y = 3(x² - 2x - 24)
y = 3x² - 6x - 72
3x²-6x-72. The quadratic equation whose roots are -4 and 6 with a leading coefficient of 3 is 3x²-6x-72.
The solutions of a quadratic equation are x = -4 and x = 6 with a leading coefficient of 3. The solutions are two real numbers which means that (x + 4) and (x - 6) are the factors of our unknown quadratic equation and the leading coefficient is 3.
[tex]3(x+4)(x-6)=0[/tex]
Expand (x+4)(x-6):
[tex]3(x^{2} -2x-24)=0\\3x^{2} -6x-72=0[/tex] which is our quadratic equation.