[tex]\text{Given that,}~f(x)=x^3-2x^2\\\\f(i)=i^3-2i^2\\\\~~~~~~=i^2 \cdot i -2(-1)~~~~~;[i^2=-1]\\\\~~~~~~=-i+2\\\\~~~~~~=2-i[/tex]
The expression equivalent to f(i) is 2-i.
What is expression?The expression is mathematical statement which consist of variables, numbers and connected by at least one operation.
Given that, a function f(x) = x³ - 2x², we need to find the expression equivalent to f(i),
To find the same we will put x = i,
So,
f(i) = i³ - 2i² [i = √-1]
= (√-1)³ - 2(√-1)²
= -i - 2(-1)
= -i+2
= 2-i
Hence, the expression equivalent to f(i) is 2-i.
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can you help me solve this?
Answer:
456*567=4890998
46766-6755=566888
Answer:
FGM and reproductive health
A triangle has a perimeter of 16x + 4. If Side 1 is 3x + 2, Side 2 is 8x + 7, what is the measure of Side 3?
Answer:
5x - 5
Step-by-step explanation:
To find the missing side, add the two sides together and subtract them from the perimeter.
side 1 + side 2
3x + 2 + 8x + 7
combine like terms
11x + 9
Subtract from the perimeter
16x + 4 - (11x + 9)
rewrite as an addition problem, so you need to change the signs inside the parentheses.
16x + 4 + (-11x -9)
Now combine like terms
5x - 5
Is this correct?
(Brainliest.)
Answer:
I think it is since i already passed that i think that is correct , well good job !!
Step-by-step explanation:
I need help ASAP! I took a screenshot of the question and linked it.
Answer:
18. $5890
19. Mitsubishi Mirage
Step-by-step explanation:
The depreciated value can be found using an exponential relation. The decay rate here is given as 12.5%. The exponential function will have the form ...
y = a·b^x . . . . . a = initial value, b = decay factor = 1 - decay rate
__
18.The above equation will have a=15,000, representing the initial value of the car. It will have b=(1-0.125) = 0.875, the decay factor for the car's value. In the 7 years between your 18th and 25th birthdays, the car will have declined in value to ...
y = $15000·0.875^7 ≈ $5890.44
When you turn 25, the car will be worth about $5890.
__
19.We found three cars with a price under $15,000:
Nissan VersaChevrolet SparkMitsubishi MirageOf these, the Mirage gets the best mileage and has the most cargo space. (It also has the smallest engine.) The Spark has a continuously-variable transmission, not a 5-speed manual, so will be somewhat easier to drive. Its mileage is almost as good, but its range is about 10% less than that of the Mirage or Versa.
(Your curriculum may offer different choices. We cannot tell.)
Perhaps you got a Mitsubishi Mirage.
Write the formula of the function f(x) whose graph is shown.
Answer:
[tex]f(x)=\dfrac{1}{x+4}[/tex]
Step-by-step explanation:
Asymptote: a line which the curve gets infinitely close to, but never touches.
From inspection of the graph, we can see that there is an asymptote at [tex]x=-4[/tex], since the curve gets infinitely close to this line, but never touches it.
Therefore, the function is undefined at [tex]x=-4[/tex]
For a rational function to be undefined, the denominator must equal zero at that point. Therefore, we are looking for a rational function with a denominator that equals zero when [tex]x=-4[/tex].
Therefore, option D is the correct solution, since:
[tex]f(-4)=\dfrac{1}{-4+4}=\dfrac{1}{0} \implies \sf und efined[/tex]
PLEASE
Write an equation in slope-intercept form of the line shown.
An equation is
Answer:
y = -x - 4
Step-by-step explanation:
m = (-5-0)/(1+4) = -5/5 = -1
b = (0, -4)
y = mx + b
y = -x - 4
Answer:
y = -x - 4
Step-by-step explanation:
Slope-intercept form is:
y = mx + b
The b is the y-intercept. That is where the line crosses the y-axis. This line crosses the y-axis at -4.
You could calculate the slope, but with a graph, you can SEE the slope without doing any calculation. Find a point on the line, any point. To get to the next point, you go DOWN1 and OVER1, (down1, over1, down1, over1)
This is -1/1. The slope is -1. Fill that in for m.
Leave the x and y as-is in
y = mx + b
fill in -1 for m and -4 for b.
y = -x - 4
If your teacher/prof is expecting to see a calc for slope. Find two points on the line. Subtract y-y and put that on top. Subtract x-x and put that on the bottom. Simplify.
Given points:
(1,-5) and (-4,0)
-5 - 0 is -5, put on top.
1 - -4 is 5, put underneath. You get -5/5, which is -1. Slope is -1.
7. Given: AD || BC and AD=BC.
B
Prove: AB || DC
시
Answer:
Step-by-step explanation:
An equilateral triangle has a perimeter of 90 inches. Find the area of the equilateral triangle, I simplest form.
Answer:
389.7 square inches
Step-by-step explanation:
equilateral triangle = each side has the same lenght
90 inches / 3 = 30 inches each side
----------------------------------------------------------
Pythagoras
30^2 = 15^2 + x^2
900 - 225 = x^2
v 675 = x
25.98 = x
x = height
----------------------------------------------------------
Area = BxH/2
B = 30 inches
H = 25.98
(30 x 25.98) /2 = 389.7 square inches
Answer:
390 in²
Step-by-step explanation:
Length of the sides of the triangle = 90/3 = 30 in
area of a triangle = (base × height)/2
height of an equilateral triangle with sides of length x [tex]=\frac{\sqrt{3} }{2}x[/tex]
Then the height of our triangle [tex]=\frac{\sqrt{3} }{2} \times30=26[/tex]
Conclusion:
area of the triangle = (30 × 26)/2 = 390 in²
What is the axis of symmetry for the function f(x)=7−4x+x2?
Answer:
The axis of symmetry is x=2
Step-by-step explanation:
What is the LCD of -1 2/8 and 2 3/4?
Answer:
The least common denominator of [tex]-1\frac{2}{8}[/tex] and [tex]2\frac{3}{4}[/tex] is 8
need help with geometry (number 21)
Answer: D
Step-by-step explanation:
Adjacent sides of a rectangle are perpendicular. This means that the measure of angle HEF is 90 degrees.
Why is ten times ten?
Answer:
100
Step-by-step explanation:
10 · 10 = 100
Of course it all depends on what the symbols you’re using mean. Assuming the the * means “multiplied by,” the next question is “what is the meaning of the symbols 0 and 1,” but (conventionally) in any field, 0 denotes the additive identity and 1 the multiplicative identity. With those assumptions, the next question is “what is meant by the juxtaposition of those symbols?” Again, the commonly used convention is that, for any numeric field with base b, “10” would mean b, and 100 would be interpreted as b*b.
So, for example, if you’re working with a field where b*b = b (e.g., a modular arithmetic), then 10 and 10*10 would both be 1. On the other hand, if your field is, for example, the integers in base 10 (0, 1, …9), then the other answers would apply.
Bottom line: It all depends on what you assume. Without telling us that, it’s harder to answer your question. Note that the other replies to your question all make some (very commonly agreed upon) assumptions, e.g. that you were working in one of the commonly use, base 10, number fields (integers, real numbers, etc.) where ten sticks, each ten inches long, placed in a straight line, would form a line 100 inches long. (The modular field described above would break the sticks into one inch pieces, stack them on top of each other, and get a line one inch long.)
Simplify the expression. (–8.6)0
A)–1
B)–8.6
C)1
D)0
Answer: D
Explanation: Anything times 0 is 0.
Amy bought 14 pounds of rice for $6. How many pounds of rice did she get per dollar?
Answer:
2.3?
Step-by-step explanation:
i just divided it 14 ÷ 6
If one three-digit number ( 0 cannot be a left digit) is chosen at random from all those that can be made from the following set all digits, find the probability that one chosen is not a multiple of 2. [0,1,2,3,4,5,6,7,8]
The probability of choosing a number that is not a multiple of 2 is P = 0.44
How to find the probability?We need to count the number of options for each digit.
For the first digit, we have 8 options {1, 2, 3, 4, 5, 6, 7, 8}For the second digit, we have 9 options {0 ,1, 2, 3, 4, 5, 6, 7, 8}For the third digit, we have 9 options {0 ,1, 2, 3, 4, 5, 6, 7, 8}.The total number of combinations is the product between the numbers of options:
C = 8*9*9 = 648
If we want our number to not be a multiple of 2 then it must end in a odd digit, the combinations that meet that condition are:
For the first digit, we have 8 options {1, 2, 3, 4, 5, 6, 7, 8}For the second digit, we have 9 options {0 ,1, 2, 3, 4, 5, 6, 7, 8}For the third digit, we have 4 options {1, 3, 5, 7}.C = 8*9*4 = 288
Then the probability of selecting a 3 digit number that is not a multiple of 2 is:
P = 288/648 = 0.44
If you want to learn more about probability, you can read:
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Find fRound the answer to the nearest tenth.
A. 54.5°
B. 57.2°
C. 90.0°
D. 109.2°
Answer:
109.2 degrees
Step-by-step explanation:
Use the cos law to find angle F
3.1^2 = 2^2 + 1.8^2 - 2 (2)(1.8) cos F
shows cos f = -.329
arc cos( - .329) = angle F =109.2 degrees
How do you add 2 1/4 plus 3/4
Answer:
Step-by-step explanation: first change 2 1/4 to a improper fraction
you are going to have 9/4 next add 9/4 plus 3/4 which will be equal to12/4 which is the same as 3
Which of the following rational functions is graphed below?
Step-by-step explanation:
There is a vertical asymptote x=3 and x=-1 so our rational function will contain
(x-3)(x+1).
Since we have a horinzintal asymptote, our numerator will be either a constant function, or linear function.
we have a zero at approximately, at 1 so our numerator will include
[tex] \frac{x - 1}[/tex]
So our rational function is
[tex] \frac{x - 1}{(x - 3)(x + 1)} [/tex]
There is a vertical asymptote x=3 and x=-1 so our rational function will contain option C [tex]f(x) = \dfrac{x-1}{(x-3)(x+1)}[/tex].
When do we get horizontal asymptote for a function?The line y = a is a horizontal asymptote if the function f(x) tends to 'a' from the upside of that line y = a, or from downside of that line.
Since we have a horizontal asymptote, our numerator will be either a constant function or a linear function.
We have given a zero at approximately, 1 so our numerator will include (x-1).
So our rational function is
[tex]f(x) = \dfrac{x-1}{(x-3)(x+1)}[/tex]
Learn more about horizontal asymptotes here:
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In a particular city, 21 in 1.5 million people have been struck by lightning. What is the experimental probability of being struck by lightning in this city?
21/(1.5 million) = 0.0014%
Which of the following is an equivalent expression to the expression a^1/3 divided by a^1/4?
A. 1/a^12
B. 7/a^12
C. 1/a^12
D. 1/a^7/12
Answer:
C. 1/a¹²
Step-by-step explanation:
Formula
[tex]\frac{a^{m}}{a^{n} } = a^{m-n}[/tex]Applying that here :
[tex]\frac{a^{\frac{1}{3} } }{a^{\frac{1}{4} } } = a^{\frac{1}{3}-\frac{1}{4} }[/tex][tex]a^{\frac{4-3}{12} } = a^{\frac{1}{12} }[/tex]1/a¹²Answer:
a^1/12 or choice A
Step-by-step explanation:
Given:
[tex]\displaystyle \large{\dfrac{a^{\dfrac{1}{3}}}{a^{\dfrac{1}{4}}}}[/tex]
Law of Exponent (Division Property):
[tex]\displaystyle \large{\dfrac{a^m}{a^n} = a^{m-n}}[/tex]
Therefore:
[tex]\displaystyle \large{a^{\dfrac{1}{3}-\dfrac{1}{4}}}[/tex]
Then evaluate the fractions. Keep in mind that we can only evaluate fractions with same denominator. Therefore, calculate the LCM of 3,4 which is 12:
[tex]\displaystyle \large{a^{\dfrac{4}{12}-\dfrac{3}{12}} = a^{\dfrac{1}{12}}}[/tex]
Therefore, the solution is a^1/12 or choice A
Please help me yall… my math is due tommorrow!
Answer:
Step-by-step explanation:
Remark
I think the easiest way to do this is to calculate the probability of those that are 12 to 24. Then subtract the decimal you get from 1. That saves you adding up 3 numbers to get the same answer.
Givens
Total number of movie goers = 3880
Total number that are between 12 and 24 = 1180
Solution
Probability of a random person being drawn from 1180
people between 12 and 24 = Those between 12 and 24 = 1180
Total Number = 3880
P(12 - 24) = 1180 / 3880
P(12 -24) = 0.3041
Remember, that's not what you want. You want everyone else
P(not(12-24)) = 1 - 0.3041
Answer 0.6959
There is a bag filled with 3 blue, 4 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?
Answer:
Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.
The marbles are chosen without replacement, hence the hypergeometric distribution is used to solve this question.
What is the hypergeometric distribution formula?
The parameters are:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this problem:
There is a total of 3 + 4 = 7 marbles, hence N = 7.
Of those, 3 are blue, hence k = 3.
2 marbles will be taken, hence n = 2.
Step-by-step explanation:
Find the perimeter of the figure to the nearest hundredth.
perimeter: about
ft
A 6 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?
Answer:
The answer would be two feet.
Step-by-step explanation:
Step 1. Do 10-6 (10 being the total space and 6 being the painting)
Step 2. Get the answer of 4.
Step 3. Divide four by 2 because it needs to be centered.
Step 4. Get the answer of two feet on each side.
I hope this helps! :)
For the polynomial f(X)=2x^3-9x^2+11x-20
As
X -> -♾️,f(X) -> ♾️
A. True
B. False
Answer:
False
Step-by-step explanation:
I'm assuming its because x isn't negative infinity because the leading coefficient is positive
distance between these points
X (-3, -4 ) Y (5, 5)
Answer:
12.0
Step-by-step explanation:
The distance betwen the two points is the slope/gradient of that line.Slope/gradient = c (pythagoras theorem) : [tex]c^{2} = a^{2} + b^{2}[/tex]x = a, y = bx = 5 - (-4) = 5 + 4 = 9y = 5 - (-3) = 5 + 3 = 8[tex]c^{2} = 8^{2} + 9^{2}[/tex]
= 64 + 81
= 145
[tex]\sqrt{c^{2} } = \sqrt{145}[/tex]
Therefore,
c = 12.0 (3 s.f.)
4
Which equation does not have a solution?
A. -3d + 7 = -9
B. 8d + 7 = -4(-2d - 4)
C. 54+ 15 = 15
D. 2(d' + 6) = -2d - 12
Answer:
Option BStep-by-step explanation:
A.)
➝ -3d + 7 = -9
➝ -3d = -7 - 9
➝ -3d = -16
➝ d = -16/-3
➝ d = 16/3
Solution is d = 16/3B.)
➝ 8d + 7 = -4(-2d - 4)
➝ 8d + 7 = 8d + 16
➝ 8d - 8d = 16 - 7
➝ 0 = 9
It has no solution.C.)
➝ 5d + 15 = 15
➝ 5d = 15 - 15
➝ 5d = 0
➝ d = 5/0
➝ d = 0
Solution is d = 0D.)
➝ 2(d + 6) = -2d - 12
➝ 2d + 12 = -2d -12
➝ 2d + 2d = -12 -12
➝ 4d = 24
➝ d = 24/4
➝ d = 6
Solution is d = 6Hence,
(Option B) 8d + 7 = -4(-2d - 4) has no solution.the eye of a hurricane is a relatively calm circular region in the center of the storm the diameter of the eye is typically about 20 miles. If the eye of a hurricane is 20 miles in diameter, what is the area of the land that is underneath the eye? answer in square miles
Answer:
A= 314.159 m2
Step-by-step explanation:
Simple Give Brainliest Please
ans this please i have alot this to do help me
Answer:
3.1
Step-by-step explanation:
ok so, 3.14 rounded to the nearest tenth is 3.1
also, keep this in mind
if it is 5 and up it will be able to round up but if it is 4 round it down
how do i multiply 30 by -20
Multiplication of a positive number and negative number
⇒ is like any other multiplication
30 * -20 = 30 * ((-1) * 20) = 30 * -1 * 20 = (-1) * 600 = -600
Hope that helped!