[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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Divide and simplify the answer to lowest terms. Write the answer as a fraction or a whole number.
17/10 ÷ 11/4
17/10 ÷ 11/4=______?
When you divide by a fraction, flip the second fraction over and change divide to multiply:
17/10 / 11/4 = 17/10 x 4/11
Now multiply straight across:
(17 x 4) / (10 x 11) = 68/110
Simplify:
68/110 = 34/55
Answer: 34/55
i know how to solve it but i’m just not used to the bigger numbers. could someone still walk me through step by step?
[tex]\cfrac{42}{70}~~ = ~~\cfrac{u}{55}\implies \cfrac{(14)3}{(14)5}~~ = ~~\cfrac{u}{55}\implies \cfrac{3}{5}=\cfrac{u}{55}\implies \cfrac{3(55)}{5}=u \\\\\\ 3\cdot \cfrac{55}{5}=u \implies 3\cdot 11=u\implies 33=u[/tex]
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.
what is probability scale to the sea will disapper
Beryllium-li decomposes into boron-li with a half-life of
13.8 seconds. How long will it take 2400 g of beryllium-il
to decompose into 75 g of beryllium-il? (3 marks)
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &75\\ P=\textit{initial amount}\dotfill &2400\\ t=seconds\\ h=\textit{half-life}\dotfill &13.8 \end{cases} \\\\\\ 75=2400\left( \frac{1}{2} \right)^{\frac{t}{13.8}}\implies \cfrac{75}{2400}=\left( \frac{1}{2} \right)^{\frac{t}{13.8}}\implies \cfrac{1}{32}=\left( \frac{1}{2} \right)^{\frac{1}{13.8} t}[/tex]
[tex]\log\left( \cfrac{1}{32} \right)=\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8} t} \right]\implies \log\left( \cfrac{1}{32} \right)=t\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8}} \right] \\\\\\ \cfrac{\log\left( \frac{1}{32} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8}} \right]}=t\implies \cfrac{\log\left( \frac{1}{32} \right)}{\log\left[ \sqrt[13.8]{\frac{1}{2}} \ \right]}=t\implies 69\approx t[/tex]
Type your answer in the box. You may use numbers, a decimal point (.), and/or a negative sign (-) in
your answer.
In one design being considered for the container shaped like a cylinder, the container will have a height
of 12 inches. What will be the radius of the container, to the nearest tenth of an inch?
The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies.
Note
C
D
E
F
G
A
B
Frequency(Hz)
261.6
293.7
329.6
349.2
392.0
440.0
493.9
Determine the ratio of the note E to middle C.
a.
1.1224
c.
1.434
b.
1.2599
d.
1.3454
Answer:
b. 1.2599
Step-by-step explanation:
The ratio of the two frequencies is found by dividing the first by the second.
__
(Freq of E)/(Freq of C) = 329.6/261.6 = 1.2599
a=[4 -7 3 -2] find the determinant
Answer:
13
Step-by-step explanation:
[tex]\text{determinant of A} =\begin{vmatrix}4&-7\\ 3&-2\end{vmatrix}[/tex]
[tex]\text{determinant of A} =\left( 4\times \left( -2\right) \right) -\left( 3\times \left( -7\right) \right)[/tex]
[tex]\text{determinant of A} =-8+21=13[/tex]
julia help the teacher clean the tables in the classroom she notices that 1/4 of the tables are blue and 3/4 of the table are red. there are 8 tables in all how many are red?
The fraction illustrates that there are 6 red tables.
How to calculate the fraction?Fron the information, Julia helps the teacher clean the tables in the classroom she notices that 1/4 of the tables are blue and 3/4 of the table are red.
Therefore, the numbers that are red will be:
= Fraction of red × Total number
= 3/4 × 8
= 6
Therefore there are 6 red tables.
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Compound Shapes
Find the area of each figure, round your answer to one decimal place if necessary
12 ya
30
1)
3)
2)
3
12 yd
18
12 ya
3
20 yd
24
Area
Area
Area
4)
5)
6)
17 cm
4 cm
7.5 m
8 orn
12 cm
10 m
5 m
Area:
Area:
Area:
9)
7)
8)
35 m
3.5 m
20 in
TO in
18 in
21 m
21 in
18 in
20 in
3.5 m
21 m
Area:
Area:
Area:
Applying the formula for areas of rectangle, triangle, & circle, area of each figure is:
1. 27
2. 537.9
3. 384
4. 168.5
5. 96.3
6. 73.1
7. 357.1
8. 1,029
9. 744
What is the Area of a Circle?Area of a circle = πr², where r is its radius.
What is the Area of a Rectangle?Area of a rectangle = length × width
What is the Area of a Triangle?Where b is the height and b is the base length, area of triangle = 1/2bh.
What is the Area of a Square?Area = s², where s is the side length.
1. Area of the figure = area of square + area of rectangle = s² + length × width
Area of the figure = 3² + 6 × 3 = 27 ft²
2. Area of the figure = area of circle + area of rectangle = πr² + length × width
Area of the figure = π(7²) + 24 × 16 = 537.9 ft²
3. Area of the figure = area of smaller rectangle + area of bigger rectangle
Area = 12 × 12 + 20 × 12 = 384 yd²
4. Area of the figure = area of 1/2circle + area of triangle = 1/2πr² + 1/2bh
Area of the figure = 1/2π(8²) + 1/2(8)(17) = 168.5 cm²
5. Area of the figure = area of rectangle + area of triangle = (l)(b) + 1/2bh
Area of the figure = (10)(7.5) + 1/2(7.5)(5) = 96.3 m²
6. Area of the figure = area of 1/2circle + area of triangle = 1/2πr² + 1/2bh
Area of the figure = 1/2π(4²) + 1/2(8)(12) = 73.1 cm²
7. Area of the figure = area of 1/2circle + area of rectangle = 1/2πr² + 1/2bh
Area of the figure = 1/2π(10²) + (20)(10) = 357.1 in.²
8. Area of the figure = area of rectangle + area of triangle = (l)(b) + 1/2bh
Area of the figure = (35)(21) + 1/2(28)(21) = 1,029 m²
9. Area of the figure = area of square + area of rectangle = s² + length × width
Area of the figure = 18² + 21 × 20 = 744 in.²
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Maren is completing a wood working project. She needs 90 feet of wood. She has 8 pieces of wood that are each 6.2 feet long in her garage. How much more wood will she need to complete the wood working project?
Answer:
She needs 40.4 feet of wood.
Step-by-step explanation:
➾ She had 8 pieces of wood that are 6.2 feet each, so total length of wood she had = 8×6.2
= 49.6feet.
➾She needs total 90feet. of wood and she had already 49.6 feet of wood.
So, now wood she needed = 90-49.6
= 40.4feet.
____________________________
Hope it helps you:)
Answer:
She needs 40.4 feet of wood
Step-by-step explanation:
Given :-
Maren has 8 piece of wood which are 6.2 feet longShe needs total 90 feet of woodTo find:-
How much wood will she need moreSolution:-
Amount of wood she needs more :-
Wood she wanted to complete project — Wood she already have
by putting the value ,
90 feet — 8 × 6.2 feet
= 40.4 feet
Write the rate in lowest terms.
A printer can print 14 pages in 56 sec.
The rate in lowest terms is ______ ?
Answer:
1 page in 4 sec.
Step-by-step explanation:
To find the rate in lowest terms, divide the 14 pages by 56 seconds and find the simplest fraction.
14/56 = 1/4 in simplest terms.
This means the rate is 1 page in 4 seconds.
Which expression is equivalent to 20 + 8y − 9y − 21
Answer:
-y-1
Step-by-step explanation:
3/11 x 4/9 fraction multiplication
pls help
Answer:
[tex] \frac{1}{9} [/tex]
Step-by-step explanation:
[tex] \frac{3}{11} \times \frac{4}{9} [/tex]
[tex] \frac{12}{108} [/tex]
[tex] \frac{1}{9} [/tex]
Find the area of the square.
pls help!!
Answer:
Area of square: 9/16 m²
Step-by-step explanation:
We are given:
Side length of square: 3/4 metersThe area of the square is the side multiplied by the same side. Therefore,
⇒ Area of square: (3/4) × (3/4)⇒ Area of square: (3/4)²Using the exponents property, [(a/b)² = (a²/b²)]:
⇒ Area of square: (3²/4²)⇒ Area of square: (9/16) m²Therefore, the area of the square is 9/16 m².
Answer:
[tex]\huge\boxed{\bf{Area_{square} = \frac{9}{16}m^2}}[/tex]
Step-by-step explanation:
Given : -
Slide length of square = [tex]\frac{3}{4}[/tex]m.To Find : -
Area of squareAns : -
$\sf \to Area_{square} = (side\:length)^2$
$\sf \to Area_{square} = (\frac{3}{4}m)^2$
$\sf \to Area_{square} = (\frac{3}{4}m*\frac{3}{4})$
$\sf \to Area_{square} = (\frac{3*3}{4*4}m^2)$
$\sf \to Area_{square} = \frac{9}{16}m^2$
[tex]\:[/tex]
$\huge\colorbox{skyblue}{BlackPain}$
Find the next two numbers in the sequence 5,2,-1,…
Answer:
The answer is (-4) and (-7).
Step-by-step explanation:
Given;a₁ = 5a₂ = 2a₃ = (-1)To Find;a₄ = ?a₅ = ?Formula;aₙ = a + (n – 1) × dNow, for common difference (d)
d = a₂ – a₁ = 2 – 5 = -3
d = a₃ – a₂ = (-1) – 2 = -3
Here, common difference is same everywhere.
So, for fourth term or n = 4
aₙ = a + (n – 1) × d
a₄ = 5 + (4 – 1) × (-3)
a₄ = 5 + 3 × (-3)
a₄ = 5 – 9
a₄ = -4
Then, for fifth term or n = 5
a₅ = 5 + (5 – 1) × (-3)
a₅ = 5 + 4 × (-3)
a₅ = 5 – 12
a₅ = -7
Thus, The fourth term is (-4) and fifth term is (-7).
Find the distance between the two points in simplest radical form.
(9,-1,) and (3,3)
x1 = 9, x2 = 3
y1 = -1, y2 = 3
By using Distance formula[tex] \sqrt{ {(x2 - x1) + (y2 - y1)}^{2} } \\ \\ \sqrt{ {(3 - 9)^{2} + (3 - ( - 1))}^{2} } \\ \\ \sqrt{ {( - 6)}^{2} + {(4)}^{2} } \\ \\ \sqrt{ 36 + 16 } \\ \\ \sqrt{52} \\ \\ 7.21 \: units[/tex]
Hope it helps2) Which situation ONLY describes a purchase made with a credit card?
A) Natalie purchased a new computer with her card. The money came straight out of her checking account
B) Jackie loves using her card to make purchases because it is convenient to use, and she doesn't have to carry cash
David paid for dinner with his card. Each time he uses this card his checking account decreases by the purchase amount
D) Maggie took her mother to the movies and paid for it with her card. This charge appeared on a bill she received two weeks later,
Answer:
D is the correct answer. This charged appeared on a bill
Having trouble with the question!
Answer:
C) [tex]6r^2-9r-6[/tex]
Step-by-step explanation:
Open the parentheses, you get:
[tex]-3r^2-2r-4+9r^2-7r-2[/tex]
Then combine like terms:
[tex]-3r^2+9r^2=6r^2\\-2r-7r=-9r\\-4-2=-6\\[/tex]
Then right as a polynomial:
[tex]6r^2-9r-6[/tex]
So the answer would be C)
Answer:
6r² - 9r - 6
Step-by-step explanation:
(-3r² - 2r - 4) - (-9r² + 7r + 2)
Multiply to remove the parenthesis:
(-3r² - 2r - 4) - (-9r² + 7r + 2)
1(-3r² - 2r - 4) - 1(-9r² + 7r + 2)
1(-3r²) +1(-2r) + 1(-4) + -1(-9r²) + -1(7r) + -1(2) <== remember that multiplying 2 negatives, makes a positive
-3r² - 2r - 4 + 9r² - 7r - 2
Combine any like terms:
-3r² - 2r - 4 + 9r² - 7r - 2
6r² - 9r - 6 <== make sure that your answer is in Standard form (in decreasing degrees)
Hope this helps!
What is a major difference between parallel lines and perpendicular lines?
Answer:
Parallel lines never intersect. Perpendicular lines are lines that intersect.
Step-by-step explanation:
Hope this helps.
Answer:
Perpendicular lines meet at a 90 degree angle while parallel lines will never touch
Step-by-step explanation:
You are a teller at a bank. A customer has $252 in their checking account. They write a check for $287 (debit) that is cashed by the recipient . Will the new balance be positive or negative?
Please help me with this! God bless you
Answer:
1. The wind has blown all the leaves off the tree.
2. All the leaves have fallen to the ground.
3. My kite is being flown in the wind.
4. A shower of acorns have fallen from the sky
5. A busy squirrel dug for his acorns.
6. In the garden, pumpkins have grown.
7. Yesterday my friend and I rode to the park.
8. We have rode to the skate park.
9. My brother wrote me a letter.
10. He has written a essay.
11. Our neighbor had given us a pie.
12. Mom and Dad have spoken to me about cleaning my room.
Step-by-step explanation:
Identify the quotient in the form of a + bi.
1 + 6 divided by
−3 + 2i
The quotient of the expression in form of a + bi is 9/13 - 20/13i
Rationalizing complex expressionsGiven the following expressions
1+6i/-3+2i
Rationalizing the given rational complex number, we will have;
= 1+6i/-3+2i * -3-2i/-3-2i
= (1+6i)(-3-2i)/9+4
= -3-2i-18i-12i²/13
Simplify the result to have:
= -3+12-20i/13
= 9-20i/13
Express in the form a + bi
9/13 - 20/13i
Hence the quotient of the expression in form of a + bi is 9/13 - 20/13i
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The midpoint of AB is M(6,2). If the coordinates of A are (4,8), what are
the coordinates of B?
★ Given that,
The midpoint of AB is M(6 , 2)The coordinates of A are (4 , 8)★ To calculate,
Coordinates of point B?So here we would be using the formula of calculating the midpoint of two points.
Midpoint of two points:-
[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]★ We have :
x1 = 4 y1 = 8★ Putting the values :
Refer to the attachment.★ Therefore,
Coordinates of the point B is (8 , -4)Additional Information :★ Centroid of a triangle :-
[tex]\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar[/tex]★ Distance Formula :-
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]A company sells confetti in boxes in the shape of a triangular
pyramid. Each box contains a volume of 240 cubic centimeters of confetti, If
the height of the box is 15 centimeters, which of the following
could be the area of the base of the box?
Volume Formula:
V number:
h of the 3-D shape number:
Answer:
who is William afton family?
4 pounds of apples cost $6. how much will 6 pounds cost
Answer:10 bucks
Step-by-step explanation:
have a good day
You have been selected by the members of White House to participate in a one-mile race (1 mile = 5,280 feet) on Sports Day. Another student from Blue House will race against you. You know from some trials in PE that you run at an average rate of 12 feet per second. Since the student from Blue house runs 10 feet per second, you have been asked to let him have a 1000-ft. head start.
If both of you maintain the estimated rates, would you be able to beat your opponent in the one-mile race?
REASONING: If both of you maintain the estimated rates, would you be able to beat your opponent in a one-mile race?
Answer:
Blue wins
Step-by-step explanation:
Blue runner 4280 ft / 10 ft/sec = 428 sec to finish
Red 5280 / 12 = 440 sec Blue will win
Need help ASAP due today! I will give brainlisted for correct answer!
Answer: 15.
Step-by-step explanation: To find the slope, you need to use rise/run which is done below if you need a visual look at what I'm saying. Before we use rise/run, we need two points on the line. We'll use (2, 80), and (6, 140). We need to go 60 up and 4 to the right to make the points meet. Going up or down is the rise and left or right is the run. Our rise/run is 60/4 or 15 when you divide. Therefore, 15 is your slope for this equation of a line.
Have a great day! :)
I need help please
Answer:
48
Step-by-step explanation:
180 is the whole thing
So add 25 and 107 to make 132, then 180-132
There are 110 calories per 28.4 grams of Cereal X. Find how many calories are in 39.76 grams of this cereal
Step-by-step explanation:
28.4 g there are 110 calories
1 g there are 110/28.4 = 3.87 calories
39.76 g there are 3.87 × 39.76 = 153.87
