Answers
Answer:
[tex]81+144i[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i[/tex]
Recall that:
[tex]\displaystyle \sqrt{-a} = i\sqrt{a}[/tex]
Therefore:
[tex]\displaystyle \begin{aligned} (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i & = (-3i\sqrt{81})(-5+i\sqrt{9})+9i \\ \\ &= -(3i(9))(-5+i(3))+9i \\ \\ & = -27i(-5+3i)+9i \\ \\ & = 135i -81i^2 + 9i \\ \\ & = 144i - 81i^2 \\ \\ & = 81+144i\end{aligned}[/tex]
Note that i² = -1.
In conclusion:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9})+9i = 81 + 144i[/tex]
Related Questions
Helpppp pleaseeeeee!!!
Answers
Answer: yes.
Step-by-step explanation:
Answer: Yes
The roll of the dice is a random process that Jon has no control over (this is assuming the dice is fair of course). Whoever is selected first is not selected again, so the probability for the second selection will increase as there is a smaller pool of people to pick from.
Which system of linear inequalities is represented by
the graph?
Oy> x-2 and y < x + 1
O y< x-2 and y > x + 1
Oy x + 1
O y > x-2 and y < x + 1
Answers
Answer:
The correct option is;
y < x - 2, and y > x + 1
Step-by-step explanation:
The given graph of inequalities is made up of parallel lines. Therefore, the slope of the inequalities are equal
By examination of the graph, the common slope = (Increase in y-value)/(Corresponding increase in x-value) = (0 - 1)/(-1 - 0) = 1
Therefore, the slope = 1
We note that the there are three different colored regions, therefore, the different colored regions opposite to each inequalities should be the areas of interest
The y-intercept for the upper bounding linear inequality, (y >) is 1
The y-intercept for the lower bounding linear inequality, (y <) is -2
The two inequalities are y > x + 1 and y < x - 2
The correct option is y < x - 2, and y > x + 1.
The system of linear inequalities is represented by the graph is y> x-2 and y < x + 1
Inequalities is an expression that shows the non equal comparison of two or more variables and numbers.
Given that:
y and x are variables, plotting the inequalities using geogebra online graphing tool.The system of linear inequalities is represented by the graph is y> x-2 and y < x + 1
Find out more on linear inequalities at: https://brainly.com/question/21103162
last one hopefullly hahah
Answers
you are correct. all angles (except central) are not equal (iff TU and CB are not parallel)
the triangles are not similar
Answer:
it's A
They don't give you enough information to determine if they are similar or not
An average person's hair grows at a rate of 19cm per year how fast in inches per month does the average person hair grow in conversion factor round you answer to the nearest tenths
Answers
Answer:
Around 1.6 cm per month
Step-by-step explanation:
We can set up a proportion to find how much the hair grows per month. It's important to note that there are 12 months in a year, so we can represent a year as 12 months.
[tex]\frac{19}{12} = \frac{x}{1}[/tex]
We can now cross multiply:
[tex]19\cdot1=19\\\\19\div12=1.58\overline{33}[/tex]
1.58333... rounds to 1.6.
Hope this helped!
3m-2-5n+p terms and coefficients
Answers
Answer: Answers are in the steps.
Step-by-step explanation:
The coefficients are 3, -5, and 1
The terms are, 3m, -2,-5n and p
A personal trainer keep track of the number of minutes each of his 20 clients exercise on the treadmill and the number of calories each client burned during that time removing. which TWO of these data points will cause the correlation coefficient to decrease the most?
A). Data point A
B). Data point B
C). Data point C
D). Data point D
Answers
Answer:
Data Point B and Data point E
Step-by-step explanation:
Data point B and data point E are the farthest and are more distant away from the best line of fit compared to other data points. The more clustered data points are, the more the correlation that exists between the variables in question.
Therefore, data point B and data point E, will cause the correlation coefficient to decrease the most.
There are 9 classes of 25 students each, 4 teachers, and two times as many chaperones as teachers.
Each bus holds a total of 45 people.
What is the least number of buses needed for the field trip?
Answers
5 buses is the answer pls mark me brainliest
Least number of bus require for trip = 5 buses
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
Total number of classes = 9
Number of student in each class = 25
Number of teacher = 4
Number of chaperones = Double of teacher
Bus hold = 45 people
Now,
Total number of student = 9 × 25
= 225
Number of chaperones = 4 × 2
= 8
Total people = 225 + 8 + 4
= 237
Least number of bus require for trip = Total people / Bus hold
= 237 / 45
= 5.266
Learn more about unitary method here:
https://brainly.com/question/22056199
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divide the sum of -5,-10 and -9 by the product of 2 and -3
Answers
Answer: 1/4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
=(-5)+(-10)+(-9)/2*(-3)
=-5-10-9/-6
=-24/-6
=4 ans.....
Please please please please help
Answers
Answer:
m = 9
Step-by-step explanation:
8/12 = 6/m
8m = 72
m = 9
m=9
Working out:
12÷8=1.5
6x1.5=9
Let me know if you need an explanation.
Hope this helps :)
Un cultivo de bacterias crece y se duplica cada dos horas .¿Cu`antas veces mas grande sera el numero de bacterias en 12 horas?El numero inicial es X. Expresa usando potencias ayuda profis es para hoy ; )
Answers
Responder:
64 visitas
Explicación paso a paso:
Dado lo siguiente:
Número inicial de bacterias = x
Tasa de crecimiento = se duplica cada dos horas
¿Cuántas veces mayor será la cantidad de bacterias en 12 horas?
La cantidad de veces (n) en las que la cantidad de bacterias se duplica:
n = 12 horas / período de tasa de crecimiento
n = 12/2 = 6
Eso significa que el crecimiento de bacterias se duplicará 6 veces en 12 horas.
Por lo tanto, la cantidad de bacterias después de 12 horas será:
Después del 1er período = x * 2 = 2x
2do período = 2 ^ 2 * x = 4x
Después de n período
= 2 ^ n * x
Después de 6 períodos:
2 ^ 6 * x = 64x
Número de veces que las bacterias serán mayores en 12 horas:
Inicial = final
x = 64x
Comparando ambos
Las bacterias serán 64 veces más grandes después de 12 horas.
A delivery truck company just bought a new delivery truck and they need to know the maximum volume it can carry. In the front of the truck, there is an extra ledge that sticks out over the driver's cab for extra storage space. What is the maximum amount of cargo that can fit into the new truck?
Answers
Answer:
The answer is below
Step-by-step explanation:
To find the maximum amount of cargo the truck can carry, we need to find the volume of the truck.
Volume = length × width × height.
Firstly 1 feet (1') = 12 inches (12"),
For the extra ledge that sticks out, the height = 7'8" = 7.667 feet, the width = 16'9" - 14'3" = 16.75 - 14.25 = 2.5 feet, the length = 2'7" = 2.583 feet
Volume of extra ledge = length × width × height = 2.583 × 2.5 × 7.667 = 49.5 feet³
For the truck, the height = 7'8" = 7.667 feet, the length = 14'3" = 14.25 feet, the width = 6'6" = 6.5 feet
Volume of truck = length × width × height = 14.25 × 6.5 × 7.667 = 710.16 feet³
The maximum volume = volume of extra ledge + volume of truck = 49.5 + 710.16 = 759.66 feet³
4.
Aliyah, Brenda and Candy share a sum of money in the ratio of 3:5:6. After
Candy gives $100 to Aliyah and $50 to Brenda, the ratio becomes 2 : 3:3.
(a) Suppose Aliyah has $3x at the start, express Candy's initial sum of money in
terms of x.
(b) Find the value of x.
(c) Hence, how much money does Brenda have in the end?
Answers
Answer:
(a) Candy's initial sum as a terms of x is $6x
(b) x = $60
(c) $350
Step-by-step explanation:
The given parameters are;
The ratio in which Aliyah, Brenda and Candy share the sum of money = 3:5:6
The amount Candy later gives Aliyah = $100
The amount Candy later gives Brenda = $50
The new ratio of the sum of the shared money between Aliyah, Brenda and Candy = 2:3:3
(a) Whereby Aliyah has $3x at the start, we have;
Total sum of mony = Y
Amount of Aliyah's initial share = Y × 3/(3 + 5 + 6) = Y×3/14
Therefore, Y×3/14 = $3x
x = Y×3/14 ÷ 3 = Y/14
Amount of Candy's initial share = Y × 6/14
Therefore Candy's initial sum as a terms of x = $6x
(b) Given that Aliyah's and Candy's initial sum as a function of x are $3x and $6x, therefore, in the ratio 3:5:6, Brenda's initial sum as a function of x = $5x
Which gives;
Total amount of money = $14x
With
6x - 150, 3x + 100, and 5x + 50, the ratio =is 2:3:3
Therefore, we have;
14·x × 2/(2 + 3 + 3) = (6·x - 150)
14·x × 2/(8) = (6·x - 150)
14·x × 1/4 = (6·x - 150)
7·x/2 = (6·x - 150)
12·x - 300 = 7·x
12·x - 7·x = 300
5·x = 300
x = $60
(b) The final amount of money with Brenda = 5x + 50 = 5 × 60 + 50 = $350
The final amount of money with Brenda = $350.
solve for x and y plz 12x - 5y = -20 x + 4 = y
Answers
Answer:
(0,4)
Step-by-step explanation:
System of Equations:
[tex]\left \{ {{12x-5y=-20} \atop {x+4=y}} \right.[/tex]
x= y-4 .... Change format so you can substitute to first equation
12(y-4)-5y=-20 .... Plug in x= y-4 to first equation
12y - 48 -5y = -20 ..... Distributed
7y -48 =-20 .... Added like terms
7y=28 .... Added 48 to both sides
y=4
.... Plug y into the second equation to find x
x + 4=y
x +4 = 4 .... Plugged in y
x = 4-4 .... Subtracted 4 from both sides
x=0
Your answer is (0,4)
Hope this helps:)
The pepper plant has 2/3 as many fruits on it as the tomato plant has. The tomato plant has 9 fruits on it. How many fruits does the pepper plant have on it?
Answers
Answer:
The pepper plant has 15 fruits on it.
Step-by-step explanation:
Let the tomato plant have x plants. Let the pepper plant have y plants. Since the pepper plant has 2/3 more fruits on it than the tomato plant, we have that y - x = 2x/3
collecting like terms,
y = 2x/3 + x
The above is the number of plants the pepper plant has.
y = 2x/3 + x
y = (2x + 3x)/3
y = 5x/3
Since x = number of fruits on tomato plant = 9, then
y = 5x/3
y = 5(9)/3
y = 5 × 3
y = 15
Since y = number of fruits on pepper plant = 15
So, the pepper plant has 15 fruits on it.
Simplify the following: a) [ -6 +22 – 6 + 8 ] ÷ ( -9 ) b) 400 ÷ { 40 – (-2) -3 – ( -1)} c) 40 x -23 + 40 x -17 d) 1673 x 99 – (-1673) e) 490 x 98
Answers
Step-by-step explanation:
a) [ -6 +22 – 6 + 8 ] ÷ ( -9 )[ -6 +22 – 6 + 8 ] = 18
18 ÷ (-9) = -2
b) 400 ÷ { 40 – (-2) -3 – ( -1)}{40 – (-2) -3 – ( -1)} = { 40 + 2 -3 + 1} = 40
400 ÷ 40 = 10
c) 40 x -23 + 40 x -17(40 x 23) + (40 x -17)
920 + (-680)
= 240
d) 1673 x 99 – (-1673)(1673 x 99) + 1673
1673 x 100
= 167300
e) 490 x 98 = 48020Hope this helps ^-^
what is the sum of the interior angles of a regular hexagon
Answers
Answer:
see below
Step-by-step explanation:
The sum of the interior angles of any polygon can be found with the formula 180(n - 2) where n = number of sides. In this case, n = 6 so the answer is 180(6 - 2) = 180 * 4 = 720°.
Answer:
The sum of the interior angles of a regular hexagon is 720°
Step-by-step explanation:
As we know that the sum of interior angle is 180(n-2). So the number of sides of hexagon is 6. Now, 180(6-2)=180*4=720°
The amount of juice in a container is
normally distributed with a mean of
70 ounces and a standard deviation of
0.5 ounce. What is the probability that a
randomly selected container has more
than 70.5 ounces of juice?
Answers
Answer:
0.15866
Step-by-step explanation:
To solve for the above question, we use z score formula
z = (x - μ) / σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question,
x is the raw score = 70.5
μ is the population mean = 70
σ is the population standard deviation = 0.5
z = 70.5 - 70/ 0.5
z= 0.5/0.5
z = 1
We used the z score table to find the probability of z = 1
P( x = z) = P(x = 70.5)
= P( z = 1) = 0.84134
Hence, the probability that a randomly selected container has more than 70.5 ounces of juice is calculated as
P(x>70.5) = 1 - P(x =70.5)
P(x>70.5) = 1 - 0.84134 = 0.15866
Therefore, the probability that a randomly selected container has more than 70.5 ounces of juice is 0.15866.
Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.
Answers
Answer:
[tex]AC=20[/tex]
Step-by-step explanation:
The line segment AC is the entire length of the line. Within this segment, point B is found.
Point B, in a way, splits the segment into two, creating the segments AB and BC.
To find the length of AC, add the lengths of the lines AB and BC together:
[tex]AB=11\\BC=9\\AB+BC=AC\\11+9=AC\\20=AC[/tex]
The length of AC is 20.
:Done
Answer:
20 units.
Step-by-step explanation:
Segment AC is broken into two parts by point B. That means that the length of segment AB plus the length of segment BC equals the length of segment AC.
If BC = 9, and AB = 11, AC = 9 + 11 = 20 units.
Hope this helps!
Which of these relations are functions?
х
O
-2 6 2 -6
-5 21 15-15
y
11
y
4
2
O
x
4
-2
4
o
{(-5,-7), (-2,-7), (7,17), (-5,21)}
y
Answers
For each value of y, the number of value of x must be one. Then the correct options is D.
The complete question is attached below.
What is relation function?The relation function is given as, for every independent value, there is a dependent value.
Let the function be y = f(x).
For each value of x, the number of value of y may one or two.
But for each value of y, the number of value of x must be one.
Then the correct options is D.
More about the relation function link is given below.
https://brainly.com/question/2253924
#SPJ1
Find the perimeter of this figure. (Image down below)
Answers
Answer:
The answer is
44 ftStep-by-step explanation:
The figure above is a rectangle
To find the perimeter of a rectangle we use the formula
Perimeter of a rectangle = 2l + 2w
where
l is the length of the rectangle
w is the width of the rectangle
From the question
length = 14 ft
width = 8ft
Substituting the values into the above formula we have
Perimeter = 2(14) + 2(8)
= 28 + 16
We have the final answer as
Perimeter = 44 ftHope this helps you
a farmer has 40 4/5 of beans 3/4 of the beans are pinto beans how many pounds of pinto bean are there
Answers
Answer: Amount of pinto beaks [tex]=30\dfrac{3}{5}\text{ pounds}[/tex]
Step-by-step explanation:
Given: Amount of beans a farmer has = [tex]40\dfrac{4}{5}\text{ pounds}=\dfrac{40\times5+4}{5}\text{ pounds}[/tex]
[tex]=\dfrac{204}{5}\text{ pounds}[/tex]
Also, [tex]\dfrac{3}{4}[/tex] of the beans are pinto beans .
Amount of pinto beaks = [tex]\dfrac 34\times[/tex] (Amount of beans a farmer has)
= [tex]\dfrac34\times\dfrac{204}{5}=\dfrac{153}{5}\text{ pounds}[/tex]
[tex]=30\dfrac{3}{5}\text{ pounds}[/tex]
Amount of pinto beaks [tex]=30\dfrac{3}{5}\text{ pounds}[/tex]
A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?
Answers
Answer:
y = -x +2
Step-by-step explanation:
y =x has a slope of 1
Perpendicular lines have slopes that multiply to -1
m* 1 = -1
The slope of the perpendicular line is -1
We have a slope and a point
y = mx+b
y= -1x+b
Substitute the point into the equation
-3 = -1(5) +b
-3 =-5 +b
Add 5 to each side
-3+5 = b
2 =b
y = -x +2
I answered all my work correctly but I don’t understand this one.
Answers
Q (0-2), (-1-1)
= (-2,-2)
D (-2-2), (2-1)
= (-4, 1)
V (2-2), (4-1)
= (0,3)
J (3-2), (0-1)
= (1,-1)
You can also draw it on a graph and then translate all coordinates 2 units left and 1 down to see the end results.
PLEASE help me with this question!!! REALLY URGENT!
Answers
Answer:
B
Step-by-step explanation:
So we have a table of values of a used car over time. At year 0, the car is worth $20,000. By the end of year 8, the car is only worth $3400.
We can see that this is exponential decay since each subsequent year the car depreciates by a different value.
To find the rate of change the car depreciates, we simply need to find the value of the exponential decay. To do this (and for the most accurate results) we can use the last term (8, 3400).
First, we already determined that the original value (year 0 value) of the car is 20,000. Therefore, we can say:
[tex]f(t)=20000(r)^t[/tex]
Where t is the time in years and r is the rate (what we're trying to figure out).
Now, to solve for r, use to point (8, 3400). Plug in 8 for t and 3400 for f(t):
[tex]3400=20000(r)^8\\3400/20000=17/100=r^8\\r=\sqrt[8]{17/100}\approx0.8[/tex]
In other words, the rate of change modeled by the function is 0.8.
As expected, this is exponential decay. The 0.8 tells us that the car depreciates by 20% per year.
2 pts Question 1 Write an expression to model the phrase: Myles has $635 and is earning $120 each week as a lifeguard. (Use x as your variable) 2 pts Wuestion 2
Answers
Answer:
The equation is y= 120x+ 635Step-by-step explanation:
Hey there!!!,
in this problem we are expected to present an equation for the given scenario, and a way out is to model it after the equation of line
i.e y= mx+c
From the problem statement we can see that the constant amount Myles have is $635, and also earnings of $120 weekly.
Comparing the statement withe equation of line we have
y= 120x+ 635
as "x" is the number of weeks worked and $635 is the constant amount at hand.
Should you need further clarification on this, let me know
PLS HELP I WILL GIVE BRAINLIST AND A THANK YOU!!!!!!!! Pls help me :)
Answers
Answer:
67°
Step-by-step explanation:
CGE + AGC + AGG = 180 (angles on a straight line)
23°+90°+x=180°
x=67°
For the function f(x) = -12x + 7, find the
matching value for x when f(x) = 17. Write
your answer as a fraction.
Answers
Answer:
[tex]\large\boxed{x=-\frac{5}{6}}[/tex]
Step-by-step explanation:
f(x) is the same value as y. Therefore, y = 17. We can place this into slope intercept form (except with a defined value for y) and solve for x.
Start by subtracting 7 from both sides. Then, divide by -12 to solve for x. Finally, simplify the fraction.
17 = -12x + 7
10 = -12x
-10/12 = x
-5/6 = x
[tex]\large\boxed{x=-\frac{5}{6}}[/tex]
find the multiplicative inverse of 3 by 4 minus 5 by 7
Answers
Answer:
28
Step-by-step explanation:
[tex]\frac{3}{4}-\frac{5}{7}[/tex]
Least Common Denominator of 4 & 7 is 4 * 7 = 28
[tex]\frac{3}{4}-\frac{5}{7}=\frac{3*7}{4*7}-\frac{5*4}{7*4}\\\\\\=\frac{21}{28}-\frac{20}{28}\\\\\\=\frac{21-20}{28}\\\\\\=\frac{1}{28}[/tex]
Multiplicative inverse of [tex]\frac{1}{28}[/tex] is [tex]\frac{28}{1} = 28[/tex]
4x
5.
If 7:5 = (x + 2y): (x - y), find the value of
5y
Answers
Answer:
5/2 OR 2.5
Step-by-step explanation:
( x + 2y ) = 7 , ( x - 2y ) = 5
x = 7 - 2y , x = 5 + 2y
substitute the two eqns together:
7 - 2y = 5 + 2y
7 - 5 = 2y + 2y
2 = 4y
y = 1/2
when y = 1/2 ,
5y = 5(1/2)
= 5/2 OR 2.5
A.) Pinky bought 1. 1/2 kg of apples and 5. 1/4 kg of mangoes 1. 1/2 kg of oranges. Find the total weight of fruits B.) if her family eats 3/4 kg of apples and 2. 1/2 kg of mangoes and 1/2 kg of oranges. Find the weight of fruits left (Please say the answer with explanation who says the answer first I will mark them as the brainliest)
Answers
Answer:
A. Total weight of the fruits is 2.25 kg
B. There are no more fruits left.
Step-by-step explanation:
A.
To get the total weight of the fruits, we will first of all have to sort out the fruits and multiply the weight of the fruits by the number available.
Weight of apples:
we have one 1apple weighing 1/2 kg. The weight will be 1 |X 1/2 = 1/2 kg
Weight of mangoes:
We have five mangoes weighing 1/4 kg. Total weight will be 5 X 1/4 = 5/4 kg
Weight of oranges:
We have one orange weighing 1/2 kg. Total weight will be 1X 1/2 = 1/2 kg
Total weight of the fruits will be total weight of Mangoes + oranges + apples
= 1/2 + 5/4 + 1/2 = 2.25kg
B.
If her family begins to eat off some portions of the fruits, we will have to calculate the sum total of all the weights of fruits eaten
The portion eaten will be 3/4 + (2 X 1/2) + 1/2 = 2.25kg
If this happens the family would have eaten all of the fruits because
the original weight present is only 2.25kg of fruits to start with
