the solution of the equation x²+27 = 0 is 3√3 i
What are real and imaginary roots ?
A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.
In other words real roots can be represented in a number line where as imaginary roots can not.
In order to determine the simplification, we have to know the rule of the imaginary numbers.
The imaginary numbers are the same than real numbers, but they add just one term more, which is :
√-1 = i
So, to implicate this term, we have to use the rules of the roots:
given equation is :
x²+27 = 0
solving for x by Subtracting 27 from both sides
x²+27 -27 = -27
x² = -27
To remove square root , take square root on both sides
√x² = √-27
x = √-27
The value of √-1 is 'i' therefore,
x = i√27
x =3√3 i
Therefore, The solution of the equation x²+27 = 0 is 3√3 i
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One of the fastest recorded speeds of an alligator on land is 8.8 m/s. Approximately, what is the speed in kilometers per hour?
The given speed is = 8.8 meter per second
To convert it in kilometer per hour, we will do the following steps:
1 meter = 0.001 km
So, 8.8 meter = 0.0088 km
3600 seconds = 1 hour
1 sec = [tex]\frac{1}{3600}[/tex] hours
now, [tex]\frac{8.8meter}{second} = \frac{0.0088}{\frac{1}{3600} }[/tex]
Now multiplying 0.0088 and 3600
[tex]0.0088*3600[/tex]
= 31.68 km/h
A recipe for chocolate chip cookie calls for 3 4 th of a cup of brown sugar to make 10 cookies how much brown sugar would be needed to make 48 cookies
Answer: 3.6 cups or 3 3/5 cups
Step-by-step explanation: what i would do here is set up a proportion. Change 3/4c to .75 cups as it’s easier to place in a proportion (and less confusing).. cross multiply .... (.75 x 48= 36) then divide 36 by 10 and that will give you x
pls help!! will give brainliest and 5star
Given the table of candy distibutions below, find P(not green), the probability of selecting anything but a green candy at random from a large bag
Answer: 0.84
Step-by-step explanation:
From the given table of probability distribution P (green)= 0.16
Since , the sum of all the probabilities of all the events in a particular probability distribution is 1.
Therefore, The probability of selecting anything but a green candy at random from a large bag is given by :-
[tex]\text{P(not green)=1-P(green)}\\\\\Rightarrow\text{P(not green)}=1-0.16\\\\\Rightarrow\text{P(not green)}=0.84[/tex]
Hence, the probability of selecting anything but a green candy at random from a large bag = 0.84
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jordan and sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up or the trip and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla only has enough to make 40 necklaces.
A) write two constraints to model the problem. let x represent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells.
B) can Sharla afford the down payment with the money she earns selling all of her necklaces? explain your answer.
Thank you
A) 25x+15y=650
25x+15(40)=650
Or it could be 25x=650 and 15y=650
B) No because she makes $15 for every necklace which she only has 40 necklaces 15x40=600
A) 25x+15y=650 i think its correct
ten minutes aftee a father left for work on the bus, he noticed that he had left his briefcase at home. His soj krft home driving 60 mph, to catch the bus that was traveling at 48 mph. How lonh did it take the son to catch the bus?
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About how many kilometers are in 0.5 light-years?
there are 9461000000000 kilometers in a light year, aka 9.5 trillion
divide it by 2, you get 4730500000000
Please help me!! You don’t need a number just an expression to find the variable
Solve for y. Note the equal sign. What you do to one side, you do to the other. Isolate the y. Do the opposite of PEMDAS.
First, subtract x from both sides
y²z + x (-x) = b (-x)
y²z = b - x
Next, divide z from both sides
(y²z)/z = (b - x)/z
y² = (b - x)/z
Finally, to fully isolate the x, root both sides
√(y²) = √((b - x)/z)
y = √((b - x)/z)
y = √((b - x)/z) is your answer
hope this helps
Michael washes the Gomez family’s cars once a month they pay him $25 every 3 months for his work at this rate how much will Michael earn in one year ?
So you need to see how many times they get paid in a year. 12 months ÷ by every 3= 4. So then you multiply the $25 by 4. Which equals $100.
Final answer:
Michael will earn $100 in one year by washing the Gomez family's cars, as he is paid $25 every 3 months and there are 4 three-month periods in a year.
Explanation:
The question involves calculating how much Michael will earn in one year from washing the Gomez family's cars. Since Michael is paid $25 every 3 months, we first determine how many 3-month periods are in one year. There are 4 such periods in a year (12 months ÷ 3 months = 4). Therefore, Michael will earn $25 for each of these 4 periods.
To find the total amount Michael will earn in one year, we multiply the amount he earns every 3 months by the number of 3-month periods in a year:
$25 per period × 4 periods per year = $100 per year
how can you use an array to show the commutative property
Arrays are useful representations of multiplication concepts of the commutative property.
We need to find how can you use an array to show the commutative property.
What is the commutative property?The word 'commutative' originates from the word 'commute', which means to move around. Hence, the commutative property deals with moving the numbers around. So mathematically, if changing the order of the operands does not change the result of the arithmetic operation then that particular arithmetic operation is commutative.
An arrangement of objects, pictures, or numbers in rows and columns is called an array. Arrays are useful representations of multiplication concepts (among other ideas in mathematics).
The commutative property of multiplication can be neatly illustrated using an array. For example, the array above could be read as 2 rows of 6, or as 6 columns of 2. Or the array could be physically turned around to show that 2 rows of 6 have the same number as 6 rows of 2.
Therefore, arrays are useful representations of multiplication concepts of the commutative property.
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If someone is 1.83 meters tall, what is his or her approximate height In inches
this person is approximately 72.0472441 inches tall because 1 meter is 39.3701 inches.
The length of the flat screen tv is 5 inches less than 3 times it's width. If the perimeter of the tv is 150 inches, find the dimensions
AS we don't know the width so let consider width=x inches
According to given condition
length = (3x -5) inches
TV screen is rectangular shaped so
Perimeter= 2( length +width) =2{(3x-5)+ (x)} equation 1
also given Perimeter = 150 inches equation 2
comparing equation 1 &2
2{(3x-5)+ (x)} =150
2{3x-5+x} =150
2{4x-5} =150
8x-10 =150
Adding 10 both sides
8x -10 +10 =150+10
8x=160
dividing 8 both sides
8x/8= 160/ 8
x= 20 inches width of screen.
length =( 3x-5) ={3(20) -5}
=60-5
length =55
If the The length of the flat screen tv is 5 inches less than 3 times it's width, and the perimeter is 150 inches, then the dimension of the TV screen = 55 inches by 20 inches
Let the length of flat screen tv be represented by L
Let the width of the flat screen tv be represented by W
Three times the width of the flat TV screen = 3W
The length of the flat screen tv is 5 inches less than 3 times it's width.
L = 3W - 5........................(1)
The TV screen is rectangular in shape
The perimeter of the TV screen is given by the formula:
P = 2(L + W)
The perimeter of the TV is 150 inches
P = 150 inches
150 = 2(L + W)
L + W = 150/2
L + W = 75..........(2)
Substitute equation (1) into equation (2)
3W - 5 + W = 75
Collect like terms
3W + W = 75 + 5
4W = 80
W = 80/4
W = 20
Substitute W = 20 into equation (1)
L = 3W - 5
L = 3(20) - 5
L = 60 - 5
L = 55
The width of the TV screen = 20 inches
The length of the TV screen = 55 inches
The dimension of the TV screen = 55 inches by 20 inches
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Which of the following is the correct graph of the compound inequality 4p + 1 > −11 or 6p + 3 < 39?
a number line with closed circles at negative 3 and 6 and shading in between.
number line with open dot at negative 3 with shading to the left and an open dot at 6 with shading to the right.
number line with open dots at negative 2 and 5 with shading in between.
number line with shading everywhere.
4p + 1 > -11 or 6p + 3 < 39
-1 -1 -3 -3
4p > -12 6p < 36
[tex]\frac{4p}{4} > \frac{-12}{4}[/tex] [tex]\frac{6p}{6} < \frac{36}{6}[/tex]
y > -3 y < 6
Graph: -3 o-------------------------o 6
None of the choices you provided are correct. If you meant to type in ≥ and ≤ instead of > and <, then the first answer is correct.
Answer: D
Step-by-step explanation:
Ursula is entering a bicycle race for charity. Her mother pledges $0.75 for every 0.5 mile she bikes. If Ursula bikes 17.5 miles, how much will her mother donate?
she will donate $26.25
Megan baby-sat this weekend. She earned $12 an hour plus an additional $32. If she made a total of $140, how long did she work for?
Megan worked for a total of 9 hours.
Explanation:To find how long Megan worked, we need to subtract the additional amount she earned from the total amount she made. Let's say she worked for x hours. Her earnings can be calculated using the equation:
12x + 32 = 140. Subtracting 32 from both sides, we get 12x = 108. Dividing both sides by 12, we find that x = 9.
Therefore, Megan worked for 9 hours.
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The ages of the people who came to a birthday party are shown below.
How does finding the square root of a number compare to finding the cube root of a number? Use the number 64 in your explanation
Answer:
The square-root of a number has 2 same factors being multiplied to get that number while a cubic-root of a number has 3 same factors being multiplied to get that number. For example, the square-root of 64 is 8 because 8 x 8 is 64. However, the cubic-root of 64 is 4 since 4 x 4 = 16 x 4 = 64.
Step-by-step explanation:
Finding the square-root of a number means finding two same numbers that when multiplied equal one number, while finding the cubic-root of a number means finding three same numbers that when multiplied equal one number. For example, the square-root of 64 is 8 because 8 x 8 is 64. However, the cubic-root of 64 is 4 since 4 x 4 = 16 x 4 = 64.
The square root of a number is found by multiplying it by itself, while the cube root is found by multiplying it by itself three times.
Explanation:Finding the square root of a number is the process of finding a number that when multiplied by itself gives the original number. For example, the square root of 64 is 8, because 8 x 8 = 64.
Finding the cube root of a number is the process of finding a number that when multiplied by itself three times gives the original number. For example, the cube root of 64 is 4, because 4 x 4 x 4 = 64.
So, the main difference is that the square root involves multiplying a number by itself once, while the cube root involves multiplying a number by itself three times.
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If the measure of one interior angle of a regular polygon is 144 degrees, find
the number of sides
The number of sides in the regular polygon is 2.
Explanation:To find the number of sides in a regular polygon, we can use the formula:
Number of sides = 360 degrees/measure of each interior angle
In this case, the measure of one interior angle is given as 144 degrees. Substituting this value in the formula, we get:
Number of sides = 360 degrees/144 degrees = 2.5
Since the number of sides cannot be a decimal, we round down the answer to the nearest whole number. Therefore, the number of sides of the regular polygon is 2.
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The number of sides of a regular polygon with each interior angle measuring 144 degrees is 10.
To find n, we can use the formula for the sum of interior angles of a polygon, which is (n-2) times 180 degrees.
Since we know that each angle measures 144 degrees in this regular polygon, we can set up the equation (n-2)times 180 degrees = n times 144 degrees.
Solving for n gives us:
n times 144 degrees = (n-2) times 180 degrees
n times 144 degrees = 180n - 360 degrees
180n - 144n = 360 degrees
36n = 360 degrees
n = 10.
PLEASE HELP!!!!WILL GIVE BRAINIEST TO WHOEVER ANSWERS
1. Suppose the path of a golf ball, in a chip shot from a small hill, follows the path graphed by the quadratic function ƒ(d) = –1.6d2 + 3.3d + 0.2 where d is the horizontal distance the ball travels, and ƒ(d) is the height, in meters, of the ball at d horizontal distance. Find the total horizontal distance the ball traveled while in the air.
A. 2.12 meters horizontally
B. 2.26 meters horizontally
C. 1.84 meters horizontally
D. 2.95 meters horizontally
2. Suppose the path of a golf ball, in a chip shot, follows the path graphed by the quadratic function ƒ(d) = –1.6d2 + 3.3d + 0.2 where d is the horizontal distance the ball travels, and ƒ(d) is the height, in meters, of the ball at d horizontal meters. Identify the domain and range that matches this situation.
A. Domain: [0,2.07] horizontal meters; range: [0, 1.72] vertical meters
B. Domain: [0,2.07] horizontal meters; range: [0, 1.72] vertical meters
C. Domain: [0,2.12] horizontal meters; range: [0, 1.90] vertical meters
D. Domain: [0,2.07] horizontal meters; range: [0, 1.72] vertical meters
1. First calculate the positive root of the quadratic using your preferred formula. I got a solution [tex]d = 1/32 (33 + \sqrt{1217})=2.121...[/tex]. That gives you the distance the ball traveled from d=0 (small hill). So the answer is A.
2. The domain is [0,2.121...]. The range is from 0 to the max height. The d for which the ball is the highest is given by the formula x = -b / 2a = -3.3/(-3.2) = 1.031... so the max is 1.902... So the range is [0,1.902...] So the answer is C.
Given:MO−→− bisects ∠LMNm∠LMO = 6x−20m∠NMO = 2x+36Solve for x and find m∠LMN.
X=14
Plug it back into both angles add it together and LMN = 128 degrees
linda has 24 students in her class and she wants each student to have 3 ice cream sandwiches if there are 12 sandwiches in each box how many boxes should she buy
24 x 3 = 72
72/12 = 6
She should buy 6 boxes.
Hope this Helps!!
6 boxes
24x3=72
72/12=6
Find The Slope Of The Line.
A.) -3/4
B.) 4/3
C.) -4/3
D.) 3/4
(0,1) and (4, -2)
Slope = (1 + 2)/(0 - 4) = -3/4
Answer
A.) -3/4
The answer is D. 3/4 because
Slope= Rise/run= 3/4
does the table represent an exponential function?
x 1 2 3 4
y -2 -12 -72 -432
a) yes
b)no
Yes this is an exponential function. One way we can determine this is to notice how each y term is multiplied by 6 to get the next y term
example: -2 times 6 = -12
another example: -12 times 6 = -72
The exponential function that models this data is y = -2*6^(x-1). Note how plugging in x = 1 leads to y = -2. Plugging in x = 2 leads to y = -12, and so on.
What are the ordered pairs of a line whose slope is 5, the y intercept is 3, the rise is 5, and the run is 1?
How do I solve this??
Two plus the quotient of a number and 8 is the same as 16. Answer it as a equation
Answer:
2 + n / 8 = 16
Step-by-step explanation:
Multiply through by 8
2*8 + n = 16*8 Combine factors
16 + n = 128 Subtract 16 from both sides
16 - 16 + n = 128 - 16 Combine terms
n = 12
Let's just get the right answer plz ppl
Answer:
[tex]\large\boxed{3xy^3}[/tex]
Step-by-step explanation:
[tex]\dfrac{9x^{-1}y^{-6}}{3x^{-2}y^{-9}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=3x^{-1-(-2)}y^{-6-(-9)}=3xy^3[/tex]
one day paul ran at a rate of 0.15 mile per minute for 40 minutes. the next day paul and Jen ran together at a rate of 0.16 mile per minute to 50 minutes. how far did paul run altogether
14 miles in all which is pretty fast
The change in the value of a stock is represented by the rational number -5.90 describe in words what this means
We are given : A stock is represented by -5.90.
The given number is a negative number.
Note: When a stock is given by a negative number, it represents the decrease in stock and when a stock is given by a positive number, it represents the increase in stock.
As we are given number is a negative number, we can just say that
" The stock value is being decrease by 5.90".
The rational number -5.90 can be described as "negative five and ninety hundredths."
Explanation:
The rational number -5.90 can be described in words as "negative five and ninety hundredths." The negative sign indicates that the change in the value of the stock is a decrease. The decimal portion, 0.90, represents nine tenths, meaning that the value of the stock has decreased by 5 and 9/10 units.
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Write the following equation in the general form Ax + By + C = 0. 2 x + y = 6 2x + y - 6 = 0 2x + y + 6 = 0 2x - y - 6 = 0
2x + y - 6 = 0
given 2x + y = 6 ( subtract 6 from both sides )
2x + y - 6 = 0 ← in general form
Answer:
Option B
Step-by-step explanation:
We have to write the equation in the general form
Ax + By + c = 0
Equation is 2x + y = 6
We subtract 6 on both the sides of the equation to convert in the standard form.
2x + y - 6 = 6 - 6
2x + y - 6 = 0
where A = 2
b = 1
and c = (-6)
Option B will be the answer.