One angle in a triangle is 10 degrees larger than the smallest angle, while the third angle is 10 degrees less than twice the smallest angle. As a result, the three angles are 55°, 45°, and 80°.
Three vertices and three sides make up a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The sum of the triangle's three angles is 180 degrees.
Let's consider the three angles of the triangle as ∠P, ∠Q, and ∠R. Let's consider Q as the smallest angle. The sum of angles P, Q, and R is given as ∠P+∠Q+∠R=180°
Then, ∠P = ∠Q + 10° and ∠R = 2∠Q - 10°. Substituting these two angle values in the above equation,
\(\begin{aligned}\angle Q + 10^{\circ}+\angle Q+2\angle Q - 10^{\circ}&=180^{\circ}\\4\angle Q&=180^{\circ}\\\angle Q&=45^{\circ}\end{aligned}\)
Then,
∠P = ∠Q + 10° = 45°+ 10° = 55°
∠R = 2∠Q - 10° = 2(45°) - 10° = 90° - 10° = 80°
The answers are 55°, 45°, and 80°.
The complete question is -
One angle of a triangle measure 10 degrees greater than the smallest angle and the third angle measure 10 degrees less than twice the smallest angle find the measure of the three angles.
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Please help me with my work
Answer
m = 19b
Step-by-step explanation:
Pretty Simple Fill In The Variables
5 Minute= 95 Blinks
95 Divided by 5 Is 19 So
M = 19b
They Want you to find what is the blinks per-minute
if I had 100 presents for 8 people how many would be left
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
20 POINTS GUYS
EASY WORD PROBLEM ⦁ The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet. Find the volume of the tank.
⦁ Use 3.14 for pi and round your answer to the nearest tenth if necessary.
Answer:
26635.2
Step-by-step explanation:
pi18.8^2=~1109.8
1109.8*24=26635.2
T/F Top 40 radio played the top 40 songs repeatedly every 24 hours.
The top 40 radio stations historically played the top 40 songs repeatedly every 24 hours to engage listeners and maximize popularity, hence true.
True, top 40 radio stations traditionally played the top 40 songs repeatedly every 24 hours.
The term "top 40" refers to a format in radio broadcasting where the station plays the current 40 most popular songs.
This format originated in the 1950s and gained popularity in the 1960s and 1970s.
In the past, top 40 radio stations used to receive weekly music charts from record companies, which ranked the popularity of songs based on sales and airplay.
The station would then select the top 40 songs and create a playlist that would be repeated throughout the day.
The repetition of the top 40 songs every 24 hours was done to maximize listener engagement.
By playing the most popular songs more frequently, radio stations aimed to attract and retain a larger audience.
This strategy helped them maintain high ratings and generate revenue through advertising.
However, it is important to note that the radio landscape has evolved over time.
With the rise of digital music platforms and personalized streaming services, the traditional top 40 radio format has faced challenges.
Today, radio stations may have more varied playlists and offer different genres of music to cater to diverse listener preferences.
It's worth noting that the radio industry has undergone changes in recent years to adapt to evolving listener demands and the emergence of new technologies.
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For a population with a mean of μ = 55 and a standard deviation of σ = 23, what is the standard error of the distribution of sample means for a sample size of n=6? leave the answer to the nearest hundredths place.
The standard error is inversely proportional to the square root of the sample size; as a result, it decreases as the sample size increases.
The formula to calculate the standard error of the mean (SEM) is as follows:
SEM = σ / sqrt (n)
where σ is the population standard deviation, n is the sample size, and sqrt means the square root.
Given that the population mean is μ = 55,
the standard deviation is σ = 23,
and the sample size is n = 6,
we can calculate the SEM as follows:
SEM = σ / sqrt (n)SEM = 23 / sqrt (6)SEM
≈ 9.39Rounded to the nearest hundredth,
the standard error of the distribution of sample means is approximately 9.39.
Standard error is the standard deviation of the sampling distribution. It calculates the accuracy of sample means as compared to the true population mean, taking into account the variation caused by sampling error. Standard error is an important concept in inferential statistics because it is used to compute confidence intervals, z-scores, and t-scores. In addition, a larger sample size results in a narrower distribution of sample means, indicating a greater precision in estimating the population mean.
Therefore, by calculating the standard error, we can calculate the accuracy of our sample and determine how close we are to the true population mean. It is important to remember that standard error is not the same as standard deviation, which measures the variation of scores within a sample rather than the accuracy of sample means.
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please help, if you get it right i'll mark you brainliest!!!!!
Answer:
Step-by-step explanation:
Back
Area = L * W
L = 20
W = 8
Area = 20 * 8
Area = 160
2 Triangles
Area = 1/2 one smaller leg*other smaller leg
one smaller leg = 8
The other one = 15
Area = 1/2 8 * 15 = 60
But there are 2 of them 2 * 60 = 120
Base
L = 20
W = 15
Area = L * W
Area = 20*15 = 300
Front (slanted) Face
L = 20
W = 17
Area = L * W
Area = 20*17 340
Total 920
Brianne needs to buy a plane ticket and new backpack for her European trip. She got tired of living with her twin sister and needed a break so she's going to just go. She only had $40 left over from Xmas and Birthday money and needs a total of $1500 for the airfare, $150 for the backpack she wants, and about another $1000 for spending money. She leaves in 5 months! She realized that she needs a job for this so she got a job at Porto's making empanadas as well as doing extra chores around the house for $50 a week. She makes $1200 a month now. How much should she save each month? If she wanted to leave in 3 months, how much would she have to save?
To calculate how much Brianne needs to save each month, we'll subtract her current savings and her monthly income from her total expenses.
1. Total expenses:
- Airfare: $1500
- Backpack: $150
- Spending money: $1000
Total expenses: $1500 + $150 + $1000 = $2650
2. Current savings: $40
3. Monthly income:
- Job at Porto's: $50/week * 4 weeks = $200/month
- Extra chores: $1200/month
Total monthly income: $200 + $1200 = $1400
4. Amount needed to save each month:
Total expenses - Current savings - Monthly income = $2650 - $40 - $1400 = $1210
Therefore, Brianne needs to save $1210 each month to reach her total expenses for the European trip leaving in 5 months.
If she wanted to leave in 3 months instead, she would have less time to save. In that case, the calculation would be as follows:
1. Total expenses: $2650
2. Current savings: $40
3. Monthly income: $1400
4. Number of months: 3
5. Amount needed to save each month:
(Total expenses - Current savings) / Number of months
= ($2650 - $40) / 3
≈ $870 / 3
≈ $290
Therefore, if Brianne wanted to leave in 3 months, she would need to save approximately $290 each month to reach her total expenses for the European trip.
y = -2x + 1
4x + y = 9
Solve the system of equations without graphing. Show all the math steps needed to find the solution to this system.
Answer:
x =4 & y = -7
Step-by-step explanation:
this is the right answer
Find the probability that a randomly selected point within the circle falls in the red-shaded square.
4√2
8
8
P = [ ? ]
The probability that a randomly selected point within the circle falls in the red shaded area is P = 0.6366
Given data ,
The probability that a randomly selected point within the circle falls in the red shaded area (Square) = Area of square / Area of the circle
On simplifying , we get
Area of square = 8² = 64 units²
And , the area of the circle is = πr²
C = ( 3.14 ) ( 4√2 )²
C = 100.530 units²
So , the probability is P = 64 / 100.530
P = 0.6366
Hence , the probability is P = 63.66 %
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Answer: 0.64
Step-by-step explanation:
the other person gave a percentage, but not what the question was asking for, so I just rounded his original answer, as was asked.
Please help, this is due soon
Answer:
21 miles
Step-by-step explanation:
Each 1/6 is equal to 1 mile because 5/6 is equal to 5 miles. 1/2 is 3/6 so 3 miles. 6/6 is 6 miles so 3 is 3*6. This means it is 18+3 or 21 miles.
Have a great day!
\( \frac{1}{( \sqrt[4]{256})^{-2} } \)
1/ (^4√256)^-2
please simplify using exponent laws and then evaluate expression
Answer:
16.
Step-by-step explanation:
I have attached the work to your problem.
Please see the attachment below.
I hope this helps!
Which sequence of transformations will map figure H onto figure H'
-8
7
-6
-5
-4-
-3
-2
1
-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 11 12 13
-1
-2
3 4
587
H
-9
-10
H'
O
Rotation of 180° about the origin, translation of (x + 10, y − 2)
reflection across x = -6
Rotation of 180° about the origin, translation of (x + 10, y − 2).
reflection across y = -6
Rotation of 180° about the origin, translation of (x - 10, y + 2)
reflection across y = -6
Rotation of 180° about the origin, translation of (x - 10, y + 2)
reflection across x = -6
The sequence of transformations that will map figure H onto figure H' is: Option B: the rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across y = −6.
How to find the sequence of transformation?We are given the coordinates of the hexagon as:
Points of Hexagon H → (2,2), (2,6), (6,7), (8,6), (8,2), (6,1)
Points of Hexagon H' → (2,-8), (2,-4), (4,-3), (8,-4), (8,-8), (4,-9)
The steps that can be used to transform the hexagon H into hexagon H' are:
Step 1 - Translate the hexagon in the positive x-axis direction by a factor of 10.
Step 2 - Translate the graph obtained in the above step by factor 2 in the downward direction.
Step 3 - Rotate the graph obtained in the above step 180 degrees about the origin.
Step 4 - Then take the reflection of the graph obtained in the above step about y = -6. The resulting graph shows the graph of Hexagon H'.
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I took a loan from the bank and I paid an interest of 1,500 at what rate and I pay if the loan was 5000 for 3 years
Answer:
Step-by-step explanation:
To calculate the rate :
Interest = P x R x T
100
Here, P = 5000, T = 3, I = 1500
Therefore,
1500 = 5000 x R x 3
100
1500 = 150 R
1500 = R
15
10 = R
Thus, the rate is 10%
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find the distance of the line segment joining the two points (-4 /2 - /12) and (/32, 2/3)
Answer: \(4\sqrt{3}\) .
Step-by-step explanation:
Distance formula : Distance between points (a,b) and (c,d) is given by :-
\(D=\sqrt{(d-b)^2+(b-a)^2}\)
Distance between points \((-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3})\).
\(D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}\)
Hence, the correct option is \(4\sqrt{3}\) .
Which statement is correct regarding independent events?
Two events are independent if they have no outcomes in common and cannot occur at the same time.
Two events are independent if they have outcomes in common and can occur at the same time.
Two events are independent if the outcome of the first event does not affect the outcome of the second event.
Two events are independent if the outcome of the first event affects the outcome of the second event.
please help thank you :)
\( \: \: \: \: \: \: \red{ \underline{ \large{ \pink{ \tt{꧁ A \: N \: S \: W \: E \: R ꧂}}} }}\)
✧ \( \underline{ \underline{ \large{ \red{ \tt{G \: I\: V \: E\: N}}}} }: \)
AC bisects \( \tt{ \angle BAD\: \& \: \angle \: BCD}\)
❀ \( \underline{ \underline{ \large{ \tt{ \purple{T \: O \: \: F \: I\: N\: D}}}}} : \)
Congruence theorem which justifies ∆ ABC \( \cong\) ∆ ADC.♕ \( \underline{ \underline{ \large{ \tt{ \orange{P \: R\:O \: O \: F \: S}}} }}: \)
\(\begin{array}{ |c| c | c | } \hline \text{SN}& \text{Statement} & \text{Reason}\\ \hline \\ \text{1 \: i.}& \sf{In \triangle} \:ABC \: \& \: \triangle \: ACD \: \ \\ & \tt{ \angle ACB= \angle \: ACD(A)}\ & \sf{AC \: bisects \angle \: BCD(Given)} \\ \text{ii} \: & \tt{AC= CA(S)}& \sf{Common \: side} \\ \text{iii} \: & \tt{ \angle \: BAC = \angle \: CAD(A)}& \sf{AC \: bisects \: \angle \: BAD ( Given )}& \\ \\ \hline 2& \tt{ \triangle} \: ABC \cong \triangle{ADC}& \red{\underline{\sf{ \bold{By \: ASA\: axiom}}}} \\ \hline\end{array}\)
Hence , We can conclude :
ASA congruence theorem justifies ∆ ABC \( \cong\) ∆ ADCツ Hope I helped! ♡
♪ Have a wonderful day / night ! ✎
✎ \( \underbrace{ \overbrace{ \mathfrak{Carry \: On \:Learning}}} ☃ \)
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
What is the least common multiple of 4 and 10?
Answer:
Step-by-step explanation:
20
Least common multiple (LCM) of 4 and 10 is 20.
Answer:
20
Step-by-step explanation:
ASAP want your guys opinion about this
What do you think of when you hear the word "Math"?
Answer:
I think of hard work :)
Step-by-step explanation:
Answer:
The perfect answer would be
M-ental
A-buse
T-o
H-uman
Step-by-step explanation:
hehe, pls mark me brainliest if you can:)
A farmer wants to fence an area of 5400 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the amount of fencing needed?.
90 feet is the lengths of the sides of the rectangular field .
What do you mean by rectangular?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart.Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.Let x represent the length of the fence and y represent the width of the fence.
Since the area is 5400, hence:
Area = length * width = x * y
5400 = xy
y = 5400/x
A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:
Amount of fencing needed (P) = x + x + y + y + y = 2x + 3y
Amount of fencing needed (P) = 2x + 3(5400/x) = 2x + 16200/xTo minimize
the amount of fencing needed, dP/dx = 0, hence:
dP/dx = 2 - 16200/x²
2 - 16200/x² = 0
2 = 16200/x²
2x² = 16200
x² = 8100
x = 90 feet
y = 5400/x = 5400/90 = 90 feet
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Follow the steps to find the product of and 0.55.
Estimate the product of and 0.55.
1/4-
Convert the decimal 0.55 to a fraction.
V55/100
What is the product of the two numbers?
X 110/150 or 11/15
110/300 or 11/30
77/103
1) Estimate value of the product of 2/3 and 0.55 is, 2/3.
2) The fraction part is, 55 / 100
3) The product of the two numbers is, 11/30
We have to given that,
Estimate the product of 2/3 and 0.55.
And, Convert the decimal 0.55 to a fraction.
And, The product of the two numbers.
Now,
Estimate the product of 2/3 and 0.55,
So, we can round 0.55 to the nearest whole number, which is 1.
Then, multiply 2/3 by 1 to get an estimate of the product.
so, The correct answer is 2/3.
Now, we can convert the decimal 0.55 to a fraction,
= 0.55
= 55/100
= 11/20
Thus, The correct answer is, 55/100.
And, the product of 2/3 and 0.55,
= 2/3 x 55/100
= 110/300
= 11/30.
Hence, The correct answer is, 110/300 or 11/30
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Write this ratio another way.
120/150
The ratio 120/150 represented in the simplest form is 4 : 5 .
The given ratio is 120 /150 .
Now if we write the expression in the form of the simplest ratio we have to divide the ratio by the highest common factor.
The HCF of the number is 30. Hence the ratio in simplest form will be
120÷30 : 150÷30 = 4 : 5 .
By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.
Ratio can be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value that this fraction represents.
Ratios of counts are rational numbers that can also be rational numbers and are occasionally expressed by (non-zero) natural numbers.
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Given two dice (each with six numbers from 1 to 6): (a) what is the entropy of the event of getting a total of greater than 10 in one throw? (b) what is the entropy of the event of getting a total of equal to 6 in one throw? What is the Information GAIN going from state (a) to state (b)?
The entropy of the event for A. H = -((1/18) * log(1/18) + (17/18) * log(17/18)) and B. H = -((7/36) * log(7/36) + (29/36) * log(29/36)). By subtracting the entropy of event (b) from the entropy of event (a), we can determine the specific value of the information gained in this case.
To calculate the entropy of an event, we need to determine the probability distribution of the outcomes and apply the entropy formula.
(a) To find the entropy of getting a total greater than 10 in one throw, we analyze the possible outcomes. The only way to achieve a total greater than 10 is by rolling a 5 and a 6 or a 6 and a 5.
There are only two favourable outcomes out of 36 possible outcomes (6 choices for the first die multiplied by 6 choices for the second die). The probability of obtaining a total greater than 10 is 2/36 or 1/18.
Using the entropy formula, H = -Σ(p_i * log(p_i)), where p_i represents the probability of each outcome, the entropy of this event is:
H = -((1/18) * log(1/18) + (17/18) * log(17/18)).
(b) To find the entropy of getting a total equal to 6 in one throw, we analyze the possible outcomes. The combinations that result in a total of 6 are (1, 5), (5, 1), (2, 4), (4, 2), (3, 3), (6, 0), and (0, 6), making a total of 7 favourable outcomes out of 36 possible outcomes. The probability of obtaining a total of 6 is 7/36.
Similarly, using the entropy formula, the entropy of this event is:
H = -((7/36) * log(7/36) + (29/36) * log(29/36)).
The information gained going from state (a) to state (b) is calculated as the difference between the entropies of the two events:
Information Gain = H(a) - H(b).
Therefore, by subtracting the entropy of event (b) from the entropy of event (a), we can determine the specific value of the information gain in this case.
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Triangle MNO is transformed to produce triangle PQR. What transformations guarantee triangles MNO and PQR are congruent
Answer:
C, D, and E are corrects.
Step-by-step explanation:
Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions. The rigid transformations are reflection, rotation, and translation. The image from these transformations will not change its size or shape.
A dilation is a nonrigid transformation that can produce enlarged or reduced images from a given pre-image.
Therefore only C, D, and E are corrects.
A. a dilation, then a translation
B. a reflection, then a dilation
C. a reflection, then a rotation
D. a rotation, then a translation
E. a translation, then a reflection
The transformations guarantee triangles MNO and PQR are congruent should be considered is option C, D, and E.
What is congruent?
The two plane figures should be considered as the congruent when one should be obtained from the other via the sequence of the fixed motions. Here the right transformation could be in the form of reflection, rotation, and translation.
Also, the image arise form transformations should remain the same with respect to the size or shape.
Therefore only C, D, and E are corrects.
This is an incomplete question. Please find the options below.
A. a dilation, then a translation
B. a reflection, then a dilation
C. a reflection, then a rotation
D. a rotation, then a translation
E. a translation, then a reflection
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a 6.5-kg bowling ball rests on a uniform beam of length and mass , as in the figure. the beam is supported at two points separated by a distance where 0.75 and the bowling ball is a distance 2.7 m from support point 1. calculate the force exerted on the beam by support point 2 if 18 kg and 4.2 m.
The force exerted on the beam by support point 2 is approximately 186.4 N.
To solve this problem, we can use the principle of moments. The weight of the bowling ball and the mass of the beam are both forces acting on the beam. We can assume that the beam is in static equilibrium, meaning that the sum of the forces and moments acting on the beam is equal to zero.
First, we can calculate the weight of the bowling ball as 6.5 kg x 9.81 m/s^2 = 63.6 N. This weight acts downward at a distance of 2.7 m from support point 1, so it creates a clockwise moment of 63.6 N x 2.7 m = 171.7 Nm.
Next, we can calculate the moment created by the mass of the beam. We can assume that the mass is evenly distributed along the length of the beam, so the center of mass is at the midpoint of the beam, which is 1.5 m from support point 1. The mass of the beam is given as 18 kg + m kg, so we can write:
(18 kg + m kg) x 9.81 m/s^2 x 1.5 m = (18 kg + m kg) x g x 1.5 m
where g is the acceleration due to gravity (9.81 m/s^2). This moment acts counterclockwise, so it has a negative sign.
Finally, we can write the equation for static equilibrium:
ΣM = 0
where ΣM is the sum of the moments. This gives:
171.7 Nm - (18 kg + m kg) x g x 1.5 m - (m kg) x g x 0.75 m = 0
Solving for m, we get:
m = (171.7 Nm - 18 kg x g x 1.5 m) / (g x 0.75 m)
m ≈ 6.98 kg
Now that we know the mass of the beam, we can calculate the force exerted by support point 2 using the equation for static equilibrium:
ΣF = 0
where ΣF is the sum of the forces. This gives:
F2 - 63.6 N - (18 kg + 6.98 kg) x g = 0
Solving for F2, we get:
F2 ≈ 186.4 N
Therefore, the force exerted on the beam by support point 2 is approximately 186.4 N.
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Which theorem does it offer proof of?
Answer:
vertical angles are =
Step-by-step explanation:
A backpack that normally sells for $39 is on sale for $25. Find the
percent of change.
Answer: To find the discount, simply multiply the original selling price by the %discount:
ie: 39 x 33/100= $12.87
So, the discount is $12.87.
Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:
ie: 39- 12. 87= 26.13
So, the sale price is $26.13
what angle types are congruent
Answer:
All angles that are either interior angles, exterior angles, alternate angles or corresponding angles are all considered congruent.
Hope this answered your question!
Answer:
exterior angles, interior angles, alternate angles , corresponding angles
please i really y need help it’s due in 4 mins
Answer: 1/2 + y
Step-by-step explanation:
Answer:
DV=3√10
Step-by-step explanation:
D(-1,7) and V(8,4)
to determine the length you use the distance formula
d =√(x2-x1)²+ (y2-y1)²
in thhis case
d=√(-1-8)²+(7-4)²
d=√81 +9
d=√90
d= 3√10
There are 12,000 people attending a concert. They announce that 20% of the people that purchased tickets did not come to the concert. How many people purchased tickets to the concert? (Quickly answer this if possible
Answer:
15,000
Step-by-step explanation:
20% of 15,000 is 3,000. 15,000-3,000=12,000
find the zeros of the function.f(x) = 3x^2 + 6
f(x) = 3x^2 + 6
0 = 3x^2 + 6 (Replacing f(x) by 0)
-6 = 3x^2 (Subtracting 6 from both sides of the equation)
-6/3 = x^2 (Dividing by 3 on both sides of the equation)
-2 = x^2 (Dividing)
\(\begin{gathered} \sqrt[]{-2}\text{ = x (Taking the square root on both sides of the equation)} \\ \sqrt[]{-1}\text{ }\cdot\sqrt[]{2}\text{= x (Separating terms)} \\ \sqrt[]{2}i=x\text{ (Changing }\sqrt[]{-1}\text{ for i)} \end{gathered}\)There are no real solutions. The complex solutions are:
\(\pm\sqrt[]{2}i\)