If the difference between the same side interior angles of two parallel lines is 50 degrees, we know that those angles must sum up to 180 degrees (because they are opposite each other).are supplementary angles. As a result, each of the four angles is 65 degrees, 115 degrees, 65 degrees, and 115 degrees..
Let's call one of the angles "x". Then, the other angle must be (x+50).
Now, let's look at the angles formed by a transversal intersecting those two parallel lines. There are eight angles in total, but we only need to find four of them since the other four are congruent (due to alternate interior angles being congruent).
The angles we need to find are:
1. x (one of the same side interior angles)
2. (x+50) (the other same side interior angle)
3. the corresponding angle to x (opposite x, on the other side of the transversal)
4. the corresponding angle to (x+50) (opposite (x+50), on the other side of the transversal)
Since corresponding angles are congruent when two parallel lines are intersected by a transversal, we know that angles 3 and 4 are equal to angles 1 and 2, respectively.
To determine all four angles, we just solve for x:
x + (x+50) = 180
2x + 50 = 180
2x = 130
x = 65
Therefore, our four angles are:
1. x = 65 degrees
2. (x+50) = 115 degrees
3. the angle corresponding to x = 65 degrees
4. the corresponding angle to (x+50) = 115 degrees
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14. Simon earned 400sh as a for goods sold what Commission 15,000 worth so, 600 could be his varnings for a total sale of 7,000
His total earnings for a total sale of 7,000 could be 1450sh
How to determine his earnings for a total sale of 7,000.From the question, we have the following parameters that can be used in our computation:
Salary = 400
Commission = 15%
using the above as a guide, we have the following:
Total earnings = 400 + 15% * Total sales
So, we have
Total earnings = 400 + 15% * 7000
Evaluate
Total earnings = 1450
Hence, the total earnings is 1450
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Question
Simon earned 400sh weekly for goods sold and a commission of 15%
What could be his earnings for a total sale of 7,000.
Mahavira wrote in detail about the idea of zero. What special characteristic did he share with Paul McCartney?
what is 3 to power of 2 -4 to the power of 5=
Step-by-step explanation:
Unclear what you are asking
here is one possibility
3^2 - 4^5
9 - 1024 = - 1015
Here is another possibility
(3^(2-4) )^5 = = (3^(-2))^5 = 3 ^-10 = 1/59049
Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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Out of a pool of 26 men and 29 women what is the probability that 6 men and 6 women will be selected?
Let's evaluate the probability based on the given information.
The number of ways to choose 6 men from 26 can be calculated as:
C(26, 6) = 26! / (6! * (26-6)!) = 26! / (6! * 20!) = 230,230.
The number of ways to choose 6 women from 29 can be calculated as:
C(29, 6) = 29! / (6! * (29-6)!) = 29! / (6! * 23!) = 177,100.
The total number of possible outcomes is the combination of selecting 6 men and 6 women from the given pool of 26 men and 29 women:
Total outcomes = C(26, 6) * C(29, 6) = 230,230 * 177,100 = 40,795,315,300.
Therefore, the probability of selecting exactly 6 men and 6 women from the given pool is:
Probability = 1 / Total outcomes = 1 / 40,795,315,300 ≈ 2.45 x 10^-11.
Hence, the probability is approximately 2.45 x 10^-11.
The following cylinder has a volume of 20π cm3 and a height of 5 cm
What is the diameter of the cylinder? Remember, the diameter of a circle is two times its radius
Answer:
Step-by-step explanation:
To find the diameter of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Given:
Volume = 20π cm^3
Height = 5 cm
We can rearrange the formula to solve for the radius:
radius^2 = Volume / (π * height)
radius^2 = (20π) / (π * 5)
radius^2 = 4
radius = 2
Now, we can find the diameter by multiplying the radius by 2:
diameter = 2 * radius
diameter = 2 * 2
diameter = 4
Therefore, the diameter of the cylinder is 4 cm.
Out of a pool of 26 men and 29 women what is the probability of 12 women jurors being chosen?
The probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.
To calculate the probability of selecting 12 women jurors out of a pool of 26 men and 29 women, we need to consider the total number of possible combinations and the specific combination of interest.
The total number of ways to choose 12 individuals from a pool of 55 (26 men + 29 women) is given by the combination formula:
C(55, 12) = 55! / (12! * (55-12)!) = 22579284062370.
The number of ways to choose 12 women from a pool of 29 is given by the combination formula:
C(29, 12) = 29! / (12! * (29-12)!) = 7726160.
Therefore, the probability of selecting 12 women jurors is the ratio of the number of ways to choose 12 women to the total number of possible combinations:
P(12 women jurors) = C(29, 12) / C(55, 12) ≈ 7726160 / 22579284062370 ≈ 0.000342.
Hence, the probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.
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Use the binomial theorem to find the expansion of ( x - y + z)^3
a bread making machine pours out 50 kg of mixture in 8 minutes in 8 minutes.at what rate is the mixture being poured?
To calculate the rate at which the mixture is being poured, we divide the amount of mixture poured (in kilograms) by the time it takes (in minutes):
Rate = Amount of mixture / TimeIn this case, the amount of mixture poured is 50 kg, and the time taken is 8 minutes. Plugging these values into the formula, we have:
Rate = 50 kg / 8 minDividing 50 kg by 8 min gives us:
Rate = 6.25 kg/minTherefore, the mixture is being poured at a rate of 6.25 kilograms per minute.
Four tiles lettered M, A, T, and H are facedown on a table. A tile is selected, the letter is recorded, the tile is replaced, and the process is repeated.
What is the theoretical probability of selecting the letter T?
The theoretical probability of selecting the letter T is 1/4.
What is probability?Probability is the possibility of happening an event.
Given the four letters M, A, T, and H.
Note that the letter T occurs 1 time, therefore, the probability of selecting the letter T is:
[tex]\sf P=\dfrac{1}{4}[/tex]
Hence, the theoretical probability of selecting the letter T is 1/4.
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Solve for x:
A: 3x - 7 = -19; x =
B: 2x + 3 = -11; x =
C: -3 + 1 = -26; x =
D: 6x + 3 = -15; x =
E: -9 + 7x = 33; x =
F: -2x + 8 = 4; x =
( URGENT PLEASE SOLVE !!! )
1. At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tor bought two pairs of gloves and two hats for
930.00. Find the prices of the hats and gloves.
(k pL.)
Let x-
Let v=
(pt.)
2. Aaliyah invested $10,000 in two mutual funds.
One of the funds rose 6% in one year, and the other rose 906 in one year. Aaliyah's investment rose a total of S684 in one vear. Find the amount she invested in each fund.
1. The price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.
2. Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.
1. Let's assume the price of a pair of gloves is represented by 'x' and the price of a hat is represented by 'y'.
From the given information, we can establish the following equations based on Cody and Tor's purchases:
Equation 1: 2x + 4y = 43.00 (Cody's purchase)
Equation 2: 2x + 2y = 30.00 (Tor's purchase)
To solve this system of equations, we can use a method like substitution or elimination.
Using the substitution method, we can rearrange Equation 2 to express x in terms of y:
2x = 30.00 - 2y
x = 15.00 - y
Now, we substitute this value of x into Equation 1:
2(15.00 - y) + 4y = 43.00
30.00 - 2y + 4y = 43.00
2y = 43.00 - 30.00
2y = 13.00
y = 6.50
Substituting this value of y back into Equation 2 to find x:
2x + 2(6.50) = 30.00
2x + 13.00 = 30.00
2x = 30.00 - 13.00
2x = 17.00
x = 8.50
Therefore, the price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.
2. Let's assume Aaliyah invested an amount represented by 'x' in the mutual fund that rose 6% and an amount represented by 'y' in the mutual fund that rose 9%.
From the given information, we can establish the following equations based on the rise in investment:
Equation 1: 0.06x + 0.09y = 684 (rise in investment)
Equation 2: x + y = 10,000 (total investment)
To solve this system of equations, we can use a method like substitution or elimination.
Using the substitution method, we can rearrange Equation 2 to express x in terms of y:
x = 10,000 - y
Now, we substitute this value of x into Equation 1:
0.06(10,000 - y) + 0.09y = 684
600 - 0.06y + 0.09y = 684
0.03y = 84
y = 2800
Substituting this value of y back into Equation 2 to find x:
x + 2800 = 10,000
x = 10,000 - 2800
x = 7200
Therefore, Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.
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What is the name of an angle that measures 91°?
Answer: Obtuse Angle
Step-by-step explanation: A 90 degree angle is a right angle anything larger then a right angle is a obtuse angle.
Answer:
It would be called an obtuse angle
Step-by-step explanation: so you see if it was exactly 90 degrees it would be called a right angle. Anything above 90 (b91 92 93 etc...) degrees would be an obtuse angle and anything below 90 ( 89 88 87 etc..) would be an acute angle except an 180 degree angle would be a straight angle. Hope that helps!
have a wonderful Sunday!
Rewrite the function by completing the square.
h (x)=x^2+3x−18
Answer: (x+6)(x-3)
Step-by-step explanation:
y=x^2+3x-18
(x+6)(x-3 )
Find the probability that
event A or B takes place.
A
B
10
19
19
The probability that event A or B takes place is 17/19
Probability of an eventProbability is defined as the ratio of the required to the total possible outcomes of an event.
The probability of event A or B taking place can be defined as ;
P(A or B) = P(A) + P(B)
P(A) = 10/19
P(B) = 7/19
Hence,
P(A) + P(B) = 10/19 + 7/19
L.C.M of 19 and 19 = 1
P(A) + P(B) = (10 + 7)/19
P(A) + P(B) = 17/19
Therefore, the probability that event A or B takes place is 17/19
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¿Cuál es el valor de 6 – (3x + 1) + 2x^2, cuando x = 4?
Answer:
Para encontrar el valor de la expresión 6 - (3x + 1) + 2x^2 cuando x = 4, sustituimos el valor de x en la expresión y evaluamos:
6 - (3x + 1) + 2x^2
= 6 - (3 * 4 + 1) + 2 * 4^2
= 6 - (12 + 1) + 2 * 16
= 6 - 13 + 32
= -7 + 32
= 25
Por lo tanto, cuando x = 4, el valor de la expresión 6 - (3x + 1) + 2x^2 es igual a 25.
Step-by-step explanation:
Reema wants to build a coat rack for the front hallway. The wall is 4 feet long, and the piece of wood she has for the the rack is 28 1/4 inches long. She wants to center the coat rack on the wall. There needs to be an equal amount of space, about 7 or 8 inches, between coat hooks. The first and last hooks should be no less than 1 3/4 inches from either end of the wood. How many hooks should Reema use? What is the distance between the hooks? What is the distance of each hook from the left edge of the wood?
Reema should use 3 hooks, with a distance of 7 inches between each hook, and each hook will be positioned 5 3/8 inches from the left edge of the wood.
To determine the number of hooks Reema should use, we first need to calculate the available space on the wood for the hooks.
The total length of the wall is 4 feet, which is equivalent to 48 inches. Reema wants to center the coat rack, so she will have an equal amount of space on either side.
Therefore, each side will have (48 - 28 1/4) / 2 = 9 3/8 inches of space.
Next, we need to determine the distance between the hooks.
Reema wants about 7 or 8 inches of space between each hook.
Let's choose 7 inches for consistency.
Since there will be (n - 1) spaces between n hooks, the total space taken by the spaces will be 7 [tex]\times[/tex] (n - 1) inches.
Now, let's subtract the space taken by the spaces from the available space on the wood: 9 3/8 - 7 [tex]\times[/tex] (n - 1) = 9 3/8 - 7n + 7 inches.
Reema wants the first and last hooks to be no less than 1 3/4 inches from either end of the wood.
Therefore, we subtract twice this distance from the remaining space: 9 3/8 - 7n + 7 - 2 [tex]\times[/tex] (1 3/4) = 9 3/8 - 7n + 7 - 3 1/2 inches.
Now we have the expression 9 3/8 - 7n + 7 - 3 1/2 inches representing the remaining space.
We want this value to be greater than or equal to zero, as it should not be negative.
Simplifying the expression, we have 18 7/8 - 7n - 3 1/2 inches ≥ 0.
Now we can solve this inequality to find the range of values for n, the number of hooks.
We can then determine the distance between the hooks by dividing the remaining space by the number of spaces, and the distance of each hook from the left edge of the wood by adding the space taken by the spaces to the distance between the hooks.
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Solve for m/MNP ifm/MNO = 132° and m/PNO = 40°.
Answer:
Step-by-step explanation:
To solve for m/MNP if m/MNO = 132° and m/PNO = 40°, we can use the fact that the sum of the angles in a triangle is 180 degrees.
First, we can find the measure of angle MNO:
m/MNO + m/PNO + m/MNP = 180
132 + 40 + m/MNP = 180
m/MNP = 8
Copy
Therefore, m/MNP = 8 degrees.
I hope this helps! Let me know if you have any other questions.
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An ice cream shop has 24 flavors. Anne wants to buy a three scoop cone with three different flavors. How many cones could she buy if the order of the flavors is important.
Graph the relation shown in the table. Is the relation a function? Why or why not?
x:y
-1:3
-1:2
0:-4
4:2
No; a horizontal line passes through two graphed points.
Yes; no vertical line passes through two graphed points.
No; a vertical line passes through two graphed points.
Yes; no horizontal line passes through two graphed points.
The graph of this relation is four points on the coordinate plane (see attached diagram).
Hence option D is true.
Since we know that,
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
And a function is a special relation,
where each input x has a single output y.
This relation is not a function, because for one x (x=-1),
Here are two different possible y (y=3 or y=2).
If you consider the graph, you can see that there will be vertical line passing through the points (-1,3) and (-1,2).
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QUESTION 1 1.1 Convert the following to the appropriate units. 1.1.1 1765m to cm 1.1.2 9.4 km to cm 1.1.3 4.2 tons to grams
Answer:
1. 176,500 centimeters
2. 940,000 centimeters
3.42,000,000 grams
Step-by-step explanation:
Convertion:
1.1.1
1765m to cm
1 meter = 100 centimeters
Therefore, 1765 meters =1765*100 centimeters = 176,500 centimeters
1.1.2
9.4 km to cm
1 kilometer = 1000 meters
First convert it into m.
9.4 kilometers = 9.4*1000 meters = 9400 meters
then in cm
1 meter = 100 centimeters
Therefore, 9400 meters = 9400*100 centimeters = 940,000 centimeters
1.1.3
4.2 tons to grams
1 ton = 1000 kilograms
First convert it into kilogram
1 kilogram = 1000 grams
Therefore, 4.2 tons = 4.2*1000 kilograms = 4200 kilograms
then in grams
4200 kilograms = 4200*1000 grams = 42,000,000 grams
I hope this helps! Let me know if you have any other questions.
The following cylinder has a volume of 627.8 cm3 and a height of 19.5 cm
What is the radius of the cylinder?
Use 3.14 for π and round your answer to the nearest tenth.
5.7
3.2
1.7
10.1
Answer:
Step-by-step explanation:
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Given:
Volume = 627.8 cm^3
Height = 19.5 cm
π (pi) = 3.14
Substituting the given values into the formula:
627.8 = 3.14 * radius^2 * 19.5
Simplifying the equation:
627.8 = 60.93 * radius^2
To solve for the radius, we can divide both sides of the equation by 60.93:
radius^2 = 627.8 / 60.93
radius^2 = 10.29
Taking the square root of both sides:
radius ≈ √10.29
Rounding to the nearest tenth:
radius ≈ 3.2
Therefore, the approximate radius of the cylinder is 3.2 cm.
Answer:
3.2
Step-by-step explanation:
The volume of a cylinder is:
Vol = pi•r^2•h
Fill in what is given.
627.8 = pi•r^2•19.5
use 3.14 for pi.
627.8 = 3.14•r^2•19.5
simplify.
627.8 = 61.23r^2
divide by 61.23
10.253 = r^2
sqrt both sides
sqrt10.253 = r
3.2 = r
Question 3 Consider the input numbers: 3; 5; 7:9; 11 3.1.1 Write all the output numbers if the rule 2x is applied. (2)
The required outputs of the given rule are 6, 10, 14, 18, 22.
Given inputs are 3, 5, 7, 9, 11 and the rule is 2x.
To find the outputs by applying the given rule to the inputs.
Let x be the input, then the output is 2x.
That implies,
x = 3 then output = 2× 3 = 6.
x = 5 then output = 2× 5 = 10.
x = 7 then output = 2× 7 = 14.
x = 9 then output = 2× 9 = 18.
x = 11 then output = 2× 11 = 22.
Hence. the required outputs of the given rule are 6, 10, 14, 18, 22.
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Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14. Then he concluded that since the differences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis’s mistake?
Answer:
Step-by-step explanation:
Willis’s mistake is that he used the differences of 6, 10 and 14 instead of the differences of 7, 17 and 31. For a linear function, the y values should have a constant rate of change and not the differences.
Based on the W2 form above, how much money did Jane Doe get to take home after taxes in 2017?
Question 9 options:
$48,500
$6,835
$50,000
$725
The amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500
How to calculate the amountBased on the W-2 form above, Jane Doe's gross pay was $50,000. She had $6,835 in federal income tax withheld, $725 in state income tax withheld, and $1,000 in FICA taxes withheld. This means that her net pay was $48,500.
Net pay = Gross pay - Total taxes withheld
Net pay = $50,000 - ($6,835 + $725 + $1,000)
Net pay = $48,500
Therefore, amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500
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Heeeeeelp pleaseeeeeeeeee!!!!!!!!!!!!L 3.11.3 Quiz: Comparing and Analyzing Function Types
Question 1 of 10
How would you describe the difference between the graphs of f(x)=2x² and
g(x)=-2x²?
A. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
OC. g(x) is a reflection of f(x) over the y-axis.
D. g(x) is a reflection of f(x) over the x-axis.
The correct statement regarding the reflection rules in this problem is given as follows:
D. g(x) is a reflection of f(x) over the x-axis.
How to define the reflection?The functions f(x) and g(x) in the context of this problem are defined as follows:
f(x) = 2x².g(x) = -2x².The entire function was multiplied by -1, meaning that the signal of the function was exchanged, hence the function was reflected over the x-axis.
As the function was reflected over the x-axis, the correct option in the context of the problem is given by option D.
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If you are trying to determine which company has higher salaries, which measure of center should you use?
A table titled, Salaries of Current Employees, listing 6 salaries for 2 companies. Company A salaries are: 45,000, 55,000, 53,000, 51,000, 49,000, and 42,000. Company B salaries are: 54,000, 39,000, 51,000, 52,000, 44,000, and 48,000.
mean median mode
To determine which company has higher salaries, you can use the mean, median, or mode as measures of center. Let's calculate each of these measures for the given data:
Company A salaries: 45,000, 55,000, 53,000, 51,000, 49,000, and 42,000.
Mean (Average):
To calculate the mean, sum up all the salaries and divide by the total number of salaries.
Mean of Company A salaries = (45,000 + 55,000 + 53,000 + 51,000 + 49,000 + 42,000) / 6 = 295,000 / 6 = 49,167
Median:
To find the median, you arrange the salaries in ascending order and find the middle value. If there is an even number of values, you take the average of the two middle values.
Arranging the Company A salaries in ascending order: 42,000, 45,000, 49,000, 51,000, 53,000, 55,000
Median of Company A salaries = (49,000 + 51,000) / 2 = 50,000
Mode:
The mode represents the value(s) that appear most frequently in the dataset.
In Company A salaries, all the values occur only once, so there is no mode.
Now let's calculate the same measures for Company B salaries:
Company B salaries: 54,000, 39,000, 51,000, 52,000, 44,000, and 48,000.
Mean of Company B salaries = (54,000 + 39,000 + 51,000 + 52,000 + 44,000 + 48,000) / 6 = 288,000 / 6 = 48,000
Arranging the Company B salaries in ascending order: 39,000, 44,000, 48,000, 51,000, 52,000, 54,000
Median of Company B salaries = (48,000 + 51,000) / 2 = 49,500
Mode of Company B salaries = There are no repeating values, so there is no mode.
To summarize:
- Mean of Company A salaries: $49,167
- Median of Company A salaries: $50,000
- Mode of Company A salaries: No mode
- Mean of Company B salaries: $48,000
- Median of Company B salaries: $49,500
- Mode of Company B salaries: No mode
Based on these measures of center, we can see that the mean and median salaries of Company A are slightly higher than those of Company B. However, since there is no mode in either dataset, we cannot consider the mode as a determining factor in this case.
A camera has a listed price $859.95 of before tax. If the sales tax rate is 9.5% , find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$941.65
Step-by-step explanation:
Salex tax:We have to find the sales tax of the camera.
tax rate = 9.5%
listed price = $859.95
[tex]\sf Sales \ tax = tax \ rate * listed \ price[/tex]
= 9.5 % * 859.95
= 0.095 * 859.95
= $81.70
To find the total cost, add the sales tax to the listed price.
Total cost = 859.95 + 81.70
= $941.65
y = x² + 6x - 12
a =______
b = _____
c=______
h=______
k =_____
y-intercept=______
x-intercepts =______
and_____
Answer:
See below for answers and explanations
Step-by-step explanation:
a, b, and c are the coefficients of the quadratic, so a=1, b=6, and c=-12
(h,k) is the vertex of the parabola, so we must convert it to vertex form by completing the square:
[tex]y=x^2+6x-12\\y+21=x^2+6x-12+21\\y+21=x^2+6x+9\\y+21=(x+3)^2\\y=(x+3)^2-21[/tex]
Therefore, the vertex is (3,-21), which means h=-3 and k=-21.
The y-intercept is when x=0, or when the function passes through the x-axis:
[tex]y=x^2+6x-12\\y=0^2+6(0)-12\\y=-12[/tex]
Therefore, the y-intercept is -12 (also written as (0,-12) as an ordered pair).
The x-intercept is when y=0, or when the function passes through the y-axis:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-6\pm\sqrt{6^2-4(1)(-12)}}{2(1)}\\\\x=\frac{-6\pm\sqrt{36+48}}{2}\\\\x=\frac{-6\pm\sqrt{94}}{2}[/tex]
Therefore, the x-intercepts are (-6+√94)/2 and (-6-√94)/2.
Hope this helped!