Answer: The area of a triangle is 1036.8 square units.
To find the area of a triangle, we can use the formula
Area = (1/2) * base * height
In this case, we are given that the first base is 32 and the second base is twice the first base, or 2*32 = 64. The height is given as 21.6. Therefore, we can plug these values into the formula and solve for the area:
Area = (1/2) * (32 + 64) * 21.6
Area = (1/2) * 96 * 21.6
Area = 1036.8
Therefore, the area of the triangle is 1036.8 square units.
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(01.03 mc) a cell phone company charges $400 for a new phone and then $50 each month after the purchase. if c (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function?
the range of the function is at least $400 plus $50 for each month after the purchase. The average monthly cost of owning the cell phone can be represented as:
C(t) = 400 + 50t
Where t is the number of months after the purchase.
Since C(t) is a linear function, its range is all real numbers greater than or equal to 400, since the initial cost of the phone is 400 and the monthly cost is a positive constant. Therefore, the range of C(t) is:
Range of C(t) = {C(t) | C(t) ≥ 400} or [400, ∞)
In other words, the range of the function is all possible average monthly costs of owning the phone, which is at least $400 plus $50 for each month after the purchase.
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7. Javier shared $280.00 among his siblings Juan, Micah and Savi. Savi received 4 times as much as Juan and Micah received 1/2 of Savi's share and Juan got the balance Calculate Micah's share.
Micah received 1/2 of Savi's share and Juan got the balance.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
total amount = $280=x
savi= 4*juan= 11
micah= 1/2 savi= 1/2*280/100= 1.4
juan got balance= 267.6
Hence, Micah received 1/2 of Savi's share and Juan got the balance.
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while shopping, sofia noticed that her favorite bag of chips were on sale for $5 for 2 bags. how much would 7 bags cost?
Sofia's favorite bag of chips were on sale for $5 for two bags. If she wanted to buy seven bags, the cost would be $17.50.
To calculate this, we need to use the formula for finding the total cost of a given number of items: Total Cost = Number of Items x Cost Per Item.In this case, we need to find the total cost of seven bags, so the equation looks like this: Total Cost = 7 x $5.
We can solve this equation by multiplying the two numbers together. 7 multiplied by 5 equals 35. However, the question is asking us to find the total cost of seven bags, which is $17.50. To convert the answer from 35 to 17.50, we need to divide 35 by two: 35 divided by 2 equals 17.50.
Therefore, the cost of seven bags of Sofia's favorite chips would be $17.50.
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An aquarium tank holds 190 liters of water. How much is this in gallons? Use the following conversion: 1 gallon is 3. 8 liters. What is the Answer?
The aquarium tank that holds 190 liters of water equals to 50.15 gallons. Therefore, the answer to the given problem is 50.15 gallons.
Conversion factors are the ratios that describe the numerical relationship between two units of measurement.
The conversion factor of liters to gallons is 1 gallon is 3.8 liters.
Therefore, by multiplying the given value of liters by the conversion factor of liters to gallons, we can convert liters to gallons.
190 liters x 1 gallon/3.8 liters = 50.15 gallons
Thus, the aquarium tank that holds 190 liters of water equals to 50.15 gallons.
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Dante collects baseball cards. He would like to keep the cards in an album. He has 10 cards for each of 24 teams. How many album pages will he need if each page can hold 8 cards? Show your work. Draw a picture if it helps.
Answer: 30 album pages
Step-by-step explanation:
cards = 10
teams = 24
total cards = 240
240 / 8 = 30
a normal population with unknown variance has a mean of 20. is one likely to obtain a random sample of size 9 from this population with a mean of 24 and a standard deviation of 4.1? if not, what conclusion would you draw?
We can conclude that it is unlikely to obtain a random sample of size 9 from this population with a mean of 24 and a standard deviation of 4.1 because the sample mean of 24 is different from the population mean of 20.
To answer this question, we can use a t-test to determine if the sample mean of 24 is significantly different from the population mean of 20.
The t-test formula is:
t = (x' - μ) / (s / √(n))
Where x' is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the values given in the question, we get:
t = (24 - 20) / (4.1 / √(9)) = 2.93
To determine if this t-value is significant, we need to compare it to the critical t-value for a two-tailed test with 8 degrees of freedom (n-1). Using a t-table or calculator, we find the critical t-value to be approximately 2.31 at a 5% significance level.
Since our calculated t-value of 2.93 is greater than the critical t-value of 2.31, we can reject the null hypothesis that the sample mean is equal to the population mean.
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a 95% confidence interval for a proportion is 0.75 to 0.83. is the value given a plausible value of p?
Yes, the value of 0.75 to 0.83 for a 95% confidence interval is plausible.
A confidence interval is a range of values that has a 95% chance of containing the true population parameter, which in this case is the population proportion (p).
A 95% confidence interval has a margin of error of 5%. Thus, a range of 0.75 to 0.83 has a 95% chance of containing the true population proportion p.
The 95% confidence interval is an estimated range of values which is calculated from sample data, with a 95% chance of containing the true population parameter, p. To calculate the confidence interval, the confidence level and the margin of error must be known.
The confidence level is the probability that the confidence interval will contain the true population parameter, and the margin of error is the amount that the sample statistic can differ from the true population parameter.
A 95% confidence level has a margin of error of 5%, meaning that the sample statistic can be up to 5% away from the true population parameter.
In this case, the 95% confidence interval for the population proportion is 0.75 to 0.83. This means that the range of 0.75 to 0.83 has a 95% chance of containing the true population proportion p, and is thus a plausible value for the population proportion.
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WILL MARK AS BRAINLEIST: QUICKLY PLEASE
Picture better demonstrate the graph and equations.
Use Newton's Method to find the two solutions of e^2= 6x to six significant figures.
For this problem you will need to use the fact that the exponential equals its own derivative, i.e.,
(d/dx) e^x = e^x
Xleft =_____
Fright=_____
The two solutions to e² = 6x using Newton's method are x_left = 1.23151 and x_right = 2.157545.
What is the solution of the function?To find the solutions of e² = 6x using Newton's Method, we will follow these steps:
Let f(x) = e² - 6x. Then we want to find the roots of f(x) = 0, which are the solutions to e² = 6x.
We need to choose a starting point x₀. A good choice is x₀ = 1, since it's a reasonable approximation to the solutions.
Apply Newton's Method to find the next approximation x₁:
x₁ = x₀ - f(x₀)/f'(x₀),
where;
f'(x) = -6 is the derivative of f(x).Plugging in the values, we get:
x₁ = x₀ - (e² - 6x₀)/(-6) = x₀ + (e²/6 - x₀)
Use x₁ as the new starting point and repeat the process until we achieve the desired level of accuracy.
In this case, we want to find the solutions to six significant figures, so we will repeat the process until the difference between xₙ and xₙ₋₁ is less than 0.000005 (the sixth decimal place).
Using a calculator, we can apply Newton's Method iteratively to find the two solutions:
Iteration 1:
x₁ = x₀ - f(x₀) / f'(x₀)
x₁ = 1 - (e² - 6)/(-6) = 1.231509
Iteration 2:
x₂ = 1.231509 - (e² - 6)/(-6) = 1.463018
Iteration 3:
x₃ = 1.463018 - (e² - 6)/(-6) = 1.694527
Iteration 4:
x₄ = 1.694527 - (e² - 6)/(-6) = 1.926036
Iteration 5:
x₅ = 1.926036 - (e² - 6)/(-6) = 2.157545
The second solution to six significant figures is x_right = 2.157545
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PLEASE ANSWER AS QUICKLY AS YOU CAN!!!!!!
Answer:
(x+6)(x+6)
[tex]x^2+12x+36[/tex]
(x+8)(x-5)
[tex]x^{2}+3x-40\\[/tex]
(x-5)(x-2)
[tex]x^{2}-7x+10[/tex]
Step-by-step explanation:
Brainliest pls hope it helped^^
Answer:
a) x^(2)+12x+36
b) x^(2)+3x-40
c) x^(2)-7x+10
Step-by-step explanation:
A circular cookie cake costs $14.13. if the diameter of the cookie cake is 6 inches, what is the approximate cost per square inch of the cookie cake? use π = 3.14. a. $0.13 b. $0.25 c. $0.50 d. $0.75
The approximate price per square inch of the cookie cake is $0.50
The area of a circle is given through the formulation:
A = πr^2
In which r is the radius of the circle.
for the reason that diameter of the cookie cake is 6 inches, the radius is half of of that, or three inches.
Substituting this into the formulation, we've:
A = π(3^2) = 28.26 square inches (approximate)
The value per square inch is the overall value of the cookie cake divided with the aid of its area:
value per square inch = $14.13 / 28.26 sq.in = $0.50 (approximate)
Therefore, the approximate price per square inch of the cookie cake is $0.50
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Jordan wrote the following descirption: three fewer than one fourth of x is 12. write an equation to represent the description.
Answer:
1/4x - 3 = 12
Step-by-step explanation:
You know you have 1/4x and need to take three from it to equal 12
if you have heteroskedasticity such that the sample can be divided into groups with each group having a different error variance, what estimation technique should be used?
One possible technique to address heteroscedasticity with group-specific variances is the use of weighted least squares (WLS) estimation, where observations from each group are assigned weights that are inversely proportional to the variance of the error term in that group.
Heteroscedasticity refers to the situation where the variance of the error term in a regression model is not constant across different levels of the independent variable(s). This violates the assumption of homoscedasticity, which can lead to biased and inefficient estimates of the model parameters.
When the heteroscedasticity is related to group-specific variances, a possible solution is to use WLS estimation. This involves calculating weights for each observation based on the inverse of the estimated variance of the error term in its group. By doing so, observations with larger variances are given smaller weights, while observations with smaller variances are given larger weights, which effectively downweighs the influence of more variable observations.
The resulting WLS estimator is more efficient and less biased than the standard OLS estimator, and it can lead to more accurate inferences about the relationship between the independent and dependent variables. However, WLS requires the researcher to specify the appropriate weights for each observation, which can be challenging and subjective in practice.
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Ethan is older than Jordan. Their ages are consecutive integers. Find Ethan’s age if the sum of the square of Ethan’s age is 4 times Jordan’s age is 56.
If the square of Ethan's age is added to Jordan's age, the result is [tex]56[/tex], which equals Ethan's age. The answer is that Ethan is [tex]6[/tex] years old.
How can you calculate age using maths?A person's birth date is compared to the day on which their age has to be computed as part of the age calculation process. The age of the individual is calculated by subtracting the person's age from the given date. Provided Date - Birthdate is used to compute age.
How can ageing be quantified?A person's age is merely a measurement of how long they have been living. These metrics don't adequately describe who you are or what you have accomplished. At any age, either old or young, one may do anything.
The solution states that [tex]56[/tex] is equal to [tex]4[/tex] times Jordan's age multiplied by the square of Ethan's age. This may be expressed as an equation:
[tex]x^2 + 4(x-1) = 56[/tex]
Simplifying the equation:
[tex]x^2 + 4x - 4 = 56[/tex]
[tex]x^2 + 4x - 60 = 0[/tex]
We can solve this quadratic equation by factoring:
(x+10)(x-6) = 0
Therefore, [tex]x = -10[/tex] or [tex]x = 6[/tex]. We can discard the negative value since age cannot be negative, so Ethan's age is [tex]6[/tex].
To check, we can substitute x=6 into the original equation:
[tex]6^2 + 4(6-1) = 36 + 20 = 56[/tex]
So the solution is Ethan is [tex]6[/tex] years old.
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Help please it’s urgent
By function, The fact that this number is 1/2 indicates the half-life of the substance is 1 year.
How would you define a function in plain English?
A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output.
Every function has an associated domain, codomain, or range. A mathematical function is a rule that, given the values of one or more independent variables and the dependent variable, determines the value of the dependent variable.
300 represents the initial amount of the substance, the amount present at t=0.
0.5 is the fraction of substance remaining at the end of each year. The fact that this number is 1/2 indicates the half-life of the substance is 1 year.
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How do I solve for x and y?
Answer:
x = 80
y = 160
Step-by-step explanation:
The sum of all arc measures that make up a circle is 360°. Therefore:
[tex]\implies 200^{\circ} + y^{\circ} = 360^{\circ}[/tex]
[tex]\implies 200^{\circ} + y^{\circ} - 200^{\circ} = 360^{\circ} - 200^{\circ}[/tex]
[tex]\implies y^{\circ} = 160^{\circ}[/tex]
[tex]\implies y=160[/tex]
Tangent and Intersected Chord TheoremIf a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.
Therefore, according to the Tangent and Intersected Chord Theorem, the measure of angle x is equal to half of the measure of arc y:
[tex]\implies x^{\circ}=\dfrac{1}{2} y^{\circ}[/tex]
[tex]\implies x^{\circ}=\dfrac{1}{2} \cdot 160^{\circ}[/tex]
[tex]\implies x^{\circ}=80^{\circ}[/tex]
[tex]\implies x=80[/tex]
[tex]\hrulefill[/tex]
Circle Theorem vocabularyChord: A straight line joining two points on the circle.Tangent: A straight line that touches a circle at only one point.Arc: the curve between two points on the circumference of a circleIntercepted arc: The curve between the points where two chords or line segments intercept the circumference of a circle.the slope of a street is 0.54. if it covers 28m of horizontal distance, what is the rise of the street?
Answer: i believe its 15.12
Step-by-step explanation:
The Sport Bat Corporation manufactures baseball bats for professional baseball teams. The company needs
capital to upgrade their equipment now that they are experiencing a good level of success. They look to borrow
$2 million to perform the upgrade. Explain how this need for capital will spread through the financial system.
The need for capital by the Sport Bat Corporation will spread through the financial system as it interacts with banks, investors, and the broader financial markets.
How the need for capital will spread throughout the system?When the Sport Bat Corporation needs to borrow $2 million to upgrade their equipment, they will likely seek a loan from a financial institution, such as a bank. The bank will evaluate the creditworthiness of the company and may require collateral or a personal guarantee before approving the loan.
Once the loan is approved, the bank will add the Sport Bat Corporation's loan to their portfolio of assets. The bank may choose to sell the loan to other investors, such as insurance companies or pension funds, to diversify their portfolio and manage risk.
These investors will then receive the interest payments on the loan as a source of income. The loan may be bundled together with other loans and sold as a package, called a securitization, to other investors in the financial markets, thus representing the spread of the loan throughout the financial system.
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Larger values of r^2
imply that the observations are more closely grouped about the:
a. average value of the independent variables.
b. average value of the dependent variable.
c. least-squares line.
d. origin.
e. None of the above answers is correct.
Larger the value of r² (R²) imply that the observations are more closely grouped about the least squares line (regression line) option C.
The dependent variables on the y-axis and the independent variables on the x-axis are shown as a linear connection by a regression line. By examining the data pattern the variables' effects have created, the correlation is established.
As the (R2) is large therefore, the model is a good fit or bounded close to regression line least squares line (regression line).
In a regression graph, the regression line that is closest to the data points is shown. By changing the value of x in the regression equation, this statistical tool helps study how a dependant variable y behaves when the independent variable x changes.
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Complete question:
Larger values of r2 (R2) imply that the observations are more closely grouped about the
Group of answer choices:
average value of the dependent variableoriginleast squares line (regression line)average value of the independent variableswhen converting to a new system, which cutover method is the most conservative? a. data coupling cutover b. parallel operation cutover c. phased cutover d. cold turkey cutover
The most conservative cutover method when converting to a new system is the Phased Cutover.
This method allows for the implementation of the new system in multiple stages, thereby reducing risk. First, the new system is installed and tested. Next, a small portion of data is moved to the new system.
After data is moved, the new system is tested again. This process is repeated until all data has been moved and tested, and the new system is running smoothly.
Once the new system is running successfully, the old system is discontinued.
The phased cutover method ensures that the new system is functioning correctly, and gives time for system users to get used to the new system, before the old system is turned off.
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17. The points (0, b) and
(a, b) are graphed on a coordinate plane. What
is the distance between the points? Explain.
Therefore, the distance between the two points is simply the difference in their x-coordinates, this makes sense since both points lie on the same horizontal line, and so the vertical distance between them is zero.
What is distance?Distance is a numerical measurement of how far apart two objects or points are from each other. It is a scalar quantity that is usually expressed in units of length, such as meters, kilometers, miles, or feet. Distance is often used in physics, mathematics, and engineering to describe the spatial separation between two objects or points. It is also used in everyday language to describe how far away something is, such as the distance between two cities or the distance from a person's house to their workplace.
By the question.
The distance between two points on a coordinate plane can be found using the distance formula:
distance =[tex]\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-x_{1}^{2} ) }[/tex]
In this case, the two points are (0, b) and (a, b). We can substitute these values into the distance formula:
distance = [tex]\sqrt{(a-0)^{2}+(b-b)^{2} }[/tex]
distance = [tex]\sqrt{a^{2}+0 }[/tex]
distance = a
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In the diagram below, what is the measure of angle x?
Answer: C - 105
Step-by-step explanation:
75+75=150
360-150=210
210/2=105
find a equation of the line through the point(-6,-5) and (-1,1))
a. y=6/5x + 11/5
b. y=6/5x - 11/6
c. y=6/5x
or
d. y=6/5x + 11/6
Answer:
The slope of the line passing through the points (-6,-5) and (-1,1) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-6,-5) and (x2, y2) = (-1,1)
slope = (1 - (-5)) / (-1 - (-6)) = 6/5
Now, using point-slope form of the equation of a line, we get:
y - y1 = m(x - x1)
where m = 6/5 and (x1, y1) = (-6,-5)
y + 5 = 6/5(x + 6)
y + 5 = 6/5x + 6.72
y = 6/5x + 6.72 - 5
y = 6/5x + 1.72
Therefore, the equation of the line passing through the points (-6,-5) and (-1,1) is:
y = 6/5x + 1.72
Option (c) y=6/5x is not the correct equation of the line. The correct answer is (d) y=6/5x + 11/6.
In an election, there were three candidates;⅔ of the electors voted for the first candidates,¼ for the second candidate and the rest for the third candidate. If the third candidate got 3290 votes, how many votes did the winner get? Solve this and show All your workings
The winner of the election got 26320 votes.
Let's first find the total number of votes cast in the election. We know that 2/3 fraction of the electors voted for the first candidate and 1/4 of the electors voted for the second candidate. Therefore, the remaining 1/12 of the electors voted for the third candidate. So, we have:
2/3 + 1/4 + 1/12 = 8/12 + 3/12 + 1/12 = 12/12 = 1
This means that all the electors voted, and the total number of votes cast is equal to the total number of electors.
Now, let's find the number of votes the third candidate got, which is 1/12 of the total number of votes. We know that this is equal to 3290. So, we have
1/12 x Total Number of Votes = 3290
Multiplying both sides by 12, we get:
Total Number of Votes = 3290 x 12 = 39480
Now, we can find the number of votes the first candidate got, which is 2/3 of the total number of votes. We have:
2/3 x Total Number of Votes = 2/3 x 39480 = 26320 votes
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A certain amount of money is shared between rui feng and vishalin the ratio of 5:9 if rui feng gets 44 dollar less than vishal find total amount of money shared between the two boys
The total amount of money shared between Rui Feng and Vishal is 154 dollars.
Let's assume that the amount of money shared between Rui Feng and Vishal is x dollars.
According to the given ratio, the amount of money received by Rui Feng is 5/14 of the total amount, and the amount received by Vishal is 9/14 of the total amount.
We are also given that Rui Feng receives 44 dollars less than Vishal. We can express this as:
9/14 x - 5/14 x = 44
Simplifying the equation, we get:
4/14 x = 44
Multiplying both sides by 14/4, we get:
x = 154
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PLEASE HELP MEEEEEEEEEEE!
What is the measure of the unknown angle?
A straight angle divided into a fifty-eight-degree angle and an unknown angle.
100°
112°
120°
122°
Therefore , the solution of the given problem of angles comes out to be the right response is option d 122°.
An angle meaning is what?Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.
Here,
180 degrees is the length of a straight circle. It has been split into a 58-degree angle and an unidentified angle, as far as we are aware. So that we can determine the size of the undetermined angle, let's use subtraction:
=> Angle unknown = 180 degrees minus 58 degrees
=> Angle unknown = 122 degrees
As a result, the undetermined angle is 122° in size.
The right response is (d) 122°.
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your child is prescribed amoxicillin (40mg/kg/day; not to exceed 1500 mg per 24 hour period) to be given 3 times per day. if she weighs 81 pounds, what is the maximum dose that she should receive?
Child is prescribed amoxicillin to be given 3 times per day. If she weighs 81 pounds, the maximum dose that she should receive is 500mg.
First, we need to convert the weight of the child from pounds to kilograms. We can do this by dividing the weight in pounds by 2.205 to get the weight in kilograms:
81 pounds÷2.205=36.74 kg
Next, we can calculate the maximum dose of amoxicillin that the child should receive per day by multiplying her weight in kilograms by 40 mg/kg:
36.74 kg×40 mg/kg=1469.6 mg
Since the maximum dose should not exceed 1500 mg per 24 hour period, the child should receive no more than 1500 mg of amoxicillin per day.
Finally, we need to divide the maximum daily dose by 3 to determine the maximum dose per individual dose, since the medication is prescribed to be given 3 times per day:
1500 mg÷3=500 mg
Therefore, the maximum dose of amoxicillin that the child should receive per individual dose is 500 mg.
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Geometry, Help Please hurry!!!
In the diagram, ABCD is Similar EFGH. Find the following,
4. Scale Factor
5. EH
6. AB
Scale Factor is equal to [tex]\frac{2}{3}[/tex]. Length of EH is equal to 16 units and length of AB is equal to 9.
4. A scale factor is the ratio of the scales of an original object and a new object.
Scale factor = Ordinated dimension / original dimension
Scale factor = [tex]\frac{10}{15}[/tex]
Scale factor = [tex]\frac{2}{3}[/tex] (or) 0.67
5. Length of EH
Scale factor = [tex]\frac{EH}{AD}[/tex]
[tex]\frac{EH}{AD}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{EH}{24} = \frac{2}{3}[/tex]
EH = 2 * 8
EH = 16 units
6. Length of AB
Scale factor = [tex]\frac{EF}{AB}[/tex]
[tex]\frac{EF}{AB}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{6}{AB} = \frac{2}{3}[/tex]
AB = 3 * 3
AB = 9 units.
Therefore, Scale Factor is equal to [tex]\frac{2}{3}[/tex]. Length of EH is equal to 16 units and length of AB is equal to 9.
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a child-care center has 200 feet of fencing to enclose two adjacent rectangular safe play areas (of equal size). find the dimensions that will produce the maximum enclosed area. 5
The dimensions that will produce the maximum enclosed area for two adjacent rectangular safe play areas of equal size with 200 feet of fencing is 100 feet by 100 feet.
To solve this problem, use the area of a rectangle formula A = lw, where l is the length and w is the width.
Since the two play areas must be of equal size, let's call the length and width l and w, respectively.
We know that the total length of fencing is 200 feet, so l + w = 200 feet.
We can then solve for l by rearranging the equation as l = 200 - w.
We then substitute this into the area equation to get A = (200 - w)w.
To maximize the area, differentiate this equation to get A' = w - 200.
Set this to 0 and solve for w to get w = 100. Since l + w = 200, l = 100 as well.
Therefore, the maximum enclosed area is produced by dimensions of l = 100 feet and w = 100 feet.
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1. use the quadratic equation to find the exact solutions to this equation, and simplify your answer: 2x^2 6x 12
As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by [tex]ax² + bx + c = 0[/tex].
To solve the quadratic equation, we can use the quadratic formula given by[tex]x = (-b ± sqrt(b² - 4ac)) / 2a[/tex] Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.
Substituting these values in the quadratic formula, we get
[tex]x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2[/tex]
Hence, the exact solutions to the given equation are [tex](-3 + i√15) / 2 and (-3 - i√15) / 2.[/tex]
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Write a word sentence for the question
x - 14 = 52
Answer:
x-14=52|+14
x=52+14
x=66 candies
Step-by-step explanation: If Anna gives 14 candies to her sister, she remains with 52. How many candies does Anna have ?