The slope of the line tangent to the parabola's y-intercepty = [tex](x+2)^2-4[/tex] is 4.
We must first get the parabola's y-intercept in order to determine the slope of the line tangent to it.
We enter x=0 into the equation to obtain the y-intercept:
[tex]y = (x + 2)^2 - 4[/tex]
[tex]y = (0 + 2)^2 - 4[/tex]
y = 4 - 4
y = 0
Hence, the parabola's y-intercept is (0, 0).
The derivative of the parabola's equation must then be determined.
[tex]y = (x + 2)^2 - 4\\y = x^2 + 4x + 4 - 4\\y = x^2 + 4x[/tex]
dy/dx = 2x + 4
By adding x=0 to the derivative, we can now get the slope of the tangent line to the y-intercept:
dy/dx = 2x + 4
dy/dx = 2(0) + 4
dy/dx = 4
Hence, the slope of the line tangent to the parabola's y-intercepty = [tex](x+2)^2-4[/tex] is 4.
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Which measure is most appropriate to describe the center of the data in the stem-and-leaf plot below? Pounds of food Collected.
0. 5, 6
1. 0, 2, 3, 3, 4
2. 1, 9
3. Blank
4. 2
5. 1
A interquartile B range C median D mean range
The answer choice which is most appropriate to describe the center of the data as represented is; Median.
Which statistical measure best reflects the center of the given data?It follows from the task content that the stemans leaf plot shown in the task content is such that;
It contains outliers such as 5.1 and 4.2 and hence, the median best appropriates the central of the data distribution as it is minimally influenced by the extremes of data.
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How many hours does Diego need to work to earn the same amount of money that Mia earns for working 6 hours
Diego would have to put in 15 hours of labor to make the same amount of money as Mia does in just 6.
what is unitary method ?The unit method is a technique of challenge where you first measure the value of a specific unit, then multiply a certain value to get the answer. Simply expressed, a minimum unit value is extracted from with a specified multiple using the unit method. For contrast, 40 pens will cost you about 400 rupees, or $1.01. The method used to execute this might be standardized. a solitary nation. anything seems to have a distinctive component. (Mathematics, Algebra) Its capable of integrating and opposite are equivalent. (Molecular Algebra, Quantitative Analysis, Math and science of Matrix or Operators)
given
Diego need to work
105/7
=15$ per hour
150/15
=10$ per hour
Diego would have to put in 15 hours of labor to make the same amount of money as Mia does in just 6.
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determine if the following graphs have a slope that is positive,negative,zero,or underfined.
A line's slope might be zero, positive, negative, or undefinable. The slope of a horizontal line is zero because it does not climb vertically (y1 y2 = 0), but the slope of a vertical line is unknown because it does not run horizontally (x1 x2 = 0).
What does a positive slope look like?The slope (m = 3.5 is positive) and y-intercept (b = 4) of the line y = 3.5x + 4 are both positive. This indicates that the y-intercept, or point (0, 4), is where the line crosses.
What does a graph's zero slope mean?A line on a plane with no upward or downward slope is known as a line with zero slope in mathematics and computer science.
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A cylinder is sliced such that the cross section is perpendicular to its bases. What is the shape of the cross section?a) circleb) rectanglec) trapezoidd) triangle
Slice a cylinder so that the cross section is parallel to the bases. The cross section is rectangular in form.
What form does a cylinder's cross section take when it is cut in half so that the cross section is parallel to the bases?A cylinder's cross-section, for instance, is a circle when it is cut parallel to the base. The cross-sectional area of this slice is therefore equal to the area of a circle whose radius is the same as the radius of the cylinder supplied.
What form does the cross-section take?The cross-section has a rectangular form. It is identical in size and form to the base. We will now cut it with a plane that is parallel to the base. Keep in mind that perpendicular lines cross the base at ninety degrees.
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i need help with part a part b part c
Answer:
Step-by-step explanation: I'm not gonna give you the answer but i will explain what you need to do. First you need to draw a bar diagram and then you need to put the number equally. But first in part A is an easy question you only need to explain or tell the steps that you will do to solve the problem. For part C you only need to tell the answer but it says how how many got to fill equally so that means that there are gonna be equal number and an not so equal number. I hope this help you with your answer
(PLS HURRY!) On Melissa's 6th birthday, she gets a 2000$ CD that earns 6% interest, compounded. If the CD matures on her 14th birthday, how much money will be available?
Using compound interest formula when the CD matures on Melissa's 14th birthday, there will be $3187.69 available.
What is Compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Use the formula for compound interest to calculate the amount of money that will be available when the CD matures -
[tex]A = P(1 + r/n)^(nt)[/tex]
Where A is the amount of money available when the CD matures, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, the initial principal is $2000, the interest rate is 6%, and the CD will be held for 8 years (from Melissa's 6th to 14th birthday).
It is not given how many times per year the interest is compounded, so assume it is compounded annually.
Using these values in the formula -
[tex]A = $2000(1 + 0.06/1)^(1*8)A = $2000(1.06)^8A = $3187.69[/tex]
Therefore, the value is obtained as $3187.69.
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gotta get it done real quick b4 i get a F
Answer: The tape diagram that represents the problem is the second (7/3)
Step-by-step explanation:
3/7 isn't 7/3, and 7/7 isn't 7/3. By process of elimination, the second answer works; 7/3 = 7/3.
An electrician charges an initial service fee plus an hourly rate for all jobs. The electrician's charges are S 130 for a one-hour job and $210 for a two-hour job. Write an equation in slope-intercept form to show the total cost, y, for a job that takes x hours.
The interpretation of the slope in the context of the problem is: For every hour the electrician works, her pay will increase $28.
What is Slope of a Function?The slope of any function is the unit rate or average rate of change of the given function for that situation.
here, we have,
Given the function, E(x) = 130 + 28x, where:
E(x) is the amount an electrician charges per job
130 is the flat rate service which is the starting value or y-intercept
28 is the unit rate or slope, which is the fee charged per hour by the electrician to complete a job.
Thus, the interpretation of the slope in the context of the problem is: For every hour the electrician works, her pay will increase $28.
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HELP DUE TOMORROW!!!!!!!!!!
For the circle below, find the area of the shaded sector and the length of the arc that outlines the sector. All units are centimeters. Give your answers in terms of π.
Answer:
Step-by-step explanation:
How do you calculate optimal bundle?
To calculate the optimal bundle, you need to find the combination of goods or services that maximizes the consumer's utility while staying within their budget constraint.
The optimal bundle can be found by using the consumer's utility function and their budget constraint. The utility function specifies how much utility the consumer gets from consuming various quantities of the goods or services, while the budget constraint specifies the combinations of goods or services that the consumer can afford given their income and the prices of the goods or services.
To find the optimal bundle, follow these steps:
Write down the consumer's utility function, such as U(x, y) where x and y are the quantities of two goods.
Write down the consumer's budget constraint, such as P_x x + P_y y = I where P_x and P_y are the prices of the goods, I is the consumer's income, and x and y are the quantities of the two goods.
Find the marginal utility of each good by taking the partial derivative of the utility function with respect to each good. For example, the marginal utility of x is given by dU/dx.
Set the marginal utility per dollar spent on each good equal to each other, since the consumer should allocate their spending so that the marginal utility per dollar spent is the same for both goods. That is, set dU/dx / P_x = dU/dy / P_y.
Solve the resulting equations for the quantities of the goods that maximize the consumer's utility subject to their budget constraint.
The resulting combination of goods that solves the optimization problem is the consumer's optimal bundle. It represents the combination of goods that maximizes the consumer's utility given their budget constraint.
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algebra 2
help it’s due at 12 i need to come up with my own stuff
The vertex form equation is illustrated below.
How to explain the equationDirectrix (d): The directrix is the horizontal line y = -2.
Focus (F): The focus is the point (0, 2).
Vertex (V): The vertex is the point (0, 0).
Equation: The equation of the parabola is y = 1/4x^2.
The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) is the vertex. We already know the vertex of this parabola, which is (0, 0). To find the value of a, we can use the fact that the distance between the focus and the vertex is equal to the distance between the directrix and the vertex.
The distance between the focus (0, 2) and the vertex (0, 0) is 2 units. The distance between the directrix y = -2 and the vertex (0, 0) is also 2 units. Therefore, we can say that 1/(4a) = 2, or a = 1/8.
So, the vertex form equation of the parabola is y = 1/8(x-0)^2 + 0, which simplifies to y = 1/8x^2.
Vertex: The vertex is (0, 0).
Axis of Symmetry (AOS): The axis of symmetry is the vertical line x = 0.
Domain: The domain of the parabola is all real numbers, because the parabola continues indefinitely in both directions along the x-axis.
Range: The range of the parabola is y >= 0, because the lowest point on the parabola is the vertex (0, 0).
Transformations: The only transformation applied to the basic parabola y = x^2 is a vertical compression by a factor of 1/8.
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1:
Sam arrives at an amusement park with $61 that he
can spend at the amusement park. The entrance fee at
the amusement park is $20. It costs $3 to play a game
and $4 for each ride. He plays 6 games and goes on x.
rides. The inequality shown below represents this
situation.
38+4x≤61
The solution of the inequality is x ≤ 5.75. Based on the
solution, which statement must be true?
A.Sam went on at most 5 rides
B.Sam went on at most 6 rides
C.Sam went on more than 6 rides
D.Sam went on fewer than 5 rides
Using the inequality 38+4x≤61 shown to represent the situation, based on the solution that x ≤ 5.75, the true statement is A. Sam went on at most 5 rides.
What is inequality?Inequality is an algebraic statement showing that two or more mathematical expressions are unequal.
Inequalities are represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total amount Sam has to spend at the amusement park = $61
The entrance fee = $20
The unit cost of a game = $3
The unit cost of a ride = $4
The total number of games Sam plays = 6
The amount spent on games = $18 ($3 x 6)
The total known cost = $38 ($20 + $18)
Let the number of rides Sam goes on = x
Inequality:38 + 4x ≤ 61
Thus, the correct statement about the inequality is Option A.
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How many lb in 60 kg?
To convert between pounds and kilogrammes, multiply the number of pounds by 0.45359237, and to do the opposite, multiply the number of kilogrammes by 2.20462.
So, the value of 60 kg is equal to 132.2772 lbs.
The fundamental mass unit in the metric system is the kilogramme (kg). A kilogramme and 1,000 cubic centimetres of water have fairly similar masses.
One pound is approximately equal to 454 grams. One kilogram is the same as 2.20462 lbs.
One pound is equal to 0.45359237 kilograms.
To convert kilograms (kg) to pounds (lbs), you can use the following formula:
To convert kilograms to pounds, multiply your figure by 2.20462
To convert 60 kg to lbs, you can multiply 60 by 2.20462:
60 kg X 2.20462 lbs/kg
= 132.2772 lbs
Therefore, 60 kg is approximately equal to 132.2772 lbs.
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Solve the system using addition. Use pencil and paper. Explain why the addition method is a good choice for solving the system. If you wanted to solve for x first, is the addition method still a good choice? Explain.
x-5.2y= -5.4
-x+4.3y=3.6
Answer:
x = 5, y = 2
Step-by-step explanation:
x - 5.2y = -5.4
+ (-x + 4.3y = 3.6)
-------------------------
-0.9y = -1.8
y = 2
x - 5.2(2) = -5.4
x - 10.4 = -5.4
x = 5
The addition (elimination) method is a good choice for solving this system because the x's are already opposites, and will cancel out when the two equations are added together. If one was to solve for x first, this method wouldn't be as good of a choice since it involves extra steps to eliminate the y's from the equation.
What’s the difference between descriptive and inferential statistics?
The characteristics of a data set are enumerated by descriptive statistics. You can test a hypothesis or determine whether your data can be applied to a larger population by using inferential statistics.
To summarize a given data set, which may be a sample of a population or a representation of the entire population, brief informational coefficients known as descriptive statistics are used.
The two primary subcategories of descriptive statistics are measures of central tendency and measures of variability (spread). Descriptive statistics are thus used to summarize the data. Descriptive statistics can only ever make claims about the data set from which they were derived, using only the data that you have.
Statistical inference is the process of determining characteristics of an underlying probability distribution through the use of data analysis. Inferential statistical analysis, for instance, infers characteristics of a population by testing hypotheses and producing estimates.
Inferential statistics looks to identify some characteristic or overarching pattern about a large group through the study of a smaller sample size in the hopes that the results will apply to the larger group.
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What is superposition principle explain with example?
The superposition is the imposing of one wave on the other and resulting in the change of the amplitude of the final wave.
When two or more waves travel through the same space in superposition, their combined amplitudes equal the amplitudes they would have produced individually. For instance, two waves moving in the same direction will pass through each other without causing any distortion on the other side.
The pattern you see when shining light through two slits, the sounds you hear in acoustically sound rooms and music halls, the interference radios receive when moved close to other electronic devices, and any tone produced by a musical instrument are all examples of the superposition principle in action.
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If 3 pizzas cost $26.97, one pizza is $ ____
Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the trapezoid.
Answer:
0.06
Step-by-step explanation:
Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle either is in the hexagon or in the circle
Area of rectangle = 26.2 * 13 = 340.6 sq inch
Area of Hexagon = 3√3(side)²/2 = 3√3 (1.8)²/2 = 8.42 sq inch
Area of circle = π(radius)² = 3.14 * (2)² = 12.56 sq inch
Area of hexagon + area of circle = 12.56 + 8.42 = 20.98 sq inch
Probability of selecting point inside the hexagon or in the circle = 20.98/340.6
= 0.06
explain the Alternate Exterior Angles Theorem
The Alternate Exterior Angles Theorem states that when a pair of parallel lines is intersected by a transversal, the pairs of alternate exterior angles formed on opposite sides of the transversal are congruent.
If line AB and line CD are parallel, and line EF intersects both lines at points G and H respectively, then the angles formed on opposite sides of line EF and on the exterior of the parallel lines are congruent.
The Alternate Exterior Angles Theorem states that when a pair of parallel lines is intersected by a transversal, the pairs of alternate exterior angles formed on opposite sides of the transversal are congruent.
In symbols, the theorem can be written as:
∠1 ≅ ∠4
where ∠1 and ∠4 are alternate exterior angles.
This theorem is useful in solving problems involving angles and parallel lines, and it is commonly used in geometry proofs.
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28. Invitations On Monday, you invited 2 friends to your party. On
Tuesday, each friend invited 2 other friends. On Friday, each of
those friends invited 2 more friends. How many
people were
invited on Friday? Write your answer as a power. Then find the
value of the power.
Number of people were invited on Friday is 2^3 = 8 and the value of the power is 3
Let's track the number of invitations over the course of the week:
Monday: 2 invitations
Tuesday: Each of the 2 friends invited 2 more friends, for a total of 2 x 2 = 4 invitations
Friday: Each of the 4 friends invited 2 more friends, for a total of 4 x 2 = 8 invitations
So on Friday, there were a total of 8 invitations. We can write this as 2^3, since we started with 2 invitations and multiplied by 2 three times (once for each round of invitations). Therefore, the value of the power is 3.
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Yes or no please helpp
Answer:
Step-by-step explanation:
No, the point is not (1,0)
Solve for x explain how
answer : x(2)x(-3--6)
HELP ASAP, 100 POINTS, WILL GIVE BRIANLIEST,
A two-sided tile has black on one side and white on the other side. Determine the sample space for flipping the tile three times.
Toss 1 Toss 2 Toss 3
Black Black White
Black White White
Black White Black
White White Black
White Black Black
White Black White
Toss 1 Toss 2 Toss 3
Black Black Black
Black Black White
Black White White
Black White Black
Toss 1 Toss 2 Toss 3
Black Black Black
Black Black White
Black White White
Black White Black
Black Black Black
White White White
White White Black
White Black Black
White Black White
White White White
Toss 1 Toss 2 Toss 3
Black Black Black
Black Black White
Black White White
Black White Black
White White White
White White Black
White Black Black
White Black White
The possible outcomes for flipping a two-sided tile once are:
Toss 1 Toss 2 Toss 3
Black Black Black
Black Black White
Black White White
Black White Black
White White White
White White Black
White Black Black
White Black White
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Now, If we flip the tile three times, the sample space will consist of all possible outcomes of the three flips.
Hence, Each flip is independent, so the total number of possible outcomes is the product of the number of outcomes for each flip, which is 2.
Therefore, the sample space for flipping the tile three times is:
BBB,
BBW,
BWB,
BWW,
WBB,
WBW,
WWB,
WWW
Where,
B = the black side facing up, and
W = the white side facing up.
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please help me solve this paragraph proof for geometry, i’ll mark brainliest
The triangle AEC is a right angled triangle.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
To prove that triangle AEC is a right angled triangle, we need to show that the angle at vertex E is a right angle (i.e., measures 90 degrees).
BD≅CD
we can say that angle BDC is approximately equal to angle CBD.
∠ABD=∠ACD since they are opposite angles.
AB≅AC
∠ABC =∠ACB.
Therefore, angles ABD and ACD are also approximately equal to angle BAC.
we can say that angle
∠BAC=∠ ABC,
which means that angle EAC is approximately equal to angle ECB.
∠EAC and ∠ ECB add up to approximately 90 degrees
we can say that the angle at vertex E measures approximately 90 degrees.
Therefore, we have shown that triangle AEC is a right angled triangle.
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write the ratio of 30c to $4.50 in simplest form.
what is critical t value calculator
A critical t-value calculator is an online tool that helps you determine the critical value for the t-distribution for a given level of significance (alpha) and degrees of freedom (df). The critical t-value is the value that separates the area under the t-distribution curve into the rejection region and the non-rejection region for a two-tailed hypothesis test.
In statistical hypothesis testing, the t-distribution is used when the sample size is small, and the population standard deviation is unknown. The t-distribution is a family of distributions that depend on the degrees of freedom (df) and is bell-shaped, with a mean of 0 and a standard deviation of 1.
To use a critical t-value calculator, you need to input the significance level (alpha) and the degrees of freedom (df) and select whether the test is one-tailed or two-tailed. The calculator will then provide you with the critical t-value that separates the rejection and non-rejection regions for the given alpha and df.
It's important to note that the critical t-value depends on the level of significance (alpha) and the degrees of freedom (df). As the level of significant increases or the degrees of freedom decrease, the critical t-value also changes. Therefore, it's essential to use a critical t-value calculator to obtain the correct value for your hypothesis test.
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A critical t-value calculator is a tool used to calculate the critical value of t in a Student's t-test for a given significance level (alpha) and degrees of freedom (df).
When the sample size is small or the population standard deviation is unknown, the t-distribution is used to estimate the population mean.
The critical t-value in a Student's t-test is the value of t that separates the rejection region from the non-rejection region in a t-distribution. The null hypothesis is rejected if the calculated t-value is greater than the critical t-value, indicating that there is a significant difference between the sample mean and the population mean.
To use a critical t-value calculator, enter the t-significance test's level (alpha) and degrees of freedom (df). The degrees of freedom are defined as the number of observations minus one and are proportional to the sample size. The calculator will output the critical t-value for the given significance level and degrees of freedom once you enter these values.
For example, the degrees of freedom for a two-tailed t-test with a sample size of 20 and a significance level of 0.05 would be 20-1=19. The critical t-value at a significance level of 0.05 and 19 degrees of freedom is approximately 2.093, according to a critical t-value calculator.
Knowing the critical t-value is useful in hypothesis testing because it allows you to compare the calculated t-value from the sample data to the critical t-value to determine whether the null hypothesis should be rejected
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Which of the following attributes describes a right pyramid?
1. 2 apexes
2. triangular faces
3. circular base
4. curved surface
Attribute that describes right pyramid is triangular faces.
What is pyramid?A pyramid is a three-dimensional shape. A pyramid has a polygonal base and a flat triangular face that join at a common point called the apex. A pyramid is formed by connecting the base and apex. Each edge of the base connects to the top and forms triangular faces called sides.
Given, properties of right pyramid
1. 2 apexes - A right pyramid has only one apex
2. Triangular faces - A right pyramid has flat triangular faces.
3. Circular base - A right pyramid has polygonal base, not circular base
4. curved surface - A right pyramid has flat surface, not curved surface.
Hence, Property of triangular faces is present in a right pyramid.
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the line plot shows the cost of 5 books.A teacher buys all 5 books.She pays with a $100 bill. How much change should she get?
Answer:
Look at the screenshot
Step-by-step explanation:
WILL MARK BRAINLIEST!! Find the area of the figure. Round to the nearest square unit.
Type the answer in the box below.
___ square units
Rounding to the nearest square unit, the area is approximately 21 square units.
What is quadrilateral?A quadrilateral is a polygon with four sides, four vertices (corners), and four angles. Some examples of quadrilaterals include rectangles, squares, parallelograms, trapezoids, and rhombuses. Quadrilaterals can have sides and angles of different lengths and sizes. However, the sum of the angles in a quadrilateral always adds up to 360 degrees. Quadrilaterals are commonly studied in geometry, where their properties and characteristics are analyzed and used to solve various problems related to area, perimeter, and other geometric concepts.
Here,
To find the area of the figure ABCE, we need to find the height of the triangle ABCE with respect to base AB.
Let's call the point where the height meets base AB as D. Since angle E is 65 degrees, we know that angle AED is 180 - 65 = 115 degrees (since the sum of the angles in triangle AED is 180 degrees).
We also know that angle ADB is a right angle (since AD is perpendicular to AB), so angle EDB is 180 - 115 - 90 = 25 degrees.
Using trigonometry, we can find that the length of AD is:
AD = AB * sin(25) = 10 * sin(25) ≈ 4.24 units.
Therefore, the area of quadrilateral ABCE is:
Area = (1/2) * base * height = (1/2) * AB * AD ≈ (1/2) * 10 * 4.24 ≈ 21.2 square units.
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Equations with roots that are whole numbers and fractions
The quadratic equations with roots that are whole numbers and fractions are listed below:
Case 2: 9 · x² - 78 · x - 27 = 0
Case 3: 7 · x² - 26 · x - 8 = 0
Case 4: 4 · x² + 2 · x - 32 · x - 16 = 0
Case 6: 4 · x² - 5 · x - 6 = 0
Case 7: 7 · x² + 38 · x - 24 = 0
How to factor a quadratic equation
In this problem we find eight cases of quadratic equations of the form a · x² + b · x + c = 0, where a, b, c are real coefficients. All roots can be found by means of algebra properties:
Case 1
5 · x² + 8 · x + 4 = 0
5 · [x² + (8 / 5) · x + 4 / 5] = 0
5 · (x + 4 / 5 - i 2 / 5) · (x + 4 / 5 + i 2 / 5)
Case 2
9 · x² - 78 · x - 27 = 0
9 · [x² - (26 / 3) · x - 3] = 0
9 · (x - 9) · (x + 1 / 3) = 0
Case 3
7 · x² - 26 · x - 8 = 0
7 · [x² - (26 / 7) · x - 8 / 7] = 0
7 · (x - 4) · (x + 2 / 7) = 0
Case 4
4 · x² + 2 · x - 32 · x - 16 = 0
4 · x² - 30 · x - 16 = 0
4 · [x² - (15 / 2) · x - 4] = 0
4 · (x - 8) · (x + 1 / 2) = 0
Case 5
2 · x² - 20 · x + 32 = 0
2 · (x² - 10 · x + 16) = 0
2 · (x - 8) · (x - 2) = 0
Case 6
4 · x² - 5 · x - 6 = 0
4 · [x² - (5 / 4) · x - 3 / 2] = 0
4 · (x - 2) · (x + 3 / 4) = 0
Case 7
7 · x² + 38 · x - 24 = 0
7 · [x² + (38 / 7) · x - 24 / 7] = 0
7 · (x - 4 / 7) · (x + 6) = 0
Case 8
x² - 5 · x - 6 = 0
(x - 6) · (x + 1) = 0
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