The zeros of function f(x) = x² -x - 2 are: x = 2 and x = -1
Consider given polynomial function f(x)=x² -x - 2
As we know the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.
To find the zeros of function f(x), we need to equate f(x) to zero then solve it for x.
⇒ f(x) = 0
⇒ x² -x - 2 = 0
using the Quadratic Formula where
a = 1, b = -1, and c = -2
[tex]\Rightarrow x=\frac{-b\pm \sqrt{b^2 -4ac} }{2a}\\\\\\ \Rightarrow x = \frac{1\pm \sqrt{9} }{2}\\\\\\\Rightarrow x = \frac{1\pm 3 }{2}[/tex]
Thus x = 2 and x = -1 are zeros.
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The complete question is:
What are the zeros of f(x)=x² -x - 2 ?
On Thursday, 4 out of the first 10 students who ate a school lunch chose spaghetti. Based on this information, if 640 students ate a school lunch on Thursday, how many students could be expected to have chosen spaghetti?
Answer:
256
Step-by-step explanation:
Given the function h(x)=-x²+4x+12, determine the average rate of change of the function over the interval -1≤x≤8
Step-by-step explanation:
the average rate of change is
(h(interval end) - h(interval begin)) /
(interval end - interval begin)
in our case this is
(h(8) - h(-1)) / (8 - -1) = (108 - 9) / 9 = 99/9 = 11/1 = 11
What is the relation between mean median and mode Class 10?.
The relation between mean, median and mode the difference between mean and mode is equal to three times the difference between the mean and median.
The average of a set of numerical data is referred to as the arithmetic mean. Either a weighted average or a basic average is possible. Adding up all the data from the data set, we divide it by the total frequency to get the simple average.
When a data set is ordered in either a descending or an ascending order, the median is the number that falls in the middle of the range. Because it removes the outliers, the median is far more useful than the mean.
The most frequent number in a dataset is referred to as the mode. There could be one mode, several modes, or none at all for a given collection of integers.
(Mean - Median) = 1/3 (Mean - Mode).
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Determine the missing step for solving the quadratic equation by completing the square.
0 = –6x2 + 24x – 5
5 = –6x2 + 24x
5 = –6(x2 – 4x)
inside the parentheses and
.
–19 = –6(x – 2)2
StartFraction 19 Over 6 EndFraction = (x – 2)2
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot = x – 2
The two solutions are
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot
Answer:2 = x
The missing step is:
Take the square root of both sides of the equation to get the value of x, which is:
x = 2 ± √(19/6)
Now we have our solutions, x = 2 + √(19/6) and x = 2 - √(19/6) which are the solutions of the quadratic equation.
Step-by-step explanation:
Answer: 1) Add 4 2) Subtract 24 from 5 3) 2
Correct on Edge 2023 :)
Which set of numbers contains only solutions to the inequality 2-3x>17?
A. x= -5, -3, 0, 1
B. x= -12, -9, -8, -5
C.x= -9, -8, -7, -6
D. x= -2, -1, 0, 1
To find the solution set for the inequality 2 - 3x > 17, we can start by solving for x:
2 - 3x > 17
3x < 15
x < 5
So, the solution set for the inequality is all values of x that are less than 5.
Of the options given, only the set C, x = -9, -8, -7, -6, contains only numbers that are less than 5. Therefore, the set of numbers that contains only solutions to the inequality is C, x = -9, -8, -7, -6.
What is the condition for two lines to be perpendicular?.
The condition for two lines to be perpendicular lines :
the two lines meet each other at the right angle
We know that the two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90°
Since these lines are inclined at 90° to each other, hence they create right angles.
This means, the condition for two lines to be perpendicular lines is that the two lines must meet each other at the right angle
This property of lines is said to be perpendicularity.
Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.
For example, if two lines l₁ and l₂ are perpendicular to each other then they are represented as l₁ ⊥ l₂.
The product of slopes of perpendicular lines is always -1.
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Can someone please tell me how to do equivalent ratio tables
What is the standard form of Y =- 5x 3?.
A polynomial equation can be written in a particular format by using its standard form. A polynomial equation is written in its standard form when the terms are written in descending order of their exponents and the leading coefficient, or the coefficient of the term with the highest exponent, is 1, as in the example above.
The term with the highest exponent in the equation Y = -5x3 is x3, which has a coefficient of -5. The entire equation must be divided by -5 in order to be written in standard form, which will set the coefficient of the x3 term to 1 and convert the equation to standard form.
The zero coefficients have been included in the equation when written in this form, however when the equation is read, we only take the term for the non-zero coefficients into account.
So, the standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.
Therefore ,the answer is Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.
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The standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.
The term with the highest exponent in the equation Y = -5x3 is x3, which has a coefficient of -5. The entire equation must be divided by -5 in order to be written in standard form, which will set the coefficient of the x3 term to 1 and convert the equation to standard form.
The zero coefficients have been included in the equation when written in this form, however when the equation is read, we only take the term for the non-zero coefficients into account.
So, the standard form of Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.
Therefore ,the answer is Y = -5x^3 is -5x^3 + 0x^2 + 0x + 0 = 0.
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1. Draw a proportional line with a slope of 3/2
*desmos graphing calculator*
The bisector of one of the angles of a rectangle also bisects the side of a rectangle. Find the perimeter of the rectangle if you know that the shorter side of the rectangle is equal to 10 cm.
If the bisector of one of the angles of a rectangle also bisects the side of a rectangle. The perimeter of the rectangle if you know that the shorter side of the rectangle is equal to 10 cm is 60cm.
How to find the perimeter of the rectangle?If we look at triangle BCE, we will see that triangle BCE is isosceles based on the fact that both angles are equal to 45 degrees.
Hence,
BC = CE =10 cm
Lengths of the base and height = 20 and 10
Now let find the perimeter of the rectangle
Perimeter of the rectangle = 20 + 10+20+10
Perimeter of the rectangle = 60cm
Therefore the perimeter of the rectangle is 60cm.
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Daffynition decoder answers page 16. 7? hints are ozone and mistletoe from the punchline algebra book b
The answer for the Daffynition Decoder is 7.
The formula is O3 - M2 = 7. The calculation is to take the ozone (O3) and subtract the mistletoe (M2). O3 stands for ozone, which is composed of three atoms of oxygen and is represented by the number 3. M2 stands for mistletoe, which is composed of two atoms of oxygen and is represented by the number 2. The formula used to calculate the answer is m = 2o + 1, where m is the number of mistletoes and o is the number of ozones. The calculation is as follows: if there are 2 ozones, then the number of mistletoes is 2(2) + 1 = 5. Therefore, the answer is 7 (5 mistletoes and 2 ozones). This formula is useful for quickly calculating the total number of items when you know the number of each type of item.Therefore, if we subtract the mistletoe from the ozone, we get the answer of 7. In summary, O3 - M2 = 7.
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What is Y =- 2 on a graph?.
The equation y = -2 is represented on the graph as shown below :
Use the slope-intercept form to find the slope and y-intercept.
The slope, m, represents the steepness of a line. The slope of the line is also termed as gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.
The slope-intercept form is
y = mx + b, where m is the slope and b is the y-intercept.
y = mx + b
Find the values of m and b, using the slope-intercept equation.
y = -2
m = 0, b = -2.
The slope of this line = m = 0
The y-intercept = -2, therefore a point on the line = (0,-2)
Finding two points on the line:
(0,-2), (1,-2)
Thus, the equation y = -2 on graph is shown below.
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Arc length of GH = 7pi cm
r =
The formula for a circle's arc length is L = r * θ, where L is the arc length, r is the circle's radius, and θ is the arc's central angle, expressed in radians.
What is the radius r in the given question?We can calculate the radius of the circle by dividing the arc length by the central angle because we know the value of L (7 cm) and that can be calculated from the arc's measure (degrees or radians):
r = L / θ
It is crucial to keep in mind that in order to calculate the radius, you must first know the arc's central angle's measurement in radians.
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What is the maximum possible value of the greatest common divisor of two consecutive terms of the sequence $a_n = n! + n$, where $n \ge 0$?
Answer:
2
Step-by-step explanation:
You want the largest possible greatest common divisor of consecutive terms of the sequence an = n! +n.
SequenceThe sequence starts off 2, 4, 9, 28, 125, ...
The first two terms have a GCD of 2. The remaining pairs of terms have a GCD of 1.
The maximum possible GCD of adjacent terms is 2.
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How many degrees is a 360?.
The measure in degrees of the angle, the 1/360 of a circle is equals to one degree.
First note the following information: Degrees is an angular unit. The One rotation around the circle is equals to the 360 degrees. Angles measured in degrees always require the unit "degrees" after either a number or the degree symbol °. For example, 90 degrees = 90°. Rotation is 360 degrees, so angles greater than 360 degrees indicate more than a full rotation. The resulting direction that, when plotted on a circle, makes the endpoint of that angle the same as any other angle between 0 and 360 degrees. These angles are called coends. The arc should be proportional to the angle. The circle should be 360 degrees. Therefore, the degree of the angle is = 1/360 ( 360°) = 1 degree. From this we can conclude that the degree of the angle is 1 degree.
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Complete question:
How many degrees is a circle of 1/360?.
The first of two numbers decreased by five
times the second number equals -10. The first
number decreased by two times the second
number equals -1. Find the numbers.
Answer:
First number = 5, second number = 3
Step-by-step explanation:
we can write this as x–5y = –10 and x – 2y = –1 so we know now that 3y = 9 so we divide both by 3 to get: y = 3
now that we know the second number we can multiply it by 2 to get 6 and now we just have to figure out what – 6 is –1 which would be 5
The decreased numbers are first number is 2. and the second number is -9.
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
Given that, there are two numbers, first of two numbers decreased by five times the second number equals -10. The first number decreased by two times the second number equals -1.
x - y = 0
The first number decreased 5 times
-5 -y = -10
-y = -10 + 5
-y = -5
y = 5
The second number decreased 2 times
x - (-2) = -1
x + 2 = -1
x = -1 -2
x = -3
Now,
the first number is
-3 - 5 = -10
-8 = -10
10-8 = 0
2 = 0
the second number is
-3 - 5 =-1
-8 = -1
-8 +1 =0
-9 = 0
Hence, the answer is 2, -9.
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I’m a sample of 2000 people, 430 people have their ears pierced. Two unrelated people are selected at random without replacement. Find the probability that both people have their ears pierced
The probability that both people have their ears pierced is calculated by dividing the number of people with pierced ears by the total number of people in the sample. This can be expressed as a fraction, with 430/2000 = 0.215, or 21.5%.
What is a probability?Probability is a measure of how likely an event is to occur. It is stated as a number between 0 and 1, with 0 indicating that the occurrence is impossible and 1 indicating that the event is unavoidable.
In this question, by dividing the number of persons with pierced ears by the total number of participants in the sample to find the chance that both people have their ears pierced. In this situation, the answer is 430/2000 = 0.215.
This may be read as follows: 430 persons out of every 2000 get their ears pierced. Therefore the chance of picking two persons at random from this sample who both had their ears pierced is 0.215, or 21.5%.
This may also be stated as a fraction, with the numerator being the number of persons with pierced ears (430) and the denominator representing the total number of participants in the sample (2000). As a result, the likelihood is 430/2000, or 0.215.
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What is the plot of a graph?.
A scatter plot is a form of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a collection of data.
It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram. A plot is a visual representation of a data collection, typically in the form of a graph illustrating between two or more variables.
But you may also do this with data that is offered in tabular form. Graphs may also be used to count off the value of an unknowing variable plotted as a function of a known variable if a scale or ruler is available.
Graphs and charts are useful visual aids because they make information accessible and quick to understand. When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.
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How do you write a logarithmic expression?.
Write a logarithmic expression in the form [tex]log_{b}M[/tex] = N.
In an exponential equation, the variable is expressed as an exponent. A logarithmic equation uses the logarithm of an expression including a variable to solve the problem. Check to determine if you can write both sides of an exponential equation as powers of the same number before attempting to solve it. If you can't, use property after taking the common logarithm of both sides of the equation.
Use the properties of logarithms to express the equation in the form [tex]log_{b}M[/tex] = N, then convert it to exponential form, M = [tex]b^{N}[/tex], to solve an equation requiring logarithms.
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An equation i modeled on a number line which equation doe thi model repreent a. 7/8-1-4 =6/8 b. 7/8 1/4= 9/8 c. 7/8- 1/4 = 5/8 d. 7/8 2/8=9/16 pl help
The equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".
What is algebraic equation ?
An algebraic equation is a mathematical statement that uses mathematical symbols (such as numbers, variables and mathematical operations) to express the equality of two expressions. It is used to represent mathematical relationships and to find solutions to problems. The most common operations used in algebraic equations are addition, subtraction, multiplication, and division.
This is an algebraic equation and it represents the mathematical relationship between different values.
The equation is , 7/8 - 1/4 = 5/8
This equation states that if we subtract 1/4 from 7/8 we get 5/8.
It can be verified by solving the equation:
7/8 - 1/4 = (7/8) - (1/4) = (74/84) - (18/48) = 28/32 - 8/32 = 20/32 = 5/8
So, the equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".
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The equation is , 7/8 - 1/4 = 5/8
This equation states that if we subtract 1/4 from 7/8 we get 5/8.
It can be verified by solving the equation:
7/8 - 1/4 = (7/8) - (1/4) = (74/84) - (18/48) = 28/32 - 8/32 = 20/32 = 5/8
So, the equation modeled on the number line represents "c. 7/8 - 1/4 = 5/8".
Write log 4 + log 7 - log 2 as a single logarithm. Which of the following is the answer
1) log 14
2) log 25
3) log 28
4) log 56
The answer is Option 3: log 28.
What is logarithm?Logarithm is a mathematical function that is used to determine the exponent of a given number. For example, the logarithm of 8 is equal to 3, since 2 to the power of 3 is equal to 8. Logarithm is also known as log and is commonly used in scientific calculations to simplify complex equations.
This can be derived by using the logarithmic rule of multiplication and addition: log(ab) = log(a) + log(b). In this case, log 4 + log 7 - log 2 = log(4*7) - log 2 = log 28.
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51 is 20% of what number?
Answer:
255
Step-by-step explanation:
51 x 100/20
The drawing below shows three squares joined at their vertices to form a right triangle. The area of square A is 9 ft2 and the area of
square B is 16 ft². What is the side length of square C?
25
7
8
5
The side length of square C is given as follows:
5 ft.
How to obtain the side length of square C?The area of a square of side length is given as follows:
A = s².
Hence the side length of A and B are given as follows:
A = 3, as the square has area of 9 ft².B = 4, as the square has area of 16 ft².Then the side length of square C is the hypotenuse of a right triangle, and applying the Pythagorean Theorem, it's length is obtained as follows:
C² = 3² + 4²
C² = 25
C = 5 ft.
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10x + 2 ≤ 14 solve the inaqualty
Answer:
[tex]x\le \cfrac{6}{5}[/tex]
Step-by-step explanation:
[tex]10x+2\le \:14[/tex]
[tex]10x\le \:12[/tex]
[tex]\cfrac{10x}{10}\le \cfrac{12}{10}[/tex]
[tex]x\le \cfrac{6}{5}[/tex]
express 52 Kobo as a decimal of 1.00
We have expresses 53 Kobo as a decimal of 0.52 Naira.
What is decimal?A number that is not a whole is written using decimals. Between whole numbers are decimal numbers. 12.5, a decimal number that falls between 12 and 13, serves as an illustration of this. It is less than 13, but it is greater than 12. It's crucial to remember that fractions and decimal numbers are equivalent; the only difference is how they are expressed.
In keeping with the previous illustration, the mixed number 12 12 and 12.5 are equivalent numbers. No matter how complex the decimal is, this is true. For instance, 0.75 and 3/4 are equivalent. If you wanted to go even further, you could say that 0.75 is equivalent to 75%.
We know that 1 Kobo = 0.01 naira
Therefore, 52 kobo = 0.01 × 52 naira
= 0.52 naira
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What are the 4 laws of logarithms?.
The 4 laws of logarithms are product rule, division rule, power rule and change of base rule.
Product rule - According to this principle, multiplying two logarithmic numbers is equivalent to adding their individual logarithms.Division rule - The difference between each logarithm is equivalent to the division of two logarithmic values.Power rule/Exponential Rule - According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.Change of base rule - A logarithm in one base is changed to a logarithm in another base using the change of base rule.To learn more about logarithms here:
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer: The area of a rectangular room is 750 square feet and the width of the room is 5 feet less than the length of the room.
Three equations that can be used to solve for y, the length of the room are:
y(y + 5) = 750: This equation uses the formula for the area of a rectangle, which is length x width. Since the width is 5 feet less than the length, we can substitute y-5 for the width.
750 – y(y – 5) = 0: This equation uses the same method as the first equation, but it is rearranged to solve for y.
(y + 25)(y – 30) = 0: This equation uses the quadratic formula to solve for the length of the room, this equation is also useful when the length is an irrational number.
Note that the fourth equation y(y – 5) + 750 = 0 is not valid because it is not possible to have negative area, hence y(y-5) should not be added to 750.
The fifth equation (y+25)(y-30)=0 is also not valid because it gives y = -25 and y = 30 as solutions but the length of the room can't be negative.
Step-by-step explanation:
How do you find the standard deviation of 4?.
The standard deviation of 4:
Calculate the Mean (the simple average of the numbers)Subtract the Mean from each value, then square the result.Calculate the mean of those squared differences next.We're done when we take that's square root!The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
In descriptive statistics, the standard deviation measures how widely the data points vary from the mean. It describes how values are distributed throughout the data sample and measures how widely apart data points are from the mean. The square root of the variance is used to calculate the standard deviation of a sample, statistical population, random variable, data collection, or probability distribution.
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What is the inverse of a relation?.
The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.
Let R be a relation from a set A to another set B. Then R is of the form. The inverse relationship of R is denoted by R-1 and its formula is R-1 ={(y, x): y∈B and x∈A}.
The first element of each ordered pair of R = the second element of the corresponding ordered pair of R-1 and
The second element of each ordered pair of R = the first element of the corresponding ordered pair of R-1.
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Samera placed the congruent ide of thee two triangle together to form a quadrilateral. Which tatement are true of the quadrilateral he contructed? Select three option
A parallelogram is created when two congruent triangles with the same orientation are connected along equal sides.
When two congruent triangles with different orientations are joined along equal sides, they can be used to make a kite or a dart.
Here, ABC and ACD, two triangles that are mirror reflections of one another, combine to make a dart.
Darts and kites both feature two adjacent pairs of equal sides. The sole distinction is that darts are concave whereas kites are convex.
A quadrilateral can be produced if there are more than two congruent triangles. At least two of the sides of such a quadrilateral will be equal if each of its sides is one of the sides of the triangles.
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