An example of rational roots can be given as:
Let the polynomial be: 4x³ + 3x² + 6x + 9;
Then,
coefficient of the variable with the highest degree = 4
coefficient having the variable with degree 0 = 9
Factors of 4 are: 1, 2;
Factors of 9 are: 1, 3;
The possible rational roots for such an equation will be: 3, 1, 1/2, 3/2, -3, -1, -1/2, -3/2;
Rational roots are the roots or solutions of equations of any polynomial consisting of one variable of any power.
Where all the coefficients are integers.
Let the solution/root of a polynomial be p/q. Then the root would be rational if and only if the coefficient of the variable with the highest degree is divisible by 'q' , and the coefficient independent of the variable or having the variable with degree 0 is divisible by 'p'
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The product of three conecutive whole number i 46620. What i the um of thee number?
The required three consecutive numbers are 35, 36, 37
Let the three consecutive numbers as per the questions are x , x+1 , x+2
Since, According to the question, the product of these three consecutive numbers are 46620
Therefore, we can write
x ( x+1 )( x+2 ) = 46620
x([tex]x^{2}[/tex] + 2x + x + 2 ) = 46620
[tex]x^{3}[/tex]+ [tex]2x^{2}[/tex] + [tex]x^{2}[/tex] + 2x = 46620
Now, [tex]x^{3}[/tex] + [tex]2x^{2}[/tex] + [tex]x^{2}[/tex] + 2x - 46620 = 0
[tex]x^{3}[/tex] + [tex]3x^{2}[/tex] + 2x - 46620 = 0
After factorization, we get
( x- 35 )( [tex]x^{2}[/tex] + 38x + 1332 ) = 0
x - 35 = 0 Since ( [tex]x^{2}[/tex] + 38x + 1332 ) will always be a positive number
Therefore, x = 35
So, x + 1 = 35 + 1 = 36
x + 2 = 35 + 2 = 37
Therefore, the numbers are 35 , 36 , 37
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The most important condition for sound conclusions from statistical inference is usually.
The data can be thought of as a random sample from the population of interest. So the option a is correct.
In the given question we have to find the most important condition for sound conclusions from statistical inference is usually.
The given statements are:
(a) the data can be thought of as a random sample from the population of interest.
(b) the population distribution is exactly Normal.
(c) the data contain no outliers.
The results of the hypothesis testing will still be accurate even if the population distribution is not perfectly normal, according to the Central Limit Theorem.
Statistical techniques can be used to identify and prevent outliers if the data contains them.
However, the results of the hypothesis testing will not be reliable for non-random samples.
The data can be thought of as a random sample from the population of interest. So the option a is correct.
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The right question is:
The most important condition for sound conclusions from statistical inference is usually that
(a) the data can be thought of as a random sample from the population of interest.
(b) the population distribution is exactly Normal.
(c) the data contain no outliers.
archer can paint a room in 4 hours, while ollie can do it in 3. if they work together, how long will it take them to paint two rooms? express your answer as a decimal rounded to the nearest tenth.
If Archer can paint a room in 4 hours, while Ollie can do it in 3 hours. If they work together then it will take 206 minutes to paint two rooms.
What is the relation between work and time?
Work Problems are word problems that involve different people or entities doing work but at different rates.
Work = Efficiency x Time
According to the given question:
Archer paints a room in = 4 hours
Work done by him in an hour =1/4
Ollie paints a room in = 3 hours
Work done by him in an hour = 1/3
So, work done by them in an hour W = (1/4 +1/3)= 7/12.
They both will complete the work in = 1/W
= 1/7/12
= 12/7 hours
≈ 103 minutes
Therefore it take 103 minutes to paint one room together.
To paint two rooms it will take 103 x 2 = 206 minutes together.
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Ayden is preparing for a job interview later today. He is deciding what to wear to the interview. He has 6 shirts, 4 pairs of pants, 3 ties, and 2 pairs of shoes. If an outfit consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes, how many different outfits can ayden make?.
If an outfit consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes, then 144 different outfits Ayden can make.
In the given question we have to find how many different outfits can ayden make.
Ayden has 6 shirts, 4 pairs of pants, 3 ties, and 2 pairs of shoes.
We have to choose outfit for interview consists of 1 shirt, 1 pair of pants, 1 tie and a pair of shoes.
We have to choose 1 shirt and he has 6 shirts. So he can choose different shirts in 6 ways.
Similarly;
We have to choose 1 pair of pants and he has 4 pair of pants. So he can choose different pair of pants in 4 ways.
We have to choose 1 tie and he has 3 ties. So he can choose different ties in 3 ways.
We have to choose one pair of shoes and he has 2 pair of shoes. So he can choose different pair of shoes in 2 ways.
So the total different outfits that he select = 6*4*3*2 = 144
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please someone help me
In order to keep the Bermuda Triangle on the Flat Earth from toppling over, it was balanced on the hole which leads to the interior of the hollow Earth. If the vertices of the Bermuda Triangle are given by (1,3) , (2,7) , and (6,2). In order to find the hole we will need to find the intersection of at least 2 lines. Name 2 points through which one of those lines will pass (in the form (x,y),(x,y))
The two lines are given as follows:
y = 4x - 1.y = -1.25x + 10.5.Their intersection is:
(2.19, 7.76).
The two points in which the line y = 4x - 1 passes are:
(2.19, 7.76) and (3,11).
How to define the linear functions?The format of the linear function is given by:
y = mx + b.
The linear function is defined taking a pair of points, and then:
The slope is the change in y divided by the change in x.The intercept is found replacing one point into the equation y = mx + b after the slope is found.For the first line, the two points are:
(1,3) and (2,7).
The slope is:
m = (7 - 3)/(2 - 1) = 4.
Hence:
y = 4x + b.
When x = 1, y = 3, hence the intercept b is obtained as follows:
3 = 4 + b
b = -1.
Then the first line is:
y = 4x - 1.
For the second line, the points are:
(2,7) and (6,2).
Hence the slope is of:
m = (2 - 7)/(6 - 2) = -5/4 = -1.25.
Then:
y = -1.25x + b.
When x = 2, y = 7, hence the intercept b is obtained as follows:
7 = -1.25(2) + b
b = 10.5.
Hence the second line is:
y = -1.25x + 10.5.
The x-coordinate of the intersection is given as follows:
4x - 1 = -1.25x + 10.5
5.25x = 11.5
x = 11.5/5.25
x = 2.19.
The y-coordinate of the intersection is:
y = -1.25(2.19) + 10.5 = 7.76.
Another point in which the line y = 4x - 1 passes is:
y = 4(3) - 1 = 11.
Hence point (3,11).
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for every nonzero rational number x, write x as p/q where p, q are integers with no common factors and q > 0. f(x)
f(xn) = 1 /nq → 0 ,while f(x0) = 1/q != 0
Given ε > 0,
Let N ∈ N such that , N < ε, and let δ = min(δ1, . . . , δN ).
Then if |x − x0| < δ, it means that x is either irrational or of the rational form p/q for some q > N.
Therefore , if |x − x0| < δ, it means
|f(x) − f(x0)| = |f(x)| < 1/N < ε
Rational numbers : when p and q are integers and q is not equal to 0, the representation of a rational number is in the p/q form. The integer p can be either positive, negative, or even zero. Example: 2/3
Irrational numbers are defined as decimal numbers that are not represented in fractional form. The reason for this is that there are countless repeating and non-repeating phrases after the decimal point. Example: 1.414
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In it expanded form a number include three power of 10 and a five. What might the anwer be
Using Expanded form formula,
the Expanded form of 1005 is { (1000×1 ) + (1×5)}.
Expanded from:
Breaks a number into its digits and expands to display the value of each digit.
For example, an extended form of 943 is
9 × 100 + 4 × 10 + 3 × 1 = 900 + 40 + 3
Find expanded form:
To write a number in expanded form:
Gets a number in its simplest form.Determine the position using the position table.Multiplies a number by its place value.All numbers must be displayed as the product of the number and the digit value.
we have given that,
Number = three power of ten and five = 1000+5
= 1005
Expanded from of given number is
one's place number is 5 and its expanded
from 1× 5
ten's place number is zero and it's expanded form 10×0
hundred's place number is zero and it's expanded form is 100×0
thousand's place number is 1 and it's expanded from is 1,000× 1
so, the expanded from of given number is
= (1,000× 1 ) + (100×0) + (10×0)+(1× 5)
=( 1,000× 1) + (1× 5) = 1,000 + 5
Hence , required form is result occurred.
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which is the biconditional of the following statement: if a polygon is a triangle, then it has exactly three sides. responses a polygon is a triangle if and only if it has exactly three sides. a polygon is a triangle if and only if it has exactly three sides. if a polygon does not have exactly three sides, then it is not a triangle. if a polygon does not have exactly three sides, then it is not a triangle. if a polygon has exactly three sides, then it is a triangle. if a polygon has exactly three sides, then it is a triangle. a polygon is not a triangle if and only if it does not have three sides
The biconditional statement,
→ If a polygon is a triangle, then the polygon has exactly three sides.
→ If a polygon has exactly three sides then it is a triangle.
Given statement;
If a polygon has three sides, then it is a triangle. If a polygon is a triangle, then it has three sides.
The biconditional of the given statement is,
→ If a polygon is a triangle, then the polygon has exactly three sides.
→ If a polygon has exactly three sides then it is a triangle.
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Ue Newton' method to find the abolute maximum value of the function f(x) = 2x in x, 0 ≤ x ≤
The absolute maximum value of the given function f(x) = 2x is 8.
Given, a function f(x) = 2x
we have to find the absolute maximum value of the function f(x) = 2x in x,
0 ≤ x ≤ 4
So, as it is clear that the given function is a one-one function and therefore it is either increasing or decreasing function.
then, the given function f(x) = 2x will be maximum at the maximum value in the domain of the function i.e. 4.
So, the absolute maximum value be
f(4) = 2(4)
f(4) = 8
8 is the absolute maximum value of the given function f(x) = 2x.
Hence, the absolute maximum value of the given function f(x) = 2x is 8.
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an 79-kghiker climbs to the summit of mount mitchell in western north carolina. during one 2.0-hh period, the climber's vertical elevation increases 540 mm.
The change in gravitational potential energy of the climber-Earth system,=4.49*10^5j.
What is Potential Energy?An object can store energy depending on its position. For example, heavy balls in demolition machines store energy when held high. This stored potential energy is called potential energy.A tense bow can also store energy due to its position. However, the position of the arc stores energy when its position is changed from its normal equilibrium position. This stored potential energy is called potential energy. Potential energy is the stored potential energy of an object.To determine the gravitational potential energy of an object, we first need to arbitrarily assign a zero elevation location. The bottom is usually considered the zero height position. But that's just an arbitrarily assigned position that most people agree with.Since many of our labs are performed on benchtops, it's common to have a benchtop height position of 0. Again, this is arbitrary. When the tabletop is at zero position, the object's potential energy is based on its height relative to the tabletop.According to our question-
Vertical height of climber, h = 540 m
Climbers need to find changes in the gravitational potential energy of the Earth system. We know that gravitational potential energy is generated when an object changes position. It is given as
Hence, The change in gravitational potential energy of the climber-Earth system,=4.49*10^5j.
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Jess starts doing her science assignment at 4:30 p.m. She takes 40 minutes to do the assignment.
What time does Jess finish her assignment?
Answer:
Time when Jessie starts doing her he: 4:30
Time talked to complete the hw : 40minutes
Time Jessie finishes the hw: 5:10
Suppose you enter the formula =D2/E2 in an Excel spread-
sheet and an error message appears.
What error message did you receive?
When formula =D2/E2 is enter in Excel spreadsheet then we receive an error which is #DIV/0! .
Excel spreadsheet Error :
Microsoft Excel shows #DIV/0. Error when dividing a number by zero (0). This happens when you enter a simple formula like =5/0, or when the formula refers to a cell that contains 0 or is blank, as shown in this image.
Easiest way to suppress #DIV/0! The error is using the IF function to evaluate the existence of the denominator. If 0 or no value, display 0 or no value as the result of the formula instead of
#DIV/0.
For example, use =IF(A3,A2/A3,0) to return 0 if the formula returning the error is =A2/A3
The function or formula is not null or an empty cell.Change the cell reference in the formula to another cell that does not have a zero (0) or blank value.Enter #N/A in reference cellTo learn more about Excel spreadsheet error , refer:
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What should we multiply to eliminate fractions in an equation?.
Fractions can be defined as the representation of a part of a whole. A fractions consists of the numerator and the denominator.
let f(x) = [tex]\frac{p}{q}[/tex]
then 'p' represents the numerator; while 'q' represents the denominator;
where p and q belong to integers for simple fractions, while when p and q belong to other sets they can from complex fractions.
To convert a fraction into an integer we need to multiply the fraction with the the denominator so that it cancels out leaving only the numerator behind.
For fractions present in equations to get rid of all the fractions we new to multiply the equation by the LCM of the denominator of all the fractions.
Where LCM is the least common multiple.
To give an example:
let y = [tex]\frac{3}{4}[/tex]X + [tex]\frac{9}{5}[/tex]
Then the LCM for 4 and 5 will be 20;
as factor of 4 are 1,2 and that of 5 are 1,5
then to eliminate the fractions from the equation
Multiplying both sides by 20
y x 20= [tex]\frac{3}{4}[/tex]X x 20 + [tex]\frac{9}{5}[/tex] x 20
20y= 3 x 5X + 9 x 4
20y = 15X + 36
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Hillary exercises Monday through Friday for 5/6 hours per day how many hours does she exercise per week
Answer: 4 hours and 10 minutes per week
Step-by-step explanation:
She exercises for 5 days per week (week days only).
(5/6 hr/day) x 5 days = 25/6 = 4.17 hours = 4 hours and 10 minutes per week
Think of 5 positive integers that have a
mode of 3 and 4, a median of 4 and a
mean of 6.
The 5 positive integers are 3,3,4,4,16, for them mode is 3 and 4, a median is 4 and mean is 6.
What is median?The median is a middle number of sequence, more precisely when the series is shorted descending to ascending order the middle term is median.
Let the number 3 repeats m times,
The number 4 repeats n times,
and any other number is x,
Mean of series is 6, therefore,
(3m+4n+x)/5 = 6
3m+4n +x = 30
Since, mode of 5 number is 3 and 4
So, the value of m can be 2 and value of n can also be 2,
3(2) + 4(2) + x = 30
x = 30-14
x = 16
Therefore, the 5 numbers are 3,3,4,4,16
And median for this number is 4 and mean is 6.
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What are the 3 representation of sets?.
The 3 representation of sets Semantic form, Roster form and Set builder form
There are varoius types of set notations used for the representation of sets depending upon the way in which the elements are listed. The three set notations used for representing sets are:
a) Semantic form.
The semantic notation describes a statement to show what are the elements of a set.
b) Roster form.
In here, the elements of the sets are enclosed in curly brackets separated by commas.
c) Set builder form.
It uses a vertical bar in its representation, with a text describing the character of the elements of the set.
Therefore, Semantic form, Roster form and Set builder form are the three ways to represent a set.
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which of the following functions are one-to-one? [more than one function may qualify.] hint: use a graphing calculator to view the behavior of the function on its domain.
A relation where each input has precisely one output was described as a function. Each input is mapped to a single output value, in other words. Every input value is translated into a single distinct output value in a one-to-one function. Another way to phrase it is that no two input items produce the same output value.
The function f(x)=x +2 is depicted in the graph above. This graph does not map the same x-value to the same y-value everywhere, indicating that it is a one-to-one function.
Here are some additional one-to-one functions:
Because no 2 input values have the same cube root and thus do not produce the same outputs, X³+1 is a one-to-one function.
Because different inputs might result in the same outputs, X² is not a function. Consider the numbers -1 and 1. These two values both produce the value 1, indicating that this equation is not one-to-one.
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x + 11 / 2x - 5 = 2
find x
Answer:
[tex]\huge\boxed{\sf x = 7}[/tex]
Step-by-step explanation:
Given Equation:[tex]\displaystyle \frac{x+11}{2x-5} =2\\\\Multiply \ 2x-5 \ to \ both \ sides\\\\x+11=2(2x-5)\\\\Distribute\\\\x+11=4x-10\\\\Subtract \ x \ to \ both \ sides\\\\11 = 4x-x-10\\\\11=3x-10\\\\Add \ 10\ to \ both \ sides\\\\11+10=3x\\\\21=3x\\\\Divide \ 3 \ to \ both \ sides\\\\7 = x\\\\x = 7\\\\\rule[25]{25}{2}[/tex]
the triangle with the vertices (4, 5, 1), (0, 8, 2), (4, 7, 8) is translated three units to the right along the y-axis. determine the coordinates of the translated triangle. (give your vertices in the same order as the original vertices.)
(4, 8, 1), (0, 11, 2), and (4, 10, 8) are the translated vertices right along the y-axis.
it is given that,
A(4, 5, 1)
B(0, 8, 2)
C(4, 7, 8)
Which are in x, y, and z, format.
here we need to translate three units to the right along the y-axis.
Right means addition and we have to choose only y- coordinates.
A(4, 5, 1) → A'(4, 5+3, 1)
B(0, 8, 2) → B'(0, 8+3 , 2)
C(4, 7, 8) → C'(4, 7+3, 8)
This gives us,
(4, 5, 1) → (4, 8, 1) → (x, y, z)
(0, 8, 2) → (0, 11, 2) → (x, y, z)
(4, 7, 8) → (4, 10, 8) → (x, y, z)
thus, these are our required vertices.
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If 5(x - y) =18, find 10x-10y
Answer:
36
Step-by-step explanation:
5(x-y)=18
5x-5y=18
To make it 10x-10y we multiply entire equation by 2
5x-5y=18
*2. *2. *2
10x+10y=36
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Please HELP NE WITH THIS MATH PROBLEM
The simplified expression of the radical expression ∛54 is 3∛3
Expression:
Expression is also known as equation is the combination of number, variable and the mathematical operator.
Given,
Here we have the radical expression ∛54.
Now, we have to simplify the expression and to find the simplest form of it.
Here we have to radical expression
=> ∛54.
Now, we have to expand this equation, then we get,
=> ∛(27 x 3)
We know that the value of ∛27 = 3,
Therefore, when we apply these on the expression, then we get,
=> 3∛3.
Therefore, the simplified expression is 3∛3.
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The pumpkin patch had two corn mazes, as shown by the shaded and non-shaded sections in the model below.
A model with 4 rows of 7 squares, representing 28 acres, and 2 rows of 7 squares, representing 14 acres.
Which expression is shown by the model?
28 + 14 = 7 (4 + 14)
28 + 14 = 4 (7 + 2)
28 + 14 = 4 (14 + 28)
28 + 14 = 7 (4 + 2)
The expression represents a model with 4 rows of 7 squares, representing 28 acres, and 2 rows of 7 squares, representing 14 acres will be 28 + 14 = 7 (4 + 2). The correct option is D.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a model with 4 rows of 7 squares, representing 28 acres, and 2 rows of 7 squares, representing 14 acres.
The expression will be written as,
28 + 14 = 7 (4 + 2)
Therefore, the expression represents a model with 4 rows of 7 squares, representing 28 acres, and 2 rows of 7 squares, representing 14 acres will be 28 + 14 = 7 (4 + 2). The correct option is D.
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One of the legs of a right triangle measures 17 cm and its hypotenuse measures 19 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
The length of the other leg is 8.48 cm
What is Pyhtagorean Theorem?
The Pythagorean theorem states that the sum of the squares on the legs of a right triangle equals the square on the hypotenuse (the side opposite the right angle)
Solution:
Given that:
Length of One Leg = 17 cm
Length of Hypotenuse = 19 cm
To Find:
Length of the other leg
= We know that by pythagorean theorem
[tex]base^{2} + length^{2} = hypotenuse^{2}[/tex]
17*17 + x^2 = 19*19
289 + x^2 = 361
x^2 = 72
x = 8.48 cm
The length of the other leg is 8.48 cm
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What is another way to express 11 + 77
Another way to express 11 + 77 is to using absolute values making it equal to
|-11 + -77|How to find another way to express equationThe use of equality sign introduces a number or equation which is equal and hence can be used to replace another item
solving this expression gives 11 + 77 = 88
The equation can also be replace in equation terms using absolute values
where it can be written as
|-11 + -77|
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Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?
A.2520 B.2880 C.1320 D.3250 E.3750
The total number of different colorings possible are c)3120.So, correct option is c.
We know very well that Probability is the defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We need to take care that each vertex of convex pentagon has been assigned a color.
We are given that we can choose 6 colors , and we need to take care that the ends of each diagonal must have different colors.
So, we need to try all different combinations,
Let PQRST are the vertex of the pentagon.
Let vertex P be any vertex, then vertex Q be one of the diagonal vertices to P, R be one of the diagonal vertices to Q, and so on. We consider cases for this problem.
In the case that,
R has the same color as P,
S has a different color from P
and so,
T has a different color from P and S.
In this case, the choices are
P = 6
Q = 5
R = 1
S = 5
T = 4
So, total number of combinations are =6 x 5 x 1 x 5 x 4 = 600 combinations.
Similarly, R has a different color from P and
S has a different color from P,
In this kind of situations,
P has 6 choices,
Q has 5 choices,
R has 4 choices
S has 4 choices,
and T has 4 choices,
So, total number of combinations is
=> 6 x 5 x 4 x 4 x 4 = 1920
Next case, R has a different color from P and S has the same color as P, So,
P has 6 choices,
Q has 5 choices,
R has 4 choices,
S has 1 choice, and
T has 5 choices,
=> total number of combinations=6 x 5 x 4 x 1 x 5 = 600
On Adding all those combinations up, we get
=> 600 + 1920 + 600 = 3120
Hence, total colorings are c)3120.
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(Complete question) is:
Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?
A.2520 B.2880 C.3120 D.3250 E.3750
Is 5 a geometric sequence?.
The number 5 can be either a geometric sequence or a arthimetic sequence
A geometric sequence is a series in which each term is found by multiplying the preceding term by the same value. Its general term is. aₙ= a₁rⁿ⁻¹.
The r represents the common ratio, and a is the initial term. r is found by taking any term in the sequence and dividing it by its preceding term.
The example of a geometric sequence with 5 as initial term is
5, 10, 20, 40.....
In an arithmetic sequence, the difference between consecutive terms is always the same.
aₙ = a + (n - 1)d
The example of a arithmetric sequence with 5 as initial term is
5, 7, 9, 11 .....
Therefore, The number 5 can be either a geometric sequence or a arthimetic sequence.
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Solve for x in the equation x squared minus 10 x 25 = 35.
The solution x is x= 5+√35 and 5-√35
What in mathematics is a quadratic equation?
A quadratic equation, or second-order polynomial equation with a single variable, is x ax2 + bx + c = 0. a 0. Since it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution. The solution could be straightforward or difficult.
x2-10x+25=35
There were two options found:
x =(10-√140)/2=5-√ 35 = -0.916
x =(10+√140)/2=5+√ 35 = 10.916
Rearrange:
Add what is to the right of the equal sign to both sides of the equation, then rewrite the equation as follows:
x^2-10*x+25-(35)=0
Step-by-step answer:
Step 1 :
Attempting factoring by dividing the middle term
Factoring x2 – 10 – 10
x2 is the initial term, and it has a coefficient of 1.
The coefficient of the middle term, which is -10x, is -10.
"The constant," the final word, is -10.
Step 1: Multiply the constant by the coefficient of the first term. 1 • -10 = -10
Step 2 is to identify two factors of -10 whose combined value is equal to the middle term's coefficient, which is -10.
-10 + 1 = -9\s-5 + 2 = -3\s-2 + 5 = 3\s-1 + 10 = 9
No two of these factors can be discovered!!
Trinomial cannot be factored, thus.
Equation following the first step:
Step 2: x2 - 10x - 10 = 0.
Finding the Vertex of a Parabola:
2.1 Locate the vertex of y = x2 – 10x – 10.
The Vertex is the highest or lowest point of a parabola. Our parabola widens, and as a result, it has a lowest point, also known as the absolute minimum. We are aware of this even before graphing "y," as the first term's coefficient, 1 is a positive number (greater than zero).
A vertical line of symmetry runs across the vertex of every parabola. The line of symmetry would, for instance, run through the middle of the two x-intercepts (roots or solutions) of the parabola as a result of this symmetry. If the parabola actually has two true solutions, that is.
Many real-world scenarios, such as the height of an object thrown into the air that has risen after some time, can be modeled using parabolas. We can learn information from the parabola's vertex, such as the highest height an object thrown upwards can travel. We need to be able to determine the vertex's coordinates for this purpose.
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The diagram shows a right-angled triangle.
11 cm
7 cm
Find the size of angle X.
Give your answer correct to 1 decimal place.
The value of angle x is x = 50.5°
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be ΔABC
where AB = 7 cm
AC = 11 cm
∠BAC = x°
Let the angle x = θ
Now , from the trigonometric relations , we know that
sin θ = opposite / hypotenuse
So ,
sin θ = BC / AC
Now ,
From Pythagoras Theorem ,
Hypotenuse² = Base² + Height²
AC² = AB² + BC²
So , substituting the values , we get
BC² = AC² - AB²
BC² = 11² - 7²
BC² = 121 - 49
BC² = 72
BC = √72
BC = 6√2
Therefore , the value of BC is 6√2
Now ,
sin θ = BC / AC
sin θ = 6√2 / 11
So , the value of θ is
θ = sin⁻¹ ( 6√2 / 11 )
θ = 50.478°
Therefore , the value of θ = 50.5° and x = 50.5°
Hence , The value of angle x is x = 50.5°
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Select the correct answer. What is the solution to this system of equations? 5x + 2y = 29 x + 4y = 13.
The solution to this system of equations is x = 5 and y = 2.
Given:
5x + 2y = 29 and x + 4y = 13.
on solving eq 1 - 5*eq 2:
5x + 2y - 5(x+4y) = 29 - 13*5
5x + 2y - 5x - 20y = 29 - 65
2y - 20 y = 29 - 65
-18y = -36
18y = 36
divide by 18 on both sides
18y/18 = 36/18
y = 36/18
y = 2
substitute y = 2
5x+2y = 29
5x + 2*2 = 29
5x + 4 = 29
5x = 29-4
5x = 25
divide by 5 on both sides
x = 25/5
x = 5
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a memory is a memory from a real event that was encoded, stored, but not retrieved for a long period of time; it is retrieved after some later event brings it suddenly to consciousness.
Implicit or Doubtful memory of actual events that was stored encrypted, but was not retrieved for a long time until subsequent events suddenly brought it back to consciousness. The establishing, stabilizing like processes include in this memory.
Implicit Memory is a type of long-term memory and it is also known as unconscious memory or automatic memory. Implicit memory draws on past experiences to remember things without thinking. The power of tacit memory is made possible by past experiences, regardless of how long ago those experiences were.
Second stage of long-term memory formation.
Implicit memory, a subset of procedural memory, allows you to perform many everyday physical activities, such as walking and cycling, without having to think about it. Most of the implicit storage is procedural in nature.
For example:
typing on a keyboard brushing your teeth. Riding a bicycle Most people find it easy to ride a bike, even after years of not riding.To learn more about Implicit Memory, refer:
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