Answers
Each of the quadratic function should be factorized as follows;
x² - 6x + 8 ⇒ (x - 4)(x - 2).
x² - 4x - 32 ⇒ (x - 8)(x + 4).
x² + x - 42 ⇒ (x - 6)(x + 7).
What is a quadratic function?In Mathematics, the standard form of a quadratic function is given by this mathematical expression;
ax² + bx + c = 0
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant.Next, we would solve each of the quadratic function by using the factorization method as follows;
x² - 6x + 8 = 0
x² - 4x - 2x + 8 = 0
x(x - 4) - 2(x - 4) = 0
(x - 4)(x - 2) = 0
x² - 4x - 32 = 0
x² - 8x + 4x - 32 = 0
x(x - 8) + 4(x - 8) = 0
(x - 8)(x + 4) = 0
x² + x - 42 = 0
x² - 6x + 7x - 42 = 0
x(x - 6) + 7(x - 6) = 0
(x - 6)(x + 7) = 0
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Related Questions
Farmer Quect started with 110 rews on his farm. Every hour, he destoryed 6 more of them. Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them?
Write a systems of equations in slope intercept form. Farmer's rews (y), hours (x)
Answers
The systems of equations in slope intercept form is
y = -6x + 110
y = 9x + 54
What is Slope- intercept form?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
As, We know Slope-intercept form is
y = mx + b
where b is the starting value and m is the change per day.
Farmer Quect started with 110 rews on his farm. Every hour he destroyed 6 more of them.
So, the Equation to show the Situation
y = -6x + 110
and, Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them.
So, the Equation to show the Situation
y = 9x + 54
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Simplify.
Rewrite the expression in the form 8n.
(8−8)(8³) =
Answers
The above expression in terms of 8n can be written as 8(0).
What is expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.
We are given a an expression (8-8)(8³)
Now the first bracket after simplifying we get an answer is 0.
Hence the expression can be given in the form of 8(n) as 8(0)
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96 Vistors in 6 Hours. How many visitors per hour?
Answers
Answer:
16 visitors per hour
Step-by-step explanation:
96/6 = 16
16
Explanation:
To calculate the average number of visitors per hour, we need to divide the total number of visitors by the number of hours.
In this case, 96 visitors in 6 hours means an average of 96 / 6 = 16 visitors per hour.
Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.\dfrac{8x}{x^2-49}+\dfrac{5}{x^2-4x-21}= x 2−498x + x 2−4x−215 =start fraction, 8, x, divided by, x, squared, minus, 49, end fraction, plus, start fraction, 5, divided by, x, squared, minus, 4, x, minus, 21, end fraction, equals
Answers
The simplified expression after factoring numerator and denominator is (x + 7) / x.
We can start by factoring the numerator and denominator of the first fraction:
x^2 - 49 = (x + 7)(x - 7)
The denominator can also be factored using the quadratic formula or by factoring as a product of two binomials:
x^2 - 4x - 21 = (x - 7)(x + 3)
So, the first fraction can be simplified as:
(x + 7)(x - 7)/[(x - 7)(x + 3)]
We can cancel out the (x - 7) factor in the numerator and denominator, leaving:
(x + 7)/(x + 3)
Next, we can simplify the second fraction by canceling out the common factor of (x + 3) in both the numerator and denominator:
(x + 3)/x
Putting it all together, we get:
[(x + 7)/(x + 3)] * [(x + 3)/x] = x + 7 / x
Therefore, the simplified expression is (x + 7) / x.
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____The given question is incorrect, the correct question is given below:
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
Simplify (x^2-49)/(x^2-4x-21)*(x+3)/x
Find the prime factorization of
the number 90.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[?] × [ ] × [ ] × [ ]
X
X
Enter the number that belongs in the green box.
Answers
Answer:
2
Step-by-step explanation:
the prime factorization of the number 90 is
2, 3, 3, 5
There are 28 students in a class.
13 of the students are boys.
Two students from the class are chosen at random.
a) If the first person chosen is a boy, what is the probability that
the second person chosen is also a boy?
Give your answer as a fraction.
b) What is the probability that both students chosen are girls?
Give your answer as a fraction.
Answers
a) The probability that the second person chosen is also a boy is; 13/28
b) The probability that both students chosen are girls is; 5/18
How to find the probability of selection?The parameters given in the question are;
Total number of students in the class = 28 students
Number of boys in class = 13 students
Number of girls = 28 - 13 = 15 students
a) Probability of the first student being selected as a boy is;
P(First is boy) = 13/28
b) The probability that both students chosen are girls is;
P(both girls) = (15/28) * (14/27) = 5/18
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Scatter Plot 8 grades, help please!!!
Answers
The of association represented in the graph is positive linear association.
option C
What is a positive correlation?
A positive correlation is a statistical relationship between two variables such that as one variable increases, the other variable also increases, and as one variable decreases, the other variable decreases as well.
In other words, positive correlation means that as the value of one variable goes up, the value of the other variable also goes up, and vice versa. The correlation is said to be positive because both variables move in the same direction.
The strength of the correlation can be measured using a correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, while a correlation coefficient of 0 indicates no correlation.
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Perform the operation and simplify the resulting fraction: 7/3a - 8/5 + 4/15a
Answers
After solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.
What are fractions?A fraction in mathematics is a number that is stated as a percentage, such as 1/2 or 2/3.
The number on top denotes the component of the unit under consideration, while the number at the bottom indicates the total number of parts that make up one unit.
An element of a whole is a fraction.
The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
So, we have the operations:
7/3a - 8/5 + 4/15a
Now, solve as follows:
7/3a - 8/5 + 4/15a
7/3a + 4/15a - 8/5
7*5 + 4 /15a - 8/5
39/15a - 8/5
Therefore, after solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.
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do you believe that this conjectures "all numbers coming from the question p=n²-n+41 are prime numbers"?
Answers
Answer: No
Step-by-step explanation:
Valid only for numbers less than 40.
P(40) = 412 which is not a prime number
find the value of x y and z
Answers
The values of x, y and z are;
x. x = 60° y = 55°
xi. x = 68° y = 56° z = 56°
xiii. x = 40° y = 50°
xiv. x = 40° y = 50°
What is a Triangle?A triangle is a 3-sided polygon that has three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle that always equals 180 degrees. This property is called angle sum property of triangle.
x. x = 60° (corresponding angles are equal)
y + 65° + 60° = 180° (Sum of angles in a triangle equals 180°)
y + 125° = 180°
y = 180° - 125°
y = 55°
xi. y = 56° (corresponding angles are equal)
y = z = 56° (angles in equal sides of a triangle are equal)
x + 56° + 56° = 180° (Sum of angles in a triangle equals 180°)
x + 112° = 180°
x = 180° - 112°
x = 68°
xiii. x + 140° = 180° (sum of angles on a straight line equals 180°)
x = 180° - 140°
x = 40°
y + 90° + 40° = 180° (sum of angles in a triangle equals 180°)
y + 130° = 180°
y = 180° - 130°
y = 50°
xiv. y + 130° = 180° (sum of angles on a straight line equals 180°)
y = 180° - 130°
y = 50°
x + 90° + 50° = 180° (sum of angles in a triangle equals 180°)
x + 140° = 180°
x = 180° - 140°
x = 40°
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Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
ASA
SAS
AAS
None
Answers
As a result, no particular postulate can be used to demonstrate their congruence due to a lack of adequate data. So "None" is the correct response.
What in mathematics is a similarity?If two figures share the same form, congruent corresponding angles (which means the angles in the same locations of each shape are the same), and identical scale factors, they are said to be "similar figures." Equal scale factors signify a matched ratio between the lengths of their respective sides.
Two triangles can be seen in the illustration, and their corresponding angles are both equal.As a result, they match the AAA similarity requirement. However, no more details are provided to demonstrate their consistency.Although comparable triangles may not be congruent, congruent triangles are known to be similar.To know more about similarity visit:
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Answer: None
Step-by-step explanation: I Just did it
Can anybody answer the question I attached?
Answers
Answer:
36 bottles
Step-by-step explanation:
You want to know the number of bottles that must be painted and sold in order to make a profit of $120, given that 3 bottles can be purchased for $11, and each bottle can be sold for $7.
ProfitThe profit on each bottle is the difference between its cost and what it is sold for. The cost of 1 bottle is 1/3 of the cost of 3 bottles.
profit = selling price - purchase price
profit = $7/bottle - ($11/(3 bottles)) = $(21/3 -11/3)/bottle = $(10/3)/bottle
BottlesTo make a profit of $120, you need n bottles such that ...
(10/3)n = 120
n = 36 . . . . . . . . . multiply by 3/10
The club needs to buy, paint, and sell 36 bottles to raise $120.
FIND THE PERIMETER AND AREA OF THE EQUILATERAL TRIANGLE
Answers
The area of an equilateral triangle is 16√3 m² and the perimeter of an equilateral triangle is 24 m.
What is area of an equilateral triangle?In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4 ×a².
From the given figure, side of the equilateral triangle is 8 m.
Now, area of an equilateral triangle is
√3/4 ×8²
= √3/4 ×64
= 16√3 m²
The perimeter of an equilateral triangle is 3a.
Now, the perimeter is 3×8
= 24 m
Therefore, the area of an equilateral triangle is 16√3 m².
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John wants to have 600 copies. His local print shop charges $10 for the First 200 copies and $15 for every additional 100 copies
Part A: How much will the 600 copies cost, including a sale tax of 6%?
Part B: If the number of sets of 100 is represented by x, write an equation to express the cost, y.
Part C: Use the equation to determine the cost of 900 copies. Include the 6% sales tax in the total final cost.
Answers
The cost of 600 copies is $90.10
The cost of 900 copies is $137.80.
The equation that expresses cost is y = 1.06 x ($10 + $15x)
What is the equation that expresses cost?The equation that represents the information in the question is:
Total cost = 1 + sales tax x [cost of the first 100 copies + (x x cost of every additional 100 copies)]
y = 1.06 x ($10 + $15x)
Cost of 600 copies:
x = (600 - 100) / 100 = 500 / 100 = 5
y = (1 + 6/100) x [$10 + (5 x $15)]
y = 1.06 x [$10 + $75)
y = 1.06 x $85
y = $90.10
Cost of 900 copies:
x = (900 - 100) / 100 = 800 / 100 = 8
y = (1 + 6/100) x [$10 + (8 x $15)]
y = 1.06 x [$10 + $120)
y = 1.06 x $130
y = $137.80
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the relationship between the amount of time a basketball player spent practicing the day before a game and the number of points he scored in the game is graphed on the scatter plot shown. scatter plot titled basketball players, with the x axis labeled time practicing in minutes and the y axis labeled points scored with points at 0 comma 10, 10 comma 15, 15 comma 18, 25 comma 25, 30 comma 28, 30 comma 30, 45 comma 35, 70 comma 40, 70 comma 45, 80 comma 45, 90 comma 50, and 120 comma 60 describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
Answers
By examining the shape and degree of association on the scatter plot, we can gain insights into the nature of the relationship between the variables and make predictions about their behavior in the future.
A scatter plot is a graphical representation of a set of data that shows the relationship between two variables.
The type of association between the two variables can be identified by the shape of the scatter plot. If the points on the plot form a linear pattern, then the association is said to be linear. If the points on the plot form a curved pattern, then the association is said to be nonlinear.
The degree of association between the two variables can be determined by the strength of the correlation coefficient, which is a measure of how closely the points on the scatter plot follow a linear pattern. The correlation coefficient ranges from -1 to 1, where a correlation coefficient of 1 indicates a perfect positive linear association, a correlation coefficient of -1 indicates a perfect negative linear association, and a correlation coefficient of 0 indicates no association between the two variables.
In this scenario, if the scatter plot shows a linear pattern and the correlation coefficient is positive, it means that there is a positive association between the amount of time the player spent practicing and the number of points he scored in the game.
On the other hand, if the correlation coefficient is negative, it means that there is a negative association between the two variables, which implies that the more time the player spent practicing, the lower the number of points he scored in the game.
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a person rolls a standard six-sided die 10 times. in how many ways can he get 6 fives, 3 ones, and 1 two?
Answers
There are 840 ways for the person to get 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die.
To calculate the number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die, we can use the formula for combinations with repetition.
The number of ways to choose 6 rolls to be fives out of 10 is given by the combination formula:
C(10, 6) = 10! / (6! * (10 - 6)!) = 210
Similarly, the number of ways to choose 3 rolls to be ones out of the remaining 4 rolls is:
C(4, 3) = 4! / (3! * (4 - 3)!) = 4
Finally, there is only one way to choose the remaining roll to be a two.
Therefore, the total number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die is:
210 * 4 * 1 = 840.
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read the story. clara snacked on a mix of almonds and pecans. she ate 3 almonds for every 1 pecan. pick the diagram that models the ratio in the story. if clara ate 10 more almonds than pecans, how many nuts did she eat altogether?
Answers
In all together, Clara ate 20 nuts.
A system of equations is a set of one or more equations involving a number of variables.
The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Given that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.
Let the number of pecans be x and the number of almonds is y.
We can write the system of equations as:
y = 3x
y = x + 10
Equating the value of {y}, we get -
3x = x + 10
2x = 10
x = 5 ...(1)
y = x + 10 = 15
y = 15 ...(2)
x + y = 15 + 5 = 20
Therefore, in together, Clara ate 20 nuts.
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Holly's height decreased by 21 is 62.
Use the variable h to represent Holly's height.
Answers
The algebraic expression is h - 21 = 62
How to represent as an algebraic expressionIf we let "h" be Holly's original height,
The phrase "Holly's height decreased by 21 is 62" can be translated into an algebraic expression as:
h - 21 = 62
This equation represents the relationship between Holly's original height and her current height, after a decrease of 21 units.
We can solve for h by adding 21 to both sides of the equation:
h - 21 + 21 = 62 + 21
h = 83
Hence, Holly's original height was 83 units.
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if we have four variables, then how many equations will we have in our system of linear equations? 5 2 3
Answers
For four variables the required number of system of linear equations are at least option d. 4 equations.
Variable is represented by small alphabets : a , b, x, y , z, m , n ... so on.System of linear equations are set of equation relating variables with degree one. To solve the system of linear equations we need to have number of equations same as the number of variables.If there are two variables then we need to have minimum two system of linear equations .If there are n variables then there should be n system of linear equations.Therefore, if there are four variables in the system of linear equations then we should have option d. 4 equations.
The above question is incomplete , the complete question is:
If we have four variables, then how many equations will we have in our system of linear equations?
a. 5 b. 2 c. 3 d. 4
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Keisha must choose a shirt and a pair of pants for today's outfit. She has 4 shirts and 2 pairs of pants to choose from. How many different outfits can she make?
Answers
answer: 12
explanation:
Anna ate 5/8 of an orange and gave the other 3/8 to her brother.
Answers
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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The complete question is
Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
Four children are playing a card game. The chart shows the number of cards each child has in his or her stack.
Name Number of Cards
Chris 7
Mike 8
Sally 10
Susan 25
Which is equivalent to Mike’s portion of the total number of cards?
A.) 2/25
B.) 16%
C.) 8/25
D.) 80%
(PLEASE EXPLAIN HOW YOU GOT THIS ANSWER)
Answers
The requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
From the given data,
Name Number of Cards
Chris 7
Mike 8
Sally 10
Susan 25
Total cards = 50
Now equivalent to Mike’s portion of the total number of cards is given as ,
= Mike cards/total card
= 8 / 50 × 100%
= 4/25×400%
= 16%
Thus, the requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
Answers
Answer:
the iqr is the best measure of variability
The IQR is the best measure of variability, and it equals 4.
Option C is the correct answer.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
The appropriate measure of variability for the data is the interquartile range (IQR), which is the range of the middle 50% of the data.
In other words, it is the difference between the third quartile (Q3) and the first quartile (Q1).
From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.
This means that Q1 is 17 and Q3 is 21.
The IQR is:
IQR = Q3 - Q1 = 21 - 17 = 4
Thus,
The IQR is the best measure of variability, and it equals 4.
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A bag contains 2 red marbles and 3 black marbles. If Abby picks a marble without looking, returns it to the bag, and then draws a second marble, what is the probability that both marbles are red? Write your answer as a fraction.
Answers
The probability of getting both the marbles to be red will be 4/25.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.
Probability = Number of favorable outcomes / Number of samples
Given that two red and three black marbles are in a bag. If Abby takes a marble out of the bag without looking, puts it back, and then draws another marble.
The probability of getting red in the first draw,
P = 2 / 5
Now the marble is returned and again the probability of getting the red marble is,
P = 2 / 5
The probability of getting both the marbles red will be,
Pb = ( 2/ 5 ) x ( 2 / 5 )
Pb = 4 / 25
Therefore, there is a 4/25 chance that both marbles will be red.
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Solve the word problem below. Enter your answer in simplest terms, using the
slash (/) to represent the fraction bar.
A recipe for a soup calls for 2/4 cup of chopped onion and 1/6 cup of chopped
celery. What is the total amount of celery and onion needed for the soup
Answers
Answer:
2/3 cups
Step-by-step explanation:
The recipe calls for 2/4 cup of onion and 1/6 cup of celery. To find the total, we need to add the two fractions together; the amount of onions(2/4 cup or 1/2 a cup if simplified), and the amount of celery(1/6). To do this, we need to find a common denominator. We can do this buy finding a common multiple between 2 and 6.
Multiples of 2: 2, 4, 6, 8, 10, 12...
Multiples of 6: 6, 12, 18, 24, 30...
A common multiple is 6. 1/2x3/3=3/6 <--- an equivalent fraction of 1/2
Now both fractions have the same denominator:
Onions: 3/6
Celery: 1/6
3/6+1/6 = 4/6
4/6 simplifies to 2/3.
The total amount of celery and onion need for the soup is 2/3 cup
Answer:
2/3 cups
Step-by-step explanation:
I increased a number by 5% twice how much id it increase by in percent.
Answers
Answer:
10%
Explanation:
You increased it by 5% twice, which is basically 5+5 or 5x2 which equals 10
Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
Answers
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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A right triangle has acute angles c and d . If c=15/8 and sin d=8/17, what are cos d and cos c?
Answers
The value of the right triangle cos d = 15/17 and cos c = 8/17.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given that, the value of tan c = 15/8 and the value of sin d = 8/17.
From the trigonometric functions we can conclude that:
Opposite side to c = 15
Adjacent side to c = 8
Hypotenuse = 17
Opposite side to d = 8
Adjacent side to d = 15
The values of cos d is:
cos d = Adjacent side to d / Hypotenuse = 15/17
cos c = Adjacent side to c / Hypotenuse = 8/17
Hence the value of the right triangle cos d = 15/17 and cos c = 8/17.
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What is the standard function of f? F(x)=4(x+6)2+5
Answers
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
What is the definition of a function?
A function is defined as a connection between a set of inputs and a single output. A function is a link between inputs that corresponds to exactly one output. Every function has a domain, a co-domain, and a range. A function is often denoted as f(x), where x represents the input. The general representation of a function is y = f(x).
There are several types of functions in mathematics. Here are a few examples:
An injective function or a one to one function exists when there is a mapping for a range for each domain between two sets.
Surjective functions, also known as Onto functions, are employed for transferring more than one element from domain to range.
A polynomial function is a function composed of polynomials.
Functions that may be used to inverse another function are known as inverse functions.
Now,
Given function is F(x)=4(x+6)2+5
=(4x+24)2+5
=8x+48+5
=8x+53
hence,
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
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(a) without adding new vertices, add a single edge to the graph so that the new graph will have an euler path. which vertices does your new edge connect?
Answers
To add a single edge to a graph to create an Euler path, we must connect two existing vertices with an odd degree.
In graph theory, an Euler path is a path that visits every edge of a graph exactly once. However, not all graphs have an Euler path. If a graph has an Euler path, it must have either zero or two vertices with an odd degree. In this scenario, we are given a graph and are asked to add a single edge to create an Euler path.
To add a single edge to the graph, we must connect two existing vertices that have an odd degree. This is because adding a new vertex would change the degree of the graph and potentially affect the existence of an Euler path. Therefore, we must carefully consider the degree of each vertex before adding the edge.
Let's consider a graph:
A
/ \
B---C
/ \ / \
D---E---F
In this graph, vertices B, E, and F have an odd degree. To create an Euler path, we must connect two of these vertices with a new edge. Let's choose B and E, and add the edge (B, E) to the graph.
A
/ \
B---C
/ \ / \
D---E---F
Now, the graph has only one vertex with an odd degree, which is C. This means that the graph has an Euler path that starts at C, visits every edge exactly once, and ends at A.
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