The correct statement regarding the value of n is given as follows:
c) any odd number.
How to obtain the value of n?The expression for this problem is given as follows:
(-1)^n+(-1)^4n.
The numeric value for the expression is given as follows:
0.
The n powers of -1 are given as follows:
Negative 1 if n is odd.Positive 1 if n is even.(-1)^4n will always be an even power due to the multiplication by the even number 4, hence it is positive.
As (-1)^4n is always positive and the numeric value of the expression is of zero, we have that (-1)^n is always negative one, meaning that the value of n is an odd number.
This means that option c is correct.
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Find an equation of the plane consisting of all points that are equidistant from (1, 4, 4) and (-4, 1, 2).
the required equation is 5x - 6y + 5z = 7
Given that;
points : (1, 4,4) and (-4, 1,2).
mid point : ( [(1-4)/2], [(4-1)/2], [(4+2)/2]
⇒ midpoint : ( -3/2, 3/2, 3 )
x₀ y₀ z₀
Direction vector n = [-4-(1)], [ 1-4], [ 2-4]
⇒ Direction vector n = < -5, -3, -2 >
General equation plane : n(x-x₀, y-y₀, z-z₀) = 0
so we substitute
⇒ (-5,-3,-2) (x-3/2, y-(-2), z-(-5/2) ) = 0
⇒ (-5,-3,-2) (x - 3/2, y + 2, z + 5/2) ) = 0
⇒ 5(x - 3/2) - 6(y + 2 ) + 5(z + 5/2) = 0
⇒ 5x - 15/2 - 6y - 12 + 5z + 25/2 = 0
⇒ 5x - 6y + 5z = 15/2 + 12 - 25/2
⇒ 5x - 6y + 5z = 7
Therefore, the required equation is 5x - 6y + 5z = 7
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Which of these constructions always gets you a 90° angle?
(There’s more than one answer)
Answer:
A, C, E
Step-by-step explanation:
What is improper fraction in Maths for Class 5?.
When the numerator of the fraction is greater than the denominator, the the fraction is an improper fraction.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
consider a fraction 1/6.
Here, numerator is 1, denominator is 6
When certain thing is divided into 6 equal parts then each part of is represented by fraction1/6
As we the types of fractions are: Proper fraction, Unit Fraction ,Improper fraction, Mixed fraction, Like fractions, Unlike fractions and Equivalent fractions
An improper fraction is a fracton in which the numerator of the fraction is greater than the denominator.
For example, 8/7 is an improper fraction.
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a bakery makes 40 different flavors of muffins. 25% of the falvors have chocalte. draw a tape diagram show how many flavors have chocolate and how many don't
A possible tape diagram that shows the proportion of muffins with and without chocolate is one that displays 1/4 or 10 flavors with chocolate and 30 flavors without chocolate.
What is a tape diagram?This is a simple diagram that uses segments of a tape to illustrate fractions.
How to create a tape diagram?It is known 25% of the flavors have chocolate, but let's calculate the exact number:
40/100 = 0.4 x 25= 10 flavors have chocolate and therefore 30 flavors do not have chocolate.
Based on this, here is the diagram (green shows the chocolate flavors):
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How do you write algebraic expressions and equations?.
Algebraic expressions and equations are written using mathematical symbols and letters to represent numbers and operations.
Algebraic expressions: An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. For example, 3x + 2y is an algebraic expression that contains the variables x and y and the operations of addition and multiplication.
Algebraic equations: An algebraic equation is a statement that shows two algebraic expressions are equal. For example, 3x + 2y = 12 is an algebraic equation that shows the left-hand side (3x + 2y) is equal to the right-hand side (12).
To write an algebraic expression or equation, you need to follow these steps:
Identify the numbers and variables in the problem.
Write the problem using mathematical symbols and operations.
Use the correct order of operations (PEMDAS) to simplify the expression or equation.
Use the equal sign (=) to write the equation.
For example, if you are given the problem "Three times a number plus two times another number equals 12", you can write the algebraic equation as:
3x + 2y = 12
In this equation, x and y are the variables and 3 and 2 are the coefficient. The equation represents the relationship between x and y and it can be used to solve for one of the variables if the other one is known.
Therefore, In short, algebraic expressions and equations are written using mathematical symbols and letters to represent numbers and operations. To write an algebraic expression or equation, you need to identify the numbers and variables in the problem, use mathematical symbols and operations, use the correct order of operations and use the equal sign (=) to write the equation.
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How is the intensity of an earthquake decided on the Richter scale?.
The intensity of an earthquake decided on the Richter scale by the following formula,
10ᴬ⁻ᴮ , where A and B are magnitude of earthquake recorded by Richter Scale.
The Richter magnitude scale was developed in 1935 by Charles F. Richter of the California Institute of Technology as a mathematical device for comparing the magnitude of earthquakes. The size of an earthquake is determined from the logarithm of the amplitude of the waves recorded by seismographs. Adjustments are included for the change in distance between different seismographs and the epicenter of the earthquake. The Richter scale is a logarithmic scale with a base of 10, meaning that each order is 10 times more intense than the previous one. In other words, a two is 10 times more intense than a one, and a three is 100 times greater. In the case of the Richter scale, there is an increase in the amplitude of the wave.The Formula used to measured the intensity of an earthquake is A is x times intense than B, x = 10ᴬ⁻ᴮ.
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Solve for f.
11f = 352
Answer:
f=32
Step-by-step explanation:
11f = 352
11x32=352
Answer:
[tex] \sf \: f = 32[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of f.
The equation is,
→ 11f = 352
Then the value of f will be,
→ 11f = 352
→ f = 352 ÷ 11
→ [ f = 32 ]
Hence, the value of f is 32.
How much higher i checkpoint 4 than checkpoint 3. If checkpoint 4 i -99 and checkpoint 3 i -207
Checkpoint 4 will be higher than Checkpoint 3 by 108.
In our question, it is given that the Checkpoint 4 value is -99 and the Checkpoint 3 value is -207.
We will use Subtraction. What is Subtraction?
The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).
The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller. For instance, your friends consumed 7 of the 9 cupcakes you purchased for your birthday party. You are now down to two cupcakes. This can be expressed as a subtraction formula: 9 - 7 = 2, which means "nine less seven equals two." The result of subtracting 7 from 9 is 2, or (9 - 7) Here, we divided two numbers, 9, and 7, by one another to get the difference of 2.
Subtracting the value of Checkpoint 3 from Checkpoint 4, we get:
Checkpoint - Checkpoint 3 = -207 -(-99)
= -207 + 99 = 108.
Therefore Checkpoint 4 will be higher than Checkpoint 3 by 108.
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(Need it urgently, thank you!)
Write a two-column proof.
Given: AC bisects ZBAD, ZBCA ZDCA
Prove: BC= DC
Left Column: AC bisects ZBCA ZDCA. Right Column: Angle ZBAC = Angle ZDCA (Angle Bisector Theorem).
What is an angle bisector theorem?Angle bisector theorem states that in any triangle, the line that bisects an angle also divides the opposite side into two segments that are proportional to the other two sides of the triangle. This theorem can be used to prove that the angle bisector of any triangle is the perpendicular bisector of the opposite side. In other words, the line that bisects the angle of a triangle will also divide the opposite side into two segments with lengths that are equal to the ratio of the other two sides of the triangle.
Left Column Right Column
1. AC bisects ZBAD 1. AC bisects ZBCA ZDCA
2. ZBAD = ZBCA + ZDCA 2. Angle ZBAC = Angle ZDCA (Angle Bisector Theorem)
3. Angle ZBAC = Angle ZBCA + Angle ZDCA 3. BC = DC (Congruent Sides of Congruent Triangles)
4. Angle ZBCA = Angle ZDCA
5. BC = DC (Congruent Sides of Congruent Triangles)
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What are the factors of x2 XY − 2xz − 2yz?.
Since a square is either positive or zero, negative numbers don't have real square roots.
No, we are unable to compute the negative number's square root. Positive is always the result of adding two numbers with the same sign.
How is a negative square root treated?Theorem: Square Roots of a Negative Number Simplifying an expression involving the square root of a negative number by simplifying the number as if it were a positive number and putting an i in front of it as a coefficient is one method. To put it another way, x=ix x = i x for every x where x is a positive number and where x is a negative number.
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Is Y =- 3x 10 a linear function?.
Yes, Y = -3x + 10 is a linear function.
A linear function is a function that can be written in the form of y = mx + b, where m is the slope (or rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The equation Y = -3x + 10 can be written in this form, with m = -3 (the coefficient of x) and b = 10 (the constant term).
Linear functions represent straight lines on a graph, and their slope and y-intercept can be used to determine the characteristics of the line, such as its direction and position. In this case, the slope of the function is -3, which means that for every unit increase in x, there is a corresponding decrease of 3 units in y. The y-intercept of this function is (0,10), which means that the line crosses the y-axis at the point (0, 10)
In summary, Y = -3x + 10 is a linear function because it can be written in the form of y = mx + b, and it represents a straight line on a graph.
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A roller skating rink charges a skate rental fee and an hourly rate to skate. The total cost to skate for 2 hours is $9. 50 and for 5 hours is $18. 50. Assume the relationship is linear.
The initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.
The initial value, b = $3.50 is the skate rental fee
The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink based on the query we have;
The roller skating rink's fees are comprised of a skate rental fee and an hourly rate.
Skating for two hours will cost you a total of $9.50.
Five hours of skating will cost you $18.50 in total.
Skating's overall cost and its duration in hours are related in a linear fashion.Let 'x' be the number of hours spent skating, and 'y' denote the overall cost;
The equation has the form y = mx + b.
Where;
m = The linear relationship's rate of change
b = The starting point (y-intercept)
X = 2 and Y = 9.50
Consequently, we can write;
9.50 = 2·m + b..(1) (1)
X = 5 and Y = 18.50
Consequently, we can write;
18.50 = 5·m + b..(2) (2)
Equation (1) minus equation (2) results in;
18.50 - 9.50 = 5·m - 2·m + b - b = 3·m
9.0 = 3 × m
∴ m = 9.0/3 = 3.0
m = 3.0 is the rate of change.
Likewise, we have;
We obtain from equation (1);
9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b
9.50 = 6.0 + b
∴ b = 9.50 - 6.0 = 3.50
The starting point is 3.50.
As a result, the initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.
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Is 45 and 36 a Coprime number?.
No, 45 and 36 are not a Co-prime numbers, because the two numbers have a common prime factor i.e., 9 .
A co-prime number is a number that has exactly one common divisor, which is 1. This means that a pair of numbers is co-prime if their greatest common divisor is 1. Consider x and y are two positive integers, they are called relatively prime if and only if their only common divisor is 1, so gcd(x, y) = 1. There are two numbers 45 and 36. First we determine the divisors of both numbers, then check the greatest common divisor. So, the factors of 45 are 1,3,5,9,15,45.
=> 45 = 1× 3×3× 5
and factors of 36 are 1, 3,2,4,6,9,12,36
=> 36 = 1×2×2×3×3
Now, greatest commen factor between 45 and 36 is 9, i.e., gcd(45,36) = 9 ≠ 1. Therefore, 45 and 36 are not co-prime numbers.
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Complete question:
Are 45 and 36 a Coprime number?.
4 bags of candy each contain 5 butterscotch candies and some
peppermint candies.Altogether, the bags contain 52 candies.
The required number of Peppermint candies in each bag is 8.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the number of peppermint candies be x in each bag,
Butterscotch candies in 5 bags = 5 × 4 = 20 candies
Peppermint candies in 5 bags = x × 4 = 4x candies
According to the quesiton, Altogether, the bags contain 52 candies.
20 + 4x = 52
x = 8
Thus, the required number of Peppermint candies in each bag is 8.
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How do you find the mean and standard deviation of the sampling distribution of the sample proportion?.
The standard deviation of the sampling distribution of a sample proportion using the formula σ^p=√p(1−p)N σ p ^ = p ( 1 − p ) N. The standard deviation of the sampling distribution of a sample proportion is about 0.054.
In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.
Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.
The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.
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How to solve a function?.
Step-by-step explanation:
a function with a single input variable x is usually defined like
y = f(x) = expression in x
to "solve" it means either to have a value for x and then calculate y.
or to have a value for y and find the corresponding value for x, so that f(x) = y. this usually involves finding and using the inverse function of f(x).
the details depend on the functions and operations used in the function expression.
Write the relation as a set of ordered pairs. A relation. An arrow goes from 1 to negative 1, from 2 to 0, from 3 to 1. a. ordered pairs: {(–1, 1), (2, 0), (3, 1)} b. ordered pairs: {(–1, 1), (0, 2), (1, 3)} c. ordered pairs: {(1, –1), (0, 2), (1, 3)} d. ordered pairs: {(1, –1), (2, 0), (3, 1)} Please select the best answer from the choices provided A B C D
The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.
What is a set ?A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.
An ordered pair consists of two items. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it might be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.
The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.
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Answer:
D
Step-by-step explanation:
A large concrete block is used for the cornerstone of a building. The block is 18 yd deep, 23 yd wide, and 16 yd long. What volume of concrete is needed to make this block?
Answer:
Step-by-step explanation:
To find the volume of concrete needed to make this block, you need to calculate the volume of the block using the formula:
Volume = Length x Width x Height
In this case:
Volume = 18 yd x 23 yd x 16 yd = 7,648 cubic yards
So, 7,648 cubic yards of concrete are needed to make this block.
Alternatively, you can use the formula:
V=LWH, where V is the volume, L is the length, W is the width and H is the height.
Which inequality represents all values of x for which the product below is defined? square root 5x times square root x + 3
The values of x for which the product:
√(5x)*√(x + 3)
Is defined are:
x ≥ 0
For which values of x is the product not defined?Here we want to see for which values of x is the following product not defined.
√(5x)*√(x + 3)
Ok, remember that the argument of the square root must be zero or larger, then we have two inequalities here:
5*x ≥ 0
x + 3≥ 0
We can simplify both of these inequalities to get:
x ≥0
x≥ -3
We take the first one, which is more restrictive, the values of x for which the product is defined are:
x ≥0
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Please help me with this!!!
Step-by-step explanation:
the area of a rectangle is
length × width.
so, it's simply a problem of multiplying 2 fractions.
it is
2 3/5 × 3 1/4
first we need to convert the numbers into true fractions.
2 3/5 = (2×5 + 3)/5 = 13/5
3 1/4 = (3×4 + 1)/4 = 13/4
the beauty of a multiplication (compared to addition) is that we don't need to bring the fractions to the same denominator. we can simply calculate with what they are.
you remember,
a/b × c/d = (a×c)/(b×d)
therefore,
13/5 × 13/4 = (13×13)/(5×4) = 169/20 =
= (8×20 + 9)/20 = 8 9/20
the area of the rectangle is 8 9/20 in²
A family at retaurant the bill i $42 they leave a tip in total they give $49. 77 how much wa the percentage of the tip?
The tip left by the family at the restaurant is 18.48% of the total bill.
To determine the percentage of the tip, we need to divide the amount of the tip by the total bill, and then multiply by 100 to get the percentage.
The amount of the tip can be calculated by subtracting the cost of the bill from the total amount paid: $49.77 - $42 = $7.77
So the percentage of the tip is:
$7.77 / $42 x 100 = 18.48%
Therefore, the tip left by the family at the restaurant is 18.48% of the total bill.
The percentage is a relative term that expresses a number as a fraction of 100. It is commonly used to express a proportion or rate in terms of a hundred. For example, 45% is equal to 45 out of 100, or 0.45. The percentage can be used to represent any ratio, such as a ratio of two numbers, a fraction of a whole, or a proportion of a total.
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Which techniques can be used to evaluate the expression 12.75 = 1.5? Select all that apply.
The evaluation of the expression 12.75 ÷ 1.5 is 51 / 6.
How to evaluate expression?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Therefore, let's evaluate the expression as follows:
Hence,
12.75 ÷ 1.5
Let's convert each decimal to fractions for easy evaluation
Therefore,
12.75 = 1275 / 100
1.5 = 15 / 10
Therefore,
1275 / 100 ÷ 15 / 10
Let's change the division sign to multiplication sign.
1275 / 100 × 10 / 15
1275 / 150
Therefore,
255 / 30 = 51 / 6
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in the figure angle APC is equal to angle BQD prove that AB is parallel to CD
From the given proof below, we have shown that AB is parallel to CD.
How to prove parallel lines?From the attached diagram showing the triangles inside the circle, we are given that;
<APC = <DQB [ Given]
Now, we know that in cyclic quadrilaterals that Equal angles subtend equal arcs and therefore; Arc(AC = BD)
From the statement above showing that Equal angles subtend equal arcs. we can conclude that AB is parallel to CD
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Max puts a stopper in the bathtub and turns on the faucet at t = 0.
After 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub.
Write an equation that relates the number of gallons, g, to the time, t.
Does the relationship represent a linear function? Justify your response.
The equation is y = 2.2x. Yes, it represents a linear function.
What is a linear function?
A linear function is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear function with exponents greater than 1. Such an equation on the graph, forms a straight line.
We are given that
Stopper is applied at t = 0
At t = 5 minutes ; water in tub = 11 gallons
At t = 10 minutes ; water in tub = 22 gallons
We know that a general form of a linear function is y = mx + c.
Where c is the intercept ; m is the Slope ; y and x are dependent and independent variables respectively
Here, the intercept is gallon of water at t = 0 ;
Since, it is not mentioned, therefore it will be taken as 0.
Slope = change in y / change in x
Slope = (22 - 11) / (10 - 5)
Slope = 11 / 5
Slope = 2.2
Therefore, the equation becomes
y = 2.2x + 0
y = 2.2x
Yes, it represents a linear function because the highest degree is 1.
Hence, the equation is y = 2.2x. and it represents a linear function.
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Mybankaccount pay 4% interet at the end of each year. Suppoe that I have $x in my bank account at the tart of thi year, and that I never add money to the account or take money out of the account. (a) Howmuchwill be in the account at the end thi year (after the interet i paid)? (b) Howmuchwill be in the account at the end of next year (again, after the interet)? (c) Find an expreion for the amount in the account after N year
a) The amount in the account at the end of this year after the interest is paid will be 1.04x.
b) The amount in the account at the end of this year after the interest is paid will be 1.08x.
c) The expression for the amount in the account after N years will be x + 0.04xn.
a) From the information, Mybankaccount pays 4% interest at the end of each year. The person has $x in the bank account at the start of this year. The amount in the account at the end of this year after the interest is paid will be:
= x + (x*0.04*1)
= x + 0.04x
= 1.04x
b) The amount in the account at the end of 2 years after the interest is paid will be:
= x + (x*0.04*2)
= x + 0.08x
= 1.08x
c) The expression for the amount in the account after N years will:
= x + (x*0.04*n)
= x + 0.04xn
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What is the formula for the sum of a sequence?.
The formula for the sum of an arithmetic sequence is [tex]S_n[/tex]=[tex]n/2[/tex][2a+(n−1)d], [tex]S_n[/tex] = [tex]n/2[/tex] [2a +( n − 1 )d ], where: n = the number of terms to be added. a = the first term in the sequence. d = the constant value between terms.
In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.
Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.
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What type of triangle is a 3 4 5 triangle?.
A triangle with a right angle is a 3 4 5 triangle.
A right triangle is a particular kind of triangle that only has one right (90°) angle.A mathematical formula for determining the length of the third side of a right triangle given the lengths of the other two sides was developed by the Greek mathematician Pythagoras.
The sides of variables a and b make up the right angle of the triangle. Any side may make use of any variable. The variable c stands for the left side, or the side that leans away from the right angle. The longest side, or side c, is always present and is known as the hypotenuse.
So the right angle triangle is a triangle with sides of 3, 4, and 5.
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What is the formula for finding the axis of symmetry for a quadratic function in standard form?.
The formula for finding the axis of symmetry for a quadratic function in standard form is y = a (x-h)² + k
The term axis of symmetry in math is defined as an imaginary straight line that divides a shape into two identical parts hereby creating one part as the mirror image of the other part.
Here we need to identify the formula for finding the axis of symmetry for a quadratic function in standard form.
According to the definition of axis of symmetry, the general formula is written as
Here the quadratic equation in vertex form is written as,
=> y = a (x-h)² + k
Here the values (h, k) refers the vertex of the parabola.
And here we have also given that the axis of symmetry formula is x = h.
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a grocery store is selling apples and grapes at the rate of $5.00 per pound and $3.99 per pound respectively. a person has $11.00 on him. they come to the grocery store to buy apples and grapes. A represents the amount of apples, in pounds, and G represents the amount of grapes, in pounds. which inequality represents the maximum amount of apples and grapes they can buy?
The inequality that represents the maximum amount of apples and grapes they can buy will be 5a + 3.99 ≤ 11.
How to calculate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Therefore, the inequality that represents the maximum amount of apples and grapes they can buy will be 5a + 3.99g ≤ 11.
where a= Apple
g = grape.
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21=3(y+3)
Responses
y = 3
y, = 3
y = 4
y, = 4
y = 5
y, = 5
y = 6
y , = 6
Answer:
y = 4
Step-by-step explanation:
21/3 = 7
7 - 3 = 4
