Enlargements of the picture or reductions of the image are both types of dilations.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.
The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.
Even in the enlarged picture, parallel and perpendicular lines are still discernible.
A dilated image's side's midway matches the pre-exactly. image's
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the graph shows the total weight of abox of cereal, y, as a function of the amount of cereal in the box, x. what is the weight of the box when it is empty?
Answer:
3
Step-by-step explanation:
This is algebra 2, please help me by using elimination to solve.
The correct option regarding the solutions of the system of equations for this problem are given as follows:
The solutions are (-1.19, 4.47) and (2.52, 27.92).
How to solve the system of equations?The system of equations for this problem is defined as follows:
4x² + x - y = 0.-x² - 5x + y - 9 = 0.Adding the two equations, we can eliminate the variable y, hence:
3x² - 4x - 9 = 0.
Meaning that this is a quadratic equation with the coefficients given as follows:
a = 3, b = -4, c = -9.
Inserting these parameters into a quadratic equation calculator, the solutions for x of the quadratic equation are given as follows:
x = -1.19 and x = 2.52.
When x = -1.19, the solution for y is calculated as follows:
y = 4x² + x = 4(-1.19)² - 1.19 = 4.47.
When x = 2.52, the solution for y is calculated as follows:
y = 4x² + x = 4(2.52)² + 2.52 = 27.92.
Meaning that the correct option is given by the second option.
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1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms?
In response to the question, we may say that As a result, the orangutan's expression mass in kilogrammes is roughly 64.55 kg.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To convert pounds to kilogrammes, divide the pound weight by the conversion ratio of 2.2.
Hence, to calculate the orangutan's mass in kilos, do the following:
Divide the orangutan's weight in pounds by the conversion ratio of 2.2:
142 pounds divided by 2.2 is 64.54545... kilos (rounded to the nearest hundredth)
As a result, the orangutan's mass in kilogrammes is roughly 64.55 kg.
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Select the correct answer.
Which expression is equivalent to √48x^5, if x > 0?
O A.12³√3x
OB. 42³√3
O c. 4x²√3x
OD. 12x²√x
Step-by-step explanation:
O c. 4x²√3x expression is equivalent to √48x^5, if x > 0?
what is the difference of 1 and a number?
How do you find mass using FG?
To find the mass of an object, one can use the formula (Force x Distance) / Gravitational Constant (FG). This formula involves multiplying the force applied to an object by the distance it moves, and then dividing the result by the gravitational constant (FG). The resulting number is the mass of the object in kilograms.
Mass can be found by using the formula (Force x Distance) / Gravitational Constant (FG).
For example, if a force of 10N is applied to an object that is moving 2 meters, the mass of the object can be calculated as follows:
Mass = (10 N x 2 m) / FG
Mass = 20 / 9.8
Mass = 2.04 kg
Finding mass using the force-distance formula (FG) is a simple process. To use it, one needs to know the force applied to an object, the distance it moves, and the gravitational constant (FG). The force and distance values can be measured or calculated depending on the situation. The gravitational constant is a fixed number and is equal to 9.8 m/s2. To calculate the mass, one needs to take the force multiplied by the distance and then divide it by the gravitational constant (FG). The resulting number is the mass of the object in kilograms. This formula is useful for calculating the mass of objects in a variety of situations. It is also useful for verifying the mass of an object that has already been measured.
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Use properties of operations to complete the equivalent expressions. 3(c−4)=___c−___ 3(c−4)
Using properties of operations, the expression is 3(c-4)= 3c-12.
What are the properties of operations?
Properties of additionAddition of whole numbers is both associative and commutative.The identity for adding whole numbers is 0, or zero.Properties of MultiplicationThe identity for multiplying whole numbers is 1.Multiplication of whole numbers is both associative and commutative.Distribution favours multiplication over addition.Properties of Division and subtractionDivision is not associative.Subtraction is not commutative.Now, we are given the expression 3(c-4)
Using the properties of operation,
3(c-4)= (3*c)-(3*4)
= 3c-12
Hence, the equivalent expressions are 3(c-4)=3c-12.
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Question- Use properties of operations to complete the equivalent expressions. 3(c−4)=___c−___
A cube with volume 8 cubic centimeters is cut in half by a plane which contains two edges of the cube. What is the area of the rectangle formed by the intersection of the plane and cube ? express your answer in simplest radical form.
In simplest radical form as A = 22 = 4 cm2
The formula for the volume of a cube is V = a3, where a is the length of each of the cube's sides. In this case, we know that the volume of the cube is 8 cm3, so a3 = 8. When we take the cube root of 8, we get that a = 2 cm.
Therefore, the area of the rectangle formed by the intersection of the plane and cube is A = 2*2 = 4 cm2. This can also be expressed in simplest radical form as A = 22 = 4 cm2.
To calculate this step by step, we first use the formula V = a3 to find the length of each side of the cube. We plug in 8 cm3 for V and solve for a.
V = a3
8 cm3 = a3
Taking the cube root of both sides gives us:
a = ∛8
a = 2 cm
Next, we use the formula for the area of a rectangle, A = l*w, where l is the length and w is the width. We know that the length and width of our rectangle are both equal to 2 cm.
A = l*w
A = 2*2
A = 4 cm2
This can also be expressed in simplest radical form as A = 22 = 4 cm2.
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Which of the following is a factor of 2x^2 3x 5?
The factor of the given expression is -1 and 5/2 first we try to solve given expression as a quadratic equation then we make 2 terms equal to 0.
first, try to understand what is the factor of a quadratic equation.
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.
The roots of a quadratic equation are known as a factor. This means if we put the value of x to factor then the quadratic equation will become zero.
2x^2 - 3x - 5 = 2x^2 - (5-2)x - 5
3 can be written as 5-2.
2x^2 - 5x + 2x - 5
x(2x - 5) +1(2x-5)
(2x - 5)(x + 1)
So the factors is 2x - 5 = 0 or x + 1 = 0.
2x - 5 = 0 , x = 5/2.
x + 1 = 0 , x = -1.
Given question is incomplete complete question here:
Which of the following is a factor of 2x^2 - 3x - 5?
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A "Pick 2" lottery game involves drawing 2 numbered balls from separate bins each containing balls labeled from 0 to 9. So there are 100 possible selections in total: 00, 01, 02, ..., 98, 99. Players can choose to play a "straight" bet, where the player wins if they choose both digits in the correct order. Since there are 100 possible selections, the probability a player wins a straight bet is 1/100. The lottery pays $50 on a successful $1 straight bet, so a player's net gain if they win this bet is $49. Let X represent a player's net gain on a $1 straight bet. Calculate the expected net gain E(X). Hint: The expected net gain can be negative. E(X) = dollars
Answer:
The probability of winning a straight bet is 1/100, and the payout is $50, so the expected value of a winning bet is (1/100) * $50 = $0.50.
The probability of losing a straight bet is 99/100, and the cost of the bet is $1, so the expected value of a losing bet is (99/100) * -$1 = -$0.99.
Therefore, the expected value of a straight bet is $0.50 - $0.99 = -$0.49.
Can you help solve this.
The equation that best represents the line on the first graph is
5x + 3y = 3
Option C is the correct answer.
The equation that best represents the line on the second graph is
x - y = -7
Option A is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Pick two coordinates that the line passes through in each graph.
First graph:
(0, 1) and (-3, 6)
m = (6 - 1)/ (-3 - 0) = 5/-3 = -5/3
(0, 1) = (x, y)
1 = (-5/3)0 + c
c = 1
Now,
y = (-5/3)x + 1
3y = -5x + 3
5x + 3y = 3
Second graph:
(0, 7) and (-5, 2)
m = (2 - 7) / (-5 - 0) = -5/-5 = 1
(0, 7) = (x, y)
7 = 1 x 0 + c
c = 7
y = x + 7
x - y = -7
Thus,
The equation of the first graph is 5x + 3y = 3.
The equation of the second graph is x - y = -7.
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PLEASE SOMEONE ANSWER THIS ASAP I NEED YOUR HELP:
PQR is a non-right-angled triangle. QR is 5.1cm, RP is 7.8cm and PQ is 6.2cm. Find the area of PQR
Using Heron's formula the area of the triangle is 15.78cm²
What is Heron's FormulaHeron's formula is a formula for calculating the area of a triangle when the lengths of all three sides are known. It is named after the Greek mathematician and engineer Heron of Alexandria (c. 10–70 AD). The formula is:
Area = √s(s-a)(s-b)(s-c)
Where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter, or half the perimeter, of the triangle, given by:
s = (a + b + c)/2
Let's define the variables as;
a = 5.1b = 7.8c = 6.2s = (5.1 + 7.8 + 6.2) / 2
s = 9.55cm
The area can be calculated as;
A = √s(s - a)(s - b)(s - c)
A = √9.55(9.55 - 5.1)(9.55 - 7.8)(9.55 - 6.2)
A = 15.78cm²
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If star a is closer to us than star b, then star a's stellar parallax is __________.
O Larger than that of star B
O Larger than that of star A
O Smaller than that of star B
O Smaller than that of star A
If star A is closer to us than star B, then Star A's parallax angle is: Larger than that of Star B.
Hence, option (A) is correct choice.
The parallax of a star at a distance of 10 parsecs would be 0.1′′ since parallax is inversely proportional to distance. The parallax of Proxima Centauri, a star in the triple system of Alpha Centauri, is 0.76813′′, indicating that it is 4.24 light-years away from Earth at a distance of 1/0.76813, or 1.302 parsecs.
The apparent shift in an object's location caused by a change in the observer position is known as parallax. This apparent shift is measured (in arc seconds) is reversed to provide the distance from the background stars (in parsecs).
The definition of an object's absolute magnitude is the apparent magnitude the object would have if it were observed at a distance of precisely 10 parsecs (32.6 light-years), without light extinction.
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what are the conditions for using the normal approximation for a sampling distribution of proportions g
The normal approximation for sampling distributions of proportions can be used when the sample size is large enough.
What prerequisites must be met for a sampling distribution of proportions g in order to use the normal approximation?The conditions for using the normal approximation for a sampling distribution of proportions are as follows: The sample size (n) must be sufficiently large (usually 30 or more). The sample proportion (p) should not be close to 0 or 1. The population distribution should be normally distributed.The general rule is that if the sample size (n) is greater than or equal to 30, then the normal approximation can be used. When using the normal approximation for a sampling distribution of proportions, the sample size must be greater than or equal to 30 and the population proportion (p) must be between 5% and 95%. Furthermore, the sample size must be large enough that the expected number of successes (np) and expected number of failures (nq) are both greater than or equal to 10. Finally, the sampling distribution should be approximately normal and the sample should be randomly selected from the population. The normal approximation is a useful tool for estimating confidence intervals and the probability of extreme values, as well as for hypothesis testing. It can be used to estimate the probability of success in a given sample of proportions, which can be helpful when making decisions about a population or understanding the behavior of a system.To learn more about distribution of proportions refer to:
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What is the meaning of △?
Meaning of the △ is: the given symbol is the representation of the geometrical figure triangle.
Different symbols used to represent the different geometrical figures.The given symbol has three sides.Symbol also represents three interior angles.When three sides intersect with each other it represents the vertices.The triangle represents the 2 dimensional shape.Sum of all the measure of the three interior angles is equal to 180 degree.Symbol of triangle in the geometrical shape is given by △.There are different shape such as square, rectangle, circle and many more.Therefore, the meaning of the given symbol △ is the representation of the triangle.
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What is the inverse of the inverse of P → Q?
The inverse of ∼P→∼Q is P->Q.
Given ∼P→∼Q
Its inverse, ∼(∼P)→∼(∼Q), means that P→Q.
If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue. A conditional statement that has been modified or rearranged is referred to as a related conditional. An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. It is noted that p→q. Read this: if p, then q.
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How do u work this out ?
Answer:
[tex]\frac{d}{c}[/tex]
Step-by-step explanation:
[tex]\frac{cxcxdxdxd}{cxcxcxdxd}[/tex] You can cross out 2 c's from the top and the bottom and 2 d's from the top and the bottom. It now looks like this
[tex]\frac{d}{c}[/tex]
I need help with this please
Answer in explanation:
*change the problem to [tex]\frac{5}{6}[/tex] x [tex]\frac{3}{1}[/tex]
(change 3 into a fraction by putting 1 in the place of a denominator)
next cross multiply
5 x /1
/2 1
3 can go into 6- 1 time
since anything multiplied by 1 is 1, the answer is [tex]\frac{5}{2}[/tex]
Hope this helps ya!
*(disclaimer lol: alternatively, you could cross multiply without changing 3 to a fraction and get the same answer-- however, I wanted to explain as clearly as possible, and figured it was less confusing this way!)
Which of the following would NOT cast doubt of the usefulness of sample? data? Choose the correct answer below.
a. Order of questions in a survey
b. Missing data
c. Nonresponse
d. An effective sampling method
An effective sampling method is not cast doubt on the usefulness of the sample
The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.
Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.
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According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most recent month. Let's assume the standard deviation is 4.5% of students. Joseph collects data from 186 students at a medium-sized school in Iowa and finds that only 11% reported this rate of bullying. What is his 95% confidence interval?
Select one:
A. [8.75, 13.25]
B. [10.353, 11.647]
C. [10.5, 19.5]
D. [6.5, 15.5]
c) A concern or risk of reporting significant mean differences between groups is that people may
If Joseph collects data from 186 students from a medium sized school in Iowa and finds that only 11% students has reported rate of bullying , then the 95% confidence interval is option (b) [tex](10.353, 11.647)[/tex] .
the students who report bullying in middle sized school is ⇒ [tex]15[/tex] percent ;
the standard deviation is given as ⇒ 4.5% = 0.045 .
the sample size is ⇒ 186 students ;
the sample proportion is ⇒ 11% = 0.11 .
we know that the for the 95 percent confidence interval the value of z score is 1.96 .
The formula to calculate the upper and lower limit of 95 percent confidence interval is :
= [tex]( Sample Proportion \pm \frac{Zscore \times Standard Deviation}{\sqrt{Population Size} })[/tex]
So , the lower limit of the interval will be calculated as :
= [tex]( 0.11 - \frac{1.96 \times 0.045}{\sqrt{186} })[/tex]
On simplifying ,
we get
= [tex]0.1035[/tex] = [tex]10.35\%[/tex] ;
So , the upper limit of the interval will be calculated as :
= [tex]( 0.11 + \frac{1.96 \times 0.045}{\sqrt{186} })[/tex]
On simplifying ,
we get ;
= [tex]0.1165[/tex] = [tex]11.65 \%[/tex]
Therefore , the required interval is [tex](10.353, 11.647)[/tex].
The given question is incomplete , the complete question is
According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most recent month. Let's assume the standard deviation is 4.5% of students. Joseph collects data from 186 students at a medium-sized school in Iowa and finds that only 11% reported this rate of bullying. What is his 95% confidence interval ?
(a) (8.75, 13.25)
(b) (10.353, 11.647)
(c) (10.5, 19.5)
(d) (6.5, 15.5)
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A recipe for 3 people uses 150 g of flour. How much flour is needed to
make the same recipe for 6 people? Give your answer in grams (g).
600 g flour is needed to make the recipe which needs 150 g flour for 3 people, for 6 people.
Given that a recipe for 3 people uses 150 g of flour.
We know that the relation between quantity of flour and number of people for whom recipe will be prepared is directly proportional.
So if the number of people will increase so the quantity of flour will be needed more.
The flour needed to make the recipe for 1 people is = 150/3 = 50 g.
The flour needed to make the recipe for 6 people will be = 50 * 6 = 300 g.
Hence 600 g flour is needed to make the same recipe for 6 people.
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In a jar, the ratio of dimes to nickels is 3.4. Given that there are 60 nickels in the jar, how many more nickels are in the jar than dimes?.
Answer:
15
Step-by-step explanation:
the nickels ratio is 4. I then divided 60 : 4 = 15. I then timesed 15 with 3 and then came out 45. I then subtracted 60 with 45 which gave me the answer of 15.
50 POINTS!! Pls make sure the answers are correct and the work is shown
Answer all pls and show work
Answer:
it 33 pts not 50
How to answer this question
The value of x to the nearest degree will be 112°.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
There are three angles are shown in figure.
That is,
⇒ 59°, 108°, and 81°.
Now, We know that;
Sum of all four angles is 360°.
So, We can formulate;
⇒ 59° + 108° + 81° + x = 360°
⇒ 248° + x = 360°
⇒ x = 360° - 248°
⇒ x = 112°
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How many dollars will Ms. Davis have saved after 30 weeks?
Ms. Davis has $54. 50 saved
• She will save $33. 25 each week for the next 30 weeks
• She will not spend any of the money
Enter your response here:
$1052 is the total saving og Ms. Davis after 30 weeks from the given point .
Given that:
Inital saving of Ms. Davis = $54.50
Ms. Davis has already saved $54.50 and plans to save an additional $33.25 each week for the next 30 weeks. This means that she will be adding a total of $33.25 x 30 = $997.50 to her savings over the next 30 weeks.
If she does not spend any of the money she has saved, her total savings will be :
sum of Initial saving and saving after 30 weeks
$54.50 + $997.50 = $1,052.00.
so the total saving is $1052.
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A researcher has collected the following sample data. The mean of the sample is 5 "3 5 12 3 2" Refer to Exhibit 1. The range is: O 1 O 2 O 10 O 12
The range of a sample data collected by a researcher is 10 . So, correct answer is option (C).
Range of a sample data is calculated by using the formula to determine the difference between the highest and lowest value in sample set of values.
R = Highest Value (H) - Lowest Value (L)
Range Formula, R = H - L
Where, R --> range
H --> the highest value
L --> the lowest value
We have, a reaseacher collected a sample data .
Sample data values are following,
3 5 12 3 2
The mean of sample data = 5
Range of sample data = highest data value - lowest data value
There is highgest data value = 12
and lowest data value = 2
Range = 12 - 2 = 10
So, the required range of sample data is 10.
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Complete question:
A researcher has collected the following sample data. The mean of the sample is 5
"3 5 12 3 2"
Refer to Exhibit 1. The range is:
A)1
B)2
C)10
D) 12
3.) In a proportional relationship, y=2 when x = 8. Which of the following equations would describe this relationship? (1) y=1/4x (2) y = 4x (3) y=x-6 (4) y =1/2x-2
The correct option is y=1/4x.Because it holds the directly proportional relationships.
What is directly proportional?Two values x and y are said to be directly proportional to each other when the ratio x:y always remains the same. Directly proportional relationship between a quantity y and a quantity x that has a constant of proportionality k is represented by the equation y = kx.
How do you find if an equation is a proportional relationship?A relationship is proportional if each pair of data values are related in the same way by multiplying by a factor. You can recognize a proportional relationship by looking at data.When two quantities x and y are in direct proportion then they are written as x ∝ y. Symbol “∝” stands for 'is proportional to'.
NOW we find
according to directly proportion
y∝x
y=kx
y/x=k
2/8 =k
1/4 =k
Now we get
y = 1/4x
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Solve this problem?
step by step
The value of x is 9.32 after solving using the Pythagoras theorem.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The diagram has 4 corners namely - A, B, C and D.
Draw a perpendicular through B.
The intersecting point at line AD is named as E.
It can be seen in figure that EDCB is a rectangle and falls under the category of parallelogram.
So, angle ADC = angle DEB = angle AEB = 90° .
Now, side BC = ED = 5.
So, side AE = 18 - 5 = 13.
Here, it can be seen that triangle ABE is a right-angled triangle.
So, to get the measurement of side BE, apply the Pythagoras theorem -
c^2 = a^2 + b^2
Where, a is perpendicular, b is base and c is hypotenuse.
So, according to the diagram -
(16)^2 = (13)^2 - (BE)^2
(BE)^2 = (16)^2 - (13)^2
(BE)^2 = 256 - 169
(BE)^2 = [tex]\sqrt{87}[/tex]
(BE)^2 = 9.32
Now, as EDCB is a rectangle so, side BE = side CD.
Therefore, the value for side CD = x = 9.32.
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How does the parabola open? Is the vertex a minimum or maximum value?
f(x) = 5x²-3x
The parabola is open upward direction. The vertex is the minimum value of the parabola.
What is a parabola?
A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.
Given quadratic function is
f(x) = 5x² -3x
The leading term of the given function is 5x².
The sign of the leading term is positive, thus it is open upward direction.
Rewrite the given function in the form f(x) = a(x - h)² + k
f(x) = 5x² -3x
f(x) = 5( x² - 3/5 x)
f(x) = 5( x² - 3/5 x + 9/100 - 9/100)
f(x) = 5( x² - 3/5 x + 9/100) - 5 × 9/100
f(x) = 5( x - 3/10)² - 9/20
f(x) = 5( x - 3/10)² + (-9/20)
The vertex of the parabola is (3/10, -9/20).
Since the parabola opens upward direction, thus the vertex of the parabole is a minimum value.
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Brian has 64 flowers for a big party decoration. In addition, he is considering buying flower arrangements that have 18 flowers each. All of the arrangements cost the same. Brian can buy up to 5 arrangements given the amount of money he has. Let x represents the number of flower arrangements Brian buys. Write a function rule to describe how many flowers Brian will have based on the number of arrangements he buys. Find a reasonable range for the function.
The function which can which can define the number of flowers in the arrangement is f(x) = 64 + 18x. The domain is found to be [ 0 , 5 ] and the range is [ 64 , 154 ].
Let the number of flowers which is to be calculated be x,
now we know that she already have 64 flowers and that each arrangement will have 18 flowers.
Therefore, the number of flowers can be given by the function , f(x) = 64 + 18x.
Now , we know that the maximum number of flowers which she can buy externally is 5 , which means the domain becomes [0,5] .
To find the range we will put the value of domain in the given function.
when x = 0 ,
f(0) = 64
when x = 5,
f(5) = 154
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