Substitution is the best method to use when one of the equations in the system is already solved for one variable. This involves substituting the solved equation into the other equations in the system, allowing the variable to be eliminated, and then solving the resulting equation.
Substitution is the best method to use when one of the equations in the system is already solved for one variable. This method involves substituting the solved equation into the other equations in the system, allowing the variable to be eliminated. The resulting equation will have fewer variables, making it easier to solve. Additionally, this method can be used to eliminate variables from equations that cannot be solved directly. For example, if two equations are given that cannot be solved for a common variable, substitution can be used to eliminate the variable from both equations and turn them into equations in one variable. This makes it easier to solve the system of equations.
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Zach made a popcorn snack. He mixed 5/8 gallon of popcorn with 1/2 gallon of dried apple rings. Did he use more dried apple rings or more popcorn?
sand is falling off of a conveyor belt onto a conical pile at the rate of 20 feet^3 per minute. the diameter of the base of the cone is four times the altitude. at what rate is the height of the pile changing when it is 8 feet high>
The rate is the height of the pile changing when it is 8 feet is:
dh/dt=60/256π
The volume of a cone is defined as the amount of space or capacity a cone occupies, and it is measured in cubic units like cm³, m³, and in³.
The volume of a cone is given as V = (1/3)πr²h.
If the radius of the base of the cone is "r"
height of the cone is "h",
Let r = radius of the base at time t
h = height at time t
V = volume of cone at time t
Given: dV/dt = 20
Find dh/dt when h = 8
V = (1/3)πr²h Since 2r = 4h, r = 2h
V = (1/3)π[2h]²h
= (2/3)πh³
dV/dt = (4/3)πh²(dh/dt)
Now, substitute the values we get
20 = (4/3)π(8)²(dh/dt)
20=4/3π×64(dh/dt)
20=256π/3(dh/dt)
60/256π=dh/dt
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What is the slope of the line passing through the points 3 2 and (- 2 2?
The slope of the line passing through the points (3, 2) and (-2, 2) is 0.
In the given question, we have to find an equation of the line that passes through the points (3, 2) and (-2, 2).
The point-slope approach is typically used when two points that sit on a specific line are specified.
A line's equation is written as y - y(1) = m(x - x(1)), where y(1) is the Y-axis coordinate, m is the slope, and x(1) is the X-axis coordinate.
Firstly we find the value of m using the formula
m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
From the given points x(1) = 3, y(1) = 2, x(2) = -2, y(2) = 2.
Now putting the value
m = [tex]\frac{2-2}{-2-3}[/tex]
Now solving
m = [tex]\frac{0}{-5}[/tex]
m = 0
Hence, the slope of the line passing through the points (3, 2) and (-2, 2) is 0.
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The complete question is:
What is the slope of the line passing through the points (3, 2) and (-2, 2)?
Convert 81/10 into mixed number
Answer:
Step-by-step explanation:
its 8 1/10
Which of the following is the solution of the quadratic equation xଶ 3x − 10 0?
The solutions of the quadratic equation x^2 + 3x - 10 = 0 are x = 4 and x = -1.
The solution of the quadratic equation x^2 + 3x - 10 = 0 can be found by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where (a, b, and c) are 1, 3, and -10
So, the solutions of the equation x^2 + 3x - 10 = 0 are:
x = (-3 ± √(3^2 - 4(1)(-10)) ) / 2(1)
x = (-3 ± √(9 + 40)) / 2
x = (-3 ± √49) / 2
x = (-3 ± 7) / 2
x = (4, -1)
Complete question:
Which of the following is the solution of the quadratic equation x^2 - 3x − 10 = 0?
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An arithmetic sequence is given below.
- 3, 4, 11, 18,
th
Write an explicit formula for the n'
term an
Answer:-3+(n-1)*7
Step-by-step explanation:
Nth term = -3+(n-1)*7
K
Catherine bought apples and pears for a school picnic. The total number of pieces of fruit that she
bought was less than 100. She bought more apples than pears. Use this information for the following
problem.
www
elp
Apples and pears were purchased by Catherine for the school picnic. The right formula will be y = 100-x and y < x if the total number of fruits is less than 100.
What is meant by equation?Equations are mathematical expressions with two algebraic operators on either side of the equal (=) symbol. To illustrate this relationship, the phrases on the left and right are shown to be equal to one another. A basic, straightforward equation is L.H.S. = R.H.S. (left-hand side = right side).
As per the given data in the equation,
Catherine bought apple and pears.
The overall quantity is less than 100
Let the number of apples is x and,
The number of pears is y.
She bought more apples than pears,
y < x.
And y < 100 - x.
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Suppose that the probability that a person will die in the next 20 years is
18. 1452%. If this person has a life insurance policy that will pay out $25,000
to the beneficiaries of the policy if the person dies in the next 20 years, what
is the premium of the policy? Assume that the administrative costs of the
policy amount to $45.
The premium of the policy will be $4,536.30. The goal of insurance is to spread the risk of potential losses among a large group of people, so that any individual loss is not too devastating for one person to bear.
Insurance is a contract between an individual or organization and an insurance company, where the individual or organization pays a premium to the insurance company in exchange for financial protection or reimbursement in the event of an unforeseen loss or event. The insurance company agrees to pay for any covered losses or damages, up to the limits specified in the insurance policy. Insurance can be used to protect against a variety of risks, including death, injury, property damage, and liability.
The premium of the policy can be calculated using the formula:
Premium = (Probability of death * Benefit amount) + Administrative costs
In this case, the probability of death is 18.1452%, the benefit amount is $25,000, and the administrative costs are $45.
Then, the premium of the policy would be:
(0.181452 * 25,000) + 45 = $4,536.30
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Answer: $4581.30
Step-by-step explanation:
Select the correct answer from each drop-down menu. Complete the steps to construct a square inscribed in a circle. Step 1: Start by drawing a circle. Step 2: On the circle, . Label its endpoints A and C. Step 3: Set the width of the compass larger than the radius of the circle. , centered at A and C, on each side of the diameter. Step 4: and the center of the circle. Label the points of intersection with the circle as B and D. Step 5: Draw chords , , , and .
The angle subtends by the endpoints of the diagonal at any point on the circle will be 90 degrees. Draw the two perpendicular diagonals. Then join the endpoints of the diagonals.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
here, we have,
Construct a square inscribed in a circle using the construction tool. Insert a screenshot of the construction here.
We know that the angle subtends by the endpoints of the diagonal (longest chord of a circle) at any point on the circle will be 90 degrees.
Then for the construction of the square, we have
First, draw the two perpendicular diagonals.
Then join the endpoints of the diagonals.
Thus, the result is a square.
The angle formed by the diagonal's endpoints at any point on the circle will be 90 degrees. Create two parallel diagonals. Then connect the diagonal endpoints.
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How do you draw a 2 x graph?
Drawing a 2 x graph is a simple process that requires only a few basic steps.
To start, you'll need a ruler, a pencil, and a piece of paper. Begin by using the ruler to draw two parallel lines that cross your paper.
These two lines will form the axis of your graph.
Next, use your ruler to evenly space out small tick marks along each line. These tick marks will help you create the “x” and “y” values that will form the data points on your graph.
Finally, connect the data points with lines or dots to create your 2 x graph. You can now use your graph to display the data in an easy-to-understand format.
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To try increase profits a theater owner increases the price of a ticket by $25 every month describe what a scatter plot might look like if x represents the number of months and y represents the profits explain your reasoning
The scatter plot will start looking like an upward line if the owner starts increasing the price by $25 every month.
A scatter plot is a graphical representation of a set of data points, where the position of each point on the x and y-axis represents the values of two variables.
If we use a scatter plot to represent the relationship between the number of months (x-axis) and the profits (y-axis) of a theater as the price of a ticket increases by $25 every month, we might expect to see the following:
A positive correlation between the number of months (x-axis) and the profits (y-axis). This means that as the number of months increases, the profits will also increase.
A linear pattern of data points, with the data points lying on or close to a straight line. This is because the price of a ticket is increasing by a fixed amount ($25) every month, so the profits will also increase by a fixed amount every month.
The slope of the line will be positive, representing the increase in profits each month.
It might look like a line that starts at low profits and as the months progress the line moves upward to the right, representing the increase in profits.
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Select all the correct answers.
If the measure of angle is , which statements are true?
0
0
The measure of the reference angle is 60°.
sin (0) =
The measure of the reference angle is 45°.
tan(0) = 1
The measure of the reference angle is 30°.
cos (0) = √3
The measure of the reference angle is: [tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]
What is reference angle?The acute angle in mathematics is the reference angle, which is smaller than 90 degrees. It consistently creates the shortest angle and aligns the angle's terminal side with the x-axis. The reference angle for an angle is the size angle, t, formed between the horizontal axis and the angle's terminal side. Use reference angles to get the sine and cosine of the original angle. Reference angles can also be used to calculate the coordinates of a point on a circle.The reference angle of an angle is the smallest acute angle between the terminal arm of a quadrant and the x-axis.
Given that:
[tex]$$\theta=\frac{11 \pi}{6}$$[/tex]
First, we convert to degrees
[tex]& \theta=\frac{11 \pi}{6} * 180 \pi \\[/tex]
[tex]& \theta=\frac{11}{6} * 180 \\[/tex]
[tex]& \theta=11 * 30 \\[/tex]
[tex]& \theta=330^{\circ}[/tex]
[tex]$$\alpha=30$$[/tex]
Hence, the measure of the reference angle Is: [tex]$30^{\circ}\alpha=30[/tex]$ means that the reference angle is in the first quadrant [tex]$\theta=330^{\circ}$[/tex] means that this angle is in the fourth quadrant
In the first and the fourth quadrants,
[tex]$$\cos (\theta)=\cos (\alpha)$$[/tex]
Substitute [tex]$\alpha=30$[/tex]
[tex]$$\cos (\theta)=\cos (30)$$[/tex]
In trigonometry:
[tex]$$\cos (30)=\frac{\sqrt{3}}{2}$$[/tex]
So:
[tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]
[tex]$$\cos (\theta)=\frac{\sqrt{3}}{2}$$[/tex]
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7-10 TEKS 6E
1) Choose the figure below that satisfies the
definition
of a kite. Explain your answer choice.
A.
B.
C.
D.
0
Explain:
justification = 2 pts
answer = 1 pt
definition of a kite is option c
Area of Kite?Area of kite is the space enclosed by a kite. A kite is a quadrilateral in which two pairs of adjacent sides are equal. The elements of a kite are its 4 angles, its 4 sides, and 2 diagonals. In this article, we will focus on the area of a kite and its formula.The area of a kite can be defined as the amount of space enclosed or encompassed by a kite in a two-dimensional plane. Like a square, and a rhombus, a kite does not have all four sides equal. The area of a kite is always expressed in terms of units2 for example, in2, cm2, m2, etc. Let us learn about the area of a kite formula in our next section.The area of a kite is half the product of the lengths of its diagonals. The formula to determine the area of a kite is: Area = ½ × (d)1 × (d)2. Here (d)1 and (d)2 are long and short diagonals of a kite.The area of kite ABCD given below is ½ × AC × BD.To learn more about Area of Kite refers to:
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in a stem-and-leaf display, . a. one or more digits are used to define each stem, and one or more digits are used to define each leaf b. one or more digits are used to define each stem, and a single digit is used to define each leaf c. a single digit is used to define each stem, and one or more digits are used to define each leaf d. a single digit is used to define each stem, and a single digit is used to define each leaf
In a stem-and-leaf display a single digit is used to define each stem, and a single digit is used to define each leaf.
In order to help visualize the shape of a distribution, a stem-and-leaf display or stem-and-leaf plot is a tool for presenting quantitative data in a graphical manner, comparable to a histogram.
While a stem plot is another name for a stem-and-leaf plot, it frequently refers to a different kind of chart. The term "simple stem plot" may refer to the mapping of a matrix of y values to a common x axis, along with the identification of the common x value by a vertical line and the individual y values by symbols on the line.
In order to give the reader a fast summary of the distribution, stem-and-leaf displays are helpful for illustrating the relative density and form of the data. The majority of the original numerical data is retained, frequently in complete fidelity. They are helpful for detecting the mode and emphasizing outliers as well. However, stem-and-leaf displays are only effective for data sets that are of a reasonable size (around 15–150 data points).
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Teshome bought 6 pencils and 2 rubber erasers from a shop and paid a total of Birr 3. Meskerem also paid a total of Birr 3 for 4 pencils and 3 rubber erasers.
Solving equations using elimination, we get the cost of pencil = 0.3, cost of rubber = 0.6
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
How is the elimination approach used to solve equations?Both equations should be written in standard form.Make the opposites of a single variable's coefficients.Step 2's equations are combined to remove one variable.Calculate the value of the last variable.In one of the original equations, substitute the step-four solution.Given,
Teshome bought 6 pencils and 2 rubber erasers from a shop and paid a total of Birr 3.
Meskerem also paid a total of Birr 3 for 4 pencils and 3 rubber erasers.
Let cost of pencil = x
cost of rubber = y
As per the question,
6x + 2y = 3
4x + 3y = 3
Upon solving the above equations using elimination,
6x + 2y = 3 × 3
4x + 3y = 3 × 2
18x + 6y = 9
8x + 6y = 6
On subtracting the above equations,
⇒ 10x = 3
⇒ x = 3/10 = 0.3, on substituting the value of x, we get,
y = 6/10 = 0.6
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Complete Question -
Teshome bought 6 pencils and 2 rubber erasers from a shop and paid a total of Birr 3. Meskerem also paid a total of Birr 3 for 4 pencils and 3 rubber erasers. Represent variables for the cost of:
a Each pencil and each rubber eraser in Question 1.
ii Formulate the mathematical equations representing each of the situations in Questions 1.
iii Solve each system and determine the cost of,
a Each pencil and each rubber eraser in Question 1.
A face painting artist's fee for parties is shown in the table.
Hours Fee ($)
2 49.00
3 73.50
4 98.00
5 122.50
Customers are also charged a $25 reservation fee. A school has $175 to spend on a face painting artist for their carnival. For how many full hours can they hire the artist?
The number of full hours that the school will be charged would be = 6 full hours.
How to calculate for the number of hours?The amount of money charged for 2 hour = $49
The amount of money charged for 5 hours = 122.50
Therefore the amount of money charged for an hour= 49/2 = $24.5
The amount of money charged for reservation fees = $25
The amount of money the school has to spend on artist fee alone = $175 - 25 = $150
The amount of hours they can hire the artist should be the cost that is within $150 = cost for an hour + cost for 5 hours = 122.50 + $24.5 = $147.
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Find the missing dimensions. Use the scale 1:15
The missing dimensions are 4.5 in. and 75 in. respectively.
What is image dilation?An enlargement or reduction of a figure that preserves shape but not size.All dilations are similar to the original figure.Dilations have a center and a scale factor.Given are model and actual dimensions of two items.
After the dilation, the relation between final and initial dimensions of the image is -
y = Kx
where -
{K} is a dimensionless quantity called scale factor.
For the figure skates -
{Model/Actual} = {1/15}
1/15 = {x}/67.5
{x} = 67.5/15
{x} = 4.5 in.
For the pipe -
{Model/Actual} = {1/15}
1/15 = 5/{y}
{y} = 5 x 15
{y] = 75 in.
Therefore, the missing dimensions are 4.5 in. and 75 in. respectively.
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Mr. Hall is cleaning up all the pylons after kissing and riding. All of the pylons are the same and they fit inside each other. Just one pylon is 27 cm tall. Each additional pylon adds 5 additional centimeters to the height. What is the height if Mr. Hall has 19 pylons? Create a table of values and find the algebraic expression to solve this problem.
Table of Values:
Number of Pylons: 0 | Height: 27 cm
Number of Pylons: 1 | Height: 32 cm
Number of Pylons: 2 | Height: 37 cm
Number of Pylons: 3 | Height: 42 cm
Number of Pylons: 4 | Height: 47 cm
Number of Pylons: 5 | Height: 52 cm
Number of Pylons: 6 | Height: 57 cm
Number of Pylons: 7 | Height: 62 cm
Number of Pylons: 8 | Height: 67 cm
Number of Pylons: 9 | Height: 72 cm
Number of Pylons: 10 | Height: 77 cm
Number of Pylons: 11 | Height: 82 cm
Number of Pylons: 12 | Height: 87 cm
Number of Pylons: 13 | Height: 92 cm
Number of Pylons: 14 | Height: 97 cm
Number of Pylons: 15 | Height: 102 cm
Number of Pylons: 16 | Height: 107 cm
Number of Pylons: 17 | Height: 112 cm
Number of Pylons: 18 | Height: 117 cm
Number
Please helpppp asapppp
Answer:
Step-by-step explanation:
The Answer is 29 degrees
13. EO bisects
14. MB is a perpendicular bisector of JK. Find the value of X. (4 points)
Please show work and give me a equation!!!
I’ll give 50 points!!!!
Answer:
x = 3
Step-by-step explanation:
B using the perpendicular theorem
Since MB is a perpendicular bisector of JK , then JB = BK
and Δ JMK is isosceles with congruent legs , so
JM = MK ( substitute values )
9x - 18 = 3x ( subtract 3x from both sides )
6x - 18 = 0 ( add 18 to both sides )
6x = 18 ( divide both sides by 6 )
x = 3
How many real numbers are solutions for x2 − 5x 7 0?
There are two real number solutions for x2 − 5x + 7 = 0: x = 2 and x = 7.
1. x2 − 5x + 7 = 0
2. (x - 2)(x - 7) = 0
3. x = 2 or x = 7
When solving for the real number solutions of x2 − 5x + 7 = 0, we first need to factor the equation into two linear terms: (x - 2)(x - 7) = 0. From here, we can use the Zero Product Property to determine that x = 2 and x = 7 are the two real number solutions of this equation. This means that when x is equal to 2 or 7, the equation will equal 0 and all other values of x will result in a non-zero answer. Therefore, the only two real number solutions of x2 − 5x + 7 = 0 are x = 2 and x = 7.
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80% of what = 80,000
Answer: 100000
Step-by-step explanation: If you take 80 percent of a number and get 80000, then what is that number? In other words, you know that 80 percent of a number is 80000 and you want to know what that initial number is.
To solve this problem, you multiply 80000 by 100 and then divide the total by 80 as follows: (80000 x 100) / 80.
AND I LOOKED IT UP ON GOGLE
For what value of K the quadratic equation is a perfect square?
The value of k must be 4 to make the given quadratic equation a perfect square.
What is meant by perfect square?The result of multiplying a polynomial by itself is a perfect square. A perfect square is a number that can be written as the product of an integer multiplied by itself or as the integer's second exponent.
When a number's square root, which is the product of an integer and itself, is an integer, it is said to be a perfect square or a square number.
The quadratic equation is : [tex]$k \cdot y^2-4 \cdot y+1=0$[/tex]
First to make it a complete square : Divide each term by k to make the leading coefficient of [tex]$\mathrm{x}^2=1$[/tex]
Now the equation becomes : [tex]$y^2-4 \cdot \frac{y}{k}+\frac{1}{k}=0 \ldots \ldots \ldots(1)$[/tex]
Divide the coefficient of y by [tex]$2-4 \cdot \frac{y}{2 \times k}=-2 \cdot \frac{y}{k}$[/tex] in order to make it a complete square.
The complete square of the above equation is : [tex]$\left(y-\frac{2}{k}\right)^2=0$[/tex]
Now, expanding this. We get
[tex]$y^2+\frac{4}{k^2}-\frac{4}{k} \cdot k=0$$[/tex]
Now, comparing the constant terms of the above equation with equation 1
[tex]$$\begin{aligned}& \Longrightarrow \frac{4}{k^2}=\frac{1}{k} \\& \Longrightarrow k=4\end{aligned}$$[/tex]
Therefore, the value of k must be 4 to make the given quadratic equation a perfect square.
The complete question is:
For what value of k, the quadratic equation ky²-4y +1 0, is a perfect square?
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The general formula for a sequence is f(x)=3x-7f(x)=3x−7 . One terms in the sequence is 8. Which term is this? The th term is 8.
Answer:
Step-by-step explanation:
If the arithmetic sequence is f(x) = 3x-7, x stands for the position of the number in the sequence. In other words, we are looking to solve for x when f(x) = 8:
8 = 3x - 7 and
15 = 3x so
x = 5. The position of the number 8 is the 5th position.
What does this problem ask for:
--> position of '8' in the sequence
Since our general formula: f(x) = 3x - 7
--> 'x' represents the position of the term in the sequence
--> f(x) is the term in the sequence
--> therefore, if we plug '8' into f(x)
--> we can find 'x' which is the position of 8 in the sequence
Thus:
[tex]8=3x-7\\3x=8+7\\3x=15\\x=5[/tex]
8 is the 5th term
Answer: 5th term
What is the range of x² 3?
The range of given parabolic function [tex]x^2+3[/tex] is [3,∞).
Domain: the domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The fact that the fraction's denominator is not equal to zero and that the digit inside the square root bracket is positive both point to the domain.
Range: the range of a function is the set of all possible values for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.
[tex]f(x)=x^2+3\\[/tex]
here domain of the given function is R.
and for x=0, f(x)=3 which is the lower range of given function and for higher range is infinity.
so range of given function is [3,∞).
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Part of a whole is represented by a percent that is ___ 100%
A percent is a unit of measurement used to express a ratio as part of 100. It is often used to express a proportion of a whole quantity.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
When a part of a whole is represented as a percent, it means that it is expressed as a fraction of 100.
For example, if a quantity is represented as 50%, it means that it is equal to 50/100 or 1/2 of the whole.
Therefore, part of a whole is represented by a percent that is a fraction of 100, with the numerator representing the part and the denominator representing the whole. The value of the fraction is then multiplied by 100 to express the ratio as a percentage.
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The graph shows the number yy of gallons of gasoline remaining in a car xx hours after filling the tank. a. The slope indicates that the car uses gallons of gasoline per hour. b. The y-intercept indicates that the car has gallons of gasoline after filling the tank. c. The x-intercept indicates that the car will run out of gasoline after hours.
The required slope, y-intercept, and x-intercept are -2.5, 15, and 7.5 respectively.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
Locate two points on the graph,
(0, 15) and (7.5, 0)
The slope is given as,
m = -15/7.5
m = -2.5
The slope of the graph represents the rate of fuel i.e. 2.5 gallons per hour.
Now,
y-intercept from the graph is 15, and the x-intercept in the graph is 7.5, which represents the amount of fuel initally in the car, and in 7.5 hours no fuel will be left respectively.
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what is the answer to (-2, -2); y= -1/5x+9
On solving the provided question, we can say that we have the equation
(-2, -2); y= -1/5x+9 => y = 91/10
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
Here,
we have the equation
(-2, -2); y= -1/5x+9
y = -1/-10 +9
y = 91/10
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a recipe for a rice dish calls for 6 oz of pure wild rice and 14 oz of a rice mixture that is 10% wild rice. what is the percent concentration of wild rice in the 20-ounce mixture?
A recipe for a rice dish calls for 6 oz of pure wild rice and 14 oz of a rice mixture that is 10% wild rice , the mixture is 37% wild rice.
we need to find how much wild rice is in the 14 oz of the rice mixture. We can do this by multiplying the weight of the rice mixture (14 oz) by the percentage of wild rice in the mixture (10%).
14 oz * 10% = 1.4 oz
Now we add the amount of wild rice in the rice mixture (1.4 oz) to the amount of pure wild rice (6 oz) to find the total amount of wild rice in the mixture:
1.4 oz + 6 oz = 7.4 oz
Now we divide the total amount of wild rice (7.4 oz) by the total weight of the mixture (20 oz) and multiply by 100% to find the percentage of wild rice in the mixture:
(7.4 oz / 20 oz) * 100% = 37%
So, the mixture is 37% wild rice.
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How do you find the equation of a parabola from a graph in factored form?
Factored form of the equation of the parabola from the given graph can be represented by : f (x) = A ( x - t ) ( x - q ).
As given in the question,
Standard equation of the parabola is given by :
f (x ) = ax² + bx + c
Let us consider the x - intercept of the given graph of parabola where graph of the parabola cuts x -axis at ( t , 0) and ( 0 ,q )
Then factored form for the given roots of the equation can be represented as:
f (x) = A ( x - t ) ( x - q )
t, q are the x-intercepts and A is called the leading coefficient.
Therefore, the factored form the parabola from the given graph is equal to f (x) = A ( x - t ) ( x - q ).
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