Always double-check your graph by entering various x values and ensuring that the associated y values fall along the curve you drew.
what is graph ?A graph is a picture of data that illustrates the connection between two or more factors. A graph in mathematics is typically a two-dimensional coordinate system with a horizontal x-axis and vertical y-axis (vertical). Data points are represented on a graph by points that are drawn with their x- and y-coordinates. The graph can be used to display trends, correlations, and temporal shifts as well as other patterns and connections between the variables. Graphs are used to aid in the interpretation and communication of data in a wide range of disciplines, including mathematics, science, economics, and social studies.
given
Locate the vertex: The vertex of a quadratic function is the lowest or highest spot on the graph. For the x-coordinate of the vertex, use the expression x = -b / (2a), and for the y-coordinate, use y = f(x), where f(x) is the quadratic function.
The places where the graph crosses the x-axis and the y-axis are known as the intercepts. If x = 0, then calculate f to determine the y-intercept (0).
Additional information: Plug a few x values into the function to determine the associated y values. You'll have more data points to display on the graph as a result.
Always double-check your graph by entering various x values and ensuring that the associated y values fall along the curve you drew.
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A caterer made 24 sandwiches for a company lunch. When they arrived at the location. they discovered the guest list was more than they had anticipated. They decided to cut the sandwiches into ( l)/(3) size pleces. How many ( 1)/(3) size pieces were they able to make?
The caterer was able to make 72 (1)/(3) size pieces from the 24 sandwiches.
To find this answer, we can use the following equation:
24 sandwiches × 3 (1)/(3) size pieces per sandwich = 72 (1)/(3) size pieces
This equation tells us that for every sandwich, the caterer was able to make 3 (1)/(3) size pieces. By multiplying the number of sandwiches by the number of (1)/(3) size pieces per sandwich, we can find the total number of (1)/(3) size pieces the caterer was able to make.
Therefore, the caterer was able to make 72 (1)/(3) size pieces from the 24 sandwiches.
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1. Find all real solution(s) to each equation algebraically: (a) - n + √(6n + 19) = 2 (Remember to check your solutions.) (b) x^4 - 20x^2 + 64 = 0
the real solutions to this equation are x = 2√2 and x = -2√2.
Solution:
(a) -n + √(6n + 19) = 2
To find the solution algebraically, we need to isolate the radical on one side of the equation and then square both sides to get rid of the radical.
-n = 2 - √(6n + 19)
(-n - 2)^2 = (2 - √(6n + 19))^2
n^2 + 4n + 4 = 4 - 4√(6n + 19) + 6n + 19
n^2 - 2n - 19 = -4√(6n + 19)
(n^2 - 2n - 19)^2 = (-4√(6n + 19))^2
n^4 - 4n^3 - 18n^2 + 76n + 361 = 96n + 304
n^4 - 4n^3 - 114n^2 + 76n + 57 = 0
This is a quartic equation that can be solved using the Rational Root Theorem or by factoring. However, this equation does not have any real solutions. Therefore, there are no real solutions to this equation.
(b) x^4 - 20x^2 + 64 = 0
This equation can be factored as:
(x^2 - 8)^2 = 0
x^2 - 8 = 0
x^2 = 8
x = ±√8
x = ±2√2
Therefore, the real solutions to this equation are x = 2√2 and x = -2√2.
Remember to check your solutions by plugging them back into the original equation and seeing if they make the equation true.
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I need the domain and the range of this graph! Im reposting this question please help
Based on the graph of this linear function, the domain and range are as follows;
Domain = {0, 100}.
Range = {450, 1200}.
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {0, 100}.
Range = {450, 1200}.
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Find all the missing angels
Answer:
15, 15
Step-by-step explanation:
Since this triangle is a right triangle has it's other two angles at 45 degrees, (180-90-45=45 for the last angle) we know that it's a 45-45-90 triangle and can use the rules in the image below to solve the other two sides:
Because the hypotenuse of this triangle is 15[tex]\sqrt{2}[/tex], then we know that the other two side lengths are 15[tex]\sqrt{2}[/tex]/[tex]\sqrt{2}[/tex], or in this case, just 15.
Answer: 15, 15
Step-by-step explanation:
It is a 45, 45, 90 triangle. This means that both of the legs have the same lengths and the hypotenuse is sqrt2 times the length of one of the legs.
Since sqrt2 is irrational, it is easy to look at the coefficient of it. Since the coefficient is 15, the lengths of the sides are also 15.
Identify the similar triangles.
E 6 H
F
order of size.
AFEH
Identify the similar triangles in increasing
tenth.
X =
X
~ A
G
Then find the value of x to the nearest
24
The similar triangles in increasing order are ΔEHF ~ ΔFHG ~ ΔEFG
The value of x = 13.5
What are Similar Triangles?Two triangles are similar if and only if:
All their corresponding angles are congruent.The ratios of their corresponding sides are equal.They have the same shape but not necessarily the same sizeTherefore, from the diagram, we can conclude that the similar triangles in increasing order of size is given as:
ΔEHF ~ ΔFHG ~ ΔEFG
Using the altitude rule, we will have the following proportion:
6/9 = 9/x
6x = 81
x = 13.5
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(−6, 3), (−6, 5), (2, 3)
What are the coordinates of the fourth vertex of the rectangle
The coordinates of the fourth vertex of the rectangle are (2, 5).
To find the fourth vertex of the rectangle, we need to first determine which sides of the triangle are opposite and parallel to each other. We can see that the two points (-6,3) and (-6,5) lie on a vertical line, which means they are opposite and parallel to each other.
Similarly, the two points (-6,3) and (2,3) lie on a horizontal line, which means they are also opposite and parallel to each other. The fourth vertex of the rectangle must lie at the intersection of these two lines.
The point (-6,3) is the lower left corner of the rectangle, and the point (2,3) is the lower right corner. The distance between these two points is 2 - (-6) = 8. Since the opposite sides of a rectangle are congruent, the distance between the other two corners (-6,5) and the fourth vertex must also be 8.
Since the two points (-6,3) and (-6,5) are on a vertical line, the y-coordinate of the fourth vertex must also be 5. We can find the x-coordinate by moving 8 units to the right of (-6,3), since the rectangle is parallel to the x-axis. Thus, the fourth vertex must be located at the point:
(x,y) = (-6+8, 5)
= (2, 5)
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600% of what number is 2,280
Answer:
380
Step-by-step explanation:
To find out what number is 600% of another number, we need to divide that number by 600% (or 6).
So:
x = 2,280 ÷ 6
x = 380
Therefore, 600% of 380 is equal to 2,280.
Hope this helped !
Before a computer programmer optimized a program, 450 clock cycles were required to process an input file. After optimization, the file was processed in 60 clock cycles. To the nearest percent, what
The nearest percent, the percent decrease in clock cycles after optimization is approximately 87%.
What is optimization?Optimization is the process of improving the performance or efficiency of a system, process, or algorithm by finding the best possible solution within a given set of constraints or limitations.
The percent decrease in clock cycles after optimization can be calculated using the formula:
Percent decrease = [(original value - new value) / original value] x 100%
where the original value is the number of clock cycles required before optimization, and the new value is the number of clock cycles required after optimization.
Using the given values, we have:
Percent decrease = [(450 - 60) / 450] x 100%
= (390 / 450) x 100%
= 86.67%
Therefore, to the nearest percent, the percent decrease in clock cycles after optimization is approximately 87%.
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What is the multiplicity of the zero x=1 for the function f(x)=x^(2)(x-1)^(4)(x+5)
The multiplicity of the zero [tex]x=1[/tex] for the function [tex]f(x)=x^2(x-1)^(4)(x+5)[/tex] is 4.
In a polynomial function, the multiplicity of a zero is the number of times that zero appears as a factor in the function. In other words, it is the exponent of the factor corresponding to that zero.
In the given function [tex]f(x)=x^2(x-1)^4(x+5)[/tex], we can see that the zero x=1 corresponds to the factor (x-1)^(4). This means that the multiplicity of the zero x=1 is 4, as it appears as a factor 4 times in the function.
Therefore, the multiplicity of the zero [tex]x=1[/tex] for the function [tex]f(x)=x^2(x-1)^(4)(x+5)[/tex] is 4.
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The graph shows the number of prints Tara needs to sell to make a profit. What can you learn by looking at the graph? IMAGINE MATH
This graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.
What is profit?Profit is the difference between a firm's total revenue and total expenses. It is the amount of money a business has earned after subtracting the cost of goods sold, operating expenses and taxes from its total revenue.
The graph reveals a few key pieces of information that can be used to assess the potential profitability of Tara’s prints. Firstly, the graph shows that there is a fixed cost associated with each print, regardless of how many prints are sold. This cost is represented by the straight line at the bottom of the graph. Additionally, the graph reveals that the cost of the prints increases exponentially as more prints are sold. This means that the more prints Tara sells, the more money she makes. Lastly, the graph shows that the revenue from selling prints is significantly higher than the cost of producing them, indicating that Tara can make a profit if she is able to sell enough prints. Overall, this graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.
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AB-> (2;3) AB = ?
les coordonées de mon vecteur AB-> sont ( 2;3 ) est ce que AB= racine de( 2 au carre + 3 au carée)
Answer:
Réponse :Explications étape par étapea) Le vecteur AC(xc-xa;yc-ya)vecteur AC(-6;-3
Step-by-step explanation:
Les coordonnées d'un vecteur dans un r.o.n. décrivent le déplacement qu'il représente. Ainsi, un déplacement de « 3 ...
Initially, there were only 3 weeds at a park. The weeds grew at a rate of 5% each week. The following function represents the weekly weed growth: f(x) = 3(1.05)x. Rewrite the function to show how quickly the weeds grow each day and calculate this rate as a percentage.
Answer: To rewrite the function to show how quickly the weeds grow each day, we need to use the fact that there are 7 days in a week. Let's divide both sides of the original function by 7 to get:
f(x/7) = 3(1.05)^(x/7)
This function gives the amount of weed growth after x/7 weeks, which is equivalent to x days. To find the daily weed growth rate, we need to take the derivative of this function with respect to x and evaluate it at x=0:
f'(0) = (d/dx) 3(1.05)^(x/7)
Using the chain rule, we get:
f'(0) = 3ln(1.05)/7 ≈ 0.00797
This means that the weeds grow at a daily rate of approximately 0.797%, or 0.00797 as a decimal.
Step-by-step explanation:
9. Simplify each expression: a. √(1 + cos 76° / 2) b. (sin 158.2°) / (1 + cos 158.2°) 10. Verify that each equation is an identity. a. sin 2x / 2 sin x = cos^2 x/2 – sin^2 x/2 b. tan θ/2 = csc θ – cot θ
LHS ≠ RHS and the equation is not an identity.
9. Simplify each expression:
a. √(1 + cos 76° / 2)
b. (sin 158.2°) / (1 + cos 158.2°)
10. Verify that each equation is an identity.
a. sin 2x / 2 sin x = cos^2 x/2 – sin^2 x/2
b. tan θ/2 = csc θ – cot θ
Answer:
9. a. √(1 + cos 76° / 2) = √(1 + 0.2419 / 2) = √(1 + 0.12095) = √(1.12095) = 1.0589
b. (sin 158.2°) / (1 + cos 158.2°) = (0.12088) / (1 + (-0.9927)) = 0.12088 / 0.0073 = 16.566
10. a. sin 2x / 2 sin x = cos^2 x/2 – sin^2 x/2
LHS = sin 2x / 2 sin x = 2 sin x cos x / 2 sin x = cos x
RHS = cos^2 x/2 – sin^2 x/2 = (cos x + sin x)(cos x - sin x) / 4 = (1)(cos x - sin x) / 4 = cos x - sin x / 4
Therefore, LHS ≠ RHS and the equation is not an identity.
b. tan θ/2 = csc θ – cot θ
LHS = tan θ/2 = sin θ/2 / cos θ/2
RHS = csc θ – cot θ = 1 / sin θ - 1 / cos θ = (cos θ - sin θ) / (sin θ cos θ)
Therefore, LHS ≠ RHS and the equation is not an identity.
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Find the equation of the curve with gradient function 3x2+5x4 that passes through (1,8)
The equation of the curve that passes through the point (1, 8) and has the gradient function 3x² + 5x⁴ is y = x³ + x⁵ + 6
In this problem, we are given the gradient function 3x² + 5x⁴ and the point (1, 8) through which the curve passes. To find the equation of the curve, we need to integrate the gradient function and add the constant of integration. Let's start by integrating 3x² + 5x⁴:
∫(3x² + 5x⁴)dx = x³ + x⁵ + C
where C is the constant of integration.
Now we have the general equation of the curve, but we need to find the specific value of C that will give us the curve that passes through the point (1, 8). We can do this by plugging in the values of x and y into the equation:
8 = 1³ + 1⁵ + C
8 = 1 + 1 + C
C = 6
Therefore, the equation of the curve is:
y = x³ + x⁵ + 6
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Find the measurements of X
pt
Answer:
x = 15°
Step-by-step explanation:
the inscribed angle APB is half the measure of the central angle AOB , so
x = [tex]\frac{1}{2}[/tex] × 30° = 15°
Consider the decision sapling in which you can choose either a sure thing worth $5M or a gamble that has probability of 0.4 of giving a return of $2M; otherwise the return on the gamble will be $7M. Suppose we can purchase a forecast for the gamble, where the forecast has probability p of being accurate. (So the false positive and false negative rates are both 1-p). a. What is the EMV of the gamble given the forecast is that the return will be $7M? If it is $2M? b. If the forecast is $7M, for what range of p will it be optimal to choose the gamble? c. Give an expression for the EVII as a function of p, and graph it.
The EMV (Expected Monetary Value) of the gamble is calculated as follows:
EMV = (probability of return) x (value of return)
a. If the forecast is that the return will be $7M, then the EMV of the gamble is:
EMV = (0.4) x ($7M) = $2.8M
If the forecast is that the return will be $2M, then the EMV of the gamble is:
EMV = (0.6) x ($2M) = $1.2M
b. If the forecast is $7M, the range of p for which it will be optimal to choose the gamble is when the EMV of the gamble is greater than the sure thing of $5M. This can be calculated by setting the EMV of the gamble equal to $5M and solving for p:
$5M = (0.4) x ($7M) + (1-p) x ($2M)
$5M = $2.8M + $2M - $2Mp
$2.2M = $2Mp
p = 1.1
Therefore, the range of p for which it will be optimal to choose the gamble is when p > 1.1.
c. The EVII (Expected Value of Imperfect Information) is the difference between the EMV of the gamble with the forecast and the EMV of the gamble without the forecast. This can be expressed as a function of p as follows:
EVII = (p x EMV with forecast) - (1-p) x EMV without forecast
EVII = (p x ($2.8M)) - (1-p) x ($1.2M)
EVII = $2.8Mp - $1.2M + $1.2Mp
EVII = $4Mp - $1.2M
To graph this function, plot p on the x-axis and EVII on the y-axis. The slope of the line will be $4M and the y-intercept will be -$1.2M.
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Which algebraic expression represents this word description the product of seven and the diffrence between a number and ten
The algebraic expression represents this word description is 7(x - 10) (option D).
One way to approach this problem is to break down the phrase into its components and then use mathematical symbols to represent them.
The phrase contains the word "product," which tells us we need to multiply two quantities.
The first quantity is the number seven, and the second quantity is the difference between a number and ten.
To represent the difference between a number and ten, we can use the variable x to stand for the unknown number.
Then, the difference between x and ten can be expressed as (x - 10).
Putting it all together, the expression that represents the product of seven and the difference between a number and ten is 7(x - 10).
Hence the correct option is (D).
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Complete Question:
Which algebraic expression represents this word description?
The product of seven and the difference between a number and ten
A. 10-7x
B. 7(10 - x)
C. 7x-10
D. 7(x - 10)
Dividing a polynomial by a monomial: (-15xz+18x^(6)z^(7)+25x^(5)z^(2))-:(-3x^(5)z^(2)) mplify your answer as much as possible.
The simplest form obtained by the given division is (-25 - 18x^(5)z^(6) + 15x^(4)z)/(3x^(5)z^(2)) .
To divide a polynomial by a monomial, we simply divide each term in the polynomial by the monomial. So, we will divide each term in (-15xz+18x^(6)z^(7)+25x^(5)z^(2)) by (-3x^(5)z^(2)).
First, we will divide -15xz by -3x^(5)z^(2):
-15xz/(-3x^(5)z^(2)) = 5x^(-4)z^(-1)
Next, we will divide 18x^(6)z^(7) by -3x^(5)z^(2):
18x^(6)z^(7)/(-3x^(5)z^(2)) = -6x^(1)z^(5)
Finally, we will divide 25x^(5)z^(2) by -3x^(5)z^(2):
25x^(5)z^(2)/(-3x^(5)z^(2)) = -25/3
So, our final answer is:
5x^(-4)z^(-1) - 6x^(1)z^(5) - 25/3
In simplified form, this is:
(-25 - 18x^(5)z^(6) + 15x^(4)z)/(3x^(5)z^(2))
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I am a function. My parent function is y = x. My parent function is
mapped onto me by a reflection over the line y = 0, then a horizontal shift
4 units to the right, a vertical shift 3 units up, and finally a horizontal
stretch with a factor of 3. Who am I?
Answer:
Step-by-step explanation:
If the graph of the parent function is shifted 7 units up and is steeper than the parent function, which of these could represent the function? answer choices.
Combine like terms and write the resulting polynomial in descending 2x^(7)+5x^(6)+9x^(7) Select one:
The resulting polynomial in descending order is 11x7 + 5x6
To combine like terms and write the resulting polynomial in descending order, we need to first identify the like terms and then add or subtract their coefficients. Like terms are terms that have the same variable and the same exponent.
In this case, the like terms are 2x^(7) and 9x^(7).
We can combine these like terms by adding their coefficients:
2x^(7) + 9x^(7) = 11x^(7)
Now we have:
11x^(7) + 5x^(6)
Since the exponents are different, we cannot combine these terms.
Therefore, the resulting polynomial in descending order is 11x7 + 5x6
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find the value of largest rectangular parallelopiped that can be incribed in the ellipsoid
The value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).
To find the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid, we need to use the formula for the volume of a parallelopiped. The formula is:
V = l*w*h
Where V is the volume, l is the length, w is the width, and h is the height.
Since we are looking for the largest rectangular parallelopiped, we need to maximize the volume. This can be done by finding the maximum values of the length, width, and height.
The maximum values of the length, width, and height can be found by using the semi-axes of the ellipsoid. The semi-axes of the ellipsoid are given by:
a = √(x^2/a^2 + y^2/b^2 + z^2/c^2)
Where a, b, and c are the semi-axes of the ellipsoid, and x, y, and z are the coordinates of the point on the surface of the ellipsoid.
The maximum values of the length, width, and height can be found by setting the derivatives of the volume with respect to x, y, and z to zero:
∂V/∂x = 0
∂V/∂y = 0
∂V/∂z = 0
Solving these equations will give us the maximum values of the length, width, and height. Once we have these values, we can plug them into the formula for the volume of a parallelopiped to find the largest volume.
The largest volume of the rectangular parallelopiped that can be inscribed in the ellipsoid is given by:
V = (2a)*(2b)*(2c)
Where a, b, and c are the semi-axes of the ellipsoid.
Therefore, the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).
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Use the table to write a linear function that relates to y to x. PLEASEE HELP
to get the equation of any straight line, we simply need two points off of it, let's use those two points in the picture below.
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{3}}} \implies \cfrac{ 2 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{ 2 }{ 3 }}(x-\stackrel{x_1}{3}) \\\\\\ y-7=\cfrac{ 2 }{ 3 }x-2\implies {\Large \begin{array}{llll} y=\cfrac{ 2 }{ 3 }x+5 \end{array}}[/tex]
What is the area of the parallelogram?
37 in.
31 in.
425.5 in.²
713 in. 2
851 in.2
1147 in.²
23 in.
Area of the parallelogram, using the area formula = 851 in².
What is the area of a parallelogram?The area of a parallelogram, which is expressed in square units, is the total number of unit squares that may fit inside of it (like cm², m², in² etc). It is the region that a two-dimensional parallelogram encloses or encompasses.
Hence, the following formula can be used to determine a parallelogram's area:
Area of a parallelogram is equal to b × h square units, where b is the base's length and h is its height.
Here in the question,
b = 37in.
h = 23in.
Area = b × h
= 37 × 23
= 851 in²
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Stella's family traveled
3
10
of the distance to her aunt’s house on Saturday. They traveled
4
7
of the remaining distance on Sunday. What fraction of the total distance to her aunt’s house was traveled on Sunday?
Stella's family traveled 2/5 of the total distance to her aunt's house on Sunday.
What is distance ?
Distance is a physical quantity that refers to the length between two points or the amount of space between them. It is typically measured in units such as meters, kilometers, miles, or feet.
Stella's family traveled 3/10 of the distance to her aunt's house on Saturday. Therefore, the remaining distance they had to travel was:
1 - 3/10 = 7/10
On Sunday, they traveled 4/7 of the remaining distance. Therefore, the total distance traveled on Sunday is:
(4/7) x (7/10) = 4/10
Simplifying the fraction 4/10 gives 2/5.
Therefore, Stella's family traveled 2/5 of the total distance to her aunt's house on Sunday.
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At summer camp the counselors want to order beads for crafts There are 597 campers at the camp each bead project uses 89 beads about how many beads should the counselors order
Answer:
597 x 89 = 53133.
53133 beads
Step-by-step explanation:
HELP NOW PLSSS
Solve. -7 2/3 + (-5 1/2) + 8 3/4 =
Answer:
-4.4166
Step-by-step explanation:
-23/3+(-11/2)+35/4
-24/3-11/2+35/4
use bodmas
addition first then subtract and u find your LCM.
11/2+35/4=57/4 or 14 1/4
LCM=4
-23/3-57/4=-263/12 or -21 11/12.
LCM=12
final answer= -21 11/12.
unit linear relationships student handout 1 answer key
In statistics, a linear relationship is a connection that runs in a straight line between two variables (or linear association).
What do you mean by linear relationships?Both a mathematical representation of a linear relationship, in which the dependent variable is produced by multiplying the independent variable by the slope coefficient and a constant, and a graphic representation of a linear relationship, in which the variable and constant are connected by a straight line.
A polynomial or non-linear (curved) relationship can be contrasted with a linear relationship.
A linear relationship is one that mathematically answers the question:
y = mx + b
Where,
m = slope
b = y-intercept
"X" and "Y" are two variables in this equation.
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If no one helps me on this, I will get a zero :(
Answer:
Step-by-step explanation:
A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 4 inches per year. Type B is 2 feet tall and grows at a rate of 10 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
It will take 18 years for the Type A and Type B trees to be the same height.
What is the midpoint formula?A location in the centre of a line connecting two places is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its ends. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places.
Let us suppose the number of years = y.
The height of the tree of type A is thus,
5 feet + (4 inches/year)(y)
= 5 + 4/12 y feet
= 5 + 1/3 y feet
For the type B:
2 feet + (10 inches/year)(y years)
= 2 + 10/12 y feet
= 2 + 5/6 y feet
To get the height of the two trees as equal we have:
5 + 1/3 y = 2 + 5/6 y
3 + 1/3 y = 5/6 y
3 = 1/6 y
18 = y
Hence, it will take 18 years for the Type A and Type B trees to be the same height.
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Lina hops linearly and Kavier hops exponentially
The equations of the functions are Lina: y = 2x + 3 and Kavier: y = 3(2)^x
The pattern of loops of the KangaroosLinear pattern
The table of values represent the given parameter
For Lina's distance from the tree, we can see that
As the hop increases by 1, the distance covered increases constantly by 2 feet
This represents a linear function
Exponential pattern
For Kavier's distance from the tree, we can see that
As the hop increases by 1, the distance covered doubles
This represents an exponential function
How to determine the equations
Lina Linear Function
From the question, we have the following parameters that can be used in our computation:
(0, 3) and (1, 5)
A linear function is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 3
Using the points, we have
m + 3 = 5
m = 2
So, we have
y = 2x + 3
Kavier Exponential Function
Here, we have
(0, 3) and (1, 6)
An exponential function is represented as
y = ab^x
Where
a = y when x = 0
So, we have
y = 3b^x
Using the points, we have
3b = 6
b = 2
So, we have
y = 3(2)^x
Hence, Kavier's equation is y = 3(2)^x
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