Answer:
f(x) = x^3 - x^2 + 16x - 16
Step-by-step explanation:
If a polynomial has the zeros 1, 4i, and -4i, then it must have the factors (x - 1), (x - 4i), and (x + 4i). This is because a factor of (x - a) produces a root of x = a.
To find the polynomial, we can multiply these factors together:
(x - 1)(x - 4i)(x + 4i)
= (x - 1)(x^2 - (4i)^2)
= (x - 1)(x^2 + 16)
= x^3 + 16x - x^2 - 16
So the polynomial function in standard form with real coefficients whose zeros include 1, 4i, and -4i is:
f(x) = x^3 - x^2 + 16x - 16
In 2010, the sea turtle population was twice the amount of turtles as in 2005. How many sea turtles were there in 2010?
Without knowing the exact number of turtles in 2005, we cannot determine the exact number of turtles in 2010. However, we can use the information given to set up an equation.
Let x be the number of sea turtles in 2005.
According to the problem, the number of sea turtles in 2010 was twice the amount in 2005, or 2x.
We can set up an equation:
2x = number of sea turtles in 2010
We don't know the exact value of x, so we cannot solve for the number of turtles in 2010.
Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 24x2 − 6xy − 2. The friends have already collected the following number of cans:
Jessa: 9x2
Tyree: 6x2 − 4
Ben: 4xy + 3
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
Therefore , the solution of the given problem of expressions comes out to be the buddies need to gather to reach their objective is
9x² - 10xy - 1.
What does an expression exactly mean?It is preferred to employ shifting numbers, which may also prove to be increasing, diminishing, or blocking, rather than random estimations. Only by exchanging tools, information, or answers to problems could they assist one another. The statement of truth equation may comprise the arguments, elements, or quantitative remarks for strategies like increased disagreement, production, and blending.
Here,
Part A:
=> Jasmine: 9x²
=> 6x² - 4 for Tyree
=> Ben: 4xy + 3
These three phrases added together represent the total amount of canned food collected:
=> 9x² + (6x² - 4) + (4xy + 3)
=> 15x² + 4xy - 1
As a result, the expression for how many cans of food the three buddies have so far amassed is 15x² + 4xy - 1.
Part B's collection objective is 24x² - 6xy - 2.
Collection total: 15x² + 4xy - 1
The distinction between these two phrases shows the quantity of cans the buddies still need to gather:
=> (24x² - 6xy - 2) - (15x² + 4xy - 1)
=> 9x² - 10xy - 1
As a result, the phrase for how many more cans the buddies need to gather to reach their objective is 9x² - 10xy - 1.
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The volume of the following square pyramid is
48^3. What is the length of 'l'? Round your answer to the nearest hundredth.
The length of 'l' is approximately equal to 331.13 units
Volume refers to the amount of space occupied by a three-dimensional object. In other words, it is the measure of how much space an object takes up.
The formula to calculate the volume of a square pyramid is:
Volume = (1/3) x Base Area x Height
where the base area is the area of the square base, and the height is the perpendicular distance from the apex to the base.
Let's substitute the given values in the formula and solve for the height:
48³ = (1/3) x l² x h
Multiplying both sides by 3, we get:
3 x 48³ = l² x h
Dividing both sides by l², we get:
h = (3 x 48³) / l²
Now, we can substitute the value of h in the original formula to get:
48³ = (1/3) x l² x [(3 x 48³) / l²]
Simplifying this equation, we get:
48³ = 48³
This equation is true, which means our solution is correct. Therefore, the length of 'l' is equal to the square root of (3 x 48³), which is approximately equal to 331.13 units (rounded to the nearest hundredth).
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What type of transformation is modeled?
The type of transformation modeled in the graph is Reflection across y-axis.
How many different coordinate transformations are there?The three different kinds of coordinate transformation are listed below. The motor's three-phase current and voltage are transformed by the Clark transformation from their original natural coordinates to two-phase static coordinates determined with reference to the stator.
What is the transformational rule?Because the domain or range values of the function f(x) have changed, rules of transformations assist in changing f(x) to a new function f'(x). With the use of these transformational rules, the function can be stretched or compressed as well as transformed vertically or horizontally.
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A sequence can be generated by using gn = 2(gn-1), where g1 = 1/3 and n is a whole number greater than 1.
What are the first 5 terms of the sequence?
The first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
What are the first 5 terms of the sequence?From the question, we have the following parameters that can be used in our computation:
The sequence is generated by using gn = 2(gn-1)
Such that g1 = 1/3 and n is a whole number greater than 1.
Using the above as a guide, we have the following:
The sequence means that we multiply the current term by 2 to get the next term
So, we have the following representations
a(2) = 2 * 1/3 = 2/3
a(3) = 2 * 2/3 = 4/3
a(4) = 2 * 4/3 = 8/3
a(5) = 2 * 8/3 = 16/3
Hence, the first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
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Kadeesha borrowed some money from her friend in order to help buy a new video
game system. Kadeesha originally borrowed $120 and agreed to pay back her friend
$8 per week. Make a table of values and then write an equation for L, in terms of t,
representing the amount Kadeesha owes her friend after t weeks.
Number of Weeks Amount of Money Owed
0
1
2
3
You must answer all questions above in order to submit.
attempt 1 out of 2
An equation for L, in terms of t, representing the amount Kadeesha owes her friend after t weeks is L = 8t + 120.
The table of values is as follows;
Number of Weeks Amount of Money Owed
0 $120
1 $128
2 $136
3 $144
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the amount of money that Kadeesha borrowed originally and the number of weeks respectively, and then translate the word problem into a linear equation as follows:
Let the variable L represent amount of money that Kadeesha owed.Let the variable t represent number of weeks.Since Kadeesha originally borrowed $120 and agreed to pay back her friend $8 per week, a linear equation which can be used to model the total amount of money that Kadeesha owed is given by;
L = 8t + 120
When t = 0, the value of L is given by;
L = 8(0) + 120
L = $120.
When t = 1, the value of L is given by;
L = 8(1) + 120
L = $128.
When t = 2, the value of L is given by;
L = 8(2) + 120
L = $136.
When t = 3, the value of L is given by;
L = 8(3) + 120
L = $144.
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What is the sine of 0?
The sine of angle θ is given as follows:
sin(θ) = -8/17.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
The point in this problem has the coordinates given as follows:
(15/17, -8/17).
Hence the trigonometric ratios are given as follows:
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Add 2 1/3 + 4 5/8 writ your answer as a mixed number
Usually, a mixed number is the simplest way to express an improper fraction – but sometimes, the fraction ... Don't express the answer as a decimal. Instead ... So, add the whole number back in to get a final result of 6 1/2. ... Write out the factors for the numerator of your fraction, then write out the factors for the denominator.
i really don’t understand this so i would really appreciate help
Answer:
[tex]6\sqrt{2}+3\sqrt{10}[/tex]
Step-by-step explanation:
Use the Distributive Property. Remember that you can multiply the numbers under a square root whether or not they're the same. But you can ONLY add square roots when the square root part is the same.
[tex]\sqrt{3}(2\sqrt{6}+\sqrt{30})\\= \sqrt{3}(2\sqrt{6})+\sqrt{3}(\sqrt{30})\\=2\sqrt{18}+\sqrt{90}[/tex]
Simplify each square root part:
[tex]2\sqrt{18}+\sqrt{90}\\=2(3\sqrt{2})+3\sqrt{10}\\=6\sqrt{2}+3\sqrt{10}[/tex]
Since the square root parts are different, you cannot simplify any further.
Find the endpoints of the latus rectum of the parabola below.
(y - 1)? = 16(x + 1)
Answer:
(3, 9) and (3, -7)
Step-by-step explanation:
You want the end points of the latus rectum for the parabola defined by ...
(y -1)² = 16(x +1)
Vertex and scale factorCompare the given equation to the form ...
(y -k)² = 4p(x -h)
we see that (h, k) = (-1, 1) and p = 16/4 = 4. The ordered pair (h, k) is the vertex of the parabola. The scale factor 'p' gives the distance from the vertex to the focus (and from the directrix to the focus). Larger 'p' values result in a "flatter" parabola.
Latus rectumSince the squared term is a y-term, and the value of 'p' is positive, we know the parabola opens to the right. The end points of the latus rectum are ...
(h+p, k±2p) = (-1+4, 1±2·4) = (3, 9) and (3, -7)
__
Additional comment
If the roles of x and y are interchanged (the parabola opens up or down), then the end points of the latus rectum are (h±2p, k+p).
On a graph of the parabola, the end points of the latus rectum lie on lines through the vertex with slope ±2 (parabola opens in x-direction), or with slope ±1/2 (parabola opens in y-direction).
Mr. and Mrs. Tran hope to send their son to college in twelve years. How much money should they invest now at an interest rate of 8.5% per year, compounded continuously, in order to be able to contribute $9000 to his education?
$3988.71 should be invested by them to be able to contribute $9000 to his education.
We can use the continuous compound interest formula:
[tex]A = Pe^{(rt)[/tex]
where A is the future value, P is the present value, r is the interest rate, and t is the time in years.
We know that A = $9000, r = 0.085 (8.5% expressed as a decimal), and t = 12.
Solving for P, we get:
[tex]P = A / e^{(rt)}\\\\P = 9000 / e^{(0.085*12)}\\\\P = \$ \ 3988.71[/tex]
Therefore, Mr. and Mrs. Tran should invest approximately $3988.71 now in order to have $9000 in twelve years, assuming continuous compound interest at a rate of 8.5% per year.
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A research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below.
A figure of a computer output is shown. At the top is a table with two rows. The first row reads variable, N, mean, S E mean, and standard deviation. The second row reads running time, 11, 74.81, 2.21, and 7.33. Below this is a second table with three columns labeled predictor, coefficient, and S E coefficient. The first row reads constant, 88.01, and 0.49. The second row reads exercise time, negative 2.20, and 0.07. At the bottom it reads S equals 0.76 and R squared equals 99 percent.
Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 ?
Answer:
The appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 is the t-statistic.
The t-statistic for testing the slope coefficient is calculated as follows:
t = (b1 - 0) / SE(b1)
where b1 is the estimated slope coefficient, and SE(b1) is the standard error of the estimated slope coefficient.
From the computer output, we see that the estimated slope coefficient for exercise time is -2.20, and the standard error of the estimated slope coefficient is 0.07.
Therefore, the t-statistic is:
t = (-2.20 - 0) / 0.07 = -31.43
This t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size. The sample size is not given in the output, so we cannot determine the exact degrees of freedom.
I been trying to figure this out but im bad with squares even though it sounds easy.
Answer:
13in :)
Step-by-step explanation:
KJASJDAJK its oki! The formula for the area of a square is Side x Side= Area, meaning you can just square root the area (since its a square all sides should be the same length) sqrt of 169 would give you 13!
System of equations
2x + 3y = 4
3x + 5y = 7
10x + 15y = 20
-9x - 15y = -21
Find the solution of this system of linear
equations. Separate the x- and y- values with a
comma. Enclose them in a pair of parantheses.
Enter the correct answer.
DONE
Answer:-₍1,3₎
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination to eliminate one of the variables. We can multiply the first equation by 5 and the second equation by -3, then add the two equations to eliminate $y$:
$(5)(2x + 3y = 4) \Rightarrow 10x + 15y = 20$
$(-3)(3x + 5y = 7) \Rightarrow -9x - 15y = -21$
Adding the equations, we get:
$10x + 15y - 9x - 15y = 20 - 21$
Simplifying, we get:
$x = -1$
Now we can substitute $x=-1$ into one of the original equations to solve for $y$. Using the first equation, we have:
$2(-1) + 3y = 4$
Solving for $y$, we get:
$y = 2$
Therefore, the solution to the system of equations is $x=-1$ and $y=2$. We can check this solution by substituting $x=-1$ and $y=2$ into the other two equations:
$3(-1) + 5(2) = 7$
$10(-1) + 15(2) = 20$
Both equations are true, so our solution is correct.
what is twenty-five divided bye four?
Answer: The answer is 6.25
Step-by-step explanation:
Answer:
6.25
Step-by-step explanation:
What is the answer to this question pls
51°
4
109°
The length of unknown side is,
⇒ 4.92
We have to given that;
A triangle is shown in image.
Let the length of unknown side = x
Now, From trigonometry formula we get;
⇒ tan 51° = x / 4
⇒ 1.23 = x / 4
⇒ x = 1.23 × 4
⇒ x = 4.92
Thus, the length of unknown side is,
⇒ x = 4.92
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What is the measure (in radians) of central angle θ in the circle below?
Enter an exact expression. (in radians)
HELP NEEDED ASAP
The measure (in radians) of central angle θ in the circle below is π/3.
We have,
radius = 3 cm
Arc length = π
We can use the formula relating the arc length (s) to the central angle (θ) and radius (r) of a circle:
s = r Ф
Now,
π = 3 x Ф
Ф = π/3
Thus,
The measure (in radians) of central angle θ in the circle below is π/3.
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need help asap
How many square feet of outdoor carpet will
we need for this hole?
3 ft
2 ft
12 ft
,1 ft
2 ft
ft²
The area needed for the green region is 40 square feet.
How to find the area?To do so, we can take the area of the whole green area, and then remove the areas of the two holes.
Remember that the area of any rectangle is the product of the two dimensions.
For the green one:
A = 4ft*12ft = 48 ft²
Removing the two areas for the holes we have:
a1 = 3ft*2ft = 6ft²
a2 = 1ft*2ft = 2ft²
Remove that:
green area= 48 ft² - 6ft² - 2t² = 40ft²
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2. Although Kevin has money, he is not spending it.
Complex or compound -complex
Answer:
complex
Step-by-step explanation:
The given sentence "Although Kevin has money, he is not spending it." is a complex sentence.
This is because it contains one independent clause, "he is not spending it," which can stand alone as a complete sentence. The other part of the sentence, "Although Kevin has money," is a dependent clause because it cannot stand alone as a complete sentence.
The dependent clause "Although Kevin has money" introduces a contrast or concession to the independent clause that follows it. Therefore, this sentence is an example of a complex sentence that uses a dependent clause to add meaning and complexity to the independent clause.
The 20 members of the photography club are trying to raise at least $1,400 for
new photography equipment. They have already raised $540.
Let m represent the amount of money each member must raise, on average, to meet
their goal. Write an expression for the total amount of money going to be raised.
b Write an equation that represents the club raising all the money.
с
Solve the equation. What does the solution mean in context of the scenario?
d Write an inequality representing the amount of money each member must raise,
on average, to meet or exceed their goal.
Write an inequality showing the possible average amount of money each club member
needs to raise.
Answer:
i dont know if this helps, im not sure if you are telling me to do all of these things or B, c, d are answer
Step-by-step explanation:
To find the total amount of money that the photography club will raise to meet their goal, we can multiply the average amount of money each member must raise by the number of members in the club:
Average amount of money each member must raise = m
Number of members in the club = 20
Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club
Total amount of money to be raised = m x 20
We know that the club is trying to raise at least $1,400, and they have already raised $540. Therefore, the amount of money they still need to raise is:
Amount of money still needed to reach goal = $1,400 - $540
Amount of money still needed to reach goal = $860
We can set up an equation to represent the total amount of money the club will raise to meet their goal:
Total amount of money to be raised = Amount of money still needed to reach goal
m x 20 = $860
We can solve for "m" by dividing both sides of the equation by 20:
m = $860 / 20
m = $43
Therefore, the total amount of money the club will raise to meet their goal is:
Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club
Total amount of money to be raised = $43 x 20
Total amount of money to be raised = $860
B))) We can set up an equation to represent the total amount of money the club will raise to meet their goal:
Total amount of money to be raised = Amount of money already raised + Amount of money still needed to reach goal
We know that the club has already raised $540 and they need to raise $860 more to reach their goal of $1,400. Therefore, we can substitute these values in the equation:
Total amount of money to be raised = $540 + $860
Total amount of money to be raised = $1,400
So the equation that represents the club raising all the money is:
$1,400 = $540 + $860
C)))) To solve the equation:
$1,400 = $540 + $860
We can simplify the right-hand side of the equation by adding $540 and $860:
$1,400 = $1,400
This equation is true, which means that it is a consistent equation. The solution to this equation is that the club will be able to raise all the money they need to buy the new photography equipment.
In the context of the scenario, the solution means that the club will be able to meet their goal of raising at least $1,400 for new photography equipment. They have already raised $540, and they need to raise $860 more to reach their goal. The equation shows that the total amount of money they will raise is exactly $1,400, which is the amount they need to meet their goal.
D))))) To represent the amount of money each member must raise, on average, to meet or exceed their goal, we can use the following inequality:
Average amount of money each member must raise ≥ Total amount of money still needed to reach goal / Number of members in the club
We know that the total amount of money still needed to reach the goal is $860, and there are 20 members in the club. Therefore, we can substitute these values in the inequality:
Average amount of money each member must raise ≥ $860 / 20
To simplify the right-hand side of the inequality, we can divide $860 by 20:
Average amount of money each member must raise ≥ $43
This inequality shows that each member must raise at least $43, on average, to meet or exceed their goal of raising $1,400.
To show the possible average amount of money each club member needs to raise, we can use the following inequality:
0 < Average amount of money each member must raise ≤ Total amount of money still needed to reach goal / Number of members in the club
This inequality shows that the average amount of money each member must raise is greater than 0 (since each member must contribute something), but it is less than or equal to $43 (which is the minimum amount each member must raise to meet or exceed their goal).
In complex numbers what is the multiplicative inverse of 2i
To find the multiplicative inverse of 2i, we need to find a complex number z such that:
(2i) * z = 1
Multiplying both sides by -i, we get:
z = -i/2
Therefore, the multiplicative inverse of 2i is -i/2.
I Need help pleaseeeeeee
Answer:
A
Step-by-step explanation:
according triangle inequality,
the sum of any two sides of a triangle is larger than the remaining side.
so a + b > c is correct
The lodge has 420 skis. Predict the number of skis that are likely to be defective.
A ski lodge inspects 80 skis and discovers four that are faulty. The skis that are likely to be defective are 21.
It is assumed that there are 80 skis, four of which are faulty.
As a result, the total number of outcomes is 80.
Positive outcomes = 4
Let [tex]E_{1}[/tex] represent the event of selecting a faulty. As a result, the likelihood of selecting a defective ski is expressed mathematically as follows.
[tex]E_{1}[/tex] = Favorable case of defective / Total number of skis
= 4 / 80
= 1 / 20
=0.05
Skis will be discovered in 5% of cases.
So, the event of choosing a defective is 4 / 80.
If the total number of skis is 420, then the number of defective skis will be:
4 / 80 × 420
= 1/20 × 420
= 21
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Correct question:
A ski lodge inspects 80 skis and finds 4 to be defective. The lodge has 420 skis. Predict the number of skis that are likely to be defective.
Game dice for a particular child’s game are numbered 1-10 what is the likehood of rolling a single one and ending up with an even number
Dice game for a particular child’s game are numbered 1-10. Then, the likelihood of rolling a single one and ending up with an even number is 1/20.
The probability of rolling a single one is 1/10, since there is only one die face with the number one out of ten possible outcomes.
The probability of rolling an even number is 5/10, since half of the die faces are even numbers (2, 4, 6, 8, 10) out of ten possible outcomes.
To find the likelihood of both events happening together, we need to multiply their individual probabilities;
P(rolling a single one and ending up with an even number) = P(rolling a single one) x P(ending up with an even number)
= (1/10) x (5/10)
= 1/20
Therefore, the likelihood of rolling a single one and ending up with an even number is 1/20.
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An annual depreciation rate is the percent that the value of an item decreases each year. A company purchases technology for $5,000. The company uses the function $r=1-\sqrt[3]{\frac{S}{5000}}$
to relate the annual depreciation rate $r$ (in decimal form) and the value $S$ (in dollars) of the technology after 3 years. Find $S$ when $r=0.15$ .
If someone wants to call Havana, Cuba from the United States, begins with US three digit exit code 011 followed by the two digit country code for Cuba which is 53, followed by the country code of Havana which is 7 and finally by seven-digit local telephone numbers. But this seven-digit local telephone number cannot begin with 0. How many different telephone numbers are possible?
There are possible 4,782,969 different telephone numbers.
We will multiply the number of options for each digit to calculate the total number of possible telephone numbers,.
How to calculate the total number of possible telephone numbers?Using the multiplication principle to estimate the number of possible telephone numbers for each digit:
n1 x n2 x n3 x ... x nk
Here:
the first three digits are fixed: 011
The 4th digit (the first digit of the local phone number) can be any digit from 1 - 9 (i.e. 9 options).
The remaining 6 digits (the second to seventh digit of the local phone number) can be any digit from 0 to 9, except 0 (9 options for each digit).
Therefore, the total number of possible telephone numbers:
9 x 9 x 9 x 9 x 9 x 9 x 9 = 4,782,969,
Therefore, 4,782,969 different telephone numbers are possible.
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Marc conducted a gravity experiment for a school science project. He found the experimental value of gravity to be 10.14 m/s2. The accepted value of gravity is 9.81 m/s2. What is Marc’s approximate percent error?
Answer:
3.36%
Step-by-step explanation:
(10.14-9.81)/(9.81)(100)=3.36% error
What is the answer to (x^2)+(2x)-(5)=0
The solution to the given quadratic equation is [tex]=-1\pm \sqrt{6}[/tex]
What is a quadratic equation?A quadratic equation is an equation whose highest power is raised to the power of 2. Mathematically it is written in the form ax² + bx + c. There are many ways in which we can solve a quadratic equation such as:
FactoringQuadratic formulaCompleting the square methodFrom the given information, we have:
x² + 2x - 5 = 0
Using the quadratic formula method;
[tex]=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
here;
a = 1b = 2c = -5[tex]=\dfrac{-2\pm \sqrt{2^2-4(1)(-5)}}{2(1)}[/tex]
[tex]=\dfrac{-2\pm \sqrt{4+20}}{2}[/tex]
[tex]=\dfrac{-2\pm \sqrt{24}}{2}[/tex]
[tex]=\dfrac{-2\pm 2\sqrt{6}}{2}[/tex]
[tex]=-1\pm \sqrt{6}[/tex]
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Can you help me answer this question?
Step-by-step explanation:
The constant of proportionality is just the slope of the line
using 0,0 and 3,2 points
slope = (y1-y2 ) / ( x1-x2) = (0-3) / ( 0-2) = 3/2 = constant of proportionality
The Soule's live on a corner lot. Often, children cut across
their lot to save walking distance. The diagram to the right
represents the corner lot. The children's path is
represented by a dashed line. Approximate the walking
distance that is saved by cutting across their property
instead of walking around the lot.
...
The walking distance that is saved by cutting across the lot is
feet.
X
15 feet
x+3
Answer:
The walking distance that is saved by cutting across the lot is approximately 18 feet.
