Describe the end behavior of the function -2x^3-13x^2+8x+52
Answers
Answer:
[tex]\text{as x} \to \infty, \ \text{y} \to -\infty\\\\\text{as x} \to -\infty, \ \text{y} \to \infty[/tex]
Rises to the left; falls to the right
============================================================
Explanation:
The leading term is what determines the end behavior of any polynomial function.
Given polynomial: -2x^3-13x^2+8x+52Leading term: -2x^3The leading term has the largest exponent. The other terms will have no effect on the end behavior.
As x gets really large in the positive direction, so does x^3. But the -2 out front will flip to have y go to negative infinity.
Therefore: [tex]\text{as x} \to \infty, \ \text{y} \to -\infty[/tex]
We can informally think of this as "falls to the right".
---------------------------
As x heads to the left, x^3 becomes further negative. But -2 out front makes -2x^3 to be positive.
So [tex]\text{as x} \to -\infty, \ \text{y} \to \infty[/tex] aka "rises to the left".
Whatever x does, y does the opposite. If x goes positive, then y goes negative and vice versa.
-------------------------
The end behavior is therefore
[tex]\text{as x} \to \infty, \ \text{y} \to -\infty\\\\\text{as x} \to -\infty, \ \text{y} \to \infty[/tex]
x and y are opposite.
We can summarize that notation as saying "rises to the left, falls to the right".
See the graph below. I used GeoGebra to make the graph, but you can use Desmos or any other tool you prefer.
Related Questions
Find the values of x and y.
Answers
The value of x is 5.
The value of y is 40°.
What is a triangle?It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
A composite figure that has three triangles.
Two equilateral triangles.
One isosceles triangle.
We see that,
Both equilateral triangles have the same sides and the same angles.
5x - 1 = 24
5x = 24 + 1
5x = 25
x = 5
We see that,
Let the opposite angle of 6y° = m
6y° + 60 + 60 + m = 360
6y + 120 = 360
6y = 360 - 120
6y = 240
y = 40°
Thus,
x = 5 and y = 40°
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an information technology company claims that a certain model of laptops have mean battery capacity of 5 hours. a consumer report firm wants to show that the actual mean is smaller than the company claims. what should be the null and alternative hypotheses? group of answer choices : versus : : versus : : versus :
Answers
Null Hypothesis: The actual mean is equal to the company's claim of 5 hours.Alternative Hypothesis: The actual mean is less than the company's claim of 5 hours.
Null and alternative hypotheses are applied for evaluating statistical theories. In contrast to the null hypothesis, which is a test's default assumption, the alternative hypothesis indicates how your research anticipates an effect or link between variables.
Null hypothesis: The null hypothesis states the expected outcome. In the given situation, the expected outcome is that the actual mean is equal to the company's claim of 5 hours.The alternate hypothesis conveys the null hypothesis' complete opposite.In this case, the alternative hypothesis is that the actual mean is less than the company's claim of 5 hours.
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help with example 6
Answers
In the given triangle, length of side AD is 5 unit and length of side AB is 7 unit.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
In triangle ABC,
BC is perpendicular bisector or side AC.
The length of side AC = 10, BC = 7,
Since, BD is a perpendicular bisector of AC,
Therefore, D will be midpoint of AC.
AD = DC = AC /2 = 10/2 = 5.
By angle bisector property,
AB/BC = AD / AC
AB / 7 = 5/5
AB = 7
The length of side AB is 7 and Side AD is 5.
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Paula bought a ski jacket on sale for $4 less than half its original price. She paid $89 for the jacket. What was the original price?
Answers
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a
graphing utility, use it to graph the function and verify the real zeros and the given function value.
n = 3;
-2 and 6+4i are zeros;
f(2)=128
Answers
Answer:
f(x) = x³ -10x² +28x +104
Step-by-step explanation:
You want a cubic polynomial f(x) with real coefficients, and its graph, such that one root is -2, another is 6+4i, and f(2) = 128.
Conjugate rootsA polynomial with real coefficients will have complex (or radical) roots that are conjugate pairs. That means the root 6+4i will be paired with a root 6-4i. The factored form of the required polynomial will be ...
f(x) = a(x -(-2))(x -(6 +4i))(x -(6 -4i))
f(x) = a(x +2)(x² -12x +52)
Scale factorWe can use the given value of f(2) to find the scale factor, a.
f(2) = 128 = a(2 +2)(2² -12·2 +52) = a(4)(32) = 128a
a = 1 . . . . . divide by 128
The required polynomial is ...
f(x) = (x +2)(x² -12x +52)
f(x) = x³ -10x² +28x +104
What is the radius of a circle with equation x² y² 121?
Answers
The length of the radius of a circle with the equation x² + y² = 121 is 11 units .
In the question ,
it is given that ,
the equation of the circle is ⇒ x² + y² = 121 ,
we know that the general equation of the circle is given as x² + y² = d² ;
and "d" is the radius of circle ,
On comparing both the equations ,
we get ,
d² = 121
Simplifying the above equation further ,
on taking square root on both the sides ,
we get ,
d = √121 = √(11 × 11)
the radius "d" is
d = 11 units .
Therefore , the radius of the circle is = 11 units .
The given question is incomplete , the complete question is
What is the radius of a circle with equation x² + y² = 121 ?
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I know the answer but I need help with the work
I WIL GIVE 20 POINTS AND BRAINLIST for ANSWER!!!
Jessica estimated that her family used 30% more water this month compared to last month. They used 12000 gallons of water last month. How much water did they use this month? Use the sketch tool to complete the double number line diagram if it is helpful.
Answers
Answer:
Below
Step-by-step explanation:
30% is .3 in decimal
So the family used 100 % of last month PLUS .3 of last month MORE
12 000 = 100 % now add .3 (12 000) more =
12 000 + .3 ( 12 000) = 15600 gallons this month
A blimp is fully expanded when it contains 35,000 cubic feet of gas. If the blimp is inflated with 28,700
cubic feet of gas, what percent full is it?
Answers
Answer: The blimp is 82% full
Step-by-step explanation:
To find the percentage of the blimp that is filled with gas, we need to divide the volume of the gas that is in the blimp by the total volume of the blimp and then multiply the result by 100%.
The blimp is filled with 28,700 cubic feet of gas, and it has a total volume of 35,000 cubic feet when fully expanded, so the percentage of the blimp that is filled with gas is 28,700 / 35,000 = 0.82.
To express this as a percentage, we need to multiply the result by 100%, so the blimp is 82% full.
Here's the complete solution:
The blimp is filled with 28,700 cubic feet of gas.
The blimp has a total volume of 35,000 cubic feet when fully expanded.
Therefore, the percentage of the blimp that is filled with gas is 28,700 / 35,000 = 0.82.
To express this as a percentage, we multiply the result by 100%, so the blimp is 82% full.
Which integer represents the following situation:
The scuba diver is 30 feet below sea level.
Question 3 options:
A: -3
B: 33
C: 30
D: -30
Answers
Answer:
D. -30
Step-by-step explanation:
Let's say 0 is sea level. If the diver is 30 feet below 0, then they would by 30 below 0, or -30.
If mr lebedev paid 85$ for a pair of air force ones after a 15% discount,how much was the original price?
Answers
PLEASE HURRY The function, f(x), gives the train fare, in dollars, for a child who is “x” years old based on these rules:
-free for children under 5
-$5 for children who are at least 5 but younger than 11
-$7 for children who are at least 11 but younger than 16
Graph this piecewise function
Answers
The Piecewise function is
f(x) = [tex]\left \{ \right.[/tex] 0, x<5
5, 5<x<11
7, 11<x< 16
What is Piecewise Function?A function that is defined piecemeal is one that has numerous subfunctions, each of which applies to a distinct interval in the domain. Instead of being a property of the function itself, piecewise definition is a means to express the function.
A piecewise function is a function that is constructed from bits of various functions across various time intervals.
Given:
let x be the age of person.
We have,
free for children under 5$5 for children who are at least 5 but younger than 11$7 for children who are at least 11 but younger than 16let f(x) represents the piecewise function
f(x) = [tex]\left \{ \right.[/tex] 0, x<5
5, 5<x<11
7, 11<x< 16
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What is parallel slope intercept form?
Answers
Parallel slope intercept form is a form of linear equation that describes a line parallel to a given line with slope m.
It is written as y = mx + b, where m is the slope of the line and b is the y-intercept of the line. This form is useful for finding equations of lines that are parallel to a given line.
y = mx + b
y = mx + b is an equation in the form of a straight line, where m is the slope of the line and b is the y-intercept of the line. This form can be used to determine the equation of a line that is parallel to a given line. The equation can be re-arranged to solve for x, if needed. To solve for x, the equation can be rewritten as x = (y - b) / m.
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In AABC and ADEF, mZA = 68°,
m/C= m/F = 59°, mZE = 53°, and
AB = DE = 8 units. Can you prove that
AABC = ADEF? If so, write a proof. If not,
explain why not.
Answers
Answer:
It is impossible to prove that AABC = ADEF with the information given. In order for us to prove that these two figures are congruent, we would need to know the measures of all the angles in both figures and the lengths of all the sides. Since we only have the measures of some of the angles and the lengths of two sides, we cannot prove that the figures are congruent.
Triangle PQR, with vertices P(4,6), Q(8,5), and R(5,9), is drawn inside a rectangle, as shown below.
Answers
The area of the given triangle will be A = 4.52 units².
How to find the distance between two points?Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
As per the given,
P(4,6), Q(8,5), and R(5,9)
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
PQ = [tex]\sqrt {\left( {4 - 8 } \right)^2 + \left( {6 - 5 } \right)^2 }[/tex]
PQ = √17 = 4.12
PR = [tex]\sqrt {\left( {4 - 5 } \right)^2 + \left( {6 - 9 } \right)^2 }[/tex]
PR = √5 = 2.25
QR = [tex]\sqrt {\left( {8 - 5 } \right)^2 + \left( {5 - 9 } \right)^2 }[/tex]
QR = √18 = 4.25
The area will be as, √(S(S - PQ)(S - QR)(S - PR)
Where, S = (4.12 + 2.25 + 4.25)/2 = 5.31
Area = √(5.31(5.31 - 4.12)(5.31 - 4.25)(5.31 - 2.25)
A = 4.52 units²
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Answer:
6.5 square units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7cm}\underline{Area of a triangle}\\\\$A=\dfrac{x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $(x_1,y_1), (x_2,y_2)$ and $(x_3,y_3)$ are \\ \phantom{ww}\;\;\; vertices of the triangle. \\\end{minipage}}[/tex]
From inspection of the given diagram, the vertices of the triangle are:
(x₁, y₁) = P = (4, 6)(x₂, y₂) = Q = (8, 5)(x₃, y₃) = R = (5, 9)Substitute the vertices into the formula to solve for area:
[tex]\implies A=\dfrac{4(5 - 9) + 8(9 - 6) + 5(6 - 5)}{2}[/tex]
[tex]\implies A=\dfrac{4(-4) + 8(3) + 5(1)}{2}[/tex]
[tex]\implies A=\dfrac{-16 + 24 + 5}{2}[/tex]
[tex]\implies A=\dfrac{13}{2}[/tex]
[tex]\implies A=6.5 \; \sf units^2[/tex]
Therefore, the area of triangle PQR is 6.5 square units.
Find the Value of sin180
Answers
PLEASE HELP ME
im stuck on it
Answers
The completed two-column table used to prove that ΔSUV ≅ ΔTVU, can be completed as follows;
Statements [tex]{}[/tex] Reasons
1. [tex]\overline{SU}[/tex] ≅ [tex]\overline{TV}[/tex] Given
2. ∠TSU ≅ ∠STV [tex]{}[/tex] Given
3. [tex]\overline{UV}[/tex]║[tex]\overline{ST}[/tex] [tex]{}[/tex] Given
4. ∠TSU ≅ ∠SUV[tex]{}[/tex] Alternate Interior Angles Theorem
5. ∠TVU ≅ ∠STV[tex]{}[/tex] Alternate Interior Angles Theorem
6. ∠STV ≅ ∠SUV [tex]{}[/tex][tex]{}[/tex] Transitive Property of Congruence
7. ∠TVU ≅ ∠SUV[tex]{}[/tex] Transitive Property of Congruence
8. [tex]\overline{UV}[/tex] ≅ [tex]\overline{UV}[/tex] [tex]{}[/tex] Reflexive Property of Congruence
9. ΔSUV ≅ ΔTVU [tex]{}[/tex] SAS
What are congruent triangles?Two triangles such as ΔSUV and ΔTUV are congruent when the three sides of triangle ΔSUV are congruent to the three sides of triangle ΔTUV.
The details of the reasons used to prove the congruency of the triangles are as follows;
Alternate Interior Angles Theorem
The alternate interior angles theorem states that the alternate interior angles formed by two parallel lines, such as [tex]\overline{UV}[/tex] and [tex]\overline{ST}[/tex] and their common transversals, [tex]\overline{TV}[/tex] and [tex]\overline{SU}[/tex], are congruent.
Transitive Property of Congruence
The transitive property of congruence states that two shapes are congruent to themselves if both shapes are congruent to a third shape.
Reflexive Property of Congruence
The reflexive property of congruence states that a shape, line, or angle is congruent to itself.
SAS
SAS, is an acronym for Side-Angle-Side congruency postulate, which states that, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
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6a+4 when a=1/3
And
5a-2/3
Answers
Step-by-step explanation:
1.6a+4 when a=1/3 is 6
2.5a-2/3=0.133
RIP BRO
How do you remove split infinitives?
Answers
To get rid of the split infinitive move the term that separates the infinitive from the split position.
In the given question we have to explain, how we remove split infinitives.
As we know that,
Split infinitives are grammatical constructions in which the "to" and "infinitive" halves of what is more often referred to as the to-infinitive in modern linguistics are separated by an adverb or adverbial phrase.
When an adverb is inserted between the word "to" and the infinitive verb, a split infinitive results. Move the term that separates the infinitive from the split position to get rid of the split infinitive.
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Which is the last sentence of the proof? because f e = 1, a2 b2 = c2. because f e = c, a2 b2 = c2. because a2 b2 = c2, f e = c. because a2 b2 = c2, f e = 1.
Answers
The last sentence of the proof is Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex]. Hence, option b is the correct answer to this question.
We have that △ABC and △CBD are right-angled triangles.
We have to prove [tex]a^{2} + b^{2} = c^{2}[/tex].
We are given the proof too.
Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA.
Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA.
The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as
[tex]a^{2}[/tex] = cf and [tex]b^{2}[/tex] = ce.
Adding [tex]b^{2}[/tex] to both sides of the first equation, [tex]a^{2}[/tex] = cf, which results in the equation [tex]a^{2} + b^{2} = cf +b^{2}[/tex].
Because [tex]b^{2}[/tex] and ce are equal, ce can be substituted into the right side of the equation for [tex]b^{2}[/tex], resulting in the equation [tex]a^{2}+b^{2}[/tex] = cf + ce.
Applying the converse of the distributive property results in the equation [tex]a^{2}+b^{2}[/tex]= c(f + e).
Now Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex] .
Hence, the last sentence of this proof is Because f+e=c, [tex]a^{2} + b^{2} = c^{2}[/tex].
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The complete question is -
Which is the last sentence of the proof?
a. Because f + e = 1, [tex]a^{2} + b^{2} = c^{2}[/tex].
b. Because f + e = c, [tex]a^{2} + b^{2} = c^{2}[/tex].
c. Because [tex]a^{2} + b^{2} = c^{2}[/tex], f + e = c.
d. Because [tex]a^{2} + b^{2} = c^{2}[/tex], f + e = 1.
Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Answer: option b
Step-by-step explanation:
Question 1 of 10
What is the first thing a lender might do if a borrower is late with a payment?
Answers
Answer:
they will probably contact them orrr charge late fees
The first thing a lender might do if a borrower is late with a payment is to send a reminder.
This reminder will usually be a phone call, email, or letter. The reminder will typically state the amount that is due, the due date, and any late fees that may be charged.
If the borrower does not make the payment after receiving the reminder, the lender may then contact the borrower directly. This contact may be made by a phone call, email, or letter. The lender may also try to work with the borrower to come up with a payment plan.
If the borrower still does not make the payment, the lender may then report the borrower to the credit bureaus. This will have a negative impact on the borrower's credit score. The lender may also start legal proceedings to collect the debt.
The specific steps that a lender will take if a borrower is late with a payment will vary depending on the lender's policies and the borrower's situation. However, sending a reminder is usually the first step.
Here are some additional things that a lender might do if a borrower is late with a payment:
Charge late fees.
Terminate the loan.
Sue the borrower.
Foreclose on the borrower's property.
It is important to note that the lender's actions will also depend on the terms of the loan agreement. The loan agreement will typically specify what happens if a borrower is late with a payment.
If you are a borrower who is late with a payment, it is important to contact your lender as soon as possible. You should try to work out a payment plan with the lender. If you do not make the payment, the lender may take legal action against you.
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The publisher of a high school yearbook charges $24 per yearbook plus a layout fee of $475. The yearbook committee has decided that the publisher will receive no more than $6100. What is the maximum number of yearbooks that can be sold?
Answers
With the help of simple mathematical operations, we know that the publisher can sell a maximum of 12 yearbooks.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
The order of operations refers to the rules that govern how to solve an expression with several operations.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).
So, the maximum number of books that can be sold are:
24 + 475 = 499
Now, the publisher can receive not more than $6100. Then,
6100/499 = 12.22
Therefore, with the help of simple mathematical operations, we know that the publisher can sell a maximum of 12 yearbooks.
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Elizabeth has half as many CDs as Jennifer. Which equation would represent the number of CDs that Jennifer has? (Let e = the number of Elizabeth's CDs and j = the number of Jennifer's CDs.)
a) 1/2e = j
b)2e = j
c)2j = e
d)1/2 + j = e
Answers
it's A
Step-by-step explanation:
i can feel the changes... i am going to gorge my eyes out :)
Please help me quick please it’s proofs and am really stuck on this question !!!
Answers
Answer:
Step-by-step explanation:
hey buddy thts supper easy just match the d and b
someone help please!!!
Answers
The coordinates of the vertices after a reflection over the line x = 2.
D = (8, 5)
E = (6, 5)
F = (4, 8)
G = (7, 8)
What is a reflection?There are two ways of translation.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
The coordinates:
D = (-4, 5)
E = (-2, 5)
F = (0, 8)
G = (3, 8)
The line x = 2.
We count the units from the line x = 2.
After the reflection, the number of units of each coordinate from the line
x = 2 must be equal to the number of units from the line x = 2 before the reflection.
Thus,
The reflected coordinates of the vertices are:
D = (8, 5)
E = (6, 5)
F = (4, 8)
G = (7, 8)
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two numeric variables x and y exhibit a negative correlation if a. the value of y tends to decrease as the value of x decreases. b. the value of y tends to increase as the value of x decreases. c. the value of y tends to increase as the value of x increases. d. the values of x and y always have the same difference.
Answers
If x and y are two numerical variables, they will have a negative correlation. As the value of x declines, the value of y tends to do the same.
Statistics uses the terms correlation or dependency to describe any statistical relationship between two random variables or bivariate data, regardless of whether it is causal or not. When two variables are negatively correlated, one drops when the other grows.Therefore, if the value of x decreases, the value of y will decrease as well.A negative correlation between x and y means that when x increases, y decreases, and when x decreases, y also decreases. This is expressed by the formula y = -x.
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find each angle measure to the nearest degree cos C= 0.7193
Answers
Answer: c≈44°
Step-by-step explanation:
cos(c)=0,7193
c=arccos(0.7193)
c≈44°
Garrick and Zan are measuring the heights of seedling plants for science class.
Use the drop-down menus to complete the statements about the measured heights and the actual heights of the plants.
Answers
The complete statements are
Garrick's plant is shorter than Zan's plant, each millimetre of error results in a 11.11% percent error.Garrick's measurement was 2 millimetres off and Zan's was 12 millimetres off. Garrick's measurement was 20% off and Zan's was 12% off.How to complete the statements?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Garrick's plant:
Actual height = 10 mmMeasured height = 8 mmZan's plant:
Actual height= 100 mmMeasured height = 88 mmGarrick's plant is shorter than Zan's plant and the difference in heights is
Actual difference = 100 mm - 10 mm = 90 mm
Measured difference = 88 mm - 8 mm = 80 mm
The percentage errors are calculated using
Percentage errors = Difference/Actual measurement * 100%
So, we have
Garrick's actual error = (10 - 8)/10 *100% = 20%
Zan's actual error = (100 - 88)/10 * 100% = 12%
Hence, Garrick's measurement was 20% off and Zan's was 12% off.
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9) y=3x+1
y=1/3x + 1
Answers
Answer:
y = 3 ; x = -3
Step-by-step explanation:
[x + 1 x y = 1/3x + 1] y = 3
SUBSTITUTE
[ x + 1 x 3 = 1/3x + 1
SIMPLIFY
[ x + 3 = 1/3x + 1]
ISOLATE X FOR X + 3 = 1/3X + 1: X = -3
solve compound inequality -3a<6 or a-5<-2
Answers
The simplified form of the compound inequality - 3a < 6 Or a - 5< - 2
is a > 3 Or a < 3.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, - 3a < 6 Or a - 5< - 2.
∴ 3a > 6 Or a < - 2 + 5.
a > 6/3 Or a < 3.
a > 3 Or a < 3.
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Ruby is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $2.50. Ruby spent $15 altogether at the carnival and the number of games she played is twice the number of rides she went on. Graphically solve a system of equations in order to determine the number of games Ruby played, x, and the number of rides Ruby went on, y.
Answers
$15 = 1.25x + 2.50y
x number of games, y = number of rides
Graphing this will show a line with coordinates (x, y) on it who 'fit' in this equation to make it = 15
I graphed points where both x and y are whole numbers.
These are answers to the equation that make it = 15.
Graph the line 2x = y (2 times the number of games is the number of rides)
Where the lines intersect is where number of rides is twice taht of games, and the price is 15.
Visually, we can determine that they intersect at (2.4, 4.8)
To verify that this is correct, plug them into the first function to see if this gives you 15.
It does equal 15.
While these are not whole numbers, they do make the equations true, but in the real world we would not have numbers like this.
Hope this helps :)
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- Jeron