Answer: 52.5
Step-by-step explanation: I used a calculator.
PLEASE HELP ASAP
Question 4(Multiple Choice Worth 2 points)
(Line of Fit MC)
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with points plotted at 1 comma 80, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 90, and 4 comma 98, and a line of fit drawn passing through the points 0 comma 70 and 1 comma 75
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
80; a student who studies for 0 hours is predicted to earn 80% on the test
70; a student who studies for 0 hours is predicted to earn 70% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
The line of fit's y-intercept is 80. This suggests that a student's anticipated test grade is 80% if they don't study at all.
What exactly is a scatter plot?A scatter plot is a type of graph that illustrates data and the connection between two variables. With one variable plotted on the x-axis and the other variable drawn on the y-axis, each data point is represented by a point on the plot. Data analysis use scatter plots to find patterns and connections between variables.
The line of fit's y-intercept is 80. This suggests that a student's anticipated test grade is 80% if they don't study at all.
This indicates that studying is positively connected with test performance in the context of the data. Higher exam scores are anticipated for students who study more. The amount of time spent studying alone may not account for other elements that may potentially affect exam performance, such as prior knowledge or test-taking techniques.
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A pan from the oven is sitting out to cool to room temperature. If the temperature difference between the pan and room temperature is currently 174°C and is decreasing by 5% every minute, how much above room temperature will the pan be in 21 minutes?
Answer: 59.26°
Step-by-step explanation:
Use the equation 174(0.95)^21
The 174 represents the temperature difference
The 21 represents the amount of time (in minutes) that has passed
To get 0.95, because the temperature is decreasing, you subtract
1-0.05=0.95 (0.05 and not 5 because you move the decimal over two places when working with percents)
That's the standard equation that you use when solving questions like these, and when you solve this equation you should get 59.26° (you need a calculator to solve it all at once)
list the possible rational roots of P(x) given by the rational roots theorem for P(x)=3x^3-4x^3-x^2-7
The possible rational roots of P(x).
According to the Rational Root Theorem, the possible rational roots of P(x) are the fractions ±p/q, where p is a factor of the constant term (-7) and q is a factor of the leading coefficient (3). The possible values for p are ±1 and ±7, and the possible values for q are ±1 and ±3. Therefore, the possible rational roots of P(x) are:
±1/1 = ±1
±7/1 = ±7
±1/3 = ±1/3
±7/3 = ±7/3
So, the possible rational roots of P(x) are ±1, ±7, ±1/3, and ±7/3.
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Find the area of the right triangle in simplest radical form that has a hypotenuse of 8 ft and a leg of 4 ft. (No decimals)
In its simplest radical form, the area of the right triangle is 8sqrt(3) square feet.
How is area determined?
The length of the other leg of the right triangle can be determined using the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where the hypotenuse is c and the triangle's legs are a and b.
We are aware that the hypotenuse c is 8 feet long and that leg an is 4 feet long. Let's work out the answer for the opposite leg's length, b:
[tex]b^2 = c^2 - a^2\sb^2 = 8^2 - 4^2\sb^2 = 64 - 16\sb[/tex]
[tex]sqrt(48) = 4sqrt(3) foot where 2 = 48 b[/tex]
Given that we know the lengths of both legs, we can use the following formula to get the triangle's area:
[tex](1/2) * Base * Height = Area[/tex]
We may use the 4 ft leg as the base and the 4sqrt(3) ft leg as the height since one leg is 4 ft and the other is 4sqrt(3) ft:
Area: (1/2) * 4 feet * 4 square feet (3)
= 8sqrt(3) square feet
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I NEED HELPP ASAP!!!!!!!!!!!!!!!!!
The measure of center that would best summarize the plot is given as follows: Median of 11.
The measure of variability is given as follows: IQR of 1.5.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.From the plot, these features are given as follows:
Minimum non-outliter value of 6.Q1 of 10.Median of 11.Q2 of 11.5.Maximum non-outlier value of 16.The median is the best measure of center of the data-set.
There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:
IQR = 11.5 - 10
IQR = 1.5.
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Emma Koonce Solve by Trinomial Factor (a)=(1) Feb 22, 8:36:18 AM Solve the quadratic by factoring. x^(2)=2x+8 Answer: x
The solutions to the quadratic equation x^(2)=2x+8 are x=4 and x=-2.
To solve the quadratic equation x^(2)=2x+8 by factoring, we need to rearrange the equation to make it equal to zero and then factor the trinomial.
Step 1: Rearrange the equation to make it equal to zero.
x^(2)-2x-8=0
Step 2: Factor the trinomial using the "AC Method."
The "AC Method" involves finding two numbers that multiply to the product of the coefficient of the x^(2) term (a) and the constant term (c), and add to the coefficient of the x term (b).
In this case, a=1, b=-2, and c=-8.
The product of a and c is (1)(-8)=-8.
The two numbers that multiply to -8 and add to -2 are -4 and 2.
Step 3: Rewrite the equation using the two numbers found in Step 2.
x^(2)-4x+2x-8=0
Step 4: Factor by grouping.
(x^(2)-4x)+(2x-8)=0
x(x-4)+2(x-4)=0
Step 5: Factor out the common factor (x-4).
(x-4)(x+2)=0
Step 6: Set each factor equal to zero and solve for x.
x-4=0 or x+2=0
x=4 or x=-2
Therefore, the solutions to the quadratic equation x^(2)=2x+8 are x=4 and x=-2.
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Mei and Ming both improved their yards by planting rose bushes and ivy they bought their supplies from the same store Mei spent 36 on 3 rose bushes and 1 pot of ivy Ming spent 168 on 9 rose bushes and 8 pots of ivy what's the cost of one rose bush and one pot of ivy..
Answer:
Mei and Ming both improved their yards by planting rose bushes and ivy they bought from the same store. Mei spent $36 on 3 rose bushes and 1 pot of ivy, while Ming spent $168 on 9 rose bushes and 8 pots of ivy. The cost of one rose bush and one pot of ivy would be $21, since the cost of one rose bush is $7 and one pot of ivy is $14
Step-by-step explanation:
PLEASE SOLVE FOR ME NEED ANSWER ASAP PLEASE
Using the leg rule and the Pythagorean theorem, we have:
x = 4
y ≈ 4.5
How to Apply the Leg Rule?The leg rule that can be use to solve the missing measures of the right triangle is given as:
hypotenuse/leg = leg/part
We have the following:
Hypotenuse = 9
Leg = 6
Part = x
Plug in the values:
9/6 = 6/x
9x = 36
x = 36/9
x = 4
Use the Pythagorean theorem to find y:
y = √(6² - 4²)
y ≈ 4.5
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Marcus found these three ordered pairs for the equation y = 52x + 150: (0, 150), (10,670), and (20,1190).
When he graphs these, what is the best range for the y-axis?
0 to 150
0 to 670
0 to 20
0 to 1190
A bank account has a monthly interest rate of 1% and initial balance of $1,000. Any earned interest is added to the account and no other deposits or withdrawals are made.
What is the account balance after 3 months. Round to the nearest dollar.
Answer: 1030.301 rounded is $1,030
Step-by-step explanation:
1000(1+.01)^3=1030.301
You multiply your initial amount by 1 and add your percent after you convert it to a decimal by moving your point two paces to the left. If you're withdrawing, you subtract your decimal. Everything is them raised to the power of 3. You then can multiply it on paper, my teacher lets us use calculators though to ensure we don't get an incorrect answer.
Find the missing degrees in the circle
The missing degrees in the circle are 260 degrees.
What is circle ?
A circle is a geometrical shape that represents a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the diameter of the circle is the distance across its widest point, passing through the center.
To find the missing degrees in the circle, we need to use the fact that the sum of the central angles in a circle is equal to 360 degrees.
In this circle, we have two central angles: one measuring 100 degrees and the other measuring x degrees. We also know that the sum of these two central angles is equal to 360 degrees.
Therefore, we can set up the following equation:
100 + x = 360
To solve for x, we can subtract 100 from both sides:
x = 260
Therefore, the missing degrees in the circle are 260 degrees.
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B it's 1/2 /8 /10 and d its 2, /2 /4
Starts work at 7:30 a.m. and finish at 4:30 p.m. he has a 45-minute lunch break how many hours does he work in a normal 5-day week
Answer: 41 hours and 15 minutes
Step-by-step explanation:
First, we count the time duration from 7:30am to 4:30pm, which is 9 hours.
Next, we subtract 45 minutes from 9 hours, which equals 8 hours and 15 minutes.
Last, we multiply that by 5 which equals 41 hours and 15 minutes.
Solving a rational equation that simplifies to linear: Denominat Solve for v. 6=(5)/(v-8)
The value of v is 8.83.
What is rational equation?A rational equation is an equation that includes one or more fractions with polynomials. It can be solved by cancelling common factors between the numerator and the denominator, and then solving the resulting equation. It is important to note that when cancelling common factors, one must always check that the original equation is still satisfied.
To solve this rational equation that simplifies to linear, you need to solve for v. To do this, first multiply both sides by the denominator:
6(v-8) = 5
Then add 8 to both sides to get rid of the variable in the denominator:
6v - 48 = 5
Finally, add 48 to both sides to isolate the variable v:
6v = 53
Finally, divide both sides by 6 to solve for v:
v = 53/6 = 8.83
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Value added tax is added at 15% for goods and services In South Africa. What will be the selling of a laptop that costs R4200 before VAT
If the VAT in South Africa is 15%, then selling price of the laptop after the VAT is R4830 .
The cost price of the laptop before the VAT is R4200,
The VAT percent on goods and services is = 15%,
In order to calculate the selling price of the laptop that costs R4200 before VAT is added at 15% in South Africa, we can use the following formula:
⇒ Selling Price = Cost Price + (Cost Price × VAT )
Substituting the values,
We get,
⇒ Selling Price = R4200 + (R4200 × 0.15)
⇒ Selling Price = R4200 + R630
⇒ Selling Price = R4830
Therefore, the selling price of the laptop, including 15% VAT, will be R4830.
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Find the area of the triangle, to the nearest tenth, of the triangle with a = 3, b = 5, and c = 6
Area of the triangle ≈ 7.5 (to the nearest tenth).
To find the area of the triangle given its side lengths, we will use Heron's formula:
s =(a + b + c)/2
A = sqrt(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, and A is the area of the triangle.
For the given triangle, we have:
a = 3
b = 5
c = 6
The semiperimeter s can be calculated as:
s = (a + b + c) / 2 = (3 + 5 + 6) / 2 = 7
Using this value of s, we can apply Heron's formula to find the area A:
A = √(s(s-a)(s-b)(s-c))
= √(7(7-3)(7-5)(7-6))
≈ 7.48
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QUESTION 6 Suppose a researcher has collected the GPAS (y variable) and Hours of Studying per week (x-variable) for 100 students. What GPA will the regression equation try to predict for students who study 10 hours per week? (NOTE: Do not use the regression equation to answer this question. The answer is not a number.) TTTT Paragraph Arial 3 (12pt) 3. T. QI %DO QE 3 TT, $x Mashup. TH
A researcher will use a regression equation to predict the relationship between the GPAS (y variable) and Hours of Studying per week (x-variable) for 100 students. The regression equation will try to predict the GPA for students who study 10 hours per week by estimating the relationship between the two variables. The regression equation is a mathematical model that is used to predict the value of one variable based on the value of another variable.
In this case, the regression equation will try to predict the GPA for students who study 10 hours per week based on the relationship between GPAS and Hours of Studying per week.
The goal of the regression equation is to provide an accurate prediction of the GPA for students who study 10 hours per week, based on the data collected by the researcher.
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twelve basketball teams will play in a tournament. Four will be given byes in the first round. They will be matched against the four first-round winners from the other eight teams. How many games will a team have to win in ordet to win the tournament
Use synthetic division an(d)/(o)r factoring to write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, given that (-(5)/(2)) is a zero of f(x).
The function f(x) in completely factored form is (4x+1)(5x-1)(x+5).
To write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, we can use synthetic division with the given zero of (-(5)/(2)).
Step 1: Set up the synthetic division with the given zero and the coefficients of the polynomial.
(-(5)/(2)) | 20 44 -17 -5
|______________
Step 2: Bring down the first coefficient, 20, and multiply it by the given zero.
(-(5)/(2)) | 20 44 -17 -5
| -50
|______________
| 20
Step 3: Add the result of the multiplication to the next coefficient and repeat the process until all coefficients have been used.
(-(5)/(2)) | 20 44 -17 -5
| -50 3 10
|______________
| 20 -6 -14 5
Step 4: The last number in the bottom row is the remainder. If it is zero, then the given zero is a factor of the polynomial. In this case, the remainder is 5, so (-(5)/(2)) is not a factor of f(x).
Since (-(5)/(2)) is not a factor of f(x), we cannot use synthetic division to write f(x) in completely factored form. Instead, we can use factoring to find the factors of f(x).
f(x) = 20x^(3)+44x^(2)-17x-5
= (4x+1)(5x-1)(x+5)
Therefore, f(x) in completely factored form is (4x+1)(5x-1)(x+5).
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4) ƒ(x) = −x³ + 4x² − 2
These are the x-coordinates of the points where the graph intersects the x-axis. We can use these points to sketch the curve of the function.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.
Here,
The function ƒ(x) = −x³ + 4x² − 2 is a cubic function, which means that it is a polynomial of degree 3. The general form of a cubic function is:
ƒ(x) = ax³ + bx² + cx + d
where a, b, c, and d are constants. In the given function, we have:
a = -1
b = 4
c = 0
d = -2
Therefore, we can rewrite the function as:
ƒ(x) = -x³ + 4x² - 2
This function can be graphed to show the shape of the curve it creates. The graph of a cubic function is a curve that can either be concave up or concave down, depending on the sign of the leading coefficient. In this case, the leading coefficient is negative, so the graph will be concave down. The function has a y-intercept of -2, which means that it intersects the y-axis at the point (0, -2). To find the x-intercepts, we can set ƒ(x) equal to zero and solve for x:
ƒ(x) = -x³ + 4x² - 2 = 0
We can use factoring or the quadratic formula to solve for x, but in this case, the equation can be simplified by factoring out a common factor of x²:
-x²(x - 4) + 2 = 0
Now we can solve for x:
x² = 2/(4 - x)
x = ±√(2/(4 - x))
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Complete question:
Solve for x when ƒ(x) = −x³ + 4x² − 2.
Fatoumata kicks a football. Its height in feet is given by ℎ ( � ) = − 16 � 2 + 96 � h(t)=−16t 2 +96t where � t represents the time in seconds after kick. What is the appropriate domain for this situation?
For the given equation of the height the appropriate domain for this situation is 0 ≤ t ≤ 6.
What role does the domain play?The collection of all feasible input values that are appropriate for the circumstance being represented is known as the domain. In this instance, the domain stands for the range of time values relevant to the height of the football following a kick. The domain helps to avoid absurd or impossible outcomes by ensuring that the function is only evaluated for legitimate inputs.
The ball with follow a parabolic path, thus the maximum height is attained at:
t = -b/2a
Substituting the values we have:
t = -96/(-32) = 3 seconds.
The ball will then follow the downward path and will take an additional 3 seconds to reach the ground.
Thus, the total time taken will be 3 + 3 = 6 seconds.
Also, the ball initially starts from rest at 0 seconds.
Hence, the domain of the situation will be represented as 0 ≤ t ≤ 6.
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how do i answer that?!
Answer:
the answer is 4.
Step-by-step explanation:
-3 squared will give you 9. 73- 9 is 64 and cube root of 64 is 4
I recently took a review test and it talked about amount of error (percent error) . The question said that , “the estimate number of balls in each bag was 86. It turned out to be 104. What is the percent of error? Round to the nearest tenth.” I wrote 17.3%. The teacher said it was wrong and claimed that you had to divide it by expected, not real. (Formula is (expected-real)/real.)) Can someone help me out, am I wrong or the teacher?
The percent of error is 20.9302%. The solution has been obtained by using percent error.
What is percent error?
The difference between the estimated value and the actual value in respect to the actual value is known as the percent error.
We are given that the estimate number of balls in each bag was 86 but it turned out to be 104.
So, the percent error is
⇒Percent error = [Estimated Value - Actual value] / Actual value
⇒Percent error = [104 - 86] / 86
⇒Percent error = 18 / 86
⇒Percent error = 20.9302%
Hence, the percent of error is 20.9302%.
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Triangle JKL is an equilateral triangle with two of its vertices at points J and K. What are the coordinates of point L?
The coordinates of point L are (s/2, s√3/2). If we know the value of s, we can determine the specific coordinates of point L.
To determine the coordinates of point L in an equilateral triangle with vertices J and K, we first need to know the location of J and K.
Since the triangle is equilateral, the distance from J to K is the same as the distance from J to L or from K to L. Let's assume that the side length of the equilateral triangle is s. Then, the distance from J to K is also s. We can assume that J is located at the origin (0,0), and K is located at (s,0).
To find the coordinates of point L, we can use some trigonometry. Let's draw a line from point K to point L, and let the angle between this line and the x-axis be θ. Since the triangle is equilateral, this angle is 60 degrees.
The x-coordinate of point L is then given by s cos θ. Since cos 60 = 1/2, the x-coordinate of point L is s/2.
The y-coordinate of point L is given by s sin θ. Since sin 60 = √3/2, the y-coordinate of point L is s√3/2.
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Mr Johns is buying a new phone. He wants to pay for the phone in 12 equal monthly payments. Work out how much Mr Johns will pay each month.
Gr8 Phones
Normal price £780
Sale price 5% off
Answer:
56.14
Step-by-step explanation:
673.36/12
27. For which values of k, if any, are u and v orthogonal? (a) u = (k. 1,3), v = (1,7,K) (b) u = (-2,k,k), v = (k. 5, k) 28. Use vectors to find the cosines of the interior angles of the triangle with vertices A(0,-1), B(1,-2), and C(4,1), 29. Use vectors to show that A(3, 0, 2), B(4,3,0), and C(8, 1.-1) are vertices of a right triangle. At which vertex is the right angle? 30. In each part determine whether the given number is a valid ISBN by computing its check digit. (a) 1-56592-170-7 (b) 0-471-05333-5 31. In each part determine whether the given number is a valid ISBN by computing its check digit. (a) 0-471-06368-1 (b) 0-13-947752-3
For two vectors to be orthogonal, their dot product should be zero.
(a) The dot product of u and v is k+21k=22k. For u and v to be orthogonal, 22k=0, which means k=0.
(b) The dot product of u and v is -2k^2+5k^2+k^2=4k^2. For u and v to be orthogonal, 4k^2=0, which means k=0.
Therefore, in both cases, the vectors are orthogonal when k=0.
Let AB and AC be vectors joining the points A(0,-1), B(1,-2), and C(4,1), respectively. Then,
AB = (1-0, -2-(-1)) = (1,-1)
AC = (4-0, 1-(-1)) = (4,2)
The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).
(a) Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(4) + (-1)(2))/sqrt(2^2+1^2 * 4^2+2^2) = 2/3
Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (4(1) + 2(-1))/sqrt(4^2+2^2 * 2^2+1^2) = 1/3
Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(3) + (-1)(-1))/sqrt(2^2+1^2 * 2^2+1^2) = 5/9
(b) Let AB and BC be vectors joining the points A(3,0,2), B(4,3,0), and C(8,1,-1), respectively. Then,
AB = (4-3, 3-0, 0-2) = (1, 3, -2)
BC = (8-4, 1-3, -1-0) = (4, -2, -1)
AC = (8-3, 1-0, -1-2) = (5, 1, -3)
The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).
Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(5) + 3(1) + (-2)(-3))/sqrt(1^2+3^2+(-2)^2 * 5^2+1^2+(-3)^2) = 0
Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (5(1) + 1(3) + (-3)(-2))/sqrt(5^2+1^2+(-3)^2 * 1^2+3^2+(-2)^2) = -7/9
Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(4) + (
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please help me i need your help. find the value of x
Answer:
122
Step-by-step explanation:
add the 2 angles together and there's your answer.
if you want to check take your answer and subtract from 180.
Answer: 122
Step-by-step explanation:
all triangles add up to 180
54+68=122
180-122=58
58=inner corner
180 (this is the measure of the line) -58 =122
hopefully this helps :))
i need helpp pp pp p
Answer:
I CAN NOT SEE THAT OML
Step-by-step explanation:
Prove that any two consecutive terms in the Fibonacci sequence
are relatively prime. (The Fibonacci sequence is given by f1 = 1,
f2 = 1, fn = fn−2 + fn−1.)
They are relatively prime.
Proof: Let fn and fn-1 be any two consecutive terms in the Fibonacci sequence. By definition, fn = fn-2 + fn-1. Since both fn and fn-1 are integers,
they must have no common factors other than 1,
so they are relatively prime.
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Which ordered pair is NOT a solution of y > 3x + 4? Responses (2, 12) (2, 12) (0, 5) (0, 5) (–2, 1) (–2, 1) (1, 7)
The ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).
What is inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
The given inequality is y > 3x + 4. To check which ordered pair is not a solution of this inequality, we need to substitute the values of x and y from each ordered pair into the inequality and check whether the inequality holds or not.
Checking the ordered pairs one by one, we have:
(2, 12): y = 12 and x = 2, so 12 > 3(2) + 4 is true. Therefore, (2, 12) is a solution of the inequality.
(0, 5): y = 5 and x = 0, so 5 > 3(0) + 4 is true. Therefore, (0, 5) is a solution of the inequality.
(-2, 1): y = 1 and x = -2, so 1 > 3(-2) + 4 is false. Therefore, (-2, 1) is not a solution of the inequality.
(1, 7): y = 7 and x = 1, so 7 > 3(1) + 4 is true. Therefore, (1, 7) is a solution of the inequality.
Therefore, the ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).
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