37. A possible solution is y(x) = ax + b, where a and b are constants. Taking two derivatives gives y''(x) = 0, which satisfies the differential equation.
38. A possible solution is y(x) = Ce^x, where C is a constant. Taking the derivative of y(x) gives y'(x) = Ce^x, which satisfies the differential equation.
39. A possible solution is y(x) = 3 + 2x^2, which can be checked by taking the derivative and plugging it into the differential equation: xy'(x) + y(x) = x(4x) + (3 + 2x^2) = 3x^2 + 2x^2 + 3 = 5x^2 + 3, which is equal to 3x^2 when x=0.
40. A possible solution is y(x) = sin(x), which can be checked by taking the derivative and plugging it into the differential equation: (y'(x))^2 + (y(x))^2 = cos^2(x) + sin^2(x) = 1.
41. A possible solution is y(x) = ex - 1, which can be checked by taking the derivative and plugging it into the differential equation: y'(x) + y(x) = e^x + e^x - 1 = 2e^x - 1.
42. A possible solution is y(x) = Asin(x) + Bcos(x), where A and B are constants. Taking the second derivative gives y''(x) = -Asin(x) - Bcos(x), which satisfies the differential equation.
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the bisection method is a root-finding tool based on the intermediate value theorem. the method is also called the binary search method. True or False
True .The bisection method is a root-finding tool based on the intermediate value theorem. the method is also called the binary search method.
The bisection technique is a root-finding approach that is used to identify the values of x for which f(x) = 0, or the roots, of a function. Using the intermediate value theorem, the approach selects the subinterval in which the function's root must reside after repeatedly bisecting an interval containing the root of the function. This approach can be repeated again until the algorithm converges to a result that accurately approximates the function's root.
The bisection method divides the interval repeatedly to approximatively determine the roots of the given equation.
The interval will be divided using this manner until an incredibly tiny interval is discovered. The bisection method is a technique for locating roots in mathematics.
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Jack has baseball practice every third day and swimming practice every second day. During the month of February, how many days will Jack have both practices? ** hint: MONTH of FEBRUARY
Answer:
Jack will have both practices for 4 days of the month.
Step-by-step explanation:
I used a calendar and marked each day he would have swimming practice in green and each day he would have baseball practice in magenta accordingly. The days that had both marks were the days he had both practices, which was 4 days in total.
LAED and LDEB are supplementary angles. (2x-17) + (x +32) = 180 3x + 15 180 3x = 165 x = 55 LDEB and ZAEC are vertical angles. mLAEC = m/DEB = (x + 32)° = (55 +32)° = 87° So, mLAEC = 87°. 1 Look at the figure in the Example. a. What is m/CEB? Show your work. (x +32) (2x-17) E D B
Considering the descriptions, angle CEB is found to be 93 degrees
How to find angle CEBAngle CEB is calculated by investigating the sketch attached
From the sketch, angle CEB and angle AEC are supplementary angles
and angle AEC is given to be 87 degrees.
Supplementary angles are angles that have their sum equal to 180 degrees.
hence In the problem, we have that
angle CEB + angle AEC = 180 degrees
where
angle AEC = 87.
substituting the value into the equation will result to
angle CEB + 87 = 180
angle CEB = 180 - 87
angle CEB = 93 degrees
We can therefore say that angle CEB = 93 degrees
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Six teammates are competing for first, second, and third place in a race.
How many possibilities are there for the top three positions?
20
30
120
240
There are 120 possibilities for the top three positions.
How to calculate the number of ways can be arranged?Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.
To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time.
Given:
Six teammates are competing for first, second, and third place in a race.
Total number of teammates= 6
Now, we need to find the number of possibilities for the top three positions
Possibility for 1st position = 6
Possibility for 2nd position = 5
Possibility for 3rd position = 4
So total number of possibilities
= 6x 5 x 3
= 120
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If JKLM is a rectangle, JN = 13x – 10, and NM = 5x + 54, find JL.
The length of JL is 9x + 22.
What are properties of rectangle?
A rectangle is a four-right-angle quadrilateral. It can also be classified as an equiangular quadrilateral because all of its angles are equal; or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.
In a rectangle, opposite sides are equal in length. So, JL is equal to KM.
We have the expressions for the lengths of JN and NM. Using this information and the fact that JKLM is a rectangle, we can set up an equation:
JN + NM = JL + KM
Substituting the given expressions, we get:
(13x - 10) + (5x + 54) = JL + KM
Simplifying the left side, we get:
18x + 44 = JL + KM
But we know that JL = KM, so we can replace both JL and KM with JL:
18x + 44 = 2JL
Now we can solve for JL:
2JL = 18x + 44
JL = (18x + 44)/2
JL = 9x + 22
Therefore, The length of JL is 9x + 22.
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Given: ⊙O with central angles ∠AOC ≅ ∠BOD Prove: AC ≅ BD Circle O is shown. Line segments O A, O C, O B, and O D are radii. Line segments connect points A and C and points B and D to form 2 triangles inside of the circle. Angles A O C and B O D are congruent. Complete the missing parts of the paragraph proof. Proof: We know that central angles are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because . Then by the congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because .
The missing statements and reasons in the two column proof are;
1. AOC and BOD.
2. All radii of a circle are congruent
3. SAS congruency theorem
4. CPCTC
How to complete two column proofs?A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons that we know those statements are true.
The two column proof of the angles is;
Statement 1: Central angles ∠AOC and ∠BOD are congruent
Reason 1: Given
Statement 2: The segments AO, CO, BO, and DO are congruent
Reason 2: All radii of a circle are congruent
Statement 3: Triangle AOC is congruent to triangle BOD
Reason 3: SAS congruency theorem
Statement 4: Chord AC is congruent to chord BD
Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
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Which process will create a figure that is congruent to the figure shown
The process that will create a congruent figure is a translation of four units up, followed by a rotation (option B).
What is the meaning of congruent?A figure is said to be congruent with another if they both have the same shape and the dimensions are the same. This means the figures are almost identical, although it is allowed that they are a reflection or that they are placed in the opposite direction.
Based on this, to create a congruent figure you need to translate the original figure and rotate it but not change its size (option B).
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write as an expression as a square of a monomial 0.16x^2y^2
The square of the monomial 0.16x^2y^2 can be expressed as:
(0.16x^2y^2)^2 = 0.16^2 * x^2 * y^2 * x^2 * y^2 = 0.0256x^4y^4
hope it helps
Instructions: Solve the following real world problem.
You and your sister are selling cookies to help raise money for
your field trip. You start out with $24 and sells each bag of
cookies, c, for $3. Your sister doesn't start out with any money but
sells her bags of cookies for $5 each. How many bags of cookies
must they sell in order for them to raise the same amount of
money?
Equating the mathematical expressions, we can determine that the siblings need to sell 12 bags of cookies for them to raise the same amount of money.
What are mathematical expressions?Mathematical expressions are the combination of variables, constants, numbers, and values using mathematical operands like addition and subtraction.
Mathematical expressions are also described as algebraic expressions.
The initial amount that you have = $24
Your selling price per bag of cookies, c, = $3
The total amount you will make is given by Expression 1: 24 + 3c
Your sister's selling price per bag of cookies, c, = $5
The total amount your sister will generate is given by Expression 2: 5c
To determine the number of bags of cookies you must sell to raise the same amount of money between the two siblings, we equate the two expressions as follows:
24 + 3c = 5c
24 = 2c
12 = c
Check:
5c = 60 (5 x 12)
24 _ 3c = 60 (24 + 36)
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Let X,Y be a random draw from the following box of tickets:0 1 1 1 1 1 2 2 21 3 3 0 1 2 0 3 39 TicketsFind P(Y > or = to 1|X = 2)
The probability of Y is greater than or equal to 1 given that X is equal to 2 i.e. P(Y ≥ 1 | X = 2) is 2/3.
To find P(Y ≥ 1 | X = 2), we will calculate the conditional probability of Y being greater than or equal to 1 given that X is equal to 2.
First, let us find the probability of X = 2, which is the number of 2 tickets in the box divided by the total number of tickets as follows -
P(X = 2) = 3/9
Next, let us find the probability of Y ≥ 1 and X = 2, which is the number of tickets with Y greater than or equal to 1 and X equal to 2 divided by the total number of tickets as follows -
P(Y ≥ 1, X = 2) = 2/9
Finally, using the formula for conditional probability to find P(Y ≥ 1 | X = 2) we get -
P(Y ≥ 1 | X = 2) = P(Y ≥ 1, X = 2) / P(X = 2)
P(Y ≥ 1 | X = 2) = (2/9) / (3/9)
P(Y ≥ 1 | X = 2) = 2/3
Therefore, the probability of Y is greater than or equal to 1 given that X is equal to 2 is 2/3.
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Simplify
p-8
7-29-9
The solution is
Write your answer using only positive exponents.
The simplified expression of p^8/p^7 is given as follows:
p.
How to simplify the expression?The expression for this problem is defined as follows:
p^8/p^7.
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the subtraction of the exponents is given as follows:
8 - 7.
Meaning that the simplified expression of p^8/p^7 is given as follows:
p.
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Let X be the minimum and Y the maximum of two random variables S and T with common continuous density f. Let Z denote the indicator function of the event (S
The distribution of the indicator function Z, which denotes the probability of S being greater than T, can be expressed in terms of the marginal density and the cumulative distribution function of the independent random variables S and T.
In probability theory, a random variable is a variable whose value depends on the outcome of a random event. The distribution of a random variable describes the probability of the variable taking on different values.
Now, let's consider the two independent random variables S and T with common continuous density f. We define X as the minimum of S and T, and Y as the maximum of S and T.
The indicator function Z is defined as the probability of the event {S > T}. In other words, Z takes on the value of 1 if S is greater than T, and 0 otherwise.
To find the distribution of Z, we need to consider the joint probability distribution of S and T. Since S and T are independent, their joint distribution is given by the product of their marginal distributions:
f(S,T) = f(S) * f(T)
Now, let's consider the event {S > T}. This event occurs when S is on the right side of the diagonal line T=S in the (S,T) plane. The probability of this event can be obtained by integrating the joint density over this region:
P(S > T) = ∫∫ {S > T} f(S,T) dS dT
We can simplify this integral by changing the order of integration:
P(S > T) = ∫∞-∞ ∫S∞ f(S,T) dT dS
= ∫∞-∞ f(S) ∫S∞ f(T) dT dS
= ∫∞-∞ f(S) (1 - F(S)) dS
where F(S) is the cumulative distribution function of the random variable T, which gives the probability that T is less than or equal to S.
Thus, we have obtained the distribution of Z as a function of the marginal density f and the cumulative distribution function F:
P(Z=1) = ∫∞-∞ f(S) (1 - F(S)) dS
P(Z=0) = ∫∞-∞ f(S) F(S) dS
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Complete Question:
Let X be the minimum and Y the maximum of two independent random variables S and T with common continuous density f, i.e X = min{S,T}, Y = max{S, T}, and let Z =>t denote the indicator function of the event {S > T}.
What is the distribution of Z?
Ava is a teacher and takes home 46 papers to grade over the weekend. She can grade
at a rate of 8 papers per hour. How many papers would Ava have remaining to grade
after working for 5 hours?
Which angles are adjacent to each other?
2
3
1
4
6 7
5 8
11
10
12
9
Answer:Angle 6 and Angle 5, Angle 3 and Angle 2
100% correct don't worry ;)
Step-by-step explanation:
Find the value of x
3x
7x+10
^imagine
The value of the x in the circle is 17.
'
How to find the centre angle in a circle?The angle measure of the central angle is congruent to the measure of the intercepted arc.
Therefore, let's find the value of x.
Hence,
180 - 3x(angle on a straight line) = 7x + 10
180 - 3x = 7x + 10
add 3x to both side of the equation
180 - 3x = 7x + 10
180 - 3x + 3x = 7x + 3x + 10
180 = 10x + 10
180 - 10 = 10x
170 = 10x
x = 170 / 10
x = 17
Therefore,
x = 17
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8 4 (x, y, z) = 3x²y-y³z², find grad & at the Paint (1, -2, -1).
find invertible matrices such that is invertible. choose so that (1) neither is a diagonal matrix and (2) are not scalar multiples of each other.
To choose that a matrix is neither a diagonal matrix and are not scalar multiples of each other. The matrices will be as:
A = [ 2 1 ; 1 2 ]
B = [ -2 1 ; 1 2 ]
The matrices shown above can be used to find invertible matrices. The sum of A and B is [0 2; 2 4], which has a non-zero determinant and is therefore invertible. This choice of A and B satisfies the given conditions because they have different eigenvalues, ensuring they are not scalar multiples of each other, and are also not diagonal matrices.
The key idea behind this choice was to use matrices with the same trace and determinant, which guarantees that their sum will have the same determinant as well. This method allows us to construct examples of invertible matrices that satisfy the given conditions.
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Write the percent as a fraction in simplest form and as a decimal. 2315%
Answer:
23:15 as a decimal and 23 3/20
Step-by-step explanation:
Just divide by 100 to get decimal. For the fraction divide by 100 and simplify
Consider the following equation.
7−6y=−38−5x
Find the x- and y-intercepts, if possible.
Use the sketch to find the range of values of x for which 2x² + 3x 2≤0
Using the sketch, the possible range of values of x for which 2x² + 3x - 2≤0 is [-2, 0.5].
What is the domain of a function?The domain of a function is a possible set of values of the independent variable. Based on the domain of a function, the codomain and range are determined.
Take the inequality as 2x²+3x-2≤0.
Solve the inequality.
2x²+3x-2≤0
(2x-1)(x+2)≤0
→ -2≤x≤0.5
The inequality is sketched in the graph and the area is also shaded for which 2x²+3x-2≤0. The range values of x mean the set of all points in the inequality -2≤x≤0.5, that is, [-2, 0.5].
Therefore, the obtained answer is [-2, 0.5].
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donuts at "hole-in-one" donut shop cost $1.20 each. how many donuts can jade purchase if she has $6.00 in her wallet?
Answer:
5
Step-by-step explanation:
6/1.2=5
Evaluate 2+8m if m = 4
Answer: 34
Step-by-step explanation:
The first step is if you multiply 8x4 you get 32
And then if you add 32+2 you get 34
According to PEMDAS
P=Parenthesis
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
Thus, you have to multiply, then add. If not you will get a way off answer. Also, because M comes before A.
Answer:
34
Step-by-step explanation:
To evaluate the expression 2 + 8m when m = 4, we can simply substitute 4 for m in the expression and simplify:
2 + 8m = 2 + 8 * 4
= 2 + 32
= 34
So, when m = 4, the value of the expression 2 + 8m is 34.
Line A passes through the points (10, 6) and (2, 15). Line 8 passes through the points (5,9)
and (14, -1).
Which statement is true?
Line A overlaps line B.
Line A intersects line B at exactly one point.
Line A does not intersect line B.
Submit
Work it out
Not feeling ready yet? These can help:
e-8/solve-a-system-of-equations-by-graph... system of equations? (91)
Solve a system of equations by graphing (60)
The true statement is that
B. Line A intersects line B at exactly one point.How to find the true statementThe equation of the two line is written by
The slope, m of the lines is calculated the formula
m = (y₀ - y₁) / (x₀ - x₁)
where
m = slope
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
The slope, m of the linear function is calculated using the points (10, 6) and (2, 15)
m = (y₀ - y₁) / (x₀ - x₁)
m = (6 - 15) / (10 - 2)
m = (-9) / (8)
m = -9/8
equation passing through point (2, 15)
(y - y₁) = m (x - x₁)
y - 15 = -9/8(x - 2)
y - 15 = -9x/8 + 9/4
y = -9x/8 + 9/4 + 15
y = -9/8 x + 17.25
For line B
The slope, m of the linear function is calculated using the points (5, 9)
and (14, -1)
m = (9 + 1) / (6 - 14)
m = (-10) / (8)
m = -5/4
equation passing through point (5, 9)
y - 9 = -5/4(x - 5)
y - 9 = -5x/4 + 25/4
y = -5x/4 + 25/4 + 9
y = -5/4 x + 15.25
plotting the lines shows the line intersects at a point
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6|x|≥72
If all real numbers are solutions, click on "All reals".
If there is no solution, click on "No solution".
IV
As a result, any real number higher than or equal to 12 or less than or equal to -12 is a solution to the inequality, implying that the answer is any real integer.
What is inequality?An inequality is a mathematical statement that compares two values and indicates whether they are equal, greater than, or less than each other. Inequalities are represented using symbols such as <, >, ≤, and ≥, which stand for "less than", "greater than", "less than or equal to", and "greater than or equal to", respectively. For example, the inequality 2 < 5 means that 2 is less than 5, and the inequality 3 ≥ 1 means that 3 is greater than or equal to 1. Inequalities are often used to describe the range of possible values for a variable, and to represent constraints in mathematical models and real-world problems. The solution of an inequality is the set of values that make the inequality true.
Here,
To solve this inequality, we first need to evaluate the expression inside the absolute value. If x is positive, then |x| = x, so the inequality becomes:
6x ≥ 72
Dividing both sides by 6, we get:
x ≥ 12
If x is negative, then |x| = -x, so the inequality becomes:
6(-x) ≥ 72
Expanding the absolute value, we get:
-6x ≥ 72
Dividing both sides by -6, we get:
x ≤ -12
Therefore, all real numbers greater than or equal to 12 or less than or equal to -12 are solutions of the inequality, meaning the solution is all real numbers.
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please help meeeeeeeeeeeeeee
Answer:10%
Step-by-step explanation:
For number one its a decrease equaling 10%
I will give brainliest and ratings if you get this correct
[tex]D(x)=\frac{f(x)}{g(x)}[/tex]
[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex]
What is quotient formula of differentiation?Quotient rule in calculus is method finding the derivative of the differentiable functions which are in the division form
There are different methods to prove the quotient rule formula, given as,
Using derivative and limit propertiesUsing implicit differentiationUsing chain ruleHere, we are using implicit differentiation method to solve this quotient rule,
Let us take a differentiable function ,
[tex]D(x)=\frac{f(x)}{g(x)}[/tex]--------(1)
So, [tex]f(x)={D(x)}*{g(x)}[/tex]
Using the product rule we get,
[tex]f'(x)= D'(x).g(x)+g'(x).D(x)[/tex] solving for [tex]D'(x)[/tex] we get,
[tex]\frac{f'(x)-g'(x).D(x)}{g(x)} = D'(x)[/tex]------(2)
substitute for D(x) sub (1) in (2)
[tex]D'(x) =\frac{f'(x)-g'(x).\frac{f(x)}{g(x)} }{g(x)}[/tex]
⇒[tex]D'(x) =\frac{f'(x)g(x)-g'(x){f(x)} }{(g(x))^{2} }[/tex]
Hence,[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex] proved.
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jacob plays basketball. he makes free throw shots 37% of the time. jacob must now attempt two free throws. the probability that jacob makes the second free throw given that he made the first is 0.52.
what is the probability that jacob makes both free throws?
The probability that Jacob makes both free throws is approximately 0.1924 or 19.24%.
The probability that Jacob makes the first free throw is 0.37, and the probability that he misses it is 0.63.
If he makes the first free throw, the probability that he makes the second free throw given that he made the first is 0.52, which means the probability that he misses the second free throw given that he made the first is 0.48.
So, the probability that Jacob makes both free throws is:
P(both made) = P(made first) [tex]\times[/tex] P(made second | made first)
= 0.37 [tex]\times[/tex] 0.52
= 0.1924
Therefore, the probability that Jacob makes both free throws is approximately 0.1924 or 19.24%.
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couple has 4 children. find each probability. 1) all boys. 2) all girls. 3) exactly 3 boys. 4) at least 1 boy. 5) at most 3 girls.
1) All boys: Probability = 1/16 , 2) All girls: Probability = 1/16, 3) Exactly 3 boys: Probability = 5/16, 4) At least 1 boy: Probability = 15/16, 5) At most 3 girls: Probability = 15/16.
1) All boys: There are 16 possible combinations of 4 children, with each gender combination having an equal probability of 1/16. Therefore, the probability of all boys is 1/16.
2) All girls: Similarly, the probability of all girls is also 1/16.
3) Exactly 3 boys: To find the probability of exactly 3 boys, we need to consider all the cases with 3 boys and 1 girl. There are 4 possible combinations of 3 boys and 1 girl, so the probability of exactly 3 boys is 4/16, or 5/16.
4) At least 1 boy: To find the probability of at least 1 boy, we need to consider all the cases with 1, 2, 3, or 4 boys. There are 15 possible combinations with at least 1 boy (1 boy, 2 boys, 3 boys, and 4 boys), so the probability of at least 1 boy is 15/16.
5) At most 3 girls: To find the probability of at most 3 girls, we need to consider all the cases with 0, 1, 2, or 3 girls. There are 15 possible combinations with at most 3 girls (0 girls, 1 girl, 2 girls, and 3 girls), so the probability of at most 3 girls is 15/16.
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Please help me solve this last question
The length of the line QR is 3 units. Options A
What are the properties of a pentagon?
The properties of a pentagon is expressed as;
The number of sides is 5The number of vertices is 5The sum of the Interior angle is 540°The sum of the exterior angle is 360°The Area is ½ × perimeter x apothem (a)Perimeter is expressed as 5 × side.Pentagons are convex, cyclic, equilateral, isogonal, isotoxalFrom the image shown, we have that;
The point from Q to R are (-8, -5)
To determine the distance, we have that;
-8-(-5)
-8 + 5
Add the values
-3
Hence, the number is 3
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The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude of an airplane and x represent the number of minutes the plane has been descending: y = -12x + 360 Part A. Create a table for the values when = 0, 5, 8, 10, 30. include worked out equation used to identify the values within the table Part B. identify the altitude after 5 minutes and after 30 minutes
Part A:
Here is the table for the values of y when x = 0, 5, 8, 10, and 30:
x y = -12x + 360
0 360
5 240
8 192
10 180
30 -360
Part B:
After 5 minutes, the altitude of the plane = 240 feet
After 30 minutes, the altitude of the plane = -360 feet.
How to make the tableTo find the value of y for each x, we substitute x into the equation y = -12x + 360:
For x = 0, y = -12(0) + 360 = 360
For x = 5, y = -12(5) + 360 = 240
For x = 8, y = -12(8) + 360 = 192
For x = 10, y = -12(10) + 360 = 180
For x = 30, y = -12(30) + 360 = -360
Part B:
After 5 minutes, the altitude of the plane can be found by substituting x = 5 into the equation
y = -12x + 360
y = -12(5) + 360 = 240 feet
After 30 minutes, the altitude of the plane can be found by substituting x = 30 into the equation
y = -12x + 360
y = -12(30) + 360 = -360 feet.
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