How do you find the sum of a polynomial function?.
A polynomial function's sum is the result of adding all of its terms together. Simply add the coefficients of each phrase together, followed by the exponents of each term, to obtain the sum.
Take the polynomial function, for instance:
f(x) = 2x² + 4x + 3
The function's sum is 2x² + 4x + 3 = 9
Determine the highest exponent before attempting to get the sum of a polynomial with many terms. Next, sum up each term's coefficients that has that exponent. Add the exponents of each phrase to the total of the coefficients after the coefficients have been added. The polynomial function's sum is the final total.
Take the polynomial function, for instance:
f(x) = 2x³ + 4x² + 3x + 5
The function's sum is 2x³ + 4x² + 3x + 5 = 14
In conclusion, you put the coefficients of each term together to determine the total of a polynomial function, and then you add the exponents of each term to the sum of the coefficients. The polynomial function's sum is the final total.
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Solve for x. Round to the nearest tenth.
Using trigonometric function the value of x is 51.3°.
What is trigonometric function?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here Let us take the given right triangle as ABC.
∠A = x , ∠B = 90° and AB = 25 , AC= 40
Now using Cosine ratio then
Cos A = [tex]\frac{adjacent}{hypotenuse}[/tex]
=> cos x = [tex]\frac{25}{40}[/tex]
=> cos x = [tex]\frac{5}{8}[/tex]
=> x = [tex]cos^{-1}\frac{5}{8}[/tex]
=> x = 51.3°
Hence the value of x is 51.3°.
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please help i dont understand it
given: m∠p=72°, m∠s = 36° and rm=16. find op
Answer: 14.31
Step-by-step explanation:
Using Law of Sines, we know that
[tex]\frac{16}{sin(72)} =\frac{PR}{sin(90)}[/tex]
Thus, [tex]PR=16.8233955878[/tex]
Then, using [tex]\frac{\alpha }{sin(\alpha)} =2R[/tex],
we know that [tex]\frac{16.8233955878}{sin(s)} =\frac{16.8233955878}{sin(36)} =28.621670112 = 2R[/tex]
Therefore, [tex]R = 14.310735056[/tex]
For what value of x 2 * 5x ends in 5?.
For x^2 * 5x to end in 5, x must be an odd number.
The last digit of a number is determined by its units digit. For example, the last digit of 123 is 3, the last digit of 789 is 9, and so on.
When you multiply two numbers, the last digit of the product is determined by the last digit of each factor. For example, the last digit of 3 * 4 is 2, the last digit of 6 * 7 is 2, and so on.
In this case, x^2 * 5x is a product of two numbers, x^2 and 5x. To find the units digit of x^2, we can square the units digit of x. The units digit of 5x is the units digit of x.
So, since we want x^2 * 5x to end in 5 , the last digit of x^2 * 5x has to be 5. The last digit of x^2 is the square of the last digit of x, and the last digit of 5x is 5 if x is odd and 0 if x is even.
--The question is not readable, answering to the question below--
"For what value of (x^2) * 5x ends in 5?"
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how many significant figures does the number 48.050 have?
The number 48.050 has five significant figures.
What do you mean by an Significant figures?
Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.
Significant figures, also known as significant digits, are the digits in a measurement or a number that carry meaning contributing to its precision. In this case, the number 48.050 has four non-zero digits (4,8,0,5) and one zero (0) between two non-zero digits, which are significant figures.
The trailing zero after the decimal point does not affect the significant figures, it is simply a placeholder to indicate the number is less than one and has a magnitude of 0.050.
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What will make the expression x2 4x+ a perfect square trinomial?.
The number that should be added to the expression x²+4x to change it into a perfect square trinomial is 4.
The general form of a perfect square trinomial is (x + y)^2, where x and y are the roots of the trinomial. To check if a trinomial is a perfect square, we can try to factor it into the square of a binomial. We can also complete the square method, which involves adding and subtracting the square of half of the x-coefficient of the linear term and then grouping the resulting terms.
It is important to note that for a trinomial to be a perfect square trinomial, the constant term must be a square of an integer and the linear term must be an even number.
Perfect square trinomials are used in solving quadratic equations and understanding their solutions, they also have applications in algebra, geometry, and trigonometry. Factoring them is a fundamental skill in algebra and is used in solving different types of mathematical problems.
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Complete Question: –
What will make the expression x²+4x a perfect square trinomial?
How are input, rule, and output related to each other in an input/output table?
A table gives the pairs input-output generated by the function.
How are the input and output related?We can define a general function as:
y = f(x)
where x is the input that we "feed" into the function, and the function gives y as the outcome.
A pair of input, output is written in a general form as (x, y).
If you have enough of these points, you can make a table:
inputs outputs
x₁ y₁
x₂ y₂
x₃ y₃
...
That means that:
f(x₁) = y₁
f(x₂) = y₂
etc...
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Hello I hope you are having an amazing day, what is 9/10 divided by (-2/5)?
Answer choices:
Answer:
A) [tex]\displaystyle -2\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{9}{10}\div\biggr(-\frac{2}{5}\biggr)=\frac{9}{10}*\biggr(-\frac{5}{2}\biggr)=\frac{9(-5)}{10(2)}=\frac{-45}{20}=\frac{-9}{4}=-2\frac{1}{4}[/tex]
Jaon wam 3 and one-half mile, then another 3 1⁄4th mile in one day. On the ame day, Rachel wam 2 2⁄3rd mile, then another 4 and one-half mile. How many more mile did Rachel wim than Jaon?
Rachel that swam 2 2⁄3rd mile then another 4 and one-half mile, did 5/12 miles more than Jason
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
To solve this problem we must perform the corresponding algebraic operations with mixed fraction.
Data of the problem:
Jason 1 = 3 1/2 mileJason 2 = 3 1/4 mileRachel 1 = 2 2/3 mileRachel 2 = 4 1/2 mileA mixed operation is solved as follows:
For the denominator: the same denominator is placed.
For the numerator:
The value of the denominator is multiplied by the integer component.The result is added to the numerator of the fraction.We transform the mixed fractions into improper fractions and we have:
3 1/2
= [(3*2) + 1)] /2
= [6+ 1] /2
7/2
3 1/4
= [(3*4) + 1)] /4
= [12+ 1] /4
13/4
2 2/3
= [(3*2) + 2)] /3
= [6+ 2] /3
8/3
4 1/2
= [(4*2) + 1)] /2
= [8+ 1] /2
9/2
Calculating how many miles Rachel did more than Jason we have:
Rachel miles more = Rachel - Jason
Rachel miles more = (8/3 + 9/2) - (7/2 + 13/4)
Rachel miles more = [(16 + 27)/6] - [(14 + 13)/4]
Rachel miles more = 43/6 - 27/4
Rachel miles more = (172 - 162)/24
Rachel miles more = 10/24
Simplifying we have:
Rachel miles more = 5/12
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Write the expression using exponents G times G times G times G times G
Answer:
G to the power of 5
Step-by-step explanation:
Since there are 5 Gs, the exponent would be 5
Answer: [tex]G^5[/tex]
Step-by-step explanation: G times G times G times G times G is G times itself 5 times, which can be rewritten as [tex]G^5[/tex]
A and D are points on a polygon. A' and D' are the points under a
translation. Find D'.
A(-2,11)
A’(8,22)
D(-10,9)
Answer:
D' is (16,20)
Step-by-step explanation:
A translation is the movement of the graphed line, either vertically or horizontally. The two given points are A and D:
A (2,11)
D (10,9)
When the line is translated, point A becomes A' (8,22).
Pint A is moved to the right by 6, and up by 11. Lets do the same for point D to make it D'
D' = (10+6, 9+11)
D' = (16,20)
See the attached graph.
Pedro and Naomi begin to hike down a mountain at the same time.
They begin at different elevations and descend at different speeds.
The equation E = 4,200-800h gives Pedro's elevation in feet as a
function of time in hours. The table shows Naomi's elevation as she hikes
at a constant rate. Who has greater elevation at 1 hour?
Time (h)
0
1
3
5.5
Naomi’s elevation (ft)
3,500
2,900
1,700
200
a. Does Pedro or Naomi have greater elevation at h = 0? How much greater?
b. Who descends at a greater speed? How do you know?
c. The base of the mountain has 0 feet elevation. Does Pedro or Naomi reach the
base of the mountain first? Show your work.
Pedro is initially 700 ft higher than Naomi
Pedro decended at a greater speed and it was 800 ft/ hr
Pedro reaches the bootom faster than Naomi.
What is Equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.
Equations can be divided into three categories based on their degree. The three categories of mathematical equations are as follows:
Linear Equations
Quadratic Equations
Cubic Equations
Pedro's Elevation in feet equation
E = 4200 - 800h
So, initial elevation at h = 0 is
E = 4200 ft for Pedro
Now Naomi's Initial Elevation is 3500 ft.
So, Pedro is 4200 - 3500 = 700 ft higher than Naomi
at h = 1hr
Pedro's Elevation = 4200 - 800*1 = 3400 ft
and Naomi's Elevation = 2900 ft
Speed of desending of Pedro is = total distance/ total time
= (4200 - 3400)/1 = 800 ft/hr
Speed of desending of Naomi is = total distance/ total time
(3500 - 2900)/1 = 600 ft/hr
For Elevation = 0 for Pedro
0 = 4200 - 800h
h = 4200/800 = 5.25 hr
Naomi's elevation when time is 5.5 is 200 ft
So, Pedro reaches the bootom faster than Naomi.
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Given triangle QRS and triangle UVT, you know the following information: For Triangle QRS, QR = 4, RS = 15, and m<T = 36
Are the figures similar? If so, explain why and give a similarity ratio. If not, explain why not.
Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles.
why and give a similarity ratio. If not, explain why not.?Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles. Then, we have to check the proportionality of the sides. If these triangles are equal, then VT/QR=UT/RS. If we calculate it, 28/7=44/11=4. This last number is the similarity ratio and since we have proportionality, ΔQRS ~ ΔVTU.
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What is the multiplication rule example?.
The multiplication rule example is calculating the probability that both the balls drawn are red from an urn containing 30 red and 10 blue balls. Two balls are pulled from a bag one after the other without replacement.
As per the multiplication rule, the probability of events A and B happening is equal to the product of the probability of B happening and the conditional probability that event A happens if event B occurs.
If A and B are dependent events, then the probability of both events happening simultaneously is given by:
P(A ∩ B) = P(B).P(A|B)
If A and B are two independent events in an experiment, then the probability of both events happening simultaneously is given by:
P(A ∩ B) = P(A).P(B)
Let's solve our given example
Let A and B represent the events that the first and the second balls are pulled, which are red balls. Now, we have to calculate P(A∩B) or P(AB).
P(A) = P(red balls in first draw) = 30/40
Now, only 10 balls of blue colour and 29 balls of red colour are left in the bag. The probability of pulling a red ball in the second draw is also an example of conditional probability, where the drawing of the second ball depends on the drawing of the first ball.
Hence Conditional probability of B on A will be,
P(B|A) = 29/39
By multiplication rule of probability,
P(A∩B) = P(A) × P(B|A)
P(A ∩ B) = 30/40 × 29/39 = 29/52
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Find the future value of a ₱3,500 monthly payable at the end of every 6 month for 3 year if money i worth 12% compounded monthly
The future value is $7,689,500.
The worth of a current asset at a future date based on an estimated rate of growth is known as future value (FV). Investors and financial planners care about future value because it helps them predict how much an investment made now will be worth in the future.
The future value formula assumes a constant rate of growth and a single up-front payment left untouched for the duration of the investment.
Given that,
P = 3500
R = 12%
T = 3 years
Future value (FV) = [tex]I*(1+R)^{T}[/tex]
where:
I=Investment amount
R=Interest rate
T=Number of years
Substituting the values in the formula given:
FV = 3500*(1+12)³= 3500*2197 = 7689500
Thus, the future value is $7689500
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Quadrilateral MNOP ha vertice M(3,-1), N(8,-4),O(6. -6), and P(1,-7). What will be the coordinate of P’ after MNOP undergoe a 180 rotation
The new points after a rotation of 180 degrees are
M' = (-3,1)
N' = (-8,4)
0' = (-6,6)
P' = (-7,1)
Quadrilateral MNOP has vertices M(3,-1), N(8,-4),O(6. -6), and P(1,-7).
Given a point (x, y) and we rotate by 180 degrees, the new point will be (-x, -y).
Given the coordinate points M(3,-1), N(8,-4), O(6. -6), and P(1,-7), if these coordinates are rotated 180 degrees, the corresponding coordinate of the pre-image will be at M'(-3,1), N' (-8,4),0'(-6,6) and P'(-7,1).
So, the resulting coordinates will be M'(-3,1), N' (-8,4),0'(-6,6), and P'(-7,1).
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How do you find the value of x in similar triangles?.
If the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.
Triangles with the same form but different sizes are referred to as comparable triangles. Examples of related objects are all equilateral triangles and squares with any side length. In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.
If two triangles have an equal number of corresponding sides and corresponding angles, they can be compared. Similar figures are objects that have the same shape but various sizes, like two or more figures.
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PLS HELP ITS DUE TODAY!!
8. Explain how you can show that KL congruent to HJ.
Step-by-step explanation:
First you show that the triangles are congruent.
Then you show that the segments are congruent by CPCTC (Corresponding parts of congruent triangles are congruent.)
Given:
Segment KM is congruent to segment JM
<L is congruent to <H
We now have 1 pair of sides and 1 pair of angles that are congruent.
Angles KML and JMH are vertical angles, so they are congruent.
Now we have 2 pairs of congruent angles and 1 pair of not included congruent sides.
By AAS, triangle KML is congruent to triangle JMH.
By CPCTC, segment KL is congruent to segment HJ.
How is Class 9 slope calculated?.
The slope is calculated by the formula : [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope is defined as the ratio of the change in the y-axis to the change in the x-axis.
The slope of a straight line will define the line’s angle of steepness from the horizontal whether it rises or falls. When the line neither rises nor falls, then its slope will be zero.
This is the case with a horizontal line where it extends infinitely to its left or right but without any sign of rise or fall.
In a coordinate system, points are represented by a pair of coordinate values. This pair is having y to values x-value and y-value.
For example (x,y) will represent a point on the geometrical plane. Also, (0,0) will represent the origin point.
Let (x₁,y₁)and(x₂,y₂) x₁, x₂ are the coordinates of x-axis and y₁,y₂ are the coordinates of y-axis
The formula to calculate slope is defined as given below,
m= y2−y1x2−x1
Where m is the slope of the line.
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How many miles of track does the crew have left to lay after 19 days
The number of miles that the crew has left to lay after 19 days is given as follows:
54 miles.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing the rate of change.b is the intercept, representing the initial value.The parameters for this problem are given as follows:
m = -6, b = 168.
Hence the function is:
y = -6x + 168.
The amount of miles left after 19 days is obtained as follows:
y = -6(19) + 168
y = 54 miles.
Missing InformationThe text of the problem is:
"A railroad crew can lay 6 miles of track each day. They need to lay 168 miles of track. "
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pls help mathematics
There are 11 trees that are more than 6m tall but not more than 12m tall.
What is the Range?
In mathematics, a range is the set of all output values, or results, of a function. In statistics, a range is a measure of dispersion, which is used to describe the distribution of a set of data.
The table provided gives the frequency of trees at different height ranges. The range for the trees more than 6m tall but not more than 12m tall is 6<h<=9, and the frequency for this range is 11. This means that there are 11 trees in the park that are taller than 6 meters but not taller than 12 meters.
Hence, There are 11 trees that are more than 6m tall but not more than 12m tall.
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take a factor out of the square root sqrt(16y^7)
The simplified rational expression of the square root of 16y^7 is given as follows:
[tex]4y^3\sqrt{y}[/tex]
How to simplify the rational expression?The rational expression for this problem is defined as follows:
[tex]\sqrt{16y^7} = (16y^7)^\frac{1}{2}[/tex]
The power of power rule states that when an exponential expression is elevated to a power, the powers are multiplied.
4 is the square root of 16, hence:
16 = 4².
Meaning that the expression is of:
(4²y^7)^0.5.
Then the simplified radicals are of:
4^(2 x 0.5) = 4.y^(7 x 0.5) = y^(3.5) = [tex]y³\sqrt{y}[/tex]Then the simplified expression is given as follows:
[tex]4y^3\sqrt{y}[/tex]
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Select the statements that describe converting the polar coordinates (6, 120°) to rectangular coordinates, (x, y) using technology.
The point is in the second quadrant.
Start by adding 180° to θ.
Substitute 6 for r.
The value of x is 3.
The value of y is approximately 5.196.
(3 right answers)
Answer:
The point is in the second quadrant.
Substitute 6 for r.
The value of y is approximately 5.196.
Step-by-step explanation:
To convert polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
The point is in the second quadrant.
-This statement is true because the polar angle (120°) is in the range of 90° < θ < 180° which correspond to the second quadrant in the cartesian plane.
Start by adding 180° to θ.
This statement is False, because when converting from polar coordinates to rectangular coordinates we don't need to add 180° to the angle, we use the given angle as it is.
Substitute 6 for r.
This statement is true. In this case, the given polar coordinates are (6, 120°), so we substitute 6 for r in the formulas.
The value of x is 3.
This statement is False, to calculate x we use the formula x = r * cos(θ), so in this case x = 6 * cos(120°) = -3, which is not equal to 3.
The value of y is approximately 5.196.
This statement is true, to calculate y we use the formula y = r * sin(θ), so in this case y = 6 * sin(120°) = 6 * 0.866 = 5.196, which is approximately equal to 5.196
Answer:
The point is in the second quadrant
Step-by-step explanation:
Factor each expression. Show your complete solution.
27m^3-64
27m^3-64 = (3m)^3 - (4)^3
= (3m-4)((3m)^2 + (3m)(4) + (4)^2)
= (3m-4)(9m^2 + 12m + 16)
The factored form of 27m^3-64 is (3m-4)(9m^2 + 12m + 16)
Answer:
(3m−4)(9m2+12m+16)
Step-by-step explanation:
this is difference of cubes (3m)^3 - (4)^3
now, apply difference of cubes formula
a^3−b^3 = (a−b)(a2+ab+b2)
where a=3m and b=4
(3m−4) ( (3)^2×(m)^2 + 4×3m + (4)^2)
(simplify)
(3m−4)(9m2+12m+16)
PLEASE HELPP!!!!
ADD OR SUBTRACT THE FOLLOWING
1/(x-3)^2 - 2/x^2-9 + 1/(x+3)^2
Answer:36/(x+3)^2*(x-3)^2
Step-by-step explanation:
What is the nature of roots of quadratic equation x² 5x 14 0?.
The Nature Of roots of quadratic equation "x² + 5x - 14 = 0 " is , that the roots are real and distinct .
In order to find the Nature of Roots of a quadratic equation , we use the Discriminant ,
Suppose the quadratic is given by : ax² + bx + c = 0 ,
then it's discriminant(D) will be written as : D = b² - 4ac,
The equation is given as : x² + 5x - 14 = 0 ;
On comparing it with the general equation , we get that ;
⇒ a = 1 , b = 5 and c = -14 .
On substituting the values ,
we get , D = 5² - 4(1)(-14) ;
⇒ D = 25 + 56 ;
⇒ D = 81 .
We see that the Discriminant (D) is greater than 0 , the roots will be Real and Distinct .
Therefore , the nature of roots is that they are Real and Distinct .
The given question is incomplete , the complete question is
What is the nature of roots of quadratic equation x² + 5x - 14 = 0 ?
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Determine the intercepts of the line. Do not round your answers. -6x+3y=-7−6x+3y=−7
For the equation -6x + 3y = -7 , the x-intercept and y-intercept is obtained as (1.167,0) and (0,-2.333) respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The given equation is -
-6x + 3y = -7
To find the x-intercept, substitute the value of y = 0.
-6x + 3(0) = -7
-6x + 0 = -7
-6x = -7
Use the arithmetic operation of division -
x = -7/-6
x = 1.167
To find the y-intercept, substitute the value of x = 0.
-6(0) + 3y = -7
0 + 3y = -7
3y = -7
Use the arithmetic operation of division -
y = -7/3
y = -2.333
So, the x-intercept is obtained as x = 1.167 and y-intercept is obtained as y = -2.333.
A graph can also be plotted to find the intercepts.
Therefore, the intercepts are x = 1.167 and y = -2.333.
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The difference of two numbers is 2. The sum of the same two numbers is 6. Find the numbers. Write the numbers from least to greatest.
The numbers are 2 and 4.
Difference in math is the result of one of the important mathematical operations, which is obtained by subtracting two numbers. It tells us by how much a number differs from the other.
Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers.
Here we have,
The difference in two numbers is 2.
2 and 4 are two numbers away from each other.
The sum of the same two numbers is 6.
2+4=6
Hence, In least to greatest order they would be written 2, 4.
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f(x)=2x^2+7x. find f(-2)
Answer:
f(-2) = -6
Step-by-step explanation:
f(x)=2x^2+7x f(-2)
We put -2 in for x and solve
f(-2) = 2(-2)^2 + 7(-2)
f(-2) = 2(4) - 14
f(-2) = 8 - 14
f(-2) = -6
Pls help step by step pls
Answer:
a₄ = 67
Step-by-step explanation:
the recursive rule allows a term to be found from the previous term
using the recursive rule
[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] - 2 , then
a₁ = - 3
a₂ = - 3a₁ - 2 = - 3(- 3) - 2 = 9 - 2 = 7
a₃ = - 3a₂ - 2 = - 3(7) - 2 = - 21 - 2 = - 23
a₄ = - 3a₃ - 2 = - 3(- 23) - 2 = 69 - 2 = 67