Answers
Given:
[tex]f(x)=\begin{cases}4x+7ifx<0{} \\ 6x+4ifx\ge0{}\end{cases}[/tex]Required:
To find the value of f(-8), f(0), f(4), and f(-100)+f(100).
Explanation:
f(-8) :
Clearly -8<0,
So
[tex]\begin{gathered} f(x)=4x+7 \\ f(-8)=4(-8)+7 \\ =-32+7 \\ =-25 \end{gathered}[/tex]f(0) :
Clearly 0=0,
[tex]\begin{gathered} f(x)=6x+4 \\ =6(0)+4 \\ =4 \end{gathered}[/tex]f(4) :
Clearly 4>0,
[tex]\begin{gathered} f(x)=6x+4 \\ f(4)=6(4)+4 \\ =24+4 \\ =28 \end{gathered}[/tex]f(-100)+f(100) :
-100<0
[tex]\begin{gathered} f(x)=4x+7 \\ f(-100)=4(-100)+7 \\ =-400+7 \\ =-393 \end{gathered}[/tex]100>0
[tex]\begin{gathered} f(x)=6x+4 \\ f(100)=6(100)+4 \\ =600+4 \\ =604 \end{gathered}[/tex][tex]\begin{gathered} f(-100)+f(100)=-393+604 \\ \\ =211 \end{gathered}[/tex]Final Answer:
[tex]\begin{gathered} f(-8)=-25 \\ \\ f(0)=4 \\ \\ f(4)=28 \\ \\ f(-100)+f(100)=211 \end{gathered}[/tex]Related Questions
The given point (-3,-4) is on the terminal side of an angle in standard position. How do you determine the exact value of the six trig functions of the angle?
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In this problem -3 will be the adyacent side, -4 will be the opposite side and wwe can calculate the hypotenuse so:
[tex]\begin{gathered} h^{}=\sqrt[]{(-3)^2+(-4)^2} \\ h=\sqrt[]{9+16} \\ h=\sqrt[]{25} \\ h=5 \end{gathered}[/tex]So the trigonometric function will be:
[tex]\begin{gathered} \sin (\theta)=-\frac{4}{5} \\ \cos (\theta)=-\frac{3}{5} \\ \tan (\theta)=\frac{4}{3} \\ \csc (\theta)=-\frac{5}{4} \\ \sec (\theta)=-\frac{5}{3} \\ \cot (\theta)=\frac{3}{4} \end{gathered}[/tex]geometric series in context
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Solution
For this case we can model the problem with a geometric series given by:
[tex]a_n=600(1+0.2)^{n-1}[/tex]And we can find the value for n=23 and we got:
[tex]a_{23}=600(1.2)^{23-1}=33123.69[/tex]And rounded to the neares whole number we got 33124
and using the sum formula we got:
[tex]S_{23}=\frac{600(1.2^{23}-1)}{1.2-1}=195742[/tex]According to the Florida Agency for Workforce, the monthly average number of unemployment claims in a certain county is given by () = 22.16^2 − 238.5 + 2005, where t is the number of years after 1990. a) During what years did the number of claims decrease? b) Find the relative extrema and interpret it.
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SOLUTION
(a) Now from the question, we want to find during what years the number of claims decrease. Let us make the graph of the function to help us answer this
[tex]N(t)=22.16^2-238.5t+2005[/tex]We have
From the graph above, we can see that the function decreased at between x = 0 to x = 5.381
Hence the number of claims decreased between 1990 to 1995, that is 1990, 1991, 1992, 1993, 1994 and 1995
Note that 1990 was taken as zero
(b) The relative extrema from the graph is at 5.381, which represents 1995.
Hence the interpretation is that it is at 1995 that the minimum number of claims is approximately 1363.
Note that 1363 is approximately the y-value 1363.278
I need some help with this (and no this is not a test)
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You have the following expression:
[tex]a_n=3+2(a_{n-1})^{2}[/tex]consider a1 = 6.
In order to determine the value of a2, consider that if an = a2, then an-1 = a1. Replace these values into the previous sequence formula:
[tex]\begin{gathered} a_2=3+2(a_1)^{2}= \\ 3+2\mleft(6\mright)^2= \\ 3+2(36)= \\ 3+72= \\ 75 \end{gathered}[/tex]Hence, a2 is equal to 75
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Z2
Find the midpoint m of z₁ = (9+7i) and Z₂ = (-7+7₂).
Express your answer in rectangular form.
m=
Re
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The midpoint m of z₁ = (9+7i) and Z₂ = (-7+7i) is 1 + 7i .
Given complex numbers:
[tex]z_{1}[/tex] = (9 + 7i) and [tex]z_{2}[/tex] = (-7 + 7i)
compare these numbers with a1+ib1 and a2+ib2, we get
a1 = 9, a2 = -7 , b1 = 7 and b2 = 7.
Mid point of complex numbers = a1 + a2 /2 + (b1 + b2 /2)i
= (9 + (-7)/2 + (7 + 7 /2)i
= 2/2 + 14/2 i
Mid point m = 1 + 7i
Therefore the midpoint m of z₁ = (9+7i) and Z₂ = (-7+7i) is 1 + 7i
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I inserted a picture of the question can you please hurry
Answers
Given:
[tex](-2,-5)\text{ and (}1,4)\text{ are given points.}[/tex][tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope}=\frac{4+5}{1+2} \\ \text{Slope}=\frac{9}{3} \\ \text{Slope}=3 \end{gathered}[/tex]Lne segment AC and BD are parallel, what are the new endpoints of the line segments AC and BD if the parallel lines are reflected across the y-axis?
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Given a point P = (x, y) a reflection P' alongside the y axis of that point follows the rule:
[tex]P=(x,y)\Rightarrow P^{\prime}=(-x,y)[/tex]We need to multiply the x coordinates of the points by (-1)
The cordinates of the points in the problem are:
A = (2, 5)
B = (2, 4)
C = (-5, 1)
D = (-5, 0)
Then the endpoints of the reflection over the y axis are:
A' = (-2, 5)
B' = (-2, 4)
C' = (5, 1)
D' = (5, 0)
Which is the second option.
Identify the constant of variation. 8y-7x=0
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A direct variation between two variables "x" and "y" is given by the following formula:
y = kx
We can rewrite the given expression 8y-7x=0 to get an equation of the form y = kx like this:
8y - 7x = 0
8y - 7x + 7x = 0 + 7x
8y = 7x
8y/8 = 7x/8
y = 7/8x
The number that is being multiplied by x should be the constant of variation k, then in this case, the constant of variation equals 7/8
(I don't know if there are tutors here right now at this time but it's worth a try.) Please help me I really really don't understand this, it's going to take me a while to understand this. X(
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by the distributive law x(y+z)=zy+xz, we have
[tex]\begin{gathered} 3b+3(5)=4(2b)-4(5) \\ 3b+15=8b-20 \end{gathered}[/tex]Then we use the properties of inequalities, we can switch both sides, and if we add or multiply something on both sides the equality remains
[tex]\begin{gathered} 3b+15=8b-20 \\ \end{gathered}[/tex]we want the variables and the numbers without variables to be in different side, so, first we add 20 to both sides, note that the -20 will be cancelled
[tex]\begin{gathered} 3b+15+20\text{ = 8b-20+20} \\ 3b+15+20=8b \end{gathered}[/tex]we want to left all the numbers with variable on the right side so we substract 3b (add -3b) to both sides. Same as before, the 3b will be cancellated (we can change the order in the sum)
[tex]\begin{gathered} -3b+3b+15+20=-3b+8b \\ 15+20=8b-3b \end{gathered}[/tex]of course, you're welcome
I was asking if you have understood my explanation so far
tell me
it doesn't matter the order, in fact, when you get used to the method you can work with both at the same time
any other question?
yes, you could substrac 3b first
For example
[tex]\begin{gathered} 2+3x=6-x \\ 2+3x+x=6-x+x \\ 2+3x+x=6 \\ -2+2+3x+x=-2+6 \\ 3x+x=6-2 \\ 4x=4 \\ \end{gathered}[/tex]sadly I will need to leave since my shift is over, but if you ask another question one of my partners will help you
Have a nice evening!!!!
then we add like terms and switch both sides
[tex]5b=35[/tex]And then we multiply by 1/5 both sides
[tex]\begin{gathered} 5\frac{1}{5}b=\frac{35}{5} \\ b=\frac{35}{5} \\ b=7 \end{gathered}[/tex]im taking geometry A and i have a hard time with the keeping the properties straight in mathematical reasoning. the question im struggling with at the moment is in the picture here:thank you for your time
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The given proposition is
[tex]m\angle UJN=m\angle EJN\rightarrow m\angle UJN+m\angle YJN=m\angle EJN+m\angle YJN[/tex]As you can observe, it was added angle YJN to the equation on both sides. The property that allows us to do that it's call addition property of equalities.
Therefore, the right answer is "addition property".Gloria's teacher asks her to draw a triangle with a 90° angle and a 42° angle.How many unique triangles can Gloria draw that meet her teacher's requirements?AOne unique triangle can be drawn because the third angle must measure 48º.BNo unique triangle can be drawn because the teacher only gave the measures of two angles.СInfinitely many unique triangles can be drawn because the side lengths of the triangles can be different sizes.DThere is not enough information to determine how many unique triangles can be drawn.
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SOLUTION
Sum of angles in a triangle must be equal to 180°
So, since one of the angle measures 90° and the other is 42°, then
90 + 42 + y = 180°, where y is the third angle
So, 132 + y = 180
y = 180 - 132 = 48°.
Therefore, one unique triangle can be drawn because the third angle must measure 48º.
Option A is the correct answer.
write each of the following numbers as a power of the number 2
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Answer
The power on 2 is either -3.5 in decimal form or (-7/2) in fraction form.
Explanation
To do this, we have to first note that
[tex]\begin{gathered} \sqrt[]{2}=2^{\frac{1}{2}} \\ \text{And} \\ 16=2^4 \end{gathered}[/tex]So, we can then simplify the given expression
[tex]\begin{gathered} \frac{\sqrt[]{2}}{16}=\frac{2^{\frac{1}{2}}}{2^4}=2^{\frac{1}{2}-4} \\ =2^{0.5-4} \\ =2^{-3.5} \\ OR \\ =2^{\frac{-7}{2}} \end{gathered}[/tex]Hope this Helps!!!
I NEED HELP
5C/2 = 20
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you would have to do this backwards
20 times 2 would remove the /2
5c=40
40 divided by 5
is
8
C=8
A. Marvin worked 4 hours a day plus an additional 5-hour day for a total of 29 hours.B. Marvin worked 9 hours a day for a total of 29 hoursC. Marvin worked 4 hours one day plus an additional 5 hours for a total of 29 hours.D. Marvin worked 4 days plus 5 hours for a total of 29 hours.
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Lisa's rectangular living room is 15 feet wide. If the length is 7 feet less than twice the width, what is the area of her living room?
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345ft²
1) Since we have the following data then we can write it down:
width: 15 ft
length: 2w-7
2) And we can write out the following equation regarding that the area of a rectangle is given by:
[tex]S=l\cdot w[/tex]We can plug into that the given data:
[tex]\begin{gathered} S=15(2(15)-7)) \\ S=15(30-7) \\ S=15\cdot23 \\ S=345 \end{gathered}[/tex]Notice we have used the FOIL acronym. And the PEMDAS order of operations prioritizing the inner parentheses.
3) So we can state that the area of her living room is 345ft²
Professor Ahmad Shaoki please help me! The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square. Help me! From: Jessie
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The length of the original square must be equal to 3 inches.
Length of the Original SquareTo find the length of the original square, we have to first assume the unknown length is equal x and then use formula of area of a square to determine it's length.
Since the new length is stretched by 5in, the new length would be.
[tex]l = (x + 5)in[/tex]
The area of a square is given as
[tex]A = l^2[/tex]
But the area is equal 64 squared inches; let's use substitute the value of l into the equation above.
[tex]A = l^2\\l = x + 5\\A = 64\\64 = (x+5)^2\\64 = x^2 + 10x + 25\\x^2 + 10x - 39 = 0\\[/tex]
Solving the quadratic equation above;
[tex]x^2 + 10x - 39 = 0\\x = 3 or x = -13[/tex]
Taking the positive root only, x = 3.
The side length of the original square is equal to 3 inches.
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Rami practices his saxophone for 5/6 hour on 4 days each week.
How many hours does Rami practice his saxophone each week?
[] 2/[] Hr
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Answer:
you take 5/6 and multiply it by 4/1.
which gives you 20/6
then reduce it by dividing the top number by the bottom number
which gives you 3 with a remainder of 2
you then place the remainder over the
This tells you he practicedfor 3 2/6
Step-by-step explanation:
Which of the following shows the expansion of sum from n equals 0 to 4 of 2 minus 5 times n ?
(−18) + (−13) + (−8) + (−3) + 0
(−3) + (−8) + (−13) + (−18) + (−23)
2 + (−3) + (−8) + (−13) + (−18)
2 + 7 + 12 + 17 + 22
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The option that indicates the required sum when n equals 0 to 4 of 2 minus 5 times n, is 2 + (−3) + (−8) + (−13) + (−18) (Option C)
What is the Sum of sequences?The sum of the terms of a sequence is called a series.
From the given sum of a sequence, we are to find the sum of the given sequence from n = 0 to n = 4
When n = 0
a(0) = 2 - 5(0)
a(0) = 2 - 0
a(0) = 2
When n = 1
a(1) = 2 - 5(1)
a(1) = 2 -5
a(1) = -3
When n = 2
a(2) = 2 - 5(2)
a(2) = 2 - 10
a(2) = -8
When n = 3
a(3) = 2 - 5(3)
a(3) = 2 - 15
a(3) = -13
When n = 4
a(4) = 2 - 5(4)
a(4) = 2 - 20
a(4) = -18
Hence the required sum is 2 + (−3) + (−8) + (−13) + (−18)
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The required sum is 2 + (−3) + (−8) + (−13) + (−18) when n equals 0 to 4 of 2 minus 5 times n, which is the correct answer that would be an option (C).
The given expression is (2 - 5n)
We to determine the sum of the given sequence from n = 0 to n = 4
Let the required sum is T₀ + T₁ + T₂ + T₃ + T₄
Substitute the value of n = 0 in the expression (2 - 5n) to get T₀
⇒ T₀ = 2 - 5(0) = 2 - 0 = 2
Substitute the value of n = 1 in the expression (2 - 5n) to get T₁
⇒ T₁ = 2 - 5(1) = 2 -5 = -3
Substitute the value of n = 2 in the expression (2 - 5n) to get T₂
⇒ T₂ = 2 - 5(2) = 2 - 10 = -8
Substitute the value of n = 3 in the expression (2 - 5n) to get T₃
⇒ T₃ = 2 - 5(3) = 2 - 15 = -13
Substitute the value of n = 4 in the expression (2 - 5n) to get T₄
⇒ T₄ = 2 - 5(4) = 2 - 20 = -18
Therefore, the required sum is 2 + (−3) + (−8) + (−13) + (−18)
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Factor the following expression using the GCF.5dr - 40rr(5 dr - 40)5 r( d - 8)r(5 d - 40)5( dr - 8 r)
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The greatest common factor (GCF) is: 5r
You multiply 5r by d to get the first term and multiply 5r by -8 to get the second term, then the factors are:
[tex]5r(d-8)[/tex]Answer: 5r(d-8)help ! it may or may not have multiple answers
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From the given problem, there are 3 computer labs and each lab has "s" computer stations.
So the total number of computers is :
[tex]3\times s=3s[/tex]Mr. Baxter is ordering a new keyboard and a mouse for each computer, since the cost of a keyboard is $13.50 and the cost of a mouse is $6.50.
Each computer has 1 keyboard and 1 mouse, so the total cost needed for 1 computer is :
[tex]\$13.50+\$6.50[/tex]Since you now have the cost for 1 computer, multiply this to the total number of computers which is 3s to get the total cost needed by Mr. Brax :
[tex]3s\times(13.50+6.50)[/tex]Using distributive property :
[tex]a(b+c)=(ab+ac)[/tex]Distribute s inside the parenthesis :
[tex]3(13.50s+6.50s)[/tex]One answer is 1st Option 3(13.50s + 6.50s)
Simplifying the expression further :
[tex]\begin{gathered} 3(13.50s+6.50s) \\ =3(20.00s) \end{gathered}[/tex]Another answer is 4th Option 3(20.00s)
write the equation for a quadratic function in vertex form that opebs down shifts 8 units to the left and 4 units down .
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STEP - BY STEP EXPLANATION
What to find?
Equation for a quadratic equation.
Given:
Shifts 8 unit to the left.
4 units down
Step 1
Note the following :
• The parent function of a quadratic equation in general form is given by;
[tex]y=x^2[/tex]• If f(x) shifts q-units left, the f(x) becomes, f(x+q)
,• If f(x) shift m-units down, then the new function is, f(x) -m
Step 2
Apply the rules to the parent function.
8 units to the left implies q=8
4 units down implies m= 4
[tex]y=(x+8)^2-4[/tex]ANSWER
y= (x+8)²- 4
A box has 14 candies in it: 3 are taffy, 7 are butterscotch, and 4 are caramel. Juan wants to select two candies to eat for dessert. The first candy will be selectedat random, and then the second candy will be selected at random from the remaining candies. What is the probability that the two candies selected are taffy?Do not round your intermediate computations. Round your final answer to three decimal places.
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Okay, here we have this:
Considering the provided information we are going to calculate what is the probability that the two candies selected are taffy. So, for this, first we are going to calculate the probability that the first is taffy, and then the probability that the second is taffy. Finally we will multiply these two probabilities to find the total probability.
Remember that the simple probability of an event is equal to favorable events, over possible events.
First is taffy:
At the beginning there are 14 sweets, and 3 are taffy, so there are 3 favorable events and 14 possible, then:
First is taffy=3/14
Second is taffy:
Now, in the bag there are 13 sweets left, and of those 2 are taffy, so now there are 2 favorable events out of 13 possible:
Second is taffy=2/13
The first and second are taffy:
First is taffy*Second is taffy=3/14*2/13
First is taffy*Second is taffy=3/91
First is taffy*Second is taffy=0.033
First is taffy*Second is taffy=3.3%
Finally we obtain that the probability that the two candies selected are taffy is aproximately 0.033 or 3.3%.
I will provide another picture with the questions to this problemBefore beginning: please note that this is lengthy, pre calculus practice problem
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I need to find the radius and the diameter but I don't understand.
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ANSWER
Radius = 3 yd
Diameter = 6 yd
EXPLANATION
We are given the circle in the figure.
The radius of a circle is defined as the distance between the centre of a circle and its circumference.
Therefore, from the circle given, the radius is 3 yards
The diameter of a circle is defined as the total distance (through the centre) from one end of a circle to another.
It is twice the radius. Therefore, the diameter of the given circle is:
D = 3 * 2
D = 6 yards
The diameter is 6 yards.
The slope of the line containing the points (-2, 3) and (-3, 1) is
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Hey :)
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Apply the little slope equation. By doing that successfully, we should get our correct slope.
[tex]\large\boldsymbol{\frac{y2-y1}{x2-x1}}[/tex]
[tex]\large\boldsymbol{\frac{1-3}{-3-(-2)}}[/tex]
[tex]\large\boldsymbol{\frac{-2}{-3+2}}[/tex]
[tex]\large\boldsymbol{\frac{-2}{-1}}[/tex]
[tex]\large\boldsymbol{-2}}[/tex]
So, the calculations showed that the slope is -2. I hope i could provide a good explanation and a correct answer to you. Thank you for taking the time to read my answer.
here for further service,
silennia[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
I need help doing this it’s the homework but I need to understand it for the test
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By similar triangle, we have:
[tex]\begin{gathered} Let\text{ the unknown measurement be x} \\ \text{Thus, we have:} \\ \frac{14}{x}=\frac{8}{15} \\ \text{cross}-\text{multiply} \\ 8x=210 \\ x=\frac{210}{8} \\ x=26.25\text{ f}eet \end{gathered}[/tex]Hence, the unknown measurement of the plan is 26.25 feet
Let f(x)=3x-2. What is f^-1 (x) ?
Answers
Given the function:
f(x) = 3x - 2
Let's find the inverse of the function f⁻¹(x).
To find the inverse of the function, apply the following steps:
• Step 1.
Rewrite y for f(x)
[tex]y=3x-2[/tex]• Step 2.
Interchange the x and y variables:
[tex]x=3y-2[/tex]• Step 3.
Solve for y.
Add 2 to both sides:
[tex]\begin{gathered} x+2=3y-2+2 \\ \\ x+2=3y \end{gathered}[/tex]• Step 4.
Divide all terms by 3:
[tex]undefined[/tex]
what is an identityA) an identity is a false equation relating to a mathematical expression to a real numberB) an identity is a true equation relating to a mathematical expression to a real numberC) an identity is a true equation relating one mathematical expression to another expressionD) an identity is a false equation relating to one mathematical expression to another expression
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The right answer is C
Find the sum of the first nine terms of the geometric series 1 – 3 + 9 - 27+....
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Hello there. To solve this question, we'll have to remember some properties about geometric series.
Given that we want the sum of
[tex]1-3+9-27...[/tex]First, we find the general term of this series:
Notice they are all powers of 3, namely
[tex]\begin{gathered} 1=3^0 \\ 3=3^1 \\ 9=3^2 \\ 27=3^3 \\ \vdots \end{gathered}[/tex]But this is an alternating series, hence the general term is given by:
[tex]a_n=\left(-3\right)^{n-1}[/tex]Since we just want the sum of the first 9 terms of this geometric series, we apply the formula:
[tex]S_n=\frac{a_1\cdot\left(1-q^n\right?}{1-q}[/tex]Where q is the ratio between two consecutive terms of the series.
We find q as follows:
[tex]q=\frac{a_2}{a_1}=\frac{\left(-3\right)^{2-1}}{\left(-3\right)^{1-1}}=\frac{-3}{1}=-3[/tex]Then we plug n = 9 in the formula, such that:
[tex]S_9=\frac{1\cdot\left(1-\left(-3\right)^9\right?}{1-\left(-3\right)}=\frac{1-\left(-19683\right)}{1+3}=\frac{19684}{4}[/tex]Simplify the fraction by a factor of 4
[tex]S_9=4921[/tex]This is the sum of the nine first terms of this geometric series and it is the answer contained in the second option.
Given a function described by the table below, what is y when x is 5?XY264859612
Answers
Given a function described by the table
We will find the value of (y) when x = 5
As shown in the table
When x = 5, y = 9
so, the answer will be y = 9