Step-by-step explanation:
Point B(2, 8) reflect to x-axis
It means the x value won't change, the only thing that will change is the y value.
According to it, we can know that B' is (2, -8)
(2, -8) → (-8, 2+4) = (-8, 6) = B''
Final answer:
To obtain the coordinates of B'' after a reflection across the x-axis and a translation of (x,y)
ightarrow(y,x+4), point B(2,8) becomes B'(2,-8) after reflection and then B''(-8, 6) after translation.
Explanation:
The student is asking about the results of performing a geometric transformation on a point in the coordinate plane. Specifically, point B(2,8) is first reflected across the x-axis, and then is translated according to the rule (x,y)
ightarrow(y,x+4). To find the coordinates of B'', we follow these steps:
Reflect B across the x-axis: The x-coordinate remains the same, but the y-coordinate changes sign, resulting in B'(2,-8).
Apply the translation rule: We then take the coordinates of B' and apply the rule. The x-value of B' becomes the y-value of B'' and the y-value of B', decreased by 4, becomes the new x-value. Therefore, B'' = (-8, 2+4) = (-8, 6).
The final coordinates of B'' after the reflection and translation are (-8,6).
Which expression is equivalent to 4x -7-4y + 18-x-y
Answer:
3x-5y+11
Step-by-step explanation:
4x-7-4y+18-x-y
4x-x-4y-y-7+18
3x-5y+11
Priya Wants to buy three tickets for a concert she has earned 135 and each ticket cost 50 she borrows the rest of the money she needs from a bank and buys the tickets how can you represent them out of money that Priyahas after buying the tickets
Answer:
y=50x-135
Step-by-step explanation:
If each ticket costs 50 then for three tickets, Priya needs 3*50=150
However, since she earned 135, then she's less 150-135=15
The best way to present the money she borrowed is
y=50x-135
Where x is the number of tickets bought
Given the info, Priya needs to borrow $15 from the bank to afford all 3 tickets, so after purchasing, she's out of her own money and in debt to the bank.
Explanation:Essentially the question asks us how much money Priya has left after buying three concert tickets. Each ticket is priced at $50. She has earned $135 herself, so let's subtract the cost of the tickets from what she has earned.
We find that Priya needs to borrow $15 from the bank in order to purchase all three tickets (because $50 * 3 - $135 = $15).
So after buying the tickets, she would be out of her own money and $15 in debt to the bank.
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1/4d + 5 Please show work too
Answer:
5 1/4
Step-by-step explanation:
add 1/4 to 5 and you get 5 1/4
Show My Work:
1/4 + 5 =
5 1/4
Answer:
1/4(d+20)
Step-by-step explanation:
1/4d+5=1/4(d+20)
What is the domain and range of the function y = 2x2 - 4x - 10?
Answer:
Step-by-step explanation:
The domain of all polynomials is all real numbers. To find the range, let's solve that quadratic for its vertex. We will do this by completing the square. To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out. That gives us:
[tex]2(x^2-2x)=10[/tex]
The second rule is to take half the linear term, square it, and add it to both sides. Our linear term is 2 (from the -2x). Half of 2 is 1, and 1 squared is 1. So we add 1 into the parenthesis on the left. BUT we cannot ignore the 2 sitting out front of the parenthesis. It is a multiplier. That means that we didn't just add in a 1, we added in a 2 * 1 = 2. So we add 2 to the right as well, giving us now:
[tex]2(x^2-2x+1)=10+2[/tex]
The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form. Completing the square gives us a perfect square binomial on the left.
[tex]x^2-2x+1=(x-1)^2[/tex] and on the right we will just add 10 and 2:
[tex]2(x-1)^2=12[/tex]
Now we move the 12 back over by subtracting and set the quadratic back to equal y:
[tex]2(x-1)^2-12=y[/tex]
From this vertex form we can see that the vertex of the parabola sits at (1,-12). This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12. Therefore, the range is R={y|y ≥ -12}
What does [tex]4![/tex] equal?
Answer:
4! = 24
Step-by-step explanation:
The "!" in math is a factorial.
A product in a four factorial is the product of all the numbers from one to 4.
[tex]4!= 1*2*3*4=24[/tex]
What is the percent of change if 40 is increased to 50?
Answer:
25%.
Step-by-step explanation:
As a fraction it will be (50 - 40)/ 40 = 10/40 = 1/4.
% change 1/4 * 100 = 25%.
• #93 ) You are testing a circuit at the factory you work
for. The load draws 1,800 watts of power and has a
voltage of 10 volts. What is the current in amps?
• A. 8.2
•B. 1,790
• C. 1,810
• D. 180
•E. 18,000
Answer:
The current flowing through the circuit is 180 ampere .
Step-by-step explanation:
Given as :
The measurement of load = p = 1800 watt
The voltage of the circuit= v = 10 volts
Let the current = i amperes
Now, As we know
Power = The electric power is define as the voltage drop at the terminal of electric circuit and the product of electric current passing through the circuit
i.e power = voltage × current
where power in watt
voltage in volt
current in ampere
Or, p = v × i
Now, From the definition of power
i = [tex]\dfrac{p }{v}[/tex]
Or, i = [tex]\dfrac{1800}{10}[/tex]
∴ i = 180 ampere
So, The current flowing through the circuit = i = 180 ampere
Hence, The current flowing through the circuit is 180 ampere . Answer
PLEASE HELP ASAP
The function f(x) = 800(1.09)3x shows the growth due to interest that Jim earns on an investment. The steps to calculate an equivalent function are shown below:
[Step 1] f(x) = 800(1.09)3x
[Step 2] f(x) = 800(1.093)x
[Step 3] f(x) = 800(1.09 ⋅ 3)x
[Step 4] f(x) = 800(3.27)x
Which of the following is the first incorrect step?
A. Step 1
B. Step 2
C. Step 3
D. Step 4
Answer:
The in the calculation the step 3 is the first incorrect step.
Step-by-step explanation:
The function [tex]f(x) = 800(1.09)^{3x}[/tex] shows the growth due to interest that Jim earns on an investment.
To get an equivalent function we are given the following steps:
[Step 1] [tex]f(x) = 800(1.09)^{3x}[/tex]
[Step 2] [tex]f(x) = 800(1.09^{3}) ^{x}[/tex]
[Step 3] [tex]f(x) = 800(1.09 \times 3)^{x}[/tex]
[Step 4] [tex]f(x) = 800(3.27)^{x}[/tex]
The in the calculation the step 3 is the first incorrect step.
And this will be [tex]1.09^{3} = (1.09)^{3} = 1.295 \neq 3.27[/tex] (Answer)
Step 3
It is multiplying three instead of doing 9x9x9 she did 9x3
Is anyone good with this? I need help finding the answer.
Which shows the expression x^2-1/x^2-x in simplest form
Answer:
[tex]\large\boxed{\dfrac{x+1}{x}=1+\dfrac{1}{x}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2-1}{x^2-x}=(*)\\\\x^2-1=x^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\=(x-1)(x+1)\\\\x^2-x=(x)(x)-(x)(1)\qquad\text{use the distributive property}\\=x(x-1)\\\\(*)=\dfrac{(x-1)(x+1)}{x(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}[/tex]
The expression x^2-1 / x^2-x in its simplest form is 1 + 1/x.
How to simplify a given expression?The given expression can be simplified by eliminating the common terms from the denominator and numerator. By doing this, the expression can be simplified.
The given expression is:
[tex]\frac{x^{2}-1 }{x^{2}-x}[/tex]
It can be simplified as shown below:
[tex]\frac{x^{2}-1 }{x^{2}-x} = \frac{(x+1)(x-1 )}{x(x-1)}[/tex]
The numerator is split using the identity :
[tex]a^{2} -b^{2} =(a+b)(a-b)[/tex]
It can be further simplified as follows:
[tex]\frac{x^{2}-1 }{x^{2}-x} = \frac{(x+1)(x-1 )}{x(x-1)}\\= \frac{x+1}{x} \\=\frac{x}{x} +\frac{1}{x} \\= 1+\frac{1}{x}[/tex]
We have simplified the given expression into 1 + 1/x.
Thus, the expression x^2-1 / x^2-x in its simplest form is 1 + 1/x.
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table
Camillo is making gourmet peanut butter and jelly sandwiches for a food challenge. What is the unit price of a loaf of bread at each store?
Store A:
Store B:
Store C:
Store D:
Answer:
Store A:
$1.98 per loaf
Store B:
$1.95 per loaf
Store C:
$2.01 per loaf
Store D:
$2.02 per loaf
Step-by-step explanation:
5.94 divided by 3 = 1.98
7.80 divided by 4 = 1.95
10.05 divided by 5 = 2.01
12.12 divided by 6 = 2.02
Answer:
Store A:
$1.98 per loaf
Store B:
$1.95 per loaf
Store C:
$2.01 per loaf
Store D:
$2.02 per loaf
Step-by-step explanation:
:)
Kyle scored 4 points in his sixth basketball game of the season, bringing his average for the season down to 9 points a game. What is the minimum and maximum that his median points per game may be at this point in the season? PLEASE ANSWER!! 25 POINTS!!!
Answer:
The minimum is 9, meaning he continued to score an avg of 9 points per game. The maximum could be infinity, because not enough info is given.
Step-by-step explanation:
Original: 9
Possible: 9, infinite
A number increased by five is equivalent to twice the same number decreased by seven
Answer:
The unknown number is 12.
Step-by-step explanation:
Let the unknown number be 'x'
Given:
A number increased by 5 is equivalent to twice the same number decreased by 7.
So, 'x' increased by 5 means add 5 to 'x'. This gives [tex]x+5[/tex]
Now, [tex]x+5[/tex] is equivalent to twice of 'x' decreased by 7.
Twice of 'x' means 2 times of 'x' which is [tex]2x[/tex]
'2x' decreased by 7 means subtract 7 from '2x'. This gives,
[tex]2x-7[/tex]
Now, [tex]x+5[/tex] and [tex]2x-7[/tex] are equivalent meaning they are equal. So,
[tex]x+5=2x-7\\5+7=2x-x\\12=x\\x=12[/tex]
Therefore, the unknown number is 12.
Find the volume of a right circular cone that has a height of 10.4 m and a base with a
radius of 6.2 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
16327.1 m^3
Step-by-step explanation:
V=13pi*r^2*h
V=13pi*(6.2)^2*(10.4)
V=16327.1
The average of five weights is 13 grams. This set of of five weights is then increased by another weight of 7 grams. What is the average of the 6 weights?
Answer:
the answer is 12
Step-by-step explanation:
You just find the total weight and divide it by the number of weights
hope this helped ;3
Answer:
12 g
Step-by-step explanation:
Recall that
Average Weight = Sum of All weights ÷ Number of Weights
in the first case we are given that average of 5 weights is 13g
i.e Average weight (of 5 weights) = 13g and number of weights = 5
or, using the formula above,
13 = sum of 5 weights ÷ 5 (rearranging)
sum of 5 weights = 13 x 5 = 65 g
we are subsequently told that one more weight of 7 g is added,
hence, new number of weights = 6
and,
sum of 6 weights = sum of original 5 weights + sum of 6th weight
= 65 g + 7 g = 72 g
once again using the first formula
Average Weight (of 6 weights) = Sum of All weights ÷ Number of Weights
= 72 ÷ 6
= 12g
-5 * 1/-7 * 4/8
........................
Answer:
5/14
Step-by-step explanation:
-5*-1/7*4/8=5/7*4/8=20/56=5/14
Two trains leave Stations 396 miles apart at the same time and travel towards each other. One train travels at 95 mph while other travels 85 mph. How long will it take two trains to meet?
It will take 2.2 hours for the trains to meet.
Step-by-step explanation:
Given,
Distance between two trains = 396 miles
Speed of one train = 95 mph
Speed of other train = 85 mph
Combined speed of trains = 95+85 = 180 mph
Distance = Speed * Time
Time = [tex]\frac{Distance}{Speed}[/tex]
Time = [tex]\frac{396}{180}[/tex]
Time = 2.2 hours
It will take 2.2 hours for the trains to meet.
Keywords: speed, distance
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The two trains will take approximately 2.2 hours to meet.
Explanation:To find the time it takes for the two trains to meet, we can use the formula:
Time = Distance/Speed
In this case, the distance between the two trains is 396 miles. The combined speed of the two trains is 95 mph + 85 mph = 180 mph. Substituting these values into the formula, we get:
Time = 396/180 = 2.2 (rounded to the nearest tenth)
So it will take approximately "2.2 hours" for the two trains to meet.
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if the sides of a square are lengthened by 3 m, the area becomes 81 m2. Find the length of a side of the original square.
Answer:
The length of a side of the original square is 6 meters
Step-by-step explanation:
Let
x ----> the length side of the original square
The area of a square is equal to
[tex]A=b^2[/tex]
where
b is the length side of the square
In this problem
The new length side of the square is [tex]b=(x+3)\ m[/tex] and the area is [tex]A=81\ m^2[/tex]
so
[tex](x+3)^2=81[/tex]
solve for x
take square root both sides
[tex](x+3)=9[/tex]
[tex]x=9-3=6\ m[/tex]
Aliyah has 75 candy canes and 45 holiday cookies. She wants to divide them into gift bags, so that each bag has an equal number of candy canes and each bag has the same number of cookies as all the other bags. What is the greatest number of gift bags that Aliyah can make? How many candy canes will be in each bag? How many cookies will be in each bag?
Answer:
1) 15 gift bags2) 3 holiday cookiesExplanation:
1) Find the greatest number that divides exactly both 75 (candy canes) and 45 (holiday cookies).
That is, find the GCF (greatest common factor) of 75 and 45.
45 = 3² × 575 = 3 × 5²GCF = common factors each raised to its least exponent: 3×5 = 15Then, the greatest number of gift bags, so that each bag has an equal number of candy canes and same number of cookies that Aliyah can make is 15.
2) How many cookies will be in each bag?
To find the number of cookies that will be in each bag, you divide the number of holiday cookies by the number of gift bags:
45 holiday cookies / 15 gift bags = 3 holiday cookies per bag.Thus, each bag will contain 3 holiday cookies.
The calculator shows the result that Enrique got after evaluating the expression 56 + 7 × (34 – 17) – 16 . He checked his work by rounding all of the values to the nearest ten and comparing it to the calculator result. Which is true regarding his estimate and the accuracy of his calculator result?
The estimated result is 140, which suggests the calculator is correct.
The estimated result is 240, which suggests the calculator is incorrect.
The estimated result is 320, which suggests the calculator is incorrect.
The estimated result is 680, which suggests the calculator is incorrect.
Answer:
The estimated result is 680, which suggests the calculator is incorrect.
Final answer:
The estimated result when rounding to the nearest ten is 130, while the exact calculator result is 159. Therefore, the given options for estimation are all incorrect. The calculator is accurate, but the estimate is lower.
Explanation:
The calculator results for the expression 56 + 7 * (34 - 17) u2013 16 can be checked by estimation. To estimate, we round the numbers to the nearest ten and perform the operations. Here are the steps for estimation:
Round 56 to the nearest ten: 60
Round 34 to the nearest ten: 30
Round 17 to the nearest ten: 20
Perform the rounded operation: 60 + 7 * (30 - 20) u2013 10
The simplified expression would be 60 + 7 * 10 u2013 10
This simplifies further to 60 + 70 u2013 10, which is 130
The exact calculator result would be:
Calculate the parentheses first: 34 - 17 = 17
Multiply by 7: 7 * 17 = 119
Add 56: 56 + 119 = 175
Subtract 16: 175 u2013 16 = 159
The estimated result is 130, and the accurate calculator result is 159. Therefore, none of the options provided are correct as the estimate should be 130, suggesting that while the calculator is accurate, the given estimate options are incorrect.
the dollar bills below show the money that Sam has saved
Answer:
Can I please have more details on what your question is?
Step-by-step explanation:
Imagine you were shopping in the city of Los Angeles and purchased the following:
Shoes: $64.99
Shirt: $34.99
Bag: $45.50
What would the subtotal be BEFORE taxes? (Be sure to use $ sign and a decimal.)
Answer:
Subtotal = $145.48
Step-by-step explanation:
Products purchased:
Shoes, Shirt and bag.
Cost of shoes = $64.99
Cost of shirt = $34.99
Cost of bag = $45.50
The subtotal of the the products purchased before taxes can be calculated by finding the sum of all the costs.
[tex]Subtotal = \textrm{Cost of shoes + Cost of shirt + Cost of bag}[/tex]
[tex]Subtotal =\$64.99+\$34.99+\$45.50 [/tex]
[tex]Subtotal = \$145.48[/tex] (Answer)
14. a. Find the prime factorization of 180.
b. Explain why every natural number with a
zero in the ones place is a composite
number.
Answer:
a. 2² * 3² * 5; b. All numbers with a zero in the ones place is even.
Step-by-step explanation:
Final answer:
The prime factorization of 180 is 2 × 2 × 3 × 3 × 5. Every natural number with a zero in the ones place is a composite number because it can be divided evenly by 2 and at least one other number.
Explanation:
a. Prime factorization of 180:
To find the prime factorization of 180, we need to find the prime numbers that divide 180 evenly. Start by dividing 180 by the smallest prime number, 2. We get 180 ÷ 2 = 90. Then divide 90 by 2 again: 90 ÷ 2 = 45. Now, divide 45 by 3: 45 ÷ 3 = 15. Finally, divide 15 by 5: 15 ÷ 5 = 3. Therefore, the prime factorization of 180 is 2 × 2 × 3 × 3 × 5.
b. Explanation of why every natural number with a zero in the ones place is a composite number:
A composite number is a number that has more than two factors. Any natural number with a zero in the ones place can be divided evenly by 2 and at least one other number, making it a composite number. For example, 10 is divisible by 2 and 5, and 20 is divisible by 2 and 10. So, every natural number with a zero in the ones place is a composite number.
2 tanx/1 - tan2x + 1/ 2 cos2x -1= cosx + sinx/ cosx - sinx
[tex]\frac{2 \tan x}{1-\tan ^{2} x}+\frac{1}{2 \cos ^{2} x-1}=\frac{\cos x+\sin x}{\cos x-\sin x}[/tex] is proved
Solution:
Given that,
[tex]\frac{2 \tan x}{1-\tan ^{2} x}+\frac{1}{2 \cos ^{2} x-1}=\frac{\cos x+\sin x}{\cos x-\sin x}[/tex]
Let us first solve the L.H.S
[tex]\text { L. H.S }=\frac{2 \tan x}{1-\tan ^{2} x}+\frac{1}{2 \cos ^{2} x-1}[/tex] --- (1)
By trignometric identities,
[tex]\tan 2 x=\frac{2 \tan x}{1-\tan ^{2} x}[/tex]
[tex]\cos 2 x=2 \cos ^{2} x-1=\cos ^{2} x-\sin ^{2} x[/tex]
By using these in (1) we get,
[tex]\text { L. H.S }=\tan 2 x+\frac{1}{\cos 2 x}[/tex]
By definition of tan,
[tex]tan x = \frac{sinx}{cosx}[/tex]
Therefore,
[tex]L. H.S =\frac{\sin 2 x}{\cos 2 x}+\frac{1}{\cos 2 x}\\\\L. H . S=\frac{1+\sin 2 x}{\cos 2 x}$[/tex] --- (ii)
By trignometric identities,
[tex]\cos 2 x=2 \cos ^{2} x-1=\cos ^{2} x-\sin ^{2} x[/tex]
[tex]\begin{aligned}&\sin 2 x=2 \sin x \cos x\\\\&\cos ^{2} x+\sin ^{2} x=1\end{aligned}[/tex]
By using these in (ii)
[tex]\text { L. H.S }=\frac{\cos ^{2} x+\sin ^{2} x+2 \sin x \cos x}{\cos ^{2} x-\sin ^{2} x}[/tex] ----- (iii)
We know that,
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]
Similarly,
[tex](cosx + sinx)^2 = cos^2x + 2cosxsinx + sin^2x[/tex]
Also,
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
Similarly,
[tex]cos^2x - sin^2x = (cosx+sinx)(cosx-sinx)[/tex]
Therefore apply these in (iii)
[tex]\begin{aligned}&\text { L. } H . S=\frac{(\cos x+\sin x)^{2}}{\cos ^{2} x-\sin ^{2} x}\\\\&\text { L. H.S }=\frac{(\cos x+\sin x)(\cos x+\sin x)}{(\cos x+\sin x)(\cos x-\sin x)}\end{aligned}[/tex]
Cancel out (cos x + sin x) on numerator and denominator
[tex]\text { L. H.S }=\frac{\cos x+\sin x}{\cos x-\sin x}[/tex]
[tex]\frac{2 \tan x}{1-\tan ^{2} x}+\frac{1}{2 \cos ^{2} x-1}=\frac{\cos x+\sin x}{\cos x-\sin x}[/tex]
Thus L.H.S = R.H.S
Thus proved
an animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog. Nick noticed that the shelter spent $164.50 caring for cats and dogs on Wednesday. Nick found a record showing that there were a total of 34 cats and dogs on Wednesday. How many cats were at the shelter on Wednesday?
Answer:
There were 9 cats at the shelter on Wednesday.
Step-by-step explanation:
Given:
An animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog.
Nick noticed that the shelter spent $164.50 caring for cats and dogs on Wednesday.
Nick found a record showing that there were a total of 34 cats and dogs on Wednesday.
Now, to find the number of cats at the shelter on Wednesday.
Let the number of cats be [tex]x[/tex].
And let the number of dogs be [tex]y[/tex].
So, total number of dogs:
[tex]x+y=34.[/tex]
[tex]y=34-x.[/tex]......( 1 )
As given animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog.
Now, total money animal shelter spent on Wednesday:
[tex]3x+5.50y=164.50[/tex]
Putting the value of equation ( 1 ) in the place of [tex]y[/tex] :
⇒ [tex]3x+5.50(34-x)=164.50[/tex]
⇒ [tex]3x+187-5.50x=164.50[/tex]
⇒ [tex]187-2.50x=164.50[/tex]
Adding [tex]2.50x[/tex] on both the sides we get:
⇒ [tex]187=164.50+2.50x[/tex]
Subtracting 164.50 on both sides we get:
⇒ [tex]22.50=2.50x[/tex]
Dividing by 2.50 on both sides we get:
⇒ [tex]9=x[/tex]
⇒ [tex]x=9.[/tex]
The number of cats = 9.
Therefore, there were 9 cats at the shelter on Wednesday.
Sarah is buying a pair of jeans that regularly cost $60. They are on sale for 40% off. What is the sales price of the jeans?
how many seconds are in a day?
Answer:
86400 seconds
Step-by-step explanation:
1 year consists of 365 days. 1 day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. 1 day = (24 hours/day) × (60 minutes/hour)(60 seconds/minute) = 86400 seconds
HOPE THIS HELPED ;3
The melting point of the chemical bromine is -7.2 C. The boiling point of bromine is 58.8 C. Write and solve an equation to find how much greater the boiling point of bromine is than the melting point. Hurry answers NOW!!!
Answer:
58.8- -7.2= 51.6
Step-by-step explanation:
Because it asked for how much greater, I subtracted.
Answer:
7.2-58.8=51.6
Step-by-step explanation:
Use the equation below to answer the question.
y = 3x + 6
Which equivalent equation is correctly matched with a key feature of the graph of the function it represents?
Answer:
The signa notation to represent the first five ten f(x) is given by [tex] f(x)=\sum\limits^{5}_{n=1}a_n[/tex]
Step-by-step explanation:
Given sequence is -5, -9, 13...
Let f(x) be the given sequence and is denoted by
[tex]f(x)=\{-5,-9,-13,...\}[/tex]
Let the first term be [tex]a_1, 2^{\textrm{nd}}[/tex] term be [tex]a_3,...[/tex]
ie, [tex]a_1=-5,a_2=-9, a_3=-13,...[/tex]
To find the common difference d:
[tex]d=a_2-a_1[/tex]
[tex]=-9-(-5)[/tex]
[tex]=-9-(+5)[/tex]
[tex]d=-4[/tex]
[tex]d=a_3-a_2[/tex]
[tex]=-13-(-9)[/tex]
[tex]=-13+9[/tex]
[tex]d=-4[/tex]
Therefore the common difference d is -4 for given sequence f(x) with [tex]a_1=-5[/tex] and d=-4, the seqence f(x) is an arithmetic sequence
By defintion of arithmetic sequence
[tex]a_n=a+(n-1)d\hfill(1)[/tex]
Now to find [tex]a_4, a_5[/tex]:
put n=4 in equation (1)
[tex]a_4=a+(4-1)d[/tex]
[tex]a_4=-5+(3)(-4)[/tex] [since a=-5, d=-4]
[tex]=-5-12[/tex]
[tex]a_4=-17[/tex]
in equation (1)
[tex]a_5=a+(5-1)d[/tex]
[tex]a_5=-5+(4)(-4)[/tex] [since a=-5, d=-4]
[tex]=-5-16[/tex]
[tex]a_5=-21[/tex]
Therefore [tex]a_4=-17[/tex] and [tex]a_5=-21[/tex]
Therefore [tex]f(x)=\{-5,-9,-13,-17,-21,...\}[/tex]
Now to represent the sum of the first five terms of f(x) using sigma notation as below
[tex]f(x)=\sum_{n=1}^5 a_n[/tex]
where [tex]\sum_{n=1}^5 a_n=a_1+a_2+a_3+a_4+a_5[/tex]
[tex]-5-9-13-17-21[/tex]
[tex]\sum_{n=1}^5 a_n=-65[/tex]
6.3 - 9.5 wroten as a fraction in simplest form
Answer:
-3 2/4
Step-by-step explanation:
I calculated so I am correct and it's not -32
its 3 2/4