[tex]\bf \textit{zeros at } \begin{cases} x = -3\implies &x+3=0\\ x = -1\implies &x+1=0\\ x = 4\implies &x-4=0 \end{cases}\qquad \implies (x+3)(x+1)(x-4)=\stackrel{y}{0} \\\\\\ (x^2+4x+3)(x-4)=0\implies x^3~~\begin{matrix}+ 4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+3x~~\begin{matrix} -4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-16x-12=0 \\\\\\ x^3-13x-12=0[/tex]
we know that f(-2) = 24, namely when x = -2, y = 24, let's see if that's true
[tex]\bf x^3-13x-12=y\implies \stackrel{x = -2}{(-2)^3-13(-2)-12}=y \\\\\\ -8+26-22=y \implies 6=y[/tex]
darn!! no dice.... hmmmm wait a second.... 4 * 6 = 24, if we could just use a common factor of 4 on the function, that common factor times 6 will give us 24, let's check.
[tex]\bf 4(x^3-13x-12)=y\implies \stackrel{x = -2}{4[~~(-2)^3-13(-2)-12~~]}=y \\\\\\ 4[~~-8+26-22~~]=y\implies 4[6]=y\implies 24=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 4x^3-52x-48=y~\hfill[/tex]
The steps to convert 23/4 to a decimal are shown below
Answer:
23/4 = 5.75
Step-by-step explanation:
Artemis took out a 30-year loan from her bank for $190,000 at an APR of
9.6%, compounded monthly. If her bank charges a prepayment fee of 6
months' interest on 80% of the balance, what prepayment fee would Artemis
be charged for paying off her loan 16 years early?
O
A. $5822.42
O
B. $7390.60
O C. $6182.58
O D. $7382.56
The prepayment fee of $6182.58 would be charged to Artemis for paying off her loan 16 years early.
Answer: Option C
Step-by-step explanation:
30 year loan at 9.6% interest yields.
Number of month = 30 (12) = 360 months
Annual percent interest of [tex]\frac{9.6 \%}{12}[/tex] = monthly percent interest of .8%
The formula for the present value of an ordinary annuity, as opposed to an annuity due, is as follows
[tex]P M T= \frac{P \times r}{1-(1+r)^{n}}[/tex]
With r and n adjusted for periodicity, where
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the interest rate (also known as the discount rate)
n = the number of periods in which payments will be made
[tex]P M T= \frac{190000 \times 0.008}{1-(1+0.008)^{-360}} = \frac{1520}{1-(1.008)^{-360}} = \frac{1520}{1-0.0567}=\frac{1520}{0.9432}[/tex]
PMT = $1611.50 per month
Her loan 16 year early. It means
[tex]\text { Worth of loan after } 14 \text { year } = 190000 \times(1.008)^{168} = 3.814 \times 190000=\$ 724641.16[/tex]
Worth of monthly payments for 14 year
[tex] = \frac{1611.50 \times\left\{(1.008)^{168}-1\right)}{0.008} = \frac{1611.50 \times(3.81-1)}{0.008} = \frac{4.534 .6}{0.008} = \$ 566825.15[/tex]
Amount still owed after 14 year = difference of the above two
=$724641.16 - $566825.18
=$157816.01
Prepayment fee = [tex](0.8 \times 157816.02) \times\left((1.008)^{6}-1\right)[/tex]
= 126252.82 (1.049-1) = 126252.82 (1.0489-1) = $6182.63
Triangles a and b are right angled. show that the two shorter sides in triangle a have the same length as the two shorter sides in triangle B
explain why the two triangles are congruent
The two shorter sides in triangle A can be demonstrated to be the same length as the two shorter sides in triangle B by showing 'a' equals 'p' and 'b' equals 'q'. The two triangles would accordingly be congruent using the Side-Side-Side (SSS) Postulate.
Explanation:Triangles A and B are right-angled triangles, which means each has one angle that measures 90 degrees. You're asking to show that the two shorter sides in triangle A have the same length as the two shorter sides in triangle B. This would mean that these sides are congruent.
Firstly, let the two shorter sides in triangle A are 'a' and 'b', and in triangle B are 'p' and 'q'. If triangle A and B are congruent, this means 'a' should equal 'p' and 'b' should equal 'q'.
Finally, the two triangles would be congruent based on the Side-Side-Side (SSS) Postulate, which states that if the three sides of one triangle are congruent to the three sides of a second triangle, then the two triangles are congruent.
Learn more about Congruent Triangles here:https://brainly.com/question/22062407
#SPJ12
Final answer:
To show that two right angled triangles are congruent, you compare the two shorter sides. If they are equal in length, then the triangles are congruent by the Side-Angle-Side (SAS) postulate, as the right angle is also congruent.
Explanation:
To demonstrate that two right angled triangles, Triangle A and Triangle B, are congruent when the two shorter sides have the same length, first let's assume they are right angled at vertex C. If the sides AC and BC are congruent to the sides A'C' and B'C' respectively in triangles ABC and A'B'C', and since right angles are always congruent, then by the Side-Angle-Side (SAS) postulate of congruency, the two triangles are congruent.
According to the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (this is expressed as c² = a² + b²), we know that if the two legs a and b are congruent in two right triangles, then the hypotenuses will also have to be congruent.
If Triangle A and Triangle B have sides of equal lengths and right angle at C, the triangles are congruent by the SAS postulate, proving that both triangles are identical in shape and size.
Rob is saving to buy a new MP3 player for every $16 he earns babysitting he saved $5 on Saturday rob earned $80 babysitting how much money did he save
Answer:
He saved $25.
Step-by-step explanation:
If Rob saves $5 for every $16 he earns, he is saving the folowing franction of his income: [tex]\frac{5}{16} =0,3125=31,25\%[/tex]. Then if his income equals $16, he will save [tex]\$16\times{0,3125}=\$5[/tex].If his income is $80, he will save [tex]\$80\times{0,3125}=\$25[/tex]Another way to understand this problem would be to think that [tex]\$80=5\times{\$16}[/tex]. Then, receiving $80 is the same as receiving 5 times $16. If he saves $5 for every $16 he receives, he would save 5 times $5 = $25.how much of the circle is shaded 1/3+2/7
Final answer:
To find out how much of the circle is shaded by adding 1/3 and 2/7, we determine the least common denominator, convert each fraction, and then add the numerators. The shaded area of the circle is 13/21.
Explanation:
The student asked how much of the circle is shaded if you add the fractions 1/3 and 2/7. To find this, we need to calculate the sum of these two fractions. Since 1/3 is less than 1/2 and 2/7 is also less than 1/2, their combined value must be less than 1. To add fractions, you need a common denominator. The least common multiple of 3 and 7 is 21, so we will convert each fraction to have a denominator of 21:
1/3 becomes 7/21,2/7 becomes 6/21.Now, we add the numerators while keeping the denominator the same:
7/21 + 6/21 = 13/21.
This represents the shaded area of the circle in fraction form. Therefore, 13/21 of the circle is shaded.
4. A local bakery sold 60 loaves of bread in one day. If 65%
of these were sold in the afternoon, how many loaves were
sold in the afternoon?
Answer: 39 loaves were sold in the afternoon
Step-by-step explanation: So basically what you do here is divide 60 by 100. That makes 0.6, 0.6 equals 1%. (60 equals 100% and that why you divide by 100) Now, you multiply 0.6 by 65. the answer is 39. 65% of the bread is 39 loaves. So 39 loaves were sold in the afternoon.
Have an amazing day! :)
Answer:
60 x 65% = 39
So 39 were sold in the afternoon
Step-by-step explanation:
Delila has 4 coins. If Delila flips all the coins at once, how many outcomes are in the sample space?
Answer:0
Step-by-step explanation:
because once you flip all of them there all in the air and there flipped
Shauna is 10 inches shorter than Ryan. Together their heights total 140 inches. How tall is each person?
Answer:
Ryan: 75
Shauna: 65
Step-by-step explanation:
x = ryan's height
x - 10 = shauna's height
x + (x - 10) = 140
2x - 10 = 140
2x = 150
x = 75
Shauna is 65 inches tall and Ryan is 75 inches tall.
Let the height of:
Shauna be represented with s
Ryan be represented with r.
Sum of their heights : s + r = 140
The equation that represents Shauna's height : r - 10
Substitute for Shauna's height in the first equation:
r - 10 + r = 140
Solve for r
2r = 150
r = 75 inches
Substitute for r in the first equation
75 + s = 140
s = 140 - 75
s = 65 inches
To learn more, please check: brainly.com/question/23589883
John wrote that 5 + 5 = 10. Then wrote that 5 + 5 + n = 10 + n. Are the equations John wrote equivalent? Explain.
Equation 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent equation
Solution:Given that
John wrote that 5 + 5 = 10 ------ (1)
Then wrote that 5 + 5 + n = 10 + n ------ (2)
Need to determine are the equations written by John are equivalent.
First we need to keep in mind that whenever we apply same operation like addition, subtraction, multiplication and division on both the sides of equation that is left hand side and right hand side, we get the equivalent equation.
As in the second equation John added same value that is n on both sides of equation, we can say that equation with n is equivalent to the previous equation without n
Other way is let’s solve equation (2) and see if we can get equation (1)
5 + 5 + n = 10 + n
On subtracting both the sides with n we get,
5 + 5 + n – n = 10 + n – n
=> 5 + 5 = 10 which is same as equation (1)
Hence we can conclude that equation 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent equation.
Final answer:
The equations 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent because adding the same number 'n' to both sides of an equation does not change the original equality.
Explanation:
Yes, the equations that John wrote are equivalent. The first equation, 5 + 5 = 10, establishes that the sum of five plus five equals ten. The second equation, 5 + 5 + n = 10 + n, simply adds n to both sides of the first equation. This does not change the equality because, according to the properties of equality, if you add the same amount to both sides of an equal sign, the two sides remain equal. This can also be seen as an application of the commutative property of addition which states that numbers can be added in any order without changing the sum, as in A + B = B + A. Therefore, the original sum of 5 + 5 on the left side remains 10 when n is added to both sides, showing that 5 + 5 + n is indeed equal to 10 + n.
A tree shadow is 95 cm long. At the same time of the day Samantha stands next to the tree in measures her shadow to be 30 cm long. Samantha is 150 cm tall. What is the height of tree in centimeters
The height of tree is 475cm.
Step-by-step explanation:
Given,
Shadow of Samantha = 30cm
Actual height of Samantha = 150cm
Ratio of Shadow to actual height of Samantha = 30:150
Shadow of tree = 95cm
Actual height of tree = x
Ratio of shadow to actual height of tree = 95:x
Using proportion,
Ratio of Shadow to actual height of Samantha :: Ratio of shadow to actual height of tree
[tex]30:150::95:x\\[/tex]
Product of mean = Product of extreme
[tex]150*95=30*x\\14250=30x\\30x=14250\\[/tex]
Dividing both sides by 30;
[tex]\frac{30x}{30}={14250}{30}\\x=475\\[/tex]
The height of tree is 475cm.
Keywords: ratio, proportion
Learn more about ratios at:
brainly.com/question/3414323brainly.com/question/3451297#LearnwithBrainly
To find the height of the tree, set up a proportion: 150 cm / 30 cm = x / 95 cm. Solving for x, the height of the tree is 475 cm.
Explanation:To find the height of the tree, we can set up a proportion using the lengths of the shadows. Let x represent the height of the tree. The proportion would be:
150 cm / 30 cm = x / 95 cm
Cross-multiplying and solving for x, we get:
x = (150 cm times 95 cm) / 30 cm = 475 cm
Therefore, the height of the tree is 475 cm.
Learn more about Finding the height of a tree here:https://brainly.com/question/31066722
#SPJ11
Help I’m stuck in algebra 2
Answer:
1. 81
2. 43
3. 14
4. 32
5. 216
6. 6,7760.25
Hope it's helpful ;)
Please answer this correctly
Is the answer
5:15pm
6:03am
2:15pm
7:03am
Answer:
2:15 PM
Step-by-step explanation:
When the plane arrives in Seattle, the time in eastern time period would be 5:15 PM. From eastern to pacific, the time goes back 3 hours. 5:15 - 3 hours is 2:15. Since the time is still in the afternoon, it is still PM.
Answer:
2:15pm
Step-by-step explanation:
1) Take 1:09pm and add 4 hours and 6 mins to the time
2) 1 hour and 9 minutes + 4 hours and 6 minutes = 5:15pm (in eastern time)
3) Subtract 3 hours from 5 hours and 15 minutes. This equals 2:15pm
This would be the answer because of the time zone change.
Inverse for h(x)=2x-4/3
Answer:
[tex]y=\frac{x}{2}+\frac{2}{3}[/tex]
Step-by-step explanation:
The inverse function [tex]f^{-1}[/tex] of a function [tex]f[/tex] must meet that if [tex]f(a)=b[/tex], then [tex]f^{-1}(b)=a[/tex]. To find the inverse function one can clear out x from the initial equation, and once obtained an expression x=f(y), replace x by y, where y=f(x).In this case, [tex]y=h(x)=2x-\frac{4}{3}[/tex].To find the inverse function, we clear out x, as follows: [tex]y=2x-\frac{4}{3}[/tex]⇒[tex]y+\frac{4}{3} =2x[/tex]⇒[tex]x=\frac{y}{2}+\frac{2}{3}[/tex].Now that we have clear out the value of x as a function of y, we just have to replace x by y: [tex]y=\frac{x}{2}+\frac{2}{3}[/tex], which is the inverse function we have been looking for.To corroborate the function is correct, we can use the fact that [tex]f(a)=b[/tex], then [tex]f^{-1}(b)=a[/tex]. If we take x=1, in the first equation [tex]f(1)=2-\frac{4}{3} = \frac{2}{3}[/tex]. If now we replace b=2/3 in the inverse function we obtain [tex]f^{-1}(\frac{2}{3})=\frac{\frac{2}{3} }{2} +\frac{2}{3} =1[/tex]y=x+5 y=3x solving systems by substitution
Answer:
x=5/2, y=15/2. (5/2, 15/2).
Step-by-step explanation:
y=x+5
y=3x
---------
x+5=3x
5=3x-x
5=2x
x=5/2
y=3(5/2)=15/2
The manager of a movie theater found that Saturdays sales were $3675. He knew that a total of 650 tickets were sold on saturday. Adult tickets cost $7.50, and children tickets cost $4.50. How many of each kind of ticket were sold?
Answer:
Adults= 250 tickets
Children= 400 tickets
Step-by-step explanation:
Answer
250 adult tickets were sold and 400 children tickets were sold
Step by Step Explanation:
Given
Saturday Sales: $3675
Total tickets: 650
Cost of adult tickets = $7.50
Cost of children tickets = $4.50
Let A represent the adult tickets and C represent the children tickets,
if there's a total of 650 tickets, then
A + C = 650
Also,
if an adult ticket cost $7.50 and a child ticket cost $4.50 then
7.5A + 4.5C = 3675
From these, we have a simultaneous equation
A + C = 650 ------- (1)
7.5A + 4.5C = 3675 ----------(2)
Make A the subject of formula in (1)
A + C = 650 becomes
A = 650 - C
Substitute 650 - C for A in (2), we have
7.5(650 - C) + 4.5C = 3675
Open the bracket
4875 - 7.5C + 4.5C = 3675
4875 - 3C = 3675
Collect like terms
-3C = 3675 - 4875
-3C = -1200
Divide through by -3
[tex]\frac{-3C}{-3} = \frac{-1200}{-3}[/tex]
C = 400
Recall that
A = 650 - C
So, A = 650 - 400
A = 250
Hence, 250 adult tickets were sold and 400 children tickets were sold
Rewrite the expression using distributive property : 30x + 6
Answer:
This cannot be done, but it can be factored as: 6(5x + 1)
Step-by-step explanation:
This expression cannot be distributed any further.
The distributive property is used when multiplying polynomials (multiplying one or more terms by two or more terms). In which case, each term in multiplied by each of the terms in the bracket, for example: .
5(x + 2) = 5x + 10
We can factor this expression however to go the opposite direction:
30x + 6
Since 30 and 6 are both divisible by 6, we can factor it out of each term.
Divide 30x by 6 and divide 6 by 6.
6(5x + 1)
a flag pole is 30 feet tall a bug crawls 14 feet up the pole then it crawls another4 feet up the pole how much firther must the bug crawl to get to the top
Answer:
12 more feet
Step-by-step explanation:
Reason why is because if you add 14 and 4 you get 18 then you add 18 with 12 and you get 30. (hope this helps)
Question 15 (2.5 points)
Which ordered pair could replace the missing value and create a
function?
{(8,5), (2, 3), (1,6), (7,4), _?_}
O (3, 6)
(2,0)
(7,9)
(1,3)
(3, 6) can replace the missing value and create a function
Step-by-step explanation:
Given relation is:
{(8,5), (2, 3), (1,6), (7,4), _?_}
In order for a relation to be a function, the first condition is that there should be no repetition in domain of the function i.e. same input cannot map to multiple outputs.
In the form of ordered pairs, the first element of each ordered pair represents the elements of domain set
So,
From all the option given, only (3,6) is suitable to be put in the blank space as it will create no repetition in the domain while other ordered pairs will cause repetition.
Hence,
(3, 6) can replace the missing value and create a function
Keywords: Relations, functions
Learn more about functions at::
brainly.com/question/10940255brainly.com/question/10941043#LearnwithBrainly
If a binomial event has a probability of success of 0.8, how many successes
would you expect out of 6000 trials?
A.4800
B.3600
C.2400
D.1200
Answer:
A) Out of 6,000 trials, one can expect 4800 successes.
Step-by-step explanation:
Here, the total number of trials = 6,000
The probability of winning each trial = 0.8
Now, as we know in a BINOMIAL EVENT:
q = n x p
⇒ The number of success out of 6,000 trials
= 6,000 x (0.8) = 4800
Hence, out of 6,000 trials, one can expect 4800 successes.
Garth has a summer job and earns $9.32 per hour. One week, he works
16 3/4 hours. He deposits $150 in a bank and decides to use the rest of the money to buy raffle tickets. Each raffle ticket costs $0.50. How many raffle tickets can Garth buy?
Answer:
12.22
Step-by-step explanation:
I don't know if 12.22 is an answer for you but if it's not I would round to 12. What you do is multiply 9.32 by 16 3/4 which gives you 156.11. Take 156.11 and subtract 150 since Garth is putting that in the bank which leaves you with 6.11. Lastly you will divide 6.11 by .5 which will give you 12.22. So Garth can buy 12 raffle tickets.
Answer:
Garth can buy 12 raffle tickets.
Step-by-step explanation:
This is because when you multiply 9.32 with 16, it is 149.12.
Then, each quarter an hour, or 15 minutes, he earns 2.33 dollars.
Multiply by 3 and you get 6.99.
Add 6.99 with 149.12 and you get 156.11
Get rid of 150$ and you have 6.11
Each dollar you can get 2 raffle tickets.
So 6 dollars or 6, multiplied by 2 is 12.
Hope this helps you!
P.S If I may, can I please have brainliest, I would greatly appreciate it.
What symbol would you use to write an algebraic expression for "three divided by a number?"
A. +
B. −
C. ×
D. ÷
Answer:
D: is the answer
Step-by-step explanation:
A. + add
B. − subtract
C. × multiply
D. ÷ divide (can also be written with a "/") as in 3/2 vs 3÷ 2
The symbol used to write an algebraic expression for "three divided by a number" is the division symbol, ÷. We write this based off the description as '3 ÷ n' or '3/n' in fractional form.
Explanation:To write an algebraic expression for "three divided by a number," you would use the division symbol which is represented as ÷. So, if our unknown number is represented by the letter 'n', the algebraic expression would be written as "3 ÷ n" or "3/n" in fractional form.
In an algebraic expression, each symbol represents a specific mathematical action. The '+' symbol is for addition, '-' is for subtraction, 'x' is for multiplication, and '÷' is for division. In this case, since the problem specifies division, the correct symbol to use would be '÷'.
Learn more about Algebraic expressions here:https://brainly.com/question/34192827
#SPJ11
Number sentence same sum as 50+6=56
Answer:
The sum of 50 and 6 is the total of 56
Answer:
Fifty plus six equals fifty-six.
Helppp me pls I can’t figure this out
Answer:
A=F
Step-by-step explanation:
It's the congruency
Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, two sides of the mat are right triangles. If the height of the mat is 28 inches shorter than the length of the mat and the hypotenuse is 8 inches longer than the length of the mat, what is the length of the mat?
Answer:
The length of the mat is 60 in.
Step-by-step explanation:
Given :
Mats are inclined to form a triangle.
two sides of the mat are right triangles.
Hence the triangle formed is right angled triangle.
Let the length be x.
Now,The height of the mat is 28 inches shorter than the length of the mat.
Height of mat = x - 28
Also, the hypotenuse is 8 inches longer than the length of the mat.
Hypotenuse = x + 8
Hence by using Pythagoras theorem we get ,
[tex]Hypotenuse^2= lenght^2+height^2\\[/tex]
[tex]x^2+(x-28)^2=(x+8)^2\\x^2+x^2-56x+784=x^2+16x+64\\x^2-72x+720=0\\x^2-60x-12x+720 = 0\\x(x-60)-12(x-60)=0\\(x-12)(x-60) = 0\\x-12=0\\x=12\\x-60=0\\x=60[/tex]
Now we get 2 values of length 12 and 60.
But height is 28 in less than length.
And when we take length value as 12 the height will be negative hence it can't be true.
Hence the Length of mat = 60 in.
Determine whether the ratio are equivalent
18 trucks and 4 cars
21 trucks and 6 cars
These two ratios are not equivalent, as 18 trucks and 4 cars simplifies to a ratio of 9:2, while 21 trucks and 6cars simplifoes down to a ratio of 7:2. Obviously, there is a difference between 9:2 and 7:2, so they are not equivalent.
what is the measure of the vertex angle of an isosceles triangle i’d one of its base angles measures 42°
The measure of the vertex angle of the isosceles Δ is 96°
Step-by-step explanation:
In the isosceles triangle
Two sides are equal in lengthsThe angle between the two equal sides is called vertex angleThe other two angles are called base anglesThe base angles are equal in measure∵ The measure of one of the base angles of an isosceles Δ = 42°
- The base angles are equal in measure
∴ The measure of the other base angle = 42°
∵ The sum of the measures of the interior angles of any Δ = 180°
∴ 42 + 42 + measure of the vertex angle = 180
∴ 84 + measure of the vertex angle = 180
- Subtract 84 from both sides
∴ measure of the vertex angle = 96°
The measure of the vertex angle of the isosceles Δ is 96°
Learn more:
You can learn more about the triangles in brainly.com/question/6530759
#LearnwithBrainly
the probability against drawing the ace of diamonds from a standard deck of 52 cards?
89%?
93%?
98%?
96%?
Answer:
98%
Step-by-step explanation:
There is 1 ace of diamonds. So the probability of drawing any other card is 51/52 ≈ 98%.
Answer:
98 percent
Step-by-step explanation:
since drawing a ace of diamonds out of the deck is 1/52 not drawing it is a 51/52 which is about 98 percent
Two whole Numbers A and B satisfy the following conditions find A and B A-B=18
Answer:
The Whole numbers that satisfies the condition A - B = 18 is
A = 25
B= 7
Step-by-step explanation:
Whole number:
Whole numbers are positive numbers, including zero, without any decimal or fractional parts.
They are numbers that represent whole things without pieces.
The set of whole numbers is represented mathematically by the set: {0, 1, 2, 3, 4, 5...}
so there are many answers to this question which satisfies A- B = 18
Few are given below
A = 19 and B = 1 ∴ 19 - 1 = 18
A = 20 and B = 2 ∴ 20 - 2 = 18
A = 18 and B =0 ∴ 18 - 0 = 18
A = 39 and B = 21 ∴ 39 - 21 = 18
A = 25 and B= 7 ∴ 25 - 7 = 18
i.e A should be always greater than B to satisfy A- B = 18 condition.
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 9, 10, 11, 12, ...
Answer:
[tex]T_n= 9+(n-1)[/tex]
Step-by-step explanation:
The Given sequence is 9, 10, 11, 12
We need to find the expression to describe the sequence.
Let [tex]T_n[/tex] be the [tex]n^{th}[/tex] term of the sequence.
Let n represent the position of the term.
Let a be the first term in the sequence.
and d be the common difference between the sequence
Hence the expression to find the above sequence is given below;
[tex]T_n= a+(n-1)d[/tex]
when n=1 d= 1 a = 9
[tex]T_1 = 9+(1-1)1 = 9 + 0 = 9[/tex]
when n=2 d= 1 a = 9
[tex]T_2 = 9+(2-1)1 = 9 + 1 = 10[/tex]
when n=3 d= 1 a = 9
[tex]T_3 = 9+(3-1)1 = 9 + 2 = 11[/tex]
when n=3 d= 1 a = 9
[tex]T_4 = 9+(4-1)1 = 9 + 3 = 12[/tex]
Hence the expression is [tex]T_n= 9+(n-1)[/tex]
The expression to describe the sequence 9, 10, 11, 12, ... is 8 + n, with n representing the position of the term in the sequence.
The sequence given is 9, 10, 11, 12, ..., which is an arithmetic sequence where each term increases by 1 from the previous term. To write an expression that represents the nth term of this sequence using n to represent the position of the term (with n = 1 for the first term), we need to find a formula that calculates the value of each term based on its position.
The first term of the sequence is 9 when n = 1. The second term is 9 + 1, and the third term is 9 + 2, and so on. Generalizing this, the nth term can be written as the first term value (9) plus the number of terms after the first one, which is (n - 1), since for the first term, n - 1 equals 0. Therefore, the final expression is:
9 + (n - 1)
We can simplify this expression as: 8 + n
This expression will give us the value of each term in the sequence based on its position n.
Chris's new car gets 42 miles per gallon. What is the equation that represents y, the total miles driven on x gallons of gas? x = 42 + y y = 42 + x y = 42x x = 42y
Answer:
y = 42x
Step-by-step explanation:
Answer:
The answer is y=42x