General Arithmetic Terms
[tex] \displaystyle \large{a_n = a_1 + (n - 1)d}[/tex]
We want to find a8; we know:
a1 = 9d = 4Substitute in the formula.
[tex] \displaystyle \large{a_n = 9 + (n - 1)4} \\ \displaystyle \large{a_n = 9 + 4n - 4} \\ \displaystyle \large{a_n = 4n + 5}[/tex]
To find a8, substitute n = 8
[tex] \displaystyle \large{a_8= 4(8) + 5} \\ \displaystyle \large{a_8= 32 + 5} \\ \displaystyle \large{a_8= 37}[/tex]
Hence, the 8th term of sequence is 37
A bag of kibble and 4 cans of cat food cost $8.40. The kibble
costs $6. Use the equation 4x+6= 8.40 to find x, the cost of
one can of cat food.
A $0.65
B $0.60
C $0.30
D$0.70
Answer:
B: $0.60
Step-by-step explanation:
4x+6=8.40
4x=2.40
2.40 / 4 = .6
.6 = 0.60 or 60 cents
Answer:$0.60
Step-by-step explanation:
A bag a kibble is 6$
Subtract the cost for the kibble to the cost of all products.
$8.40
- $6.00
$2.40... is the cost for all 4 cans of cat food.
Then divide $2.40 by 4... That will be B) $0.60
If a = 3+2✓2 then find the value of a^2+1/a^2
Pls answer first to answer get the brainliest crown
Pls answer ASAP
Answer: 34
Step-by-step explanation:
[tex]a=3+2\sqrt{2} \\\\\dfrac{1}{a} =\dfrac{1}{3+2\sqrt{2}} =\dfrac{3-2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})} =\dfrac{3-2\sqrt{2}}{3^2-2^2*2} =3-2\sqrt{2}\\\\\\a+\dfrac{1}{a} =3+2\sqrt{2}+3-2\sqrt{2}=6\\\\(a+\dfrac{1}{a})^2=6^2=36=a^2+\dfrac{1}{a^2}+2\\\\\\a^2+\dfrac{1}{a^2}=36-2=34\\[/tex]
Help!
Find the value of x for which ABCD must be a parallelogram.
PLEASE HELP
X+11/8 = -3
Show your work in details if you can, I have a hard time understanding this.
Answer:
[tex] \frac{x + 11}{8} = - 3 \\ x + 11 = - 3 .8 \\ x = - 24 - 11 \\ x = - 33[/tex]
maaf jika salah
Answer:
x=-35
Step-by-step explanation:
x+11=-3*8
x+11=-24
x=-24-11
x=-35
decomponha o número 52.489
Answer:50.000+2000+400+80+9
Step-by-step explanation:
Answer:
50.000 + 2.000 + 400 + 80 + 9
please answer my question it's urgent
a = 16
Solution:common ratio = (-1/8)/(1/16)=-2a1 = 1/6
n=9
an = a1 (r n-1)a9 = a1
a9 = 1/16 (-2 9-1)
a9 = 1/16 (-28)
a9 = 1/16 (256)
a9 = 16
I hope this helps :)
What is the area of a circle with a diameter of 8 meters? Use 3.14 for pi, nothing else. Express in pi term and number term.
The two answers you are looking for are 16π m² and 50.24 m².
Solution:
Finding the area of the circle,
First, knowing what the area of a circle formula is:
A=πr²
Since knowing that the radius is half the length of the diameter,
If the diameter is 8, then the radius must be 4.
A=π(4)²
A=16π m²
Now, you have the first answer. If you want to express it differently,
Using 3.14 as pi,
So, therefore,
A=16(3.14)
A=50.24 m²
So, now, we can conclude that the two answers you are looking for for the area of this circle are 16π m² and/or 50.24 m².
Answer:
16pi and 50.24 m squared
Step-by-step explanation:
Convert a lot size of 2/9 acre to square feet given the conversion factor: 1 acre = 43,560 ft2
Answer:
9680 ft^2
Step-by-step explanation:
1 acre = 43,560 ft^2
(2/9) acre = (2/9)*43,560 ft^2
(2/9) acre = 9680 ft^2
help me do this plz
Answer:
X= –10
[tex] \frac{1}{2} x - 5 = - 10 \\ \frac{1}{2} x = - 10 + 5 \\ \frac{1}{2} x = - 5 \\ x = - 5 \times 2 \\ x = - 10[/tex]
I hope I helped you^_^
∠2= ∠5 , because they are
(I) Corresponding angles
(II) Alternate angles
(III) Co- interior angles
(IV) Linear pair
[tex] \sf \red {alternate \: angles}[/tex]
[tex] \huge \purple{ \underbrace{ \overbrace{Hope \: it \: helps}}}[/tex]
Select all that apply please!
Answer:
x= –4/5 , x= 2
Step-by-step explanation:
5x²-6x-14=-6
5x² –6x –14 +6=0
5x²–6x –8=0
(5x+4)(x-2)=0
x=–4/5
x=2
Hi! I'm happy to help!
To solve this, we simply have to replace x with the given values.
First, we have -14, let's apply that:
(5·(-14²))-(6·(-14))-14=
Now, let's solve (using the order of operations):
(5·(-14²))-(6·(-14))-14=
(5·196)-(6·(-14))-14=
980-(6·(-14))-14=
980-(-84)-14=
980+84-14=
1064-14=
1050=
1050≠-6
Option 1 is incorrect.
Next, let's substitute 14 for x:
(5·14²)-(6·14)-14=
Now, let's solve:
(5·14²)-(6·14)-14=
(5·196)-(6·14)-14=
980-(6·14)-14=
980-84-14=
896-14=
880=
880≠-6
Option 2 is incorrect.
Now, let's substitute -7 for x:
(5·(-7²))-(6·(-7))-14=
Now, let's solve:
(5·(-7²))-(6·(-7))-14=
(5·49)-(6·(-7))-14=
245-(6·(-7))-14=
245-(-42)-14=
245+42-14=
287-14=
273=
273≠-6
Option 3 is incorrect.
Now, let's substitute 7 for x:
(5·7²)-(6·7)-14=
Now, let's solve:
(5·49)-(6·7)-14=
245-(6·7)-14=
245-42-14=
203-14=
189=
189≠-6
Option 4 is incorrect.
Now, let's substitute -2 for x, and solve:
(5·(-2²))-(6·(-2))-14=
(5·4)-(6·(-2))-14=
20-(6·(-2))-14=
20-(-12)-14=
20+12-14=
32-14=
18=
18≠-6
Option 5 is incorrect.
Now, let's substitute 2 for x and solve:
(5·2²)-(6·2)-14=
(5·4)-(6·2)-14=
20-(6·2)-14=
20-12-14=
8-14=
-6=
-6=-6
Option 6 is correct.
Now, let's substitute -1 for x and solve:
(5·(-1²))-(6·(-1))-14=
(5·1)-(6·(-1))-14=
5-(6·(-1))-14=
5-(-6)-14=
5+6-14=
11-14=
-3=
-3≠-6
Option 7 is incorrect.
Now, let's substitute 1 for x and solve:
(5·1²)-(6·1)-14=
5-(6·1)-14=
5-6-14=
-1-14=
-15=
-15≠-6
Option 8 is incorrect.
Now, let's substitute -4/5 for x and solve:
(5·(-4/5²))-(6·(-4/5))-14=
(5·0.64)-(6·(-4/5))-14=
3.2-(6·(-4/5))-14=
3.2-(-4.8)-14=
3.2+4.8-14=
8-14=
-6=
-6=-6
Option 9 is correct.
Now let's substitute 4/5 for x and solve:
(5·4/5²)-(6·4/5)-14=
(5·0.64)-(6·4/5)-14=
3.2-(6·4/5)-14=
3.2-4.8-14=
-1.6-14
-15.6
-15.6≠-6
Option 10 is incorrect.
To summarize, you should pick option 6, and option 9.
I hope this was helpful, keep learning! :D
The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t^4 – 9t^3 + 24t^2 – 20t, where t is the number of months since the restaurant opened. How many months after the franchise opens will it begin to show a profit?
5 months
3 months
2 months
1 month
(2 months isn’t the answer btw)
The profitability of the restaurant is when the function gives a value greater than 0. The franchise does not make a profit after 5, 3, 2 or 1 month of opening.
Given that:
[tex]P(t) = t^4 - 9t^3 + 24t^2 - 20t[/tex]
To calculate the profit, we simply substitute the values of t in the above equation.
(a) 5 months
This means [tex]t =5[/tex]
So, we have:
[tex]P(5) = 5^4 - 9\times 5^3 + 24 \times 5^2 - 20 \times 5[/tex]
[tex]P(5) = 0[/tex]
(b) 3 months
This means that [tex]t=3[/tex]
So, we have:
[tex]P(3) = 3^4 - 9 \times 3^3 + 24 \times 3^2 - 20 \times 3[/tex]
[tex]P(3) = -6[/tex]
(c) 2 months
This means that [tex]t = 2[/tex]
So, we have:
[tex]P(2) = 2^4 - 9 \times 2^3 + 24 \times 2^2 - 20 \times 2[/tex]
[tex]P(2) = 0[/tex]
(d) 1 month
This means that [tex]t = 1[/tex]
So, we have:
[tex]P(1) = 1^4 - 9 \times 1^3 + 24 \times 1^2 - 20 \times 1[/tex]
[tex]P(1) = -4[/tex]
For the restaurant to make a profit, the equation has to give a positive value. Since none of the values of t gives a positive value for P(t).
Then, we can say the franchise does not make a profit after 5, 3, 2 or 1 month of opening.
Read more about functions at:
https://brainly.com/question/24314573
a square playground measures 2500 ft^2 what is the distance around the edge of the playground?
Answer:
20000
Step-by-step explanation:
A hot air balloon went from an elevation of 6,813 feet to an elevation of 3,168 feet in 54 minutes. What was its rate of descent?
Please Help!!! Will give brainliest
Answer:
e) and f) doesn't exist.
Step-by-step explanation:
Other you can see in picture.
In a group 40% like football ,70% like cricket and 30% like both games
Answer:
40%
Step-by-step explanation:
40+30+70=140
180-140= 40
Carlo got a pet snake as a birthday present. On his birthday, the baby snake was just 26 cm long. He has been measuring its length weekly and has noticed that it has been growing approximately 2 cm each week.
Write an equation to represent the length of the snake in weeks since Carlo's birthday use L for length and w for weeks.
The equation to represent the length of the snake in weeks:
[tex]L=2w+26[/tex]
Given:
A snake of lenght of 26 cemtimeters grows approximately 2 centimeter long each week.
To find:
The equation to represent the length of the snake in weeks
Solution:
Let the length of the snake in' w' weeks be 'L'.
The initial length of the snake on Carlo's birthday = 26 cm
At starting very first week the length of the snake was 26 cm. And after a week the lenght of the snake becomes 28 cm and then aftertwo weeks the length becomes 30 cm and so on.
Increase in length of the snake each week = 2 cm
And increase in length of the snake in 'w' weeks = (2×w) cm
And the length of the snake in terms weeks (w) will be given by equation:
[tex]L=2\times w+ 26\\L=2w+26[/tex]
The equation to represent the length of the snake in weeks:
[tex]L=2w+26[/tex]
Learn more about equation representation here:
https://brainly.com/question/11408596
Please help
Solve the inequality.
|14 – 5x] > 8
[?]
x <
or x >
A
Answer:
x< -4/1 or x > 6/5
If our answers are different, just say so :)
7 + 3x - 12x = 3x+ 1
Solve for x
Answer:
x = 1 /2
Step-by-step explanation:
isolate the variable by dividing each side by factors that dont contain the variable
decimal form will be: x = 0.5
hope that helps>3
Help please asap first answer get brainliest
Beging you please
Answers:
12. 2 3/5+1 4/6 = (2+1)+(3/5+4/6) = 3+19/15 = 64/15
13. 2/4*4/6 = 8/24 = 1/3
14. 3/4*3/6 = 9/24 = 3/8
15. 2/6*4/6 = 8/36 = 2/9
16. 2/4*1/6 = 2/24 = 1/12
17. 3/4/1/6 = 18/4 = 9/2
18. 3/4/2/4 = 12/8 = 3/2
19. 3/6/4/6 = 18/24 = 3/4
20. 5/7+2/7 = 7/7 = 1
21. 4/5+5/7 = 53/35
22. 3/5+5/5 = 8/5
23. 1/6-1/6 = 0
24. 3/7-2/3 = -5/21
25. 3/5-2/7 = 11/35
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) {-4, 8/3, -16/9, 32/27, -64/81, . . . } an =
Step-by-step explanation:
a1 = -4 = -4/1, a2 = 8/3
r = a2/a1 = (8/3) / (-4/1) = -2/3
the formula :
an = a1. r^(n-1)
so,
an = (-4). (-2/3)^(n-1)
Step-by-step explanation:
[tex]-4, \dfrac{8}{3}, -\dfrac{16}{9}, \dfrac{32}{27}, -\dfrac{64}{81},..., (-1)^n\dfrac{2^{n + 1}}{3^{n - 1}}, ...[/tex]
Determine the gradient of line AC
Answer:
This formula can also be written as \(y - {y}_{1} = m\left(x - {x}_{1}\right)\). The standard form of the straight line equation is \(y = mx + c\) where \(m\) is the gradient and \(c\) is the \(y\)-intercept.
3)There are 9 colorful socks in a drawer: 3 green, 2
purple,
2 Navy, 1 yellow, and 1 pink. What's the
probability of picking a green putting it on and
then choosing a purple?
Answer:
1/24 chance
Step-by-step explanation:
To begin you would need to find the probability of picking a green sock which would be 3/9; and you could simplify this to 1/3.
After that you need to find the probability of picking a purple sock out of the 8 left, which would provide you with 1/8. To find the probability of both you would multiply 1/8 by 1/3 to find the combined probability which would leave you with 1/24.
Given the triangle below, find the angle θ in radians. Round to four decimal places.
Answer:
θ = 0.9626
Step-by-step explanation:
Hi there!
We're given the hypotenuse and the leg adjacent to θ in this right triangle. To find θ, we can use the cosine ratio:
[tex]\displaystyle cos\theta=\frac{adjacent}{hypotenuse}[/tex]
Plug in the given information
[tex]\displaystyle cos\theta=\frac{4}{7}[/tex]
Use the inverse cosine ratio
[tex]\displaystyle \theta=cos^-^1(\frac{4}{7})[/tex]
Plug this into your calculator (and ensure you're solving for radians instead of degrees in the settings)
[tex]\displaystyle \theta=0.9626[/tex]
Therefore, θ = 0.9626 when rounded to four decimal places.
I hope this helps!
Answer:
theta = 0.9626 radians
Step-by-step explanation:
cos theta = a/h
cos theta = 4/7 = 0.5714
so, the angle theta = arc cos 0.5714 =
55.1520 °
in radians => 55.1520 × π / 180°
= 0.9626 radians
which point is a solution to the following system:
y=-3x-13
x+2y=4
You deposit $1500 in an account that earns a simple interest at an annual rate of 3%. How long must you leave the money in the account to earn $900 in interest?
9514 1404 393
Answer:
20 years
Step-by-step explanation:
The interest earned is found using the formula ...
I = Prt
where principal P is invested at rate r for t years. Solving for t, we find ...
t = I/(Pr) = $900/($1500×0.03) = 900/45
t = 20
You must leave the money in the account for 20 years to earn $900 in interest.
1. In order to complete the square on x^2 – 3x, you would…?
Answer:
(x-1.5)^2 -2.25
Step-by-step explanation:
divide 3 by 2 which is 1.5
(x-1.5)^2 -2.25
A trapezoid has one base measuring 12', and the other measuring 13'8". What is the area in square feet if the height of the trapezoid is 9'4"?
(Remember for trapezoids A= (b1 + b2)/2 x h
Answer:
Step-by-step explanation:
buzhou一=12212+13。8.12+13.8=25.8 25.8x9.4=?242.52242.522
The area of the trapezoid is given by A = 121.26 feet²
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the area of the trapezoid be represented as A
Now , the equation will be
Let the height of the trapezium be H = 9.4 feet
The shorter base of the trapezium a = 12 feet
The longer base of the trapezium b = 13.8 feet
Now , Area of Trapezoid = ( ( a + b ) h ) / 2
On simplifying the equation , we get
Area of Trapezium A = ( ( 13.8 + 12 ) 9.4 ) / 2
Area of Trapezium A = 121.26 feet²
Hence , the area of trapezium is 121.26 feet²
To learn more about area of trapezium click :
https://brainly.com/question/12221769
#SPJ2
WILL MARK AS BRAINLIEST
Answer:
... uhh I'm only in middle school but uhh I think 25??
Can someone help me thanks!
Answer:
If it goes to the left it becomes in the hundredths place meaning it decreases
Step-by-step explanation:
