Answer:
Arithmetic Sequence
[tex]T_n = 240-60n[/tex] ---- Explicit
[tex]T_n = T_{n-1} - 60[/tex] --- Recursive
Geometric Sequence
[tex]T_n = 270* (\frac{2}{3})^n[/tex] ---- Explicit
[tex]T_n = T_{n-1} * \frac{2}{3}[/tex] ---- Recursive
Step-by-step explanation:
Given
[tex]180, 120,....[/tex]
(a) Assume it is an arithmetic sequence
The explicit formula is calculated using:
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]a = 180[/tex]
[tex]d = 120 - 180[/tex]
[tex]d = -60[/tex]
So, we have:
[tex]T_n = 180 + (n - 1)*-60[/tex]
[tex]T_n = 180 -60n + 60[/tex]
Rewrite
[tex]T_n = 180 + 60-60n[/tex]
[tex]T_n = 240-60n[/tex]
The recursive function is calculated using:
[tex]T_1 = 180[/tex]
[tex]T_2 = 120 = 180 - 60 = T_1 - 60[/tex]
[tex]T_3 = 60 = 120 - 60 = T_2 -60[/tex]
-
[tex]T_n = T_{n-1} - 60[/tex]
(b) Assume it is a geometric sequence
The explicit formula is calculated using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = 180[/tex]
[tex]r = \frac{120}{180}[/tex]
[tex]r = \frac{2}{3}[/tex]
So, we have:
[tex]T_n = 180 * (\frac{2}{3})^{n-1}[/tex]
Split
[tex]T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})^1[/tex]
[tex]T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})[/tex]
Rewrite as:
[tex]T_n = 180 * (\frac{2}{3})^n * (\frac{3}{2})[/tex]
[tex]T_n = 180 * (\frac{3}{2})* (\frac{2}{3})^n[/tex]
[tex]T_n = 180 * \frac{3}{2}* (\frac{2}{3})^n[/tex]
[tex]T_n = 90 * 3* (\frac{2}{3})^n[/tex]
[tex]T_n = 270* (\frac{2}{3})^n[/tex]
The recursive function is calculated using:
[tex]T_1 = 180[/tex]
[tex]T_2 = 120 = 180 * \frac{2}{3} = T_1 * \frac{2}{3}[/tex]
[tex]T_3 = 80 = 120 * \frac{2}{3} = T_2 * \frac{2}{3}[/tex]
-
[tex]T_n = T_{n-1} * \frac{2}{3}[/tex]
HURRRY PLEASE 3x + 2y = 7 4x - 3y = -2 How many solutions can be found for the system of linear equations represented on the graph? A) no solution B) one solution two solutions D) infinitely many solutions
Answer:
1 solution,since it cuts one time
y=2
Step-by-step explanation:
taking the equations
[tex]3x+2y=7, 4x-3y=-2\\[/tex] as equation 1 and 2 respectively,
Multipy the equation 1 by 4
Multipy the equation 2 by 3
[tex](3x+2y=7 )[/tex]×4
[tex](4x-3y=-2)[/tex]×3
[tex]12x+8y=28\\12x-9y=-6\\\\[/tex] comes as equation 3 and 4, subtract 4 from 3,
[tex]12x-12x+8y+9y=28+6\\17y=34\\y=2[/tex]
Mr.Suarez wants to paint his storage shed.He needs to calculate the lateral surface area of the shed so that he will know how much paint to buy.The shed is in the shape of a rectangular prism with the dimensions shown below.Including the doors what is the lateral surface area of the storage shed brainly
Answer:
The lateral surface area is 336 square feet
Step-by-step explanation:
Given
See attachment for storage
Required
The lateral surface area
From the attached figure, we have:
[tex]L = 14[/tex] --- Length
[tex]W = 7[/tex] --- Width
[tex]H = 8[/tex] --- Height
The lateral area is calculated as:
[tex]Area = 2 * H * (L + W)[/tex]
So, we have:
[tex]Area = 2 * 8 * (14 + 7)[/tex]
[tex]Area = 16 * (14 + 7)[/tex]
[tex]Area = 16 * 21[/tex]
[tex]Area = 336[/tex]
The line OP is a radius of a circle, centre O draw accurately the circle using compasses
Answer:
put the pointy end of the compass on the end line point then draw a circle at a measurement of 3cm 4 cm or 5 cm
PLEASE HELP GUYS AND GIRLS
Hola, ¿cómo está tu día?
Answer:
Muy bien, y usted?
Answer:
es una pregunta o necesitas eso traducido al inglés ¿?
how can I do this ???
Answer:
The triangle EFG can be constructed with the following specifications: [tex]EF = 8\,cm[/tex], [tex]FG = 7\,cm[/tex], [tex]EG = 12\,cm[/tex], [tex]E \approx 34.093^{\circ}[/tex], [tex]F \approx 106.068^{\circ}[/tex], [tex]G \approx 39.838^{\circ}[/tex].
Step-by-step explanation:
A triangle is formed by either knowing the lengths of its three sides or knowing two angles and the length of a side or knowing a angle and the lengths of two sides. By Geometry, we know that sum of internal angles in triangles equals 180°. In order to construct this triangle, we need to know the measures of angles E, F and G by means of the Law of Cosine:
Angle E
[tex]E = \cos^{-1}\left[\frac{(7\,cm)^{2}-(12\,cm)^{2}-(8\,cm)^{2}}{-2\cdot (12\,cm)\cdot (8\,cm)} \right][/tex]
[tex]E \approx 34.093^{\circ}[/tex]
Angle F
[tex]F = \cos^{-1}\left[\frac{(12\,cm)^{2} - (8\,cm)^{2} - (7\,cm)^{2}}{-2\cdot (8\,cm)\cdot (7\,cm)} \right][/tex]
[tex]F \approx 106.068^{\circ}[/tex]
Angle G
[tex]G = \cos^{-1}\left[\frac{(8\,cm)^{2}-(12\,cm)^{2}-(7\,cm)^{2}}{-2\cdot (12\,cm)\cdot (7\,cm)} \right][/tex]
[tex]G \approx 39.838^{\circ}[/tex]
The triangle EFG can be constructed with the following specifications: [tex]EF = 8\,cm[/tex], [tex]FG = 7\,cm[/tex], [tex]EG = 12\,cm[/tex], [tex]E \approx 34.093^{\circ}[/tex], [tex]F \approx 106.068^{\circ}[/tex], [tex]G \approx 39.838^{\circ}[/tex].
Find the measurement of the exterior 1
Answer:
Sorry, but I can't see this well! I am on lapton, and it is impossible to tilt the whole thing over.
Answer: A: 145 degrees
Step-by-step explanation:
Asked the wrong question minutes ago. The question I need answering is here, in the included photo.
Step-by-step explanation:
m L 1 = 180°-75° = 105° ( angles in one side)
m L 2 = 75° (corresponding angles)
Vertical angles have sum 180
m<1=
180-75105°m<2
180-10575°Cora is using successive approximations to estimate a positive solution to
f
(
x
)
=
g
(
x
)
, where
f
(
x
)
=
x
2
+
13
and
g
(
x
)
=
3
x
+
14
. The table shows her results for different input values of
x
.
By successive approximations we find that [tex]x \approx 3.3[/tex] for [tex]f(x) = g(x)[/tex].
How to find a solution of two functions by direct inspection
According to the table, the value of [tex]x[/tex] must be between 3 and 3.5. [tex]x[/tex] is the solution of [tex]f(x) = g(x)[/tex] if and only if [tex]f(x) - g(x) = 0[/tex]. Let suppose that [tex]x = 3.3[/tex], then:
[tex]3.3^{2}+13 = 3\cdot (3.3) + 14[/tex]
[tex]-0.01[/tex]
As we need only two decimals, approximation seems to be reasonable.
By successive approximations we find that [tex]x \approx 3.3[/tex] for [tex]f(x) = g(x)[/tex]. [tex]\blacksquare[/tex]
RemarkStatement is incomplete and incorrectly formatted, correct form is presented below:
Cora is using successive approximations to estimate a positive solution to [tex]f(x) = g(x)[/tex], where [tex]f(x) = x^{2}+13[/tex] and [tex]g(x) = 3\cdot x + 14[/tex]. The table shows her results for different input values of [tex]x[/tex]:
x f(x) g(x)
0 13 14
1 14 17
2 17 20
3 22 23
4 29 26
3.5 25.25 24.5
To learn more on numerical methods, we kindly invite to check this verified question: https://brainly.com/question/19034634
Please help me with my work
Answer:
If the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle.
Step-by-step explanation:
Answer:
Down below is the answer.
Step-by-step explanation:
So, lets remember that the pythagreon theorm is only useable in right traingles.
The formula for the pythagreons theorm is A^2+B^2=C^2
So basically, if this is not a right triangle, the two sides(4ft^2 and 3ft^2) will be equivelent to 5ft^2.
Lets solve the pythagroens theorm and plug in our values:
4^2+3^2=5^2
Now lets use the square roots:
16+9=25
COmbine the two numbers:
25=25
This is correct!
So yes, this is a right triangle.
HOpe this helps! :)
"Y 1
Themba deposited R100 000 in the bank which offers 5,5% per annum simple interest
His intention is to buy a car after 4 years
1.1
Write interest rate as decimal per annum
Answer:
1 ramdhjajdjejjejdnsns
Describe fully the single transformation that takes shape P to Q
Answer:
Triangle P is scaled up 3 times to become triangle Q.
Please help !!!!!!
Clare is deriving the quadratic formula by solving ax^2+bx+c=0 by completing the square.
She arrived at this equation:
(2ax+b)^2=b^2-4ac
Briefly describe what she needs to do to finish solving for I and then show the steps.
Answer:
Clare starts with:
a*x^2 + b*x + c = 0
And she gets to:
(2*a*x + b)^2 = b^2 - 4*a*c
Now we want to show the final steps to solve the equation (isolating x)
First, we apply the square root to both sides:
[tex]\sqrt{(2*a*x + b)^2} = \sqrt{(b^2 - 4*a*c)}[/tex]
Because the square root has two solutions, (one negative and one positive), we will write:
[tex]2*a*x + b = \pm \sqrt{b^2 - 4*a*c}[/tex]
Now we subtract b in both sides:
[tex](2*a*x + b) - b = \pm \sqrt{b^2 -4*a*c} - b[/tex]
[tex]2*a*x = \pm \sqrt{b^2 -4*a*c} - b[/tex]
Now let's divide by 2*a in both sides:
[tex]2*a*x/(2*a) = \frac{\pm \sqrt{b^2 -4*a*c} - b}{2*a}[/tex]
[tex]x = \frac{\pm \sqrt{b^2 -4*a*c} - b}{2*a}[/tex]
A quality control inspector tested 235 CDs and found 8 defective
What is the relative frequency of finding a defective CD?
Answer:
235 C D s =
8 =
Step-by-step explanation:
b.r.uh. these ch.a..t links be t.ripping
Answer: Ok so that is a fact for sure
Answer:
yup
Step-by-step explanation:
The costs for going to a dog beach are $7 for 1 dog, and $2 for each additional dog. Write an equation for this situation, when going to the beach with at least one dog.
Answer:
$7+$2(x-1)-y
Step-by-step explanation:
$7+$2(x-1)=y where $7 is fixed fee and $2(x-1) represents $2 more for every ADDITIONAL dog more than the first dog.
Calculate (1.6) · (0.215). Show your reasoning.
Answer:
0.344
Step-by-step explanation:
i cant show reasoning its just 1.6 times 0.215
The area of a circular plate is 625 pi square inches. If the radius of the circle is tripled, what is the area of the new circle?
A).1090 π in²
B).1270 π in²
C).6715 π in²
D).5625 π in²
Answer:
D.) 5625 pi inches squared
Step-by-step explanation:
square root of 625 = 25
25 x 3 = 75
A= pi r(squared)
A= 75squared pi
A= 5625 pi inches squared
Answer: D
Step-by-step explanation:
Determine the slope of the line.
Answer:
2/3
Step-by-step explanation:
Find the area of the shape below
Answer:
2 times 2 =4 4 times 4 =16 then you add I think
What is the distance between the integers (-15) and (-9) on a number line?
Answer: 6 Im sure
Step-by-step explanation:
thank you. please answer asap!
Answer:
96 i think
Step-by-step explanation:
I think its 96. just multiply all the sides
Can somebody plz help answer these questions correctly thanks (only if u know how to do this) :3
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST...promise :DDDD
If the graph of f(x) contains the coordinates (0, 1) and (4, 16), which of the
following coordinates must be on the graph of the inverse of f(x)?
a. (-4,-16)
b. (16,4)
c. (0,-1)
d. (-16,-4)
e. (0,1)
Answer:
b. (16 , 4)
Step-by-step explanation:
f(x): 0 -> 1 , 4 -> 16
f⁻¹(x): 1 -> 0 , 16 -> 4
Can someone help me with this
Answer:
C
Step-by-step explanation:
1. Absolute values are in the shape of a V, so the answer is automatically C.
2. If you did not know that, you can see that the graph is a function because it passes the vertical line test. This rules out option A. By looking at the graph, you can see it passes the x-axis twice, meaning that it has 2 x-intercepts. This rules out option B. X-intercepts always have a y-coordinate of 0, so we can rule out option D. The only option left after this is C.
Ms. Acton spent $205.60 at Target. If the sales tax is 10%, what was her final bill?
Answer:
$217.94
Step-by-step explanation:
Simplify this expression by combining the like terms
5m + g + 6 + 3g - 2m + k
Answer:
3m+4g+6+k
Step-by-step explanation:
Jesse and her family are painting their house. When they first started, they bought four 16-cup cans of paint. In order to paint their house, it took all of those cans plus they needed another 16-cup can of paint. How many cups of paint did it take Jesse and her family to paint their house?
Answer:
80
Step-by-step explanation:
yes
Giving brainlist to whoever answers
Answer:
14
Step-by-step explanation:
The trapezoids are similar, so you need to find which sides allign with each other. It can be seen that among the paralel sides of the trapezoid, the longer ones will be similar by the factor of 2. So, 2*7=14
Answer:
14 feet
Step-by-step explanation:
which of the following statements best describes the association
Answer:
C
Step-by-step explanation:
For one, it's negative so all positive answers can be eliminated.
Secondly, the y axis is hit on positive 3. No point even hits negative 3.
Knowing that, the only choice left is C.