Answer:
see explanation
Step-by-step explanation:
The nth term ( explicit formula) of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = - 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{\frac{4}{3} }{-2}[/tex] = - [tex]\frac{2}{3}[/tex] , then
[tex]a_{n}[/tex] = - 2 [tex](-\frac{2}{3}) ^{n-1}[/tex] ← explicit formula
Answer:
Step-by-step explanation:
The formula for an explicit geometric formula (as opposed to a recursive one) is
[tex]a_n=a_1(r)^{n-1}[/tex] where a(n) is representative of the position of a number in the sequence, a(1) is the first number in the sequence, and r is the common ratio. The common ratio is the same number that must be either multiplied in or divided out to get to the next number in the term. Notice that the top numbers in our sequence are doubling which implies we are multiplying the top numbers by -2, and the bottom numbers are going up by multiples of 3. So our common ratio is -2/3. Try it and see:
[tex]-2(-\frac{2}{3})=\frac{4}{3}[/tex] and
[tex]\frac{4}{3}(-\frac{2}{3})=-\frac{8}{9}[/tex] etc.
Therefore, the explicit geometric formula for this sequence is
[tex]a_n=-2(-\frac{2}{3})^{n-1[/tex]
You can use this formula to find any number in the sequence; for example, if you wanted to know the 100th number in this sequence, simply replace n with 100 and do the math. That's what an explicit formula is used for.
big ideas integrated 1 chapter 8 test? anyone ?
Answer:
Uh, sure! :)
Step-by-step explanation:
Please help :) will mark brainliest
Answer:
1) C: 113 m
2) C: 572.3 m²
3) B: 61.2 cm²
4) A: $2.2
6) C: 756 yd³
8) D: 3402 mm²
9) A: 25x + 125 < 500
Step-by-step explanation:
1) Formula for circumference of circle is;
C = 2πr
radius; r = 18 m
C = 2π × 18
C ≈ 113 m
2) Formula for area of a circle is;
A = πr²
Here we have diameter; d = 27
Thus, radius; r = 27/2 = 13.5 m
A = π × 13.5²
A = 3.14 × 13.5²
A ≈ 572.3 m²
3) The diameter of the semicircle is parallel to the base of the rhombus. Thus, diameter; d = 7 cm
Thus, r = 7/2 = 3.5 cm
Area of semi circle = ½πr² = ½ × π × 3.5² = 19.2 cm²
Area of rhombus = base x height = 7 × 6 = 42 cm²
Total area of object = 42 + 19.2 = 61.2 cm²
4) Cost of banana per pound = $0.4 per pound
Amount of banana bought = 5.5 pound
Amount spent = 0.4 × 5.5 = $2.2
6) Volume of triangular prism is;
V = ½bhl
b = 12 yd
h = 7 yd
L = 18 yd
Thus;
V = ½ × 12 × 7 × 18
V = 756 yd³
8) Volume of cuboid at the base;
V1 = lbh = 25 × 9 × 9 = 2025 mm²
Volume of cuboid at top;
V2 = 9 × 9 × 9 = 729 mm²
Volume of triangular prism;
V3 = ½bhl = ½ × 9 × 9 × (25 - 9) = ½ × 81 × 16 = 648 mm²
Total volume = 2025 + 729 + 648 = 3402 mm²
9) Cost per class; $25 per class
Charge for the supplies = $125
He doesn't want to spend more than $500.
Thus;
25x + 125 < 500
Decide whether the ordered pair (-2,-8) is a solution of the equation.
y = 4x
Is (-2,-8) a solution to y = 4x?
Yes or no
Answer:
Yes it is
Step-by-step explanation:
Because 4 ×-2=-8
The area of the parallelogram below is___square meters
Answer:
48 m^2
Step-by-step explanation:
Since this is a parallelogram, you can think of it as taking the triangle off of the left side and reattaching it on the right side to make a rectangle. After you visualize it as a rectangle, you just have to multiply 8 by 6 to get 48 meters squared.
What is the surface area?
Find the surface Area?
Answer:
[tex]150 km^{2}[/tex]
Step-by-step explanation:
Use the surface area equation of cylinder: [tex]A = 2\pi rh + 2\pi r^{2}[/tex]
The diameter is 6 km but you need the radius for the formula, so you divide the diameter by 2.
6÷2 = 3 --> r = 3
You already know h, aka the height.
Plug everything into the equation.
Answer:
150.72
Step-by-step explanation:
im usin 3.14 as pi btw
the term net means like imagine you unfold the shape like the walls of the shape are paper. its now a 2d net, which includes a rectangle and two circles.
so, surface area of a circle is pi r^2 so 3.14 * 3 * 3 = 28.26
times two cause theres two circles; top and bottom :3
56.52 = 28.26 * 2
rentangle surface area = h*l
the height of the rectangle is 5 and the length is the circumference of the circle
circumference is 2*3.14*r, which in this problem, is 3
2*3.14*3 = 18.84
now, h*l is 18.84*5 = 94.2
94.2 + 56.52 = 150.72
i just need a little help on this one sorry for the bother
Answer:
they look like their curved at about 70? 65? and they would be the same
Step-by-step explanation:
Answer: Both C and D are 76
Step-by-step explanation:
Because this is a isosceles triangle both C and D are the same. Subtract 28 from 180 and you get 152. So D and C combined equals to 152 so divide that by 2 an you get 76.
here is a graph of y=x^2-7x+10 for values of x from 0 to 7.
write down the roots of x^2 -7x +10=0.
ASAP please
Answer:
Roots of the function are x = 2, 5.
Step-by-step explanation:
Roots of a function are defined by the x-intercepts of the graph.
From the given graph in the question,
x-intercepts → x = 2, 5
Now confirm it by solving the equation algebraically,
x² - 7x + 10 = 0
x² - 5x - 2x + 10 = 0
x(x - 5) - 2(x - 5) = 0
(x - 5)(x - 2) = 0
x = 2, 5
Therefore, roots of the function are x = 2, 5.
< 3 Plz help 10th grad maths < 3 i don't understand
b. Calculate the equivalent resistance of the circuit.
c. Calculate the current through the battery.
d. How much current is passing through each resistor?
e. Calculate the voltage drop across each resistor.
f. How does the voltage drop across each resistor compare to the voltage of the battery?
Answer:
Step-by-step explanation:
this is math or physics
Answer:
brainliest please, sorry for the inconveniences
8. The sum of three consecutive multiples of 11 is 759. Find the multiples.
Answer:
252, 253, 254
Step-by-step explanation:
[tex] \frac{759}{3} \\ = 253[/tex]
253 is the median. so the multiples will be 252, 253, 254
use circle C
classify arc MNO in circle C
Answer:
Semicircle
Step-by-step explanation:
As we can see, the arc is bounded by the chord MO
since the chord passes through the center of the circle, we have it that the chord is a diameter
Mathematically, an arc bounded by a diameter represents half of a circle
So we can conclude that the arc MNO in circle C is a semicircle
The conjugate of complex number z = 3 + 2i is
_
z = a-bi
i think this is the answer
Pls helppp!!! Find the ninth term of the sequence
5,4,1,-4,-11...
The ninth term is??
Answer:
-20 because it's 5-1=4-3=1-5=-4-7=-11-9=-20
Answer:
-59
Step-by-step explanation:
It's subtracting each number by the next ODD number
subtract 1
subtract 3
then 5, 7, 9 and so on
how to measure latitudes
Answer:
Lines of latitude run in horizontal parallels and represent distance north or south from the equator, measured in an angle from the centre of the Earth. The equator represents 0° and each pole represents 90°
Step-by-step explanation:
Answer: Hope This Helps!
Step-by-step explanation:
Use the sight line on the top of the aiming beam to align the beam with the North Star. Use the protractor to measure the angle between the beam and the horizon (which is 90º to the plumb line). This angle is your latitude.
Find the value of x so that x – 4 = -2
Answer:
x=2
Step-by-step explanation:
[tex] - 2 + 4 = 2[/tex]
Andre has a summer job selling magazine subscriptions. He earns $25 per week plus $3 for every subscription he sells. Andre hopes to make at least enough money this week to buy a new pair of soccer cleats. Let `n` represent the number of magazine subscriptions Andre sells this week. Write an algebraic expression for the amount of money he makes this week.
Answer:
C = 25 + 3n
Step-by-step explanation:
Andre has a summer job selling magazine subscriptions.
We are told that:
Andy earns $25 per week plus $3 for every subscription he sells.
Let us represent
C = Total amount of money he makes this week
n = the number of magazine subscriptions Andre sells this week.
Hence, Our Algebraic expression =
C = $25 + $3 × n
C = 25 + 3n
Please help me with this question. The answer is $745,000 but I need working out.
Answer:
745,000
Step-by-step explanation:
200,000x.03= 6000
150,000x.025=3,750
Commission. 2,350
total. 12,100
total fees. 20,000
less above. 12,100
=.remaining fees 7,900
divide by .02(2% commission)
=remaining sales price 395,000
tier 1 200000
tier 2 150000
tier 3 395,000 (calculated above)
=. 745,000 sales price
Find the solution set of the quadratic equation over the set of complex numbers.
5x2 + 8x + 4 = 0
1+1
A)
x=-1- or -1
-
B)
X
4 2i
or
5
4
5
+
2i
5
2
5
C)
6i
5
or
2
5
+
61
5
1
3i
1
4
D)
31 or
+
4.
Answer:
c
Step-by-step explanation:
Answer:
D confirm bro............
Is this inequality true or false?
5v > 25, v = 3
Answer:
False
Step-by-step explanation: 5x3 is 15 and 25 is greater than 15 so the inequality is false.
Select all of the equations where x = 5 is the solution:
2 = 7 - x
1 + x = 6
x - 4 = 9
10 ÷ x = 2
10x = 2
can someone please answer this? i will mark brainly
Factor as the product of two binomials
x² – 4 =
Answer:
(x-2) (x+2)
Step-by-step explanation:
------------------
solve for x. round your answer to the nearest tenth if necassary.
Answer:
32.9 degrees
Step-by-step explanation:
cos (x) = 21/25
cos^1 (21/25)
= 32.856 --> round to 32.9
Answer:
32.9°
Step-by-step explanation:
You can see that relative to the angle that is x, we are given the side lengths that are adjacent and the hypotenuse. The trig function associated with this is cosine, and we get:
cos(x) = adj / hyp --> 21 / 25
To find x as the angle, we use the function arccosine,
x = arccosine(21/25)
x = 32.85988038°
And this rounds up to 32.9°
What is her average from Macy scores
Answer: 85.2
Step-by-step explanation:
The answer is correct because, to find your grades your bassicaly just looking for the mean. To find the mean you have to take all the numbers and add them after you do that you have to divide how ever much numbers you added. So in this case we do 90 plus 76 plus 88 plus 80 plus 92. That equals 426, and since we added five numbers we divide the answer by 5 and that equals 85.2.
Hope This Helps!
7.
Choose the linear inequality that describes the graph. The gray area represents the shaded region.
A. y ≥ 2x – 2
B. y ≥ 2x + 2
C. y ≥ –2x + 2
D. y ≤ 2x – 2
Answer:
A. y ≥ 2x – 2
Step-by-step explanation:
if x<-2 then x can be
Answer:
x ={-3, -4, -5 , -6, -7, ...}
Transform pentagon ABCDE according to (x, y) + (x - 2, y - 3). Which new coordinates are correct for pentagon A'B'C'D'E
A) A'(-1,3)
B) B'(3, 4)
C) C'(6,-1)
D) D'(2,-4)
E) E'(-6, -5)
The correct coordinates are A'(-1,3) and C'(6,-1)
Transformation of coordinatesFrom the given figure, we have the coordinates ABCDE under the translation (x, y) + (x - 2, y - 3)
Given the following coordinate points (1, 6), B(6, 6), C(8, 2), D(4, -2) and E(-2, -5). The resulting coordinate after transformation will be:
A = (1-2, 6-3) = (-1, 3)B = (6-2, 6-3) = B'(4, 3) C = (8-2, 2-3) = C'(6,-1) D = (4-2, -2-3) D'(2,-5) E = (-2-2, -5-3) = E'(-4, -8)Hence the correct coordinates are A'(-1,3) and C'(6,-1)
Learn more on translation here: https://brainly.com/question/12861087
LEAN CADA CONDICIÓN Y COLOQUEN UNA X A LOS NÚMEROS QUE LA CUMPLEN:
UN NÚMERO ES DIVISIBLE POR 3 CUANDO LA SUMA DE SUS CIFRAS ES MÚLTIPLO DE 3.
352 405 625 813 1.011 2.546 5.104
UN NÚMERO ES DIVISIBLE POR 4 CUANDO SUS DOS ÚLTIMAS CIFRAS SON CEROS O MÚLTIPLOS DE 4.
170 512 700 914 1.302 3.164 7.480
UN NÚMERO ES DIVISIBLE POR 6 CUANDO ES DIVISIBLE POR 2 Y POR 3.
213 460 522 720 2.310 4.503 5.316 AYUDA PLS
Answer:
I speak english srry
Step-by-step explanation:
Please help quicky!!!!!!!!!!
Answer:
≈ 2,826 cm^3
Step-by-step explanation:
V = πr^2h
V = 3.14 · 10^2 · 9
V = 3.14 · 100 · 9
V = 314 · 9
V = 2,826
Can someone please help me? i’ve asked twice but people didn’t comment to help! If you’re not gonna help please don’t comment!! I’m not able to open any files, so its best if you tell me or explain the answers..
Answer:
lenth = x= 12cm
Breadth = y = 8cm
Step-by-step explanation:
Given :
The length of a rectangle is 4 cm more than its width
The area of the rectangle is 96 cm²
To Find :
Width of the rectangle.
Solution :
Let the length of the rectangle be x cm.
Let the breadth of the rectangle be y cm.
Case 1:
➣
➣ _____(1)
Case 2 :
We have the formula for area of the rectangle as follows :
Where,
l = length → x cm
b = breadth → y cm.
➣
➣
Substitute, x = 96/y in equation 1,
➣
➣
➣
➣
➣
Divide by minus sign,
➣
➣
➣
➣
➣
➣
➣
As per assumption, y = breadth of the rectangle.
•°• y = -12 is not acceptable.
Substitute, y = 8 in equation 1,
➣
➣
➣
➣
How do you work out the area of a triangle?