Answer:
The first 5 terms of the sequence are 2, 4, 8, 16 and 32.
Step-by-step explanation:
Given:
[tex]a_{1}[/tex] = 2
[tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] -----------------(i)
To get the first 5 terms of the sequence, substitute in turn, n = 1, 2, 3, 4, 5 into equation (i).
The first term (when n = 1) has been given as:
[tex]a_{1}[/tex] = 2
The second term (when n = 2) is given as:
[tex]a_{2}[/tex] = 2[tex]a_{2-1}[/tex]
[tex]a_{2}[/tex] = 2[tex]a_{1}[/tex] (but [tex]a_{1}[/tex] = 2 )
=> [tex]a_{2}[/tex] = 2(2)
=> [tex]a_{2}[/tex] = 4
The third term (when n = 3) is given as:
[tex]a_{3}[/tex] = 2[tex]a_{3-1}[/tex]
[tex]a_{3}[/tex] = 2[tex]a_{2}[/tex] (but [tex]a_{2}[/tex] = 4 )
=> [tex]a_{3}[/tex] = 2(4)
=> [tex]a_{3}[/tex] = 8
The fourth term (when n = 4) is given as:
[tex]a_{4}[/tex] = 2[tex]a_{4-1}[/tex]
[tex]a_{4}[/tex] = 2[tex]a_{3}[/tex] (but [tex]a_{3}[/tex] = 8 )
=> [tex]a_{4}[/tex] = 2(8)
=> [tex]a_{4}[/tex] = 16
The fifth term (when n = 5) is given as:
[tex]a_{5}[/tex] = 2[tex]a_{5-1}[/tex]
[tex]a_{5}[/tex] = 2[tex]a_{4}[/tex] (but [tex]a_{4}[/tex] = 16 )
=> [tex]a_{5}[/tex] = 2(16)
=> [tex]a_{5}[/tex] = 32
Therefore, the first 5 terms of the sequence are 2, 4, 8, 16 and 32.
the length of a rectangular yard is 4 feet more than the width. the perimeter of the yard is 208 feet. write the equation that represents the perimeter of the yard. let w represent the width. solve the equation. what are the dimensions of the yard?
Answer:
Length = 54 ft.
Width = 50 ft.
Step-by-step explanation:
Let the width of the rectangle be 'w'.
According to question ,
Length = w + 4
Perimeter = 208 ft.
We know that [tex]perimeter = 2(l + w)[/tex] where l = length & w = width
So,
[tex]2(w + 4 + w) = 208[/tex]
[tex] = > 2(2w + 4) = 208[/tex]
[tex] = > 2w + 4 = \frac{208}{2} = 104 [/tex]
[tex] = > 2w = 104 - 4 = 100[/tex]
[tex] = > w = \frac{100}{2} = 50[/tex]
Width = 50 ft.
=> Length = 50 + 4 = 54 ft.
What value of x is in the solution set of 8x - 6 > 12 + 2x?
O-1
O0
O3
O5
The answer of X will be equal (3)
3y + 20 = 3 + 2y
A. -1/17
B.7 2/3
C. 23
D. -17
A ladder 12 m long is propped up against a building at an angle of 15°. How far up the wall does the ladder go?
The ladder can go as far as 3.1m
Application of SOH CAH TOAThe given set up is. a triangle with the following parameters
Angle of elevation = 15 degrees
Hypotenuse = 12m
Required
Height of the building
Using the expression
sin theta = opp/hyp
sin 15 = h/12
h = 12sin15
h = 3.1m
Hence the ladder can go as far as 3.1m
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In a series of 4 one day cricket matches, the runs scored by Pakistan and Australia are given below: (06 Marks) Match Pakistan Australia First 102 208 Second 202 192 Third 360 241 Fourth 276 203 Find: (i) What is the average score of Pakistan in one match? (ii) What is the average score of Australia in one match? (iii) Which team performed better?
Step-by-step explanation:
Scores of Australia in all four matches starting from 1st 208, 192, 241, 203 respectively.
Similarly, scores of Pakistan in all four matches starting from 1st 102, 202, 360, 276 respectively.
The avg of Pakistan in one match = (102+202+360+276)/4 = 235
The avg of Australia in one match = (208+192+241+203)/4= 211
Since, the avg score of Pakistan is more than that of Australia, Pakistan performed better.
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-15x^2+801x-5900
Answer:
The widgets should be sold for $26.7 for the company to make the maximum profit.
Step-by-step explanation:
Given the quadratic equation
[tex]f\left(x\right)=-15x^2+801x-59000[/tex]
As the leading coefficient is (-3), so the graph would be a downward Parabola.
Thus, the maximum profit would be at the vertex.
The selling price 'x' can be determined by determining the x-coordinate of the vertex.
In order to calculate the x-coordinate of the vertex, we can find this by
x = -b/2a
where a = -15 and b = 801
x = -801 / 2(-15)
x = -801/-30
x = 801/30
x = 267/10
x = 26.7
Therefore, the widgets should be sold for $26.7 for the company to make the maximum profit.
MATH PLS HELPPP BRANLIETS 5 POINTS!!!!!!!!!!
Answer:
A?
Step-by-step explanation:
I think it is A but I'm not 100% sure
Answer:
The total cost of riding in the taxi
Step-by-step explanation:
Please help me choose the right equation!!! I’m a taking a test and really want to pass!!!
Answer:
Step-by-step explanation:
Express the ratio 12:3:9 in its simplest form
Answer:
4:1:3
Step-by-step explanation:
A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100cm, calculate the radius of the circle.
Answer:
7 cm
Step-by-step explanation:
Let the side of square be x.
Perimeter of square = 4x
Diameter of circle = x
Radius of circle = x/2
Circumference of circle = 2 * 22/7 * x/2 = 22/7x
According to Question,
4x + 22/7x = 100
(28+22) / 7x = 100
50x = 700
x = 14
Hence, diameter of circle = 14 cm
Radius of circle = (14/2) cm = 7 cm
WILL GIVE BRAINLIEST!!! Which equation is modeled below? 4 x tiles and 2 negative 1 tiles = 2 x tiles and 4 1 tiles. 2 x + (negative 2) = negative 2 x + 6 4 x + (negative 2) = negative 2 x + 6 2 x + 4 = 6 x + 2 Negative 2 x + 4 = 6 x + (negative 2)
Answer:
B
Step-by-step explanation:
4x+ (-2) =-2x+6
just took the quiz
Answer:
B) 4 x + (-2) = -2 x + 6
Step-by-step explanation:
Ernesto baked 3 cakes in 2 1/2 hours. Assume that the number of cakes baked varies directly with the number of hours. Write and solve a direct variation equation to find how many cakes can he bake in 7 1/2 hours.
Answer: We assume that the number of cakes baked varies directly with the number of hours. Hence, he can bake 9 cakes in 7.5 hours.
Step-by-step explanation:
a mat is 3m long and xm wide what is the area in m²
Step-by-step explanation:
Area = Length * Width = (3m)(xm) = 3xm².
In triangle △WXY, XY ≅ WX and m∠X=38 Find m∠W
Answer:
[tex]71^{\circ}[/tex]
Step-by-step explanation:
Since two sides of the triangle are equal in length, we can conclude that [tex]\triangle WXY[/tex] is an isosceles triangle. With this information, we can draw an isosceles triangle to find [tex]m\angle W[/tex]. Since the base angles of an isosceles triangle are equal, we can solve for [tex]m\angle W[/tex]:
[tex]38 + m\angle W + m\angle Y = 180[/tex] (Angle sum of triangle is [tex]180^{\circ}[/tex])
[tex]38+2(m\angle W) = 180[/tex] (Base angles of isosceles triangles are equal, there is an image attached to show that [tex]m\angle W[/tex] is one of the base angles)
[tex]2(m\angle W) = 142[/tex]
[tex]m\angle W=71^{\circ}[/tex]
Hope this helps :)
Using Point Slope Formula, write an equation that passes through (-2, 6) and ( 8, 9)
Answer:
y - 9 = 3/10(x - 8)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Point (-2, 6)
Point (8, 9)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute [SF]: [tex]\displaystyle m=\frac{9-6}{8+2}[/tex]Subtract/Add: [tex]\displaystyle m=\frac{3}{10}[/tex]Step 3: Write Function
Plug in variables into general form.
y - 9 = 3/10(x - 8)
y - 6 = 3/10(x + 2)
I CANNOT get this one wrong. I just don't understand this.
Answer:
C. 90°
Step-by-step explanation:
ΔEFG ≅ ΔJKL
E ---> J F ---> K G ----> L
∠ J ----> ∠ E
∠ J = 90°
∠ E = 90°
In a candy mix there are 4 green bars for every 3 red bars. How many red bars are there if there are 200 green bars? A. 150 red bar's B. 199 red bars c.201 red bars d. 267 red bars
Step-by-step explanation:
4 green bars to 3 red bars
=> 200 green bars to 3 * (200/4) = 150 red bars.
There are 150 red bars. (A)
Answer:
Step-by-step explanation:
A - 150 is the a answer
4 green bars for every 3 red bars, take 3 red bars as one bucket so total we have 200/4 buckets which is 50
now 1 bucket has 3 green bars so total we have 3* 50 buckets which is 150
What is the HCF of 200 and 240
Answer:
It is 40
Step-by-step explanation:
The highest common factor of 200 and 240 is 40
Calculate the distance between each point to the store. Please help, will give brainliest
Answer:
see in this picture, the point of Lake House is (-2;5)
the point of Cabin is (6;3)
the point of Store is (-4;-5)
=> the distance between Lake House to Store is [tex]\sqrt{(-4-(-2))^{2}+(-5-5)^{2} }=2\sqrt{26}[/tex]
the distance between Cabin to Store is [tex]\sqrt{(-4-6)^{2}+(-5-3)^{2} }=2\sqrt{41}[/tex]
Step-by-step explanation:
A ball bounces from a height of 8 feet. The ball bounces to 80% of its previous height with each bounce. How high (to the nearest tenth of a foot) does the ball bounce on the fifth bounce?
Answer:
2.6 feet
Step-by-step explanation:
At each point, there is a loss of 20% (since it flies to 80%)
a) 8 - 20% of 8
= 8-1.6 = 6.4
b) 6.4 - 20% of 6.4
= 5.12
c) 5.12 - 20% of 5.12
4.096
d) 4.096 - 20% of 4.096
3.2768
e) 3.2768 - 20% of 3.2768
= 2.62144 feet
PLEASE PLEASE HELP FAST!!
Find the value of x in the figure below. Show your work. A 9 in 9 in 2x-4 44° ОС B 13 in
Answer:
x=24 degrees
Step-by-step explanation:
2x-4=44 <----The triangle is isosceles, in which the two base angles are equal
2x=48 <-----Solve the equation
x=24 <-------Answer
Solve the equation below for x:
0.25(x - 13) = 7
Answer:
x=41
Step-by-step explanation:
0.25(x-13)=7
We move all terms to the left:
0.25(x-13)-(7)=0
We multiply parentheses
0.25x-3.25-7=0
We add all the numbers together, and all the variables
0.25x-10.25=0
We move all terms containing x to the left, all other terms to the right
0.25x=10.25
x=10.25/0.25
x=41
The solution to the equation; 0.25(x - 13) = 7 as given is; x = 41
According to the question;
We are required to solve for x in the equation; 0.25(x - 13) = 7The solution to the given equation can be evaluated as follows;
0.25(x - 13) = 70.25x - 3.25 = 70.25x = 10.25x = 41.
Read more on one variable equation;
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help 6th grade math i will give brainliest
Answer:
2 * 2 * 5 * 5, or 2^2 * 5^2, or 5^2 * 2^2
Step-by-step explanation:
You can use a factoring tree to find the prime factorization of 100.
+------ 100----------------+
| |
2 +---50---------+
| |
2 +----25----+
| |
5 5
The prime factorization of 100 is 2 * 2 * 5 * 5, or 2^2 * 5^2, or 5^2 * 2^2
Step-by-step explanation:
2^2 × 5^2 =
(2×2) × (5×5) =
4 × 25 = 100
5^2 × 2^2 =
(5×5) × (2×2) =
25 × 4 = 100
2*2*5*5=100
2 and 5 are the only prime numbers in this question. 2(2)*5(5) doesnt equal 100.
Suppose m is the line with equation x=-5, line n is the equation y=1
Here is the complete question:
suppose m is the line with equation x=-5, line n is the line with equation y=1, line g is the line with equation y=x, and line h is the line with equation y=-2. Given A(9,-3), B(6,4), and C(-1,-5), what are the coordinates of the vertices of △A′B′C′ for each reflection?
1. Rx-axis
2. Ry-axis
Answer with step-by-step explanation:
1. When you get the reflecting coordinates along x-axis, the signs of the y coordinates changes. Therefore, A(9,-3), B(6,4), and C(-1,-5) becomes:
A(9, 3), B(6, -4), and C(-1, 5).
2. When you get the reflecting coordinates along y-axis, the signs of the x coordinates changes. Therefore, A(9,-3), B(6,4), and C(-1,-5) becomes:
A(-9, -3), B(-6, 4), and C(1, -5).
The perimeter of the rectangle is 10. Find the value of x.
Answer:
Hi! Is there a picture?
Step-by-step explanation:
Answer:
The area equation to solve becomes \displaystyle x(x-4)=96, or \displaystyle x^{2}-4x-96=0. To factor, find two numbers the sum to -4 and multiply to -96. -12 and 8 will work: x2 ...
I need help pls with this question
Red snapper cost $4.15 per pound find the cost of 3.5 pound round to the nearest cent
Answer:
$14.53 for 3.5 pounds of red snapper
Step-by-step explanation:
Answer:
14.52?
Step-by-step explanation:
i multiplied 4.15 by 3.5
[tex] {x}^{3} - 4x + \sqrt{{x}^{3} - 4x + 9 } = 3[/tex]
Help me please
Emily makes $24 per hour. She worked 80 hours of regular time for the last pay
period and 5 hours of overtime at $36 per
hour.
Answer: 2,100$
Step-by-step explanation:
help i don’t understand!!