Given:
[tex]a_n=-5+2(n-1)[/tex]
To find:
The arithmetic sequence using a Recursive Formula.
Solution:
We have,
[tex]a_n=-5+2(n-1)[/tex] ...(i)
The explicit formula of an AP is
[tex]a_n=a_1+(n-1)d[/tex] ...(ii)
where, a₁ is first term and d is common difference.
From (i) and (ii), we get
[tex]a_1=-5,d=2[/tex]
Now, the recursive formula of an AP is
[tex]a_n=a_{n-1}+d[/tex]
Putting d=2, we get
[tex]a_n=a_{n-1}+2[/tex]
Therefore, the arithmetic sequence using a Recursive Formula is defined as [tex]a_n=a_{n-1}+2[/tex], where n>2 and [tex]a_1=-5[/tex].
Please help due in 10 minutes
The points (-5, -22) and (4, r) lie on a line with slope 3. Find the missing coordinate r.
Step-by-step explanation:
here,
x1= -5. x2=4
y1= -22. y2=r
slope(m)=3
now we have,
m=(y2-y1)/(x2-x1)
or,3=(r-(-22))/(4-(-5))
or,3=(r+22)/(4+5)
or,3=(r+22)/9
or,27=r+22
or,r=27-22
or,r=5
PLEASE HELP ASSP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
E that's the answer if reflected it'd look like a mirror image
Answer:
The answer is E
Step-by-step explanation:
Can 5,8,12 be a triangle
Answer: For an oblique or acute triangle sure but not a right triangle
Step-by-step explanation: I guess the sides would work on a regular non right triangle but Pythagorean theorom doesn't work here so the sides don't work for a right triangle
Answer:
Step-by-step explanation:
since the two smaller numbers don't add up to more than the bigger they can. but not a right triangle :|
at tge local bookstore jim bought 2 paperback books for 13.00. Maria bought 5 paperback books for 45.00.
Translate (-7, 4) to the right 5 and up 7
will give brainliest
determine the value of sin(-240°)
Answer:
[tex]\frac{\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Given
sin(- 240°)
To obtain the positive angle measure add 360°, equivalent to one full revolution about the origin, then
ain(- 240°)
= sin(- 240 + 360)°
= sin120°
= sin( 180 - 120)°
= sin60°
= [tex]\frac{\sqrt{3} }{2}[/tex]
The number of camera phones shipped globally can be modeled by the function y = 1.28e 1.31x where x is the number of years since 1997 and y is the number of camera phones shipped (in millions). How many camera phones were shipped in 2002?
Answer: 895 phones
Step-by-step explanation:
Given that :
The function : y = 1.28e^1.31x ; is used to model the number of camera phones shipped since 1997
y = number of camera phones ; x = number of years since 1997
The number of camera phones shipped in the year 2002 can be obtained thus ;
x = 2002 - 1997 = 5 years
y = 1.28e^(1.31 * 5)
y = 1.28e^6.55
y = 1.28(699.24417)
y = 895.03254
y = 895 phones
Given f(x) = -x + 6 write an equation for f(x+3)
Answer:
Step-by-step explanation:
f(x)=-x+6
f(x+3)=-(x+3)+6=-x-3+6=-x+3
Answer:
f(x + 3) = -x + 3
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Function NotationCombining Like TermsStep-by-step explanation:
Step 1: Define
f(x) = -x + 6
f(x + 3) is x = x + 3
Step 2: Evaluate
Substitute in x: f(x + 3) = -(x + 3) + 6Distribute -1: f(x + 3) = -x - 3 + 6Combine like terms: f(x + 3) = -x + 3Sara earns a weekly salary of $400 plus commission of 6.5% on sales at the clothing store where she works. How much would she earn in one week if she sold $1200 worth of merchandise?
Answer:
Sara earns a weekly salary of $400 plus commission of 6.5% on sales at the clothing store where she works. How much would she earn in one week if she sold $1200 worth of merchandise?Step-by-step explanation:
2(3x-17) by using the distributive property
Plzzz I need help with this question I tried to solve it many times but I can't
Let x represents a length in cm where x > 1.5.
AB = 2x – 3, BC = 4x – 6,
AD = 2x + 3 and BE = 4x +1
• ABC is right triangle of area Sj.
• CBFG is a rectangle of area S2.
. ADEB is a right trapezoid of area S3.
1) Express S1, S2 and S3 in terms of x.
2) Let S = Si + S2 - Sz.
a) Show that S = (2x - 3)(5x - 9).
b) For what values of x, the areas of AFGC and ADEB are equal?
c) Expand and reduce S.
d) What is the value of x, so that the area of AFGC exceed the area of ADEB by 27?
Answer and Step-by-step explanation: Area of a right triangle, (as any other triangle), is calculated as: [tex]A1=\frac{(base)(height)}{2}[/tex]
Area of a rectangle is calculated as: [tex]A2=(side)(side)[/tex]
Area of a right trapezoid is: [tex]A3=\frac{(a+b)h}{2}[/tex], where:
a is short base
b is long base
h is height
1) Expressing areas in terms of x:
Area of triangle S1:
[tex]S1=\frac{(2x-3)(4x-6)}{2}[/tex]
[tex]S1=4x^{2}-12x+9[/tex]
Area of rectangle S2:
[tex]S2 = (4x-6)(3x-2)[/tex]
[tex]S2=12x^{2}-26x+12[/tex]
Area of trapezoid S3:
[tex]S3=\frac{(2x+3+4x+1)(2x-3)}{2}[/tex]
[tex]S3=\frac{(6x+4)(2x-3)}{2}[/tex]
[tex]S3=6x^{2}-5x-6[/tex]
2) a) [tex]S=4x^{2}-12x+9+12x^{2}-26x+12-(6x^{2}-5x-6)[/tex]
[tex]S=4x^{2}-12x+9+12x^{2}-26x+12-6x^{2}+5x+6[/tex]
[tex]S=10x^{2}-33x+37[/tex]
Which is the same as S = (2x-3)(5x-9)
b) For the areas to be the same:
[tex]\frac{(3x-2+3x-2+2x-3)(4x-6)}{2}=\frac{(6x+4)(2x-3)}{2}[/tex]
[tex]\frac{(8x-7)(4x-6)}{2}=\frac{(6x+4)(2x-3)}{2}[/tex]
[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x-12[/tex]
[tex]20x^{2}-66x+54=0[/tex]
Using Bhaskara to solve the second degree equation:
[tex]\frac{66+\sqrt{(-66)^{2}-(4.20.54)} }{2(20)}[/tex]
[tex]x_{1}=\frac{66+6}{40}[/tex] = 1.8
[tex]x_{2}=\frac{66-6}{40}[/tex] = 1.5
For the areas of AFGC and ADEB to be equal, x has to be 1.5 or 1.8.
c) Expand a polynomial (or equation) is to multiply all the terms, remiving the parenthesis. Reduce a polynomial (or equation) is to combine terms alike,e.g.:
[tex]S=(2x-3)(5x-9)[/tex]
[tex]S=10x^{2}-18x-15x+27[/tex] (expand)
[tex]S=10x^{2}-33x+27[/tex] (reduce)
d) For area of AFCG to be bigger than area of ADEB by 27:
[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x-12+27[/tex]
[tex]32x^{2}-48x-28x+42=12x^{2}+8x-18x+15[/tex]
[tex]20x^{2}-66x+27=0[/tex]
Solving:
[tex]\frac{66+\sqrt{(-66)^{2}-(4.20.27)} }{2(20)}[/tex]
[tex]\frac{66+46.86}{40}[/tex]
[tex]x_{1}=\frac{66+46.86}{40}=[/tex] 2.82
[tex]x_{2}=\frac{66-46.86}{40}[/tex] = 0.48
According to the enunciation, x cannot be less than 1.5, then, the value of x so that area AFGC exceeds the area ADEB by 27 is 2.82
Kiran says that the
Blep
pattern is growing
linearly because as the step number goes up by 1, to
number of rows and the number of columns also
increase by 1. Do you agree? Explain your reasoning
Answer:
what?
Step-by-step explanation:
A quadrilateral has a side length of x+6 inches and a perimeter of 49 inches. Which equation represents this situation? a. 4x + 6 = 49 b. 4(x + 6) = 49 c. X + 6 = 49 d. X + 24 = 49
Answer:
b. 4(x + 6) = 49
Step-by-step explanation:
Step two:
given data
A quadrilateral has a side length L of x+6 inches
Perimeter= 49 inches.
Required:
the expression for the perimeter of the quadrilateral given the situation
Step two:
A quadrilateral has four sides, assume we have a square-shaped quadrilateral
P=4L
49= 4(x+6)
A store was having an end-of-summer sale with a discount of 25% on all swimsuits. Sarah saw a swimsuit she liked that had an original price of $60. What is the swimsuit's discounted price?
Is 2/10 greater than 1/8?
Answer:
1/8 is SMALLER then 2/10
Answer:
2/10 is greater
Step-by-step explanation:
2/10 and 1/8, hard to tell since they have different denominators. So let's make them have the same denominators, multiply 2/10 with 4/4 and 1/8 with 5/5.
If u don't want to think too much to find a number they can both be multiplied too, simply multiply each fraction with the others denominator, so 2/10 times 8/8 and 1/8 times 10/10. It doesn't rlly matter what factor u choose to multiply with as long as the denominator is the same.
So back to the first one, 2/10 times 4/4 is 8/40, 1/8 times 5/5 is 5/40.
8/40 > 5/40
Therefore 2/10 is greater
help plzzz
3x - 4 = -2x + 31
Answer:
x=-7
if you were to simplify and do all the correct steps then you would be able to get the correct answer and I hope this helps you
7x/2+(-11)=3
x=?
Merry Christmas and or other holidays you celebrate!
Answer:
x = 4
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
A farmer is selling apples from his orchard. He uses the equation c = 1.6p to calculate the total cost, c, for every pound of apples, p.
a.) How much does a customer pay for 1 pound of apples?
b.) How much would 8.5 pounds of apples cost?
c.) A customer spent $5.20. How many pounds of apples did they purchase?
You are going to an amusement part.it cost $15 to get in and $2 for each ride.
PLEASE ANSWER!!!! SIMPLE MATH PROBLEM PLEASE
Can someone pleaseeee help if you’re correct I’ll give u brainlist
Answer:
a = 49°
Step-by-step explanation:
Answer: 49
Step-by-step explanation: 180-82-49= 49
Given that: SinA = a/b, then cosA =
Answer:
please see it my step solution work
John has three bags, each containing x counters. He removes one country from each of his bags. Write an expression for the total number of counters in John's bag now
Answer: 3x - 3
Step-by-step explanation:
Each bag contained x counters and there are 3 bags.
He removes one counter from each of the 3 bags so the expression for the counters in each bag is now;
= x - 1
As there are 3 bags, the expression is;
= 3 * ( x - 1)
= 3x - 3
Please I need help fast!!!
WILL MARK BRAINLIEST Select the correct answer. Consider these functions: f(x) = 3x^3 + 8x-2 k(x) = 4x What is the value of k(f(x))?
Answer:
D. 12x³ + 32x - 8
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Function NotationComposite FunctionsStep-by-step explanation:
Step 1: Define
f(x) = 3x³ + 8x - 2
k(x) = 4x
k(f(x)) is x = f(x)
Step 2: Find k(f(x))
Substitute: k(f(x)) = 4(3x³ + 8x - 2)Distribute 4: k(f(x)) = 12x³ + 32x - 8Coraline spent $78 on 4 T-shirts. How much did each T-shirt cost? Explain your answer
Answer:
$19.50
Step-by-step explanation:
You can set up a simple equation where t-shirts are represented by t and cost by c.
$78=4t.
To solve this equation, you want to get the variable isolated. To do this divide four on both sides since the t is multiplied by 4 and to undo multiplication, you divide. So you divide 4t by four, which gets you 1t, and then you divide 78 by 4 (because whatever you do to one side you have to do it to the other) which gives you 19.5. So the remaining equation is
$19.50=1t
And since t represents t-shirts, the equation is saying that $19.50 is equal to one t-shirt.
There are 5 birch trees in each row at the nursery. There are 9 rows of birch trees. How many birch trees are in the nursery?
45 Answer:
Step-by-step explanation:45
Answer:
45
Step-by-step explanation:
5x9=45
How to get that answer it to count by 5's.
5, 10, 15, 20, 25, 30, 35, 40, 45.
Another way to get there is to count by 9's
9, 18, 27, 36, 45.
The science teacher asked Ramona and Tino to make a graph illustrating the weekly plant growth with sunlight. Which type of graph would be the most appropriate for Brittney to use?
More likely a line graph
Answer:
line graph
Step-by-step explanation:
At the start of the week, you could run for 8 minutes. By the end of the week, you could run for 15 minutes. Which proportion could you use to find the percent increase in your running time? A. 7\15=n1\00 B. 8\7=n1\00 C. 7\8=n1\00 D. 8\15=n\100
Answer:
8/15=n/100
Step-by-step explanation: