Answers
Answer:
(x-4y)(x-3y) ÷(x+8y)(x-8y)×(x+8y)÷3(x-3y)
=3(x-4y)÷(x-8y)
Related Questions
Question 4 of 5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each explicit formula to its corresponding recursive formula.
(8) = 5(5)(1-1)
(n) = 3 +5(n-1)
(3) = 5+3(1-1)
7(n) = 3(5)(n-1)
$(n) = 5 +5(n-1)
f(1) = 5
(*) = 3;(n - 1), for 3
(1) = 5
(n) = f(n-1) +5, for n?
f(1) = 5
f(n) = f(n-1) + 3, for n?
Answers
Given:
The recursive formulae.
To find:
The correct explicit formulae for the given recursive formulae.
Solution:
If the recursive formula of a GP is [tex]f(n)=rf(n-1), f(1)=a, n\geq 2[/tex], then the explicit formula of that GP is:
[tex]f(n)=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
The first recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:
[tex]f(n)=5(3)^{n-1}[/tex]
Therefore, the required explicit formula for the first recursive formula is [tex]f(n)=5(3)^{n-1}[/tex].
If the recursive formula of an AP is [tex]f(n)=f(n-1)+d, f(1)=a, n\geq 2[/tex], then the explicit formula of that AP is:
[tex]f(n)=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
The second recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:
[tex]f(n)=5+(n-1)5[/tex]
[tex]f(n)=5+5(n-1)[/tex]
Therefore, the required explicit formula for the second recursive formula is [tex]f(n)=5+5(n-1)[/tex].
The third recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:
[tex]f(n)=5+(n-1)3[/tex]
[tex]f(n)=5+3(n-1)[/tex]
Therefore, the required explicit formula for the third recursive formula is [tex]f(n)=5+3(n-1)[/tex].
The number of booker borrowed from a library each week follows a normal distribution. When sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30
Answers
Answer:
2.5%
Step-by-step explanation:
Given :
Mean, μ = 190
Standard deviation, σ = 30
Probability that more than 250 books are borrowed ;
x = 250
P(Z > z)
Z = (x - μ) / σ
P[Z > (x - μ) / σ] = P[Z > (250 - 190) / 30]
P(Z > z) = P(Z > 2)
P(Z > 2) = 1 - P(Z < 2) = 1 - 0.97725
P(Z > 2) = 1 - P(Z < 2) = 0.02275
(0.02275 * 100)% = 2.275%
2.5% is closest to 2.275%
please help me solve the equations, I re-wrote the question under each of them so you can read it better. Ty
Answers
45. 13/36
46. 86/63
47. 19/42
48. 17/30
Answer:
45:13/36
46:86/63
47:19/42
48:9/10
49:1/12
The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have
Answers
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
The known value in the question includes the following
The given table of f(x) and x, from which we have;
The point of the minimum value, which is the vertex = (-3, -10)
The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)
Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6
From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2)
Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3
Therefore, we have the correct options as follows;
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
Learn more about parabola here;
https://brainly.com/question/22213822
The diagram shows a square with side length 5cm.
The length of the diagonal is y cm.
Find the exact value of y.
Answers
Answer:
5sqrt2
Step-by-step explanation:
Using the pythagorean theorem, we get 5^2+5^2=c^2. C is the diagonal here. 25+25=c^2, c^2=50. c=sqrt50. Simplifying it, we get the diagonal as 5sqrt2.
similar right triangles, i need help with this please
Answers
Answer:
Step-by-step explanation:
the answer is a)
The robotics team purchased 3 androids for the purpose of programming. Each of the robots was $398, which included tax. If the tax rate is 8%, what is the TOTAL TAX to be paid?
Answers
Answer:
$95.52
Step-by-step explanation:
Number of robots = 3
Cost of each robots = $398
Tax rate = 8%
Amount of tax of each robots = 8% of $398
= 8/100 × $398
= 0.08 × $398
= $31.84
TOTAL TAX to be paid = Amount of tax of each robots × Number of robots
= $31.84 × 3
= $95.52
TOTAL TAX to be paid = $95.52
HELP PLEASE!!! The expected value of a random variable X is 35. The variable is transformed
by multiplying X by 4 and then adding 1 to it. Find the expected value (mean)
of the transformed variable. A. 135 B.117 C. 154 D.141
Answers
Answer:
Expected value x= 35
linear transformation is defined as a + bx
here, b=4, a=1
The transformation is [tex]z=1+4x[/tex]
now, expected value, [tex]l_z=l_z(a+bx)[/tex]
[tex]=l(a)+l(bx)[/tex]
[tex]=a+b\:l\:x[/tex]
substitute the value of a=1, b=4 and l=35
[tex]l_z=1+4\times35[/tex]
[tex]=1+140[/tex]
[tex]=141[/tex]
So, the expected value of the transformed variable is 141.
OAmalOHopeO
=======================================================
Explanation:
Let's consider a set of three values such that they're all equal to 35
{35,35,35}
This rather boring set has a mean of 35 and it's hopefully very clear why this is the case. The terms "mean" and "expected value" are interchangeable.
If we multiply everything by 4, then we get the new set {140,140,140}
Then add 1 to everything and we arrive at {141,141,141}. You can quickly see that the mean here is 141.
-----------------------------
You could play around with that original set of 3 values to make things more interesting. Let's say we subtract 1 from the first item and add 1 to the last item. So we could have {35,35,35} turn into {34,35,36}. You should find that the mean is still 35 here.
If we quadruple each item, then we have {34,35,36} turn into {136,140,144}
Finally, add 1 to everything to get {137,141,145}. Computing the mean of this set leads to 141.
These are just two examples you could do to help see why the answer is D) 141
-----------------------------
In a more general theoretical sense, we're saying the following
Y = mX+b
E[Y] = E[m*X+b]
E[Y] = E[m*X] + E[b]
E[Y] = m*E[X] + b
where Y is the transformed variable based on the random variable X. In this case, m = 4 and b = 1. Also, E[X] = 35.
So,
E[Y] = m*E[X] + b
E[Y] = 4*35 + 1
E[Y] = 141
-----------------------------
Why go through all this trouble? Well consider that you know a certain distribution is centered around 35. Then consider that you want to convert those measurements to some other unit. This conversion process is us going from variable X to variable Y. Think of it like a batch conversion of sorts.
A more real world example would be something like "we know the average temperature is 35 degrees Celsius. The question is: what is the average temperature in Fahrenheit?" The numbers would be different, but the idea still holds up.
Zoe and Hanna share tips in the ratio 3:7
Last week Zoe received £24
How much did Hanna receive last week?
Answers
Answer:
56
Step-by-step explanation:
Zoe : hanna
3 7
Zoe got 24
3*8 = 24
so multiply each side by 8
Zoe : hanna
3*8 7*8
24 56
Hanna got 56
What is Index Law 2?
please give definition
Answers
LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . The a represents the number that is divided by itself and m and n represent the powers.
Answer:
The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. The a represents the number that is divided by itself and m and n represent the powers. Here is an example for this rule.
What’s the answer? I don’t understand the question and I came to see if you all can help
Answers
Answer:
15/2 that is the answer man
Find the distance between the
following points using the
Pythagorean theorem: (5, 10)
and (10, 12)
Answers
Answer:
[tex]\displaystyle d = \sqrt{29}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Step-by-step explanation:
*Note:
The distance formula is derived from the Pythagorean Theorem.
Step 1: Define
Identify
Point (5, 10)
Point (10, 12)
Step 2: Find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{5^2 + 2^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{25 + 4}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{29}[/tex]cos(30 +x) =5/3 find x
Answers
Answer:
no solution
Step-by-step explanation:
Answer:
Step-by-step explanation:
I get no solution also (the answer is imaginary).
When a coin and die are tossed together find the probability of getting:
a)coin with head and die with prime number
b)coin with head and die with composite number
c)coin with tail and die with even prime number
Answers
Answer:
a) 1/4
b) 1/6
c) 1/12
Step-by-step explanation:
Let S be the sample space.
S={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}
n(s) =12
Events
A: coin with head and die with prime number .
B:coin with head and die with composite number.
C:coin with tail and die with even prime number.
a) A={H2,H3,H5}
n(A) = 3
P(A) =n(A)/n(S)
=3/12
= 1/4
b) B={H4,H6}
n(B)= 2
P(B) = n(B)/n(S)
= 2/12
= 1/6
c) C ={T2}
n(C) = 1
P(C) = n(C)/n(S)
= 1/12
(x⁴ + 3x³ – 2x² + 5) + (2x⁴ – 5x³ + 4x – 15).
Answers
Answer:
[tex]\left(x^4+3x^3-2x^2+5\right)+\left(2x^4-5x^3+4x-15\right)[/tex]
[tex]=[/tex] [tex]x^4+3x^3-2x^2+5+2x^4-5x^3+4x-15[/tex]
[tex]=x^4+2x^4+3x^3-5x^3-2x^2+4x+5-15[/tex]
[tex]=x^4+2x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x-10[/tex]
[tex]OAmalOHopeO[/tex]
Explain the relationship of the meaning of the word isometric to the properties of an isometric or rigid transformation
Answers
Step-by-step explanation:
The iso parts of isometric means same, and It is similar becuase rigid trtransformation and the metric parts means measure. Basically isometric means same measure. Rigid transformation preserve "same measures" like angles and side lengths.
Please help!!!!!!!!!!!!!!
Answers
Answer:
choice A is the answer
Step-by-step explanation:
[tex]5 + 2.75s \leqslant 21 \\ 2.75s \leqslant 21 - 5 \\ s \leqslant 16 \div 2.75 \\ s \leqslant 5.82[/tex]
but since we only can have a whole number in the number of stops, she can only travel 5 stops with the money she has.
Joe receives a cake for his birthday. He eats $\frac{1}{4}$ of the cake on the first day. On the second day, he eats $\frac{3}{4}$ of the amount of cake that is left after the first day. What fraction of a whole cake is left for Joe to eat on the third day
Answers
Answer:
3 / 16
Step-by-step explanation:
Let The total amount = x
Fraction eaten on first day = 1/4x
Fraction left = x - 1/4x = 3/4x
Fraction of amount left eaten on second day = 3/4 of 3/4x
3/4 * 3/4x = 9/16x
Fraction left :
3/4x - 9/16x = (12x - 9x) /16 = 3/16x
Hence, fraction left = 3/16
What is the slope of the line that contains these points? x- 31, 36,41,46 y- 10,8,6,4
Answers
[tex] - \frac{2}{5} [/tex]
[tex]\text{Solve for 'x':}\\\\3(x+1)=12+4(x-1)[/tex]
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = -5[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\3(x+1)=12+4(x-1)\\----------\\\rightarrow 3x + 3 = 12 + 4x - 4\\\\\rightarrow 3x + 3 = 12 -4+4x\\\\\rightarrow 3x + 3 = 8 + 4x\\\\\rightarrow 3x + 3 = 4x + 8\\\\\rightarrow3x + 3 -3 = 4x + 8 - 3\\\\\rightarrow 3x = 4x + 5\\\\\rightarrow 3x - 4x = 4x - 4x + 5\\\\\rightarrow -x = 5\\\\\rightarrow \frac{-x=5}{-1}\\\\\rightarrow \boxed{x = -5}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=-5Step-by-step explanation:
3(x+1)=12+4(x-1)
3(x+1)=8+4x
3x+3=8+4x
3x+3−4x=8
-x+3=8
-x=8-3
-x=5
-x(-1)=5(-1)
-x(-1)=-5
x=-5
Can someone help me with this please
Answers
Answer:
.574
Step-by-step explanation:
This can be inputted in a calculator to achieve .57357643
To three decimal places that is .574
factor x^2-3x-28 using the x method
Answers
Answer:
[tex] {x}^{2} - 7x + 4x - 28 \\ = x(x - 7) + 4(x - 7) \\ = (x - 7)(x + 4)[/tex]
in how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively
Answers
Answer:
2520 ways
Step-by-step explanation:
Given
[tex]n = 10[/tex]
[tex]r = (2,3,5)[/tex]
Required
The number of selection
First, select 2 people from 10 in 10C2 ways.
There are 8 people, left.
Next, select 3 people from 8 in 8C3 ways.
There are 5 people left.
Lastly, select 5 from 5 in 5C5 ways
So, we have:
[tex]Total = ^{10}C_2 * ^8C_3 * ^5C_5[/tex]
Using combination formula
[tex]Total = 45 * 56 * 1[/tex]
[tex]Total = 2520[/tex]
Can someone please help me with this I’m struggling
Answers
Answer:
Equation: [tex]70=(x+3)x[/tex]
x = -10 or x = 7
x = 7 (width can't be negative)
x + 3 = 10
Step-by-step explanation:
Represent the width of the rectangle by x. "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression x + 3.
Area = (length)(width)
70 = (x + 3)x
Multiply out the right side.
[tex]70=x^2+3x\\x^2+3x-70=0[/tex]
Factor the left side.
[tex](x+10)(x-7)=0[/tex]
Each binomial could equal 0, so
[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]
The negative solution does not make sense as the width of a rectangle.
x = 7, making the length, x + 3 = 10
Answer:
Pls mark this as brainiest
Step-by-step explanation:
Area of the rectangle = length x breadth
consider 'x' to be width
therefore length = x+3
area = (x+3)*x
Area = 70 square
x = 7
x+3 = 7+3
= 10
verification
7 x 10
= 70
Find out the values of x and y from the following ordered pairs.
(x + y, 2) = (13, 2x – y)
Answers
Answer:
(x, y) = (5,8)
Step-by-step explanation:
Comparing the ordered pairs we get, x+y=13 and 2=2x-y. Solving it we will get, x=5 and y=8
Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.
Answers
Answer: £21007.22
Step-by-step explanation:
First, find the interest amount using the formula SI = (P × R × T) / 100.
SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22
The total amount = principle amount + interest amount
= £18790 + £2217.22 = £21007.22
Jack rides his bike 4 miles in 1/3 of an hour. What is jack unit rate in miles per hour?
Answers
Answer:
12 miles
Step-by-step explanation:
1/3 of an hour = 20 minutes = 4 miles
1 minute = 4/20 miles
60 minutes = 4/20 x 60 miles
= 4 x 3 miles
= 12 miles
60 minutes = 1 hour
=> 1 hour = 12 miles
Jacks unit rate is 12 miles/hr
Answer:
12
Step-by-step explanation:
There are two ways of doing this problem. I think the easiest way is to use a decimal in the denominator and round
4/0.333333333 = 12.000000001
The answer is obviously meant to be 12.
The other way is more sophisticated, but more accurate.
4/1 // 1/3 This is a 4 tier fraction. The rule is to invert the denominator (turn the bottom fraction upside down) and multiply.
4/1 * 3/1 = 12
The first method is easier to understand. The second is more accurate and more useful for physics.
Simplify the variable expression by evaluating its numerical part.
p-7+56 - 12
A. p + 51
B. p+37
O c. p-51
D. p + 49
Answers
i need help ASAP please
Answers
Answer:
reflection over Y axis
Step-by-step explanation:
Answer:
I believe it is D) a reflection over the Y-axis
Step-by-step explanation
it is going over the Y-axis as if it is a sort of mirror, if it were going over the x-axis it would be flipped upside down, if it was A the shape would be going over the original shape. I don't know how to explain C. (I hope this helped and I hope it was correct lol)
(c+d)^2+11(c+d)+30
Factor completely.
Answers
Answer:
firstable give c+b a polynomial value like x
so its will be x^2+11x+30
after the we have to factor it
30=6×5
and 11=6+5
so its will become
(x+6)×(x+5)=x^2+11x+30
x=c+d
(c+d+6)×(c+d+5)=(c+d)^2+11(c+d)+30
have a great day
