Answer:
10(6 - x) or 10(x - 6)
Step-by-step explanation:
Let the number be x.
Answer: 10(6 - x) or 10(x - 6)
PLEASE HELP!!!
Which expression are equal to 6³×2 6÷2³?
O12 6
O12³
O6³
O2 6×3³
O2³×3³
Answer:
(6³×2^6)÷2³=6³×2^(6-3)=6³×2³=(6×2)³=12³is your answer(1728)
You had a bag of fruit snacks that you shared with 4 friends. Each of you got 175 or fewer fruit snacks. The inequality x÷4≤175 models this situation. Solve the inequality to find the number of fruit snacks that were in the bag.
Answer:
Step-by-step explanation:
It’s 20
Which of the following is the correct factorization of the polynomial 4x2 - 11x +7?
A)
(4x - 1)(x - 7)
B)
(4x - 7)(x - 1)
C)
(4x - 7)(x + 1)
D)
(4x + 1)(x - 7)
Recall that the Fibonacci Sequence is defined by the recurrence relation, a0 = a1 = 1 and for n ≥ 2, an = an−1 + an−2 . a. Show that f(x) = 1 1−x−x 2 is the generating function of the Fibonacci Sequence. b. Find ???? and β such that 1 − x − x 2 = (1 − ????x)(1 − βx). c. Find A and B in terms of ???? and β, such that 1 1−x−x 2 = A 1−????x + B 1−βx. d. Use the results of the previous parts to obtain a formula for an.
Answer:
Step-by-step explanation:
From the given information:
[tex]a_n = a_{n-1} + a_{n-2}; \ \ \ n \ge 2 \\ \\ a_o = 1 \\ \\ a_1 =1 \ \ \ \ \ since \ \ a_o = a_1 = 1[/tex]
A)
[tex]a_n - a_{n-1} - a_{n-2} = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2}(a_n -a_{n-1}-a_{n-2} ) x^n = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2} a_nx^n - \sum \limits ^{\infty}_{n=2} a_{n-1}x^n - \sum \limits ^{\infty}_{n=2}a_{n-2} x^n = 0 \\ \\ \implies (a(x) -a_o-a_1x) - (x(a(x) -a_o)) -x^2a(x) = 0 \\ \\ \implies a(x) (1 -x-x^2) -a_o-a_1x+a_ox = 0 \\ \\ \implies a(x)(1-x-x^2)-1-x+x=0 \\ \\ \implies a(x) (1-x-x^2) = 1[/tex]
[tex]\mathbf{Generating \ Function: a(x) = \dfrac{1}{1-x-x^2}=f(x)}[/tex]
B)
[tex]If \ \ 1 -x-x^2 = (1 - \alpha x) ( 1- \beta x) \\ \\ \implies 1 -x - ^2 = 1 + \alpha \beta x^2 - ( \alpha + \beta )x \\ \\ \text{It implies that:} \\ \\ \alpha \beta = -1 \\ \\ \alpha + \beta = 1 \\ \\ \implies \alpha = ( 1-\beta) \\ \\ ( 1- \beta) \beta = -1 \\ \\ \implies \beta - \beta^2 = -1 \implies \beta - \beta^2 -1 = 0\\ \\ \beta = \dfrac{-(-1) \pm \sqrt{(-1)^2 -4(1)(-1)}}{2(1)}[/tex]
[tex]\beta = \dfrac{1\pm \sqrt{5}}{2} \\ \\ \beta = \dfrac{1 + \sqrt{5}}{2} \ \ and \ \ \alpha = \dfrac{1 - \sqrt{5}}{2}[/tex]
C)
[tex]\dfrac{1}{1-x-x^2}= \dfrac{A}{1-\alpha x}+ \dfrac{\beta}{1-\beta x} \\ \\ = \dfrac{A(1-\beta x) + B(1-\alpha x)}{(1-\alpha x) (1 - \beta x)} \\ \\ = \dfrac{(A+B)-(A\beta+B\alpha)x}{(1-\alpha x) (1-\beta x)}[/tex]
[tex]\text{It means:} \\ \\ A+B=1 \\ \\ B = (1-A) \\ \\ A\beta+ B \alpha =0 \\ \\ A\beta ( 1 -A) \alpha = 0 \\ \\ A( \beta - \alpha ) = -\alpha \\ \\ A = \dfrac{\alpha}{\alpha - \beta } \\ \\ \\ \\ B = 1 - \dfrac{\alpha }{\alpha - \beta} \implies \dfrac{\alpha - \beta - \alpha }{\alpha - \beta } \\ \\ =\dfrac{-\beta }{\alpha - \beta} \\ \\ \mathbf{B = \dfrac{\beta }{\beta - \alpha }}[/tex]
D)
[tex]\text{The formula for} a_n: \\ \\ a(x) = \dfrac{\alpha }{\alpha - \beta }\sum \limits ^{\infty}_{n=0} \alpha ^n x^n - \dfrac{\beta}{\beta - \alpha }\sum \limits ^{\infty}_{n=0} \beta x^n \\ \\ \implies \sum \limits ^{\infty}_{n =0} \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta}x^n \\ \\ a_n = \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta } \\ \\ \\ a_n = \dfrac{1}{\sqrt{5}} \Big (\Big( \dfrac{\sqrt{5}+1}{2}\Big)^{n+1}- \Big ( \dfrac{1-\sqrt{5}}{2}\Big) ^{n+1}\Big)[/tex]
As the student council treasurer, you prepare the budget for your class rafting trip. Each large raft
costs $100 to rent and each small raft costs $40 to rent. You have $1,600 to spend. Write and
solve a linear equation to find the number of small rafts you can rent if you rent 12 large rafts.
Answer:
10 small rafts
Step-by-step explanation:
(1600- 1200) / 40 = 10
1600- 1200 = 400
400 / 40 = 10
12 large rafts costs $1200 so subtract that amount from you budget. If you do that you will have $400 left. So I divided $400 by the amount of money each small raft cost whitch was $40 per small raft so i got the quotient of 10.
Sorry if i worded that weirdly but you get the point.
P.s sorry if it isn't comlety correct but i did my best so... ya
the sum of the three sisters' ages is 51. If ava is 6 years older than
Camila, and Camila is twice as old as Luna, what are the ages of the
three sisters?
Create an equation with only one variable.
9514 1404 393
Answer:
Luna is 9Camila is 18Ava is 24Step-by-step explanation:
We can express all of the ages in terms of Luna's age. Letting L represent Luna's age, we have ...
Luna's age: LCamila's age: 2LAva's age: 2L +6The total of their ages is then ...
L +2L +(2L+6) = 51 . . . . an equation with one variable
5L = 45
L = 9
Luna is 9, Camila is 18, and Ava is 24.
In triangle ABC, angle C is a right angle. If cos A = 5 8, what is the value of cos B?
Answer:
65
Step-by-step explanation:
.A boat can travel 280 miles on 56
gallons of gasoline. How much
gasoline will it need to go 110 miles
Answer:
22 gallons
Step-by-step explanation:
280 miles / 56 gallons = 5 miles per gallon
110 miles/5 mpg = 22 gallons
Analyze the results of the correlation using the given residual plot.
Answer:
Last one
Step-by-step explanation:
Answer:Analyze the results of the correlation using the given residual plot.
Residual
Step-by-step explanation:
PLEASE HELP!!!! ILL GIVE BRAINLIEST!
Explain why the two figures below are not similar. Use complete sentences and provide evidence to support your explanation.
Answer: because the figure on the left is negative and more wide open while the other one is not only smaller but also positive and it’s more shut
Step-by-step explanation:
So the X-axis of the Figure on the left is going form point -3 to 0 while the other figure on the right is going form 3 to 5. And the Y- axis of the figure on the left is 2 while the right is 1 which proves that the figure on the left is bigger then the other
Your Also supposed to add all the point like first look for the Y and the X of I with J Then look for H and K then look for G and L the look for the slope of all those and then add them,then do the same with the left one and see which ones more and how much more
Number Question ID: 15573
Drag these decimals into order from highest at the top to lowest.
8.3
8.31
8.301
8.03
8.031
Answer:
8.31
8.3
8.301
8.03
8.031
I think that's the answer.. not sure th
The cost of making a chair is $28 correct to the nearest dollar. Calculate the lower and upper bounds for the cost of making 450 chairs
Answer:
$12,375
$12820.50
Step-by-step explanation:
To obtain a rounded value of $28 (to nearest dollar) the lowest and highest possible value before rounding will be : 27.50 and 28.49
Hence,
Lower bound = $27.50
Upper bound = $28.49
Therefore. Cost of making 450 chairs ;
27.50 * 450 = $12,375 (lower bound)
28.49 * 450 $12820.50 (upper bound)
I need help please ASAP ?!!!!!!!
Answer:
B
Step-by-step explanation:
B because the number line goes from negative 6, -2, and x must be greater than negative 6 but less than or equal to 2
A square has a side of 10x. Write and simplify an expression for the perimeter of the square. Then calculate the perimeter of the square if
X=12
Answer:
Step-by-step explanation:
perimeter = 4(10x) = 40x units
if x = 12, perimeter = 480x units
Solve. -x < 20
Graph on a number lin
Answer:
x > -20
Step-by-step explanation:
-x < 20
When dividing by negative numbers, flip the inequality.
x > -20
inclusive -> open circle
greater than -> to the right
open circle at -20 going to the right
Someone help me
Right now.
a. Identify the relationship between the two
angles.
b. Write the equation used to represent the
relationship between the two angles.
c. Solve for the unknown variable.
Answer:
a - Mutual
b - (x+21)+(2x+3)=90
c - 3x +24 =90
3x=90-24
3x=66
X=22
im super confused pls help
The 1st flat-bar, or cross, or other operator means:
-9-(-7)
-9-(-7)
-9--7
-9+7
7-9
-2
---
hope it helps
Convert the angle −4.5 radians to degrees, rounding to the nearest 10th
Answer:-257.8
Step-by-step explanation:
Triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
What length of segment A'B?
The length of segment A'B' from the triangle A'B'C' is 6 units.
Given that, triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
In the given triangle ABC, AB=3 units
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
2=Dimensions of the new shape/3
Dimensions of the new shape=6 units
Therefore, the length of segment A'B' from the triangle A'B'C' is 6 units.
To learn more about the scale factor visit:
https://brainly.com/question/22312172.
#SPJ1
Four points are drawn on the coordinate plane and connected with straight lines to form a rectangle. Three of the vertices of the rectangle are located at (2, 1), (2, 4) and (4.4). a What are the coordinates of the fourth vertex of the rectangle? b. What are the dimensions of the rectangle? c What is the area of the rectangle?
You have 2 points with the same x value of 2 and 2 points with the same y value of 4.
You now need 2 points with the same x value of 4 ( you are given 1) and 2 y values of 1 ( you are given 1.
The missing point would need to be (4,1)
The width would be x2-x1 = 4-2 = 2 units
The length would be y2-y1 = 4-1 = 3 units
Area = 3x 2 = 6 square units
Find the volume of the cone th=20 in and r=8 in. Solve in terms of pi and round off the decimal to the
nearest tenths.
Answer:
426.7pi
Step-by-step explanation:
V = 1/3 pi r2h
1/3 × 22/7× 8 × 8 × 20
426.7 pi
Factorise the following expressions.
Answer:
Q.1 a²+10a+24
splitting the middle.
a²+6a+4a+24
=a(a+6)+4(a+6)
(a+6)(a+4)
Q.2 x²+9x+18
splitting the middle
x²+6x+3x+18
x(x+6)+3(x+6)
(x+6)(x+3)
If computers sell for $1020 per unit and hard drives sell for $118 per unit, the revenue from x computers and y hard drives can be represented by
Answer:
Revenue = 1020x + 118y
Step-by-step explanation:
Revenue = 1020x + 118y
This is an important question to understand. You will use it very shortly when you try and solve 2 equations with 2 unknown. Just to show you what that means, Suppose the revenue is
Revenue = 5808
and 11 items total were sold
x + y = 11 Total number of items sold
1020x + 118y= 5808 Revenue
is the kind of problem you will be solving.
Step-by-step explanation:
a computer sell for $1020
x computer will sell for $1020x
a hard drive sell for $118
y hard drive will sell for $118y
The revenue equals $1020x + $118y
A jury pool has 18 people that are married and 22 people that are not married, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of the following. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation out to 4 decimal places for example 3.3421E-6.)
Which function is shown in the graph below?
On a coordinate plane, an exponential function shows decay. It rapidly decreases into quadrant 1 and approaches y = 1 in quadrant 1.
y = (one-half) Superscript x + 3 Baseline minus 1
y = (one-half) Superscript x minus 3 Baseline + 1
y = (one-half) Superscript x minus 1 Baseline + 3
y = (one-half) Superscript x + 1 Baseline minus 3
Answer:
Option B, y = 2 Superscript x + 2 Baseline + 3
Step-by-step explanation:
I could be wrong tbh. I graphed it on a graphing website and the graph from B matched up with the graph shown in the question.
Hope this helps Bye =)
The exponential function is given by [tex]y=(\frac{1}{2})^{x-3} +1[/tex]
Exponential functionAn exponential function is in the form:
y = abˣ
Where y,x are variables, a is the initial value of y and b is the multiplication factor.
The exponential function is given by [tex]y=(\frac{1}{2})^{x-3} +1[/tex]
From the point (0, 9):
[tex]y=(\frac{1}{2})^{0-3} +1=9[/tex]
Also at point (3, 2):
[tex]y=(\frac{1}{2})^{3-3} +1=2[/tex]
Find out more on Exponential function at: https://brainly.com/question/12940982
The function f(x) = -(x + 5)(x + 1) is shown.
What is the range of the function?
10
8
O all real numbers less than or equal to 4
O all real numbers less than or equal to -3
O all real numbers greater than or equal to 4
O all real numbers greater than or equal to -3
6
2
-10
-8
4
-2
2
4
8
8
10
X
4
-6
8
-10
Answer:
a
Step-by-step explanation:
f(x)=-(x+5)(x+1)=-(x²+6x+5)=-(x²+6x+9-9+5)
=-(x+3)^2+4
Range: all numbers ≤4
what is the H.C.F of 2³×3²
A real estate agent has 17 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling less than 3 properties in one week. Round your answer to four decimal places.
Answer:
0.0011 = 0.11% probability of selling less than 3 properties in one week.
Step-by-step explanation:
For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A real estate agent has 17 properties that she shows.
This means that [tex]n = 17[/tex]
She feels that there is a 50% chance of selling any one property during a week.
This means that [tex]p = 0.5[/tex]
Compute the probability of selling less than 3 properties in one week.
This is
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{17,0}.(0.5)^{0}.(0.5)^{17} \approx 0[/tex]
[tex]P(X = 1) = C_{17,1}.(0.5)^{1}.(0.5)^{16} = 0.0001[/tex]
[tex]P(X = 2) = C_{17,2}.(0.5)^{2}.(0.5)^{15} = 0.0010[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0.0001 + 0.0010 = 0.0011[/tex]
0.0011 = 0.11% probability of selling less than 3 properties in one week.