The 1st flat-bar, or cross, or other operator means:
-9-(-7)
-9-(-7)
-9--7
-9+7
7-9
-2
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hope it helps
You inherit $25,000 and deposit it into an account that earns 4.5% compounded continuously. How much money would be in the account after 10 years?
Answer:
sf
Step-by-step explanation:
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:
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]
A cylinder has a volume of 51[tex]m^3[/tex]. What is the volume of a cone with the same diameter and height as the cylinder?
51 [tex]m^3[/tex]
8.5 [tex]m^3[/tex]
17 [tex]m^3[/tex]
153 [tex]m^3[/tex]
In the figure below, solve for the value of a. a = ______ in. (round to the nearest tenth and do NOT include units in your answer)
Answer:
6.9
Step-by-step explanation:
sinX=opposite/hypotenuse
sin35=a/12
a=12*0.57357643635
a=6.88291723621≈6.9
what is the H.C.F of 2³×3²
A piece of rope 6.54 metres long is cut
into two pieces. One piece is twice as
long as the other. What is the length of
the longest piece?
which statement regarding the number of solutions for the linear equation shown below is true?
1/4x - 13 = 1/4(x + 13)
Answer: There is no solution.
Answer:
There is no solution
Step-by-step explanation:
Here's a graph of a linear function. Write the equation that describes that function
An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 60 meters wide. The middle of the arch is 10 meters above the center of the river. Start by writing an equation for the ellipse if the x-axis coincides with the water level and the y-axis passes through the center of the arch. How high above the river is the arch at a distance of 8 meters from the center?
The arch is ____ meters above the river at a distance of 8 meters from the center. Do not round until the end. Round to the nearest tenth of a meter.
Answer:
Step-by-step explanation:
(y/10)^2+(x/30)^2=1
y^2/100+x^2/900=1
9y^2+x^2=900
9y^2=900-x^2
y^2=(900-x^2)/9, when x=8 we have
y^2=(900-8^2)/9
y^2=(900-64)/9
y^2=836/9
y=9.6 meters
The arch is 9.6 meters above the river at a distance of 8 meters from the center.
Help me please.......
Ok I dont know how to do this im so sorry
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.
Two linear functions are shown. Which function has the greater initial value?
Answer:
Function A has the greater initial value because the initial value for Function A is 6 and the initial value for Function B is 3.
Step-by-step explanation:
✔️Function A:
Initial value = y-intercept (b)
y-intercept is the value of y, when the corresponding value of x = 0
From the table, y = 6 when x = 0.
The y-intercept of function A = 6
Therefore, initial value for Function A = 6
✔️Function B:
y = 4x + 3 is given in the slope-intercept form, y = mx + b.
b = y-intercept = initial value.
Therefore
Initial value for Function B = 3
✔️Function A has the greater initial value because the initial value for Function A is 6 and the initial value for Function B is 3.
thx guysssssssssssssssssssssssssssssssssssssssss
Pls answer correctly I’ll give you brainliest
Answer:
1=2(4)+b
Step-by-step explanation:
slope intercept looks like this y=mx(or y=#x+#
if the slope is 2 the equation will be y=2x+b
to find b so x=4 and y=1 we can plug those numbers into the equation to find b
Solve for the length of a leg
I will give brainless
The numbers are
A-24
C- 25
Answer:
7
Step-by-step explanation:
To solve for B, you have to use the Pythagorean Theorem and work it to solve for B. If b^2+24^2 is equal to 25^2, you can take those numbers (for 24^2, it's 576, and 25^2 is 625) and subtract them for the squared number that B will be equal to, 49. You then take the square root of 49 and that answer will be your side B, 7.
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
Marking brainliest!!
What should I put for the second question? I am confused. HELPP
Help me with this
Please
Answer:
146.96 [tex]m^2[/tex]
Step-by-step explanation:
1. Approach
Divide this figure into two smaller shapes. Calculate the area of these smaller shapes, and then add the results. One can divide this shape into a semi-circle, and a triangle.
2. Area of the triangle
The formula to find the area of a triangle is;
[tex]\frac{base*height}{2}[/tex]
It is given that the base of the triangle is (14m) and the height is (10m). Substitute in these values, and solve for the area,
[tex]\frac{14*10}{2}\\= \frac{140}{2}\\= 70[/tex]
2. Area of the semi-circle
The area of the semi-circle can be found by finding the area of the larger circle, and then divide it by 2, since a semi-circle is half of a circle. The formula for the area of a semi-circle is;
[tex]\frac{(pi)(r^2)}{2}[/tex]
Where (pi) is the constant (3.1415...), (r) represents the radius of the circle, which by definition is half of the diameter. Substitute in the values and solve;
[tex]\frac{(pi)(7)^2}{2}\\= \frac{3.14*49}{2}\\=76.96[/tex]
3. Find the total area;
Now add up the two values for the area of the figures;
Triangle + Semi-circle
= 70 + 76.96
= 146.96
Answer: about 147 m²
Step-by-step explanation:
Cos Milky said it. Trust Milky. Milky Smart.
Solve a0 = 0, a1 = 1 and an = an−1 + an−2 + 2n , for n ≥ 2. Hints: This one involves a lot more algebra than the problems above. Solving the homogeneous problem will involve using the quadratic formula. The characteristic roots turn out to be 1 ± √ 5 2 (but show the work!). For a particular solution, try an = A2 n . You should find A = 4 (but show the work!). Put those two pieces together to write down the general solution an = A( (1 + √ 5 )/2 )^n + B( (1 − √ 5)/ 2 )^n + 4(2^n ) and the determine the values for A and B by using the two initial conditions, a0 = 0 and a1 = 1. The necessary arithmetic will be somewhat complicated, but not impossible.
Answer:
Hi yes ik I'm not that good at math but wouldn't it be
a n=1∗1 n =1
GIVING 25 PTS URGENT
Answer:
D) 76 sq in
Step-by-step explanation:
It’s 4 triangles. A=1/2bh
1/2(8)(5)=20 (two of these)
1/2(8)(6)=24
1/2(4)(6)=12
20+20+24+12=76
The price of an item yesterday was $130. Today, the price fell to $39. Find the percentage decrease.
Answer:
30% decrease
Step-by-step explanation:
We have to divide 39 by 130 and then find the percentage of it. 39/130 is equal to 3/10, and 3/10 is equal to 30%. That means that it was a 30% decrease.
Answer:
35%
Step-by-step explanation:
Find the measure of 67.
81
96
90
47 = [?]
Entor
Answer
Correct option is
A
68
Answer:
96 is the answer because vertically opposite angles are always equal
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)
y - X=-5
y = 2x2-3x-5
PLEASE HELP
(use substitution)
Answer:
x=1 y=-4
Step-by-step explanation:
Untaxi viaja
ina
velocidad de 48 mph
llegar a un destino
in 2 2 horas media.
y
¿ Cuál seria su velocidad
Si se tarda dos horas?
para
llegar
Answer:
60 millas por hora.
Step-by-step explanation:
Dado que un taxi viaja a una velocidad de 48 mph para llegar a un destino en 2 horas y media, para determinar cuál seria su velocidad si se tarda dos horas para llegar se debe realizar el siguiente cálculo:
48 x 2.5 = 120
120 / 2 = X
60 = X
Así, su velocidad, si se tardase dos horas en llegar, sería de 60 millas por hora.
Determine the volume and the total surface area of the square pyramid.if its perpendicular height is 12cm and square length is 5cm
Answer:
Volume = 100 cm³
Surface area of the square pyramid = 145 cm²
Step-by-step explanation:
Given:
Perpendicular height = 12cm
Square length = 5cm
Find:
Volume
Surface area of the square pyramid
Computation:
Area of base = side²
Area of base = 5²
Area of base = 25 cm²
Volume = (1/3)(A)(h)
Volume = (1/3)(25)(12)
Volume = 100 cm³
Surface area of the square pyramid = A + 1/2(P)(h)
Perimeter square pyramid = 4(s)
Perimeter square pyramid = 4(5)
Perimeter square pyramid = 20 cm
Surface area of the square pyramid = 25 + 1/2(20)(12)
Surface area of the square pyramid = 145 cm²
The cashier determines that the customer's groceries total $156.75. If the sales tax is four percent, how much will the customer have to pay for their groceries, including tax?
If Sam's present age is x years, what will be his age in years after 20 years from now?
31 x + 20
x - 20
20x
x/20