7/16 - 7/12 ?
common multiple of 16 and 12 = 48 ((3x16 and 12x4)
7/16 - 7/12 = (7x3) / (16x3) - (7x4) / (12x4) = 21/48 - 28/48 = - 7/48
22nd term: -2, -5, -8, -11, -14
Answer:
The pattern goes by adding -3.
Using the arithmetic sequence, you can find the 22nd term.
[tex]t_{22} = -2+(22-1)(-3)\\t_{22} = -2+21*-3\\t_{22} = -2-63\\t_{22} = -65[/tex]
Find the solution set to the given equation. Answer only in numbers.
y(y +78) – 84(y + 78)
Answer:
(y-84) (y+78
Step-by-step explanation:
Determine the Value of x for the diagram shown.
A) 30
B) 45
C) 60
D) 80
A rectangular frame has width 7 inches longer than its length. What is the width of the painting if it’s area is 18in^2
Answer:
9 inches
Step-by-step explanation:
if the function rule is y equals 3x - 4 what is range when the domain is 7?
[tex] \rm\frac{13}8 + \sum \limits_{n = 0}^{ \infty } \frac{( - {1)}^{n + 1} (2n + 1)! }{n! (n + 2)! {4}^{2n + 3} } \\ [/tex]
Rewrite the factorial parts of the summand as
[tex]\dfrac{(2n+1)!}{n!(n+2)!} = \dfrac{(2n+1)(2n!)}{(n+2)(n+1)(n!)^2} = \dfrac{2n+1}{(n+2)(n+1)} \dbinom{2n}n[/tex]
where [tex]\binom nk[/tex] is the binomial coefficient, and [tex]\binom{2n}n[/tex] are the so-called central binomial coefficients.
Expand the rational expression into partial fractions:
[tex]\dfrac{2n+1}{(n+2)(n+1)} = \dfrac3{n+2} - \dfrac1{n+1}[/tex]
Pull out a constant factor and collect the exponential terms.
[tex]\dfrac{(-1)^{n+1}}{4^{2n+3}} = -\dfrac1{64} \left(-\dfrac1{16}\right)^n[/tex]
The sum we want is now
[tex]\displaystyle \frac{13}8 - \frac1{64} \sum_{n=0}^\infty \binom{2n}n \left(\frac3{n+2} - \frac1{n+1}\right) \left(-\frac1{16}\right)^n[/tex]
Let f(x) and g(x) be functions with power series expansions
[tex]\displaystyle f(x) = \sum_{n=0}^\infty \binom{2n}n \frac{x^n}{n+1}[/tex]
[tex]\displaystyle g(x) = \sum_{n=0}^\infty \binom{2n}n \frac{x^n}{n+2}[/tex]
and recall the well-known binomial series
[tex]\displaystyle \dfrac1{\sqrt{1-4x}} = \sum_{n=0}^\infty \binom{2n}n x^n[/tex]
which converges for |x| < 1/4.
Integrating both sides yields
[tex]\displaystyle \int \frac{dx}{\sqrt{1-4x}} = \int \sum_{n=0}^\infty \binom{2n}n x^n \, dx[/tex]
[tex]\displaystyle -\frac12 \sqrt{1-4x} = C_1 + \sum_{n=0}^\infty \binom{2n}n \frac{x^{n+1}}{n+1}[/tex]
Taking x = 0 on both sides, it follows that C₁ = -1/2. We then see that
[tex]\displaystyle f(x) = \frac{1-\sqrt{1-4x}}{2x}[/tex]
Step back and multiply both sides of the binomial series identity by x, then integrate. This yields
[tex]\displaystyle \int \frac x{\sqrt{1-4x}} \, dx = \int \sum_{n=0}^\infty \binom{2n}n x^{n+1} \, dx[/tex]
[tex]\displaystyle -\frac1{12} \sqrt{1-4x} (1 + 2x) = C_2 + C_1 x + \sum_{n=0}^\infty \binom{2n}n \frac{x^{n+2}}{n+2}[/tex]
Taking x = 0 again points to C₂ = -1/12. Hence
[tex]\displaystyle g(x) = \frac{1 - \sqrt{1-4x}(1+2x)}{12x^2}[/tex]
Then the value of the sum we want is
[tex]\displaystyle \frac{13}8 - \frac1{64} \left(3g\left(-\frac1{16}\right) - f\left(\frac1{16}\right)\right) = \frac{1+\sqrt5}2 = \boxed{\phi}[/tex]
where ɸ ≈ 1.618 is the golden ratio.
Evaluate the given function
Answer:
-4
Step-by-step explanation:
P(4)= 4^2 - (5*4)
= 16 - 20
= -4
The phone company offers Rachel 12c per minute for her long distance calls. A discount company called Rachel and offered her long service for 1/2c per minute, but will charge a R46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a better deal?
Step-by-step explanation:
x = number of minutes
the cost function (in c) of the phone company is
cp(x) = 12x
and the cost function of the discount company is
cd(x) = x/2 + 4600 (R46)
we now need to calculate for what x this becomes the same cost :
12x = x/2 + 4600
24x = x + 9200
23x = 9200
x = 400 minutes
she would have to talk for at least 400 minutes long distance per month to make it an even or then better deal.
with 400 minutes being the break-even point.
so, to make it a better deal (not just equal), she has to talk for at least 401 minutes per month.
Which expression is equivalent to 56÷7?
Find the quotient. 4,216 ÷ 7 with remainder
Answer:
602 r. 2
Step-by-step explanation:
True or false? sin 45° cos 30° − cos 45° sin 30° = sin 60° cos 45° − cos 60° sin 45°.
Answer:
The statement is false.
4000 is 0.8% of what number?
Answer:
the correct answer should be 500,000 hope this helps
4000 is 0.8% of 500000.
will give 20 points + brainliest
A. y-3=-2(x-4)
B. y-6=-1\2(x-2)
C. y-3=-1/2(x-4)
D. y-6=-1/2(x+2)
E. y-6=-2(x+2)
F. y-4=-1/2(x-3)
Answers:
A. y = -2x + 11
B. y = 1/2x + 5
C. y = -1/2x + 5
D. y = -1/2x + 5
E. y = 2x + 2
F. y = -1/2x + 11/2
Hope this helped! (brainliest please)
What is the value of x?
Answer:
12
Step-by-step explanation:
(10x - 20) + (6x + 8) = 180
16x - 12 = 180
16x = 192
x= 12
Hi there!
This is an example of supplementary angles, angles that sum up to 180° (they form a straight line).
Summing these two angles up equals 180°, so:
180° = (10x - 20)° + (6x + 8)°
We can drop the ° sign for ease of solving.
180 = 10x - 20 + 6x + 8
Combine like terms:
180 = (10x + 6x) - (20 + 8)
180 = 16x - 12
Add 12 to both sides:
192 = 16x
Divide both sides by 16:
192/16 = 16x/16
x = 12°
Eliana opened a savings account and deposited $300.00. The account earns 13% interest, compounded annually. If she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike?
Answer:
$432.87Step-by-step explanation:
Use below compound interest formula and the given data.
[tex]F = P*(1 + r)^{nt}[/tex]F- future amount, P- invested amount, r - interest rate, n - number of compounds, t- time
Given:
P = $300r = 13% or 0.13t = 3 yearsn = 1Find the amount after 3 years:
[tex]F = 300(1 + 0.13)^3 = 432.87[/tex]Overview
10
Question Progress
Homework Progress
43 / 50 Marks
Which two numbers have a mean of 10 and a range of 4?
Answer:
I belive the correct answers are 8 and 12
Step-by-step explanation:
How do you do this question?
==========================================
Work Shown:
[tex]\displaystyle S_n = \sum_{k=1}^{n} \frac{1}{k}\\\\\\\displaystyle S_4 = \sum_{k=1}^{4} \frac{1}{k}\\\\\\\displaystyle S_4 = \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\\\\\\\displaystyle S_4 = \frac{12}{12}+\frac{6}{12}+\frac{4}{12}+\frac{3}{12}\\\\\\\displaystyle S_4 = \frac{12+6+4+3}{12}\\\\\\\displaystyle S_4 = \frac{25}{12}\\\\[/tex]
Note: in step 3, I'm adding terms in the form 1/k where k ranges from k = 1 to k = 4 (k being an integer)
Simplify these expressions:
a) 5x+3x+2y+4y
b) 6x - 2x + 8y - 6y
Answer:
a)8x+6y
b)4x+2y
Step-by-step explanation:
a)5x+3x+2y+4y
5x+3x=8x
2y+4y=6y
=8x+6y
b)6x-2x+8y-6y
6x-2x=4x
8y-6y=2y
=4x+2y
Answer:
a) x = -0.75y
b) x = -0.5y
Step-by-step explanation:
Simplifying
5x + 3x + 2y + 4y = 0
Combine like terms: 5x + 3x = 8x
8x + 2y + 4y = 0
Combine like terms: 2y + 4y = 6y
8x + 6y = 0
Solving
8x + 6y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6y' to each side of the equation.
8x + 6y + -6y = 0 + -6y
Combine like terms: 6y + -6y = 0
8x + 0 = 0 + -6y
8x = 0 + -6y
Remove the zero:
8x = -6y
Divide each side by '8'.
x = -0.75y
Simplifying
x = -0.75y
Simplifying
6x + -2x + 8y + -6y = 0
Combine like terms: 6x + -2x = 4x
4x + 8y + -6y = 0
Combine like terms: 8y + -6y = 2y
4x + 2y = 0
Solving
4x + 2y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2y' to each side of the equation.
4x + 2y + -2y = 0 + -2y
Combine like terms: 2y + -2y = 0
4x + 0 = 0 + -2y
4x = 0 + -2y
Remove the zero:
4x = -2y
Divide each side by '4'.
x = -0.5y
Simplifying
x = -0.5y
f(x) = x2
g(x) = 2x + 4
evaluate
f(-1) - g(2)
Answer:
–2x2 + 13
Step-by-step explanation:
( f o g)(x) = f (g(x))
= f (–x2 + 5)
= 2( ) + 3 ... setting up to insert the input formula
= 2(–x2 + 5) + 3
= –2x2 + 10 + 3
What is the value of x when h(x) = −3?
Answer:
○ -1
Step-by-step explanation:
Looking closely at this piecewise function, when the line on the left-hand side intersects at -3 = y, x is -1.
i hope this work for you
How do you do this question?
Answer:
1
Inconclusive
Step-by-step explanation:
aₙ = (-1)ⁿ / (n + 6)
aₙ₊₁ = (-1)ⁿ⁺¹ / (n + 1 + 6)
lim(n→∞)│aₙ₊₁ / aₙ│
lim(n→∞)│[(-1)ⁿ⁺¹ / (n + 1 + 6)] / [(-1)ⁿ / (n + 6)]│
lim(n→∞)│[(-1)ⁿ⁺¹ / (n + 7)] × [(n + 6) / (-1)ⁿ]│
lim(n→∞)│[(-1)ⁿ⁺¹ / (-1)ⁿ] × [(n + 6) / (n + 7)]│
lim(n→∞)│-1 × [(n + 6) / (n + 7)]│
lim(n→∞) [(n + 6) / (n + 7)]
1
The limit equals 1, so the ratio test is inconclusive.
Which of the following cosine functions has a period of 3Pi
Answer:
C
Step-by-step explanation:
Hello!
In the equation y=a cos bx, we can learn alot about the cosine graph.
a is the amplitude, or how 'long' the cosine graph is.
b is the period, which is how 'wide' one cycle of a cosine period can be. The higher the period, the wider the cycle is.
In this equation, we are focused on finding the period; so any choices that contain amplitude is not a correct answer choice for this problem, which leaves out B and C.
To find the period, we can plug b into [tex]\frac{2\pi }{b}[/tex] , which in a way converts the b value to a period.
For B) y= cos3x
[tex]\frac{2\pi }{3}[/tex]= it does not equal 3 [tex]\pi[/tex]
For C) y=cos [tex]\frac{2}{3}[/tex]x
[tex]\frac{2\pi }{\frac{2}{3}}[/tex]= equals 3 [tex]\pi[/tex] when simplified
Since C equals 3 [tex]\pi[/tex] as a period, C is the only logical answer.
What is the remainder when
8
x
3
+
6
x
2
−
7
x
−
2
is divided by
x
+
2
?
What is the missing side length in this right triangle? 9 in & 12 in
15 is the value of the missing side of the right-angled triangle.
An isosceles triangle, which consists of a pair of sides as well as sides with angles identically, is additionally recognized as a right triangle. Two 45° angles and a 90° angle make up a right isosceles triangle. The triangle's three sides add up to 180 degrees in total.
The information that is provided is with respect to the right triangle:
Side 1 is given as = 9
Side 1 is given as = 12
Applying the Pythagoras theorem:
[tex]H^{2} = S1^{2} + S2^{2} \\= 9^{2} + 12^{2} \\\\= 81 + 144\\=225\\h = \sqrt{225} \\h = 15[/tex]
Learn more about right-angle triangles, here:
https://brainly.com/question/3772264
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WHAT IS 9+8+9-2+5x5+5-25+5-4+2+-2+4-+2-5+4-2+5-4+2-5+4-1+5-4+-2+4-2+5-4+2-4
+-+
Answer:
34
Step-by-step explanation:
cause you had to doit the simple math problem
are you trying to prank on this problem
the answer is 5 because I got it correct on a quiz
Marion is 3 feet tall. She is 4 inches taller than her brother Elijah.She is 1 1/4 feet shorter than her sister Lorie. How tall are Elijah and Lorie, Show your work. (1 foot = 12 inches)
Answer:
3-4 inch= 2.8feet
11/4 = 2.75
2.8-2.75=0.05
Elijsh=2.8
lorie= 2.85
What is 52 - (36/3) x 4
Answer:
=3
Step-by-step explanation:
Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two cities at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?
A runner can travel 340 meters in 20 seconds.At this rate,how far does the runner go in 1 minute?
Answer:
1020 m
Step-by-step explanation:
340 x 3 = 1020
Answer:
6800
Step-by-step explanation:
b. El empleado de una compania tiene un sueldo mensual de L. 23, 865,00, en el mes de marzo del 2019 se le hizo una rebaja
del 20% por llegadas tarde al trabajo. Cuanto se le dedujo? ¿Qué sueldo neto saco ese mes?
Ese mes se le dedujeron $4774, y cobró un sueldo de $19,092.
Cálculo de cantidadesDado que el empleado de una compañía tiene un sueldo mensual de L. 23, 865,00, y en el mes de marzo del 2019 se le hizo una rebaja del 20% por llegadas tarde al trabajo, para determinar cuánto se le dedujo y qué sueldo neto sacó ese mes se debe realizar el siguiente cálculo:
100 - 20 = 8023,865 x 0.80 = X19,092 = X23,865 - 19,092 = 4773Por lo tanto, ese mes se le dedujeron $4774, y cobró un sueldo de $19,092.
Aprende más acerca de cálculos de cantidades en https://brainly.com/question/14342345