PLS HELP ASAP PLS PLSPLS
What is the explicit formula for this sequence?
6, 2, -2, -6, ...
Answers
Answer:
B
Step-by-step explanation:
this is just common sense. if you would have tried you could have easily answered this yourself.
the sequence starts with 6. that is a1.
so, the formula simply has to add "something" to 6.
therefore, A and D are out.
and then we see immediately that the sequence is built by subtracting 4 (or adding -4) for every step.
so, we need to add multiples of -4.
therefore, only B is correct (C adds multiples of +4).
Related Questions
What quadratic formula do I need to use to solve 3x(x+6)=-1
Answers
Answer:
[tex]\Large \boxed{x_1=\frac{9+\sqrt{51} }{3} \ \ ; \ \ x_2=\frac{9-\sqrt{51} }{3} }[/tex]
Step-by-step explanation:
[tex]\displaystyle \Large \boldsymbol{} 3x(x+6)=-10 \\\\3x^2+18x=-10 \\\\3x^2+18x+10=0 \\\\D=324-120=204 \\\\ x_{1;2}=\frac{18\pm2\sqrt{51} }{6} =\frac{9\pm\sqrt{51} }{3}[/tex]
double a number plus 54 equals 8 times the number
Answers
2x+54=8x
So. The Answer is 7
Mike and Ken shared some stamps. \frac{1}{5} 5 1 of Ken's stamps were \frac{1}{3} 3 1 of Mike's stamps. If Mike gave Ken 24 stamps, Ken would have thrice as many stamps as Mike. Find the number of stamps each of them had in the beginning.
Answers
Answer:
Mike had 72 stamps
Ken had 120 stamps
Step-by-step explanation:
Given
[tex]M \to Mike[/tex]
[tex]K \to Ken[/tex]
[tex]\frac{1}{5} * K = \frac{1}{3} * M[/tex]
[tex]K + 24 = 3 * ( M - 24)[/tex]
Required
Find K and M
Make K the subject in: [tex]K + 24 = 3 * ( M - 24)[/tex]
[tex]K = 3 * ( M - 24) - 24[/tex]
Substitute [tex]K = 3 * ( M - 24) - 24[/tex] in [tex]\frac{1}{5} * K = \frac{1}{3} * M[/tex]
[tex]\frac{1}{5} * [3 * ( M - 24) - 24] = \frac{1}{3} * M[/tex]
Open brackets
[tex]\frac{1}{5} * [3M - 72 - 24] = \frac{1}{3} * M[/tex]
[tex]\frac{1}{5} * [3M -96] = \frac{1}{3} * M[/tex]
Multiply both sides by 15
[tex]3* [3M -96] = 5 * M[/tex]
[tex]9M -288 = 5M[/tex]
Collect like terms
[tex]9M -5M= 288[/tex]
[tex]4M= 288[/tex]
Divide both sides by 4
[tex]M= 72[/tex]
Substitute [tex]M= 72[/tex] in [tex]K = 3 * ( M - 24) - 24[/tex]
[tex]K = 3 * (72 - 24) - 24[/tex]
[tex]K = 3 * 48 - 24[/tex]
[tex]K = 120[/tex]
Given a line segment that contains the points A,B, & C in order,if AB = 2x + 3, BC = 4x - 11, and AC = 28, find the length of segment AB.
Answers
Answer:
15
Step-by-step explanation:
AB+BC=AC
2X+3+(4X-11)
6X-8=28
6x= 36
x=6
then ab= 2(6)+3
=15
bc= 4(6)-11
=13
ac=ab+bc
=15+13
=28
You are standing 186 feet away from the base of a building and your clinometer
measures 23° when it's looking at the top of the building. (This angle is the one between
the ground and the top of the building). Please calculate the height of the building.
Answers
9514 1404 393
Answer:
about 79 ft
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
In this scenario, the angle is 23°, the adjacent side is the distance to the building, and the opposite side is the building height. Then we have ...
height = tan(23°)·(186 ft) ≈ 78.95 ft ≈ 79 ft
arc length of an oval that is 6ft by 5ft. i just want 1/4 of the oval. i want to find out how long i would need a wire to go from the ground to the middle of the "dome".
the picture explains it better.
in the end i want to have a wire frame around the garden and than take some netting and use that to keep out the big bugs and birds. i will of course use zip ties to attach the screen/netting to the frame. unless there is a easier and cheaper way to do this.
Answers
You can model the ellipse with the equation
(x/6)² + (y/5)² = 1
If you're comfortable with calculus, read on.
Let x = 6 cos(t ) and y = 5 sin(t ), with 0 ≤ t ≤ π/2. Then the curve C parameterized by (x(t), y(t)) traces out one quarter of the ellipse. The arc length of this curve is given by the integral,
[tex]\displaystyle\int_C\mathrm ds = \int_0^{\pi/2}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{36\sin^2(t)+25\cos^2(t)}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{25+11\sin^2(t)}\,\mathrm dt \\\\ = 5\int_0^{\pi/2}\sqrt{1+\frac{11}{25}\sin^2(t)}\,\mathrm dt[/tex]
Unfortunately, you cannot find the exact value of this integral. (Well, you can, but it involves introducing a special kind of function; I'll link it in a comment.)
But you can approximate it, and the integral above comes out to about 8.657.
I'm not sure if there's a simpler, purely geometric way to estimate the arc length. But since the semiaxes (5 ft and 6 ft) are fairly close, you could try a circle with a radius somewhere in between. The arc length would range between 7.854 ft and 9.425 ft. If the material isn't too expensive, you can always overshoot and trim off the excess or repurpose it.
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. If you randomly choose your character and tool, what is the probability that you wont be a hobbit or use an umbrella
Answers
Answer:
The probability that you won't be a hobbit=
[tex] \frac{2}{3} [/tex]
The probability that you won't choose an umbrella=
[tex] \frac{4}{5} [/tex]
Step-by-step explanation:
The characters are 3, minus the hobbit gives you 2. So the probability of that=
[tex] \frac{2}{3} [/tex]
The weapons are 5, minus the umbrella is 4. So the probability of that=
[tex] \frac{4}{5} [/tex]
anyone can help me with this
Answers
Answer:
4x-7=-5x²
or, 5x²+4x-7=0
so the standard form of the equation is,
5x²+4x-7=0
or, f(x) = 5x²+4x-7
Answered by GAUTHMATH
The curve C has parametric equations x = t², y = (2 - t)^1/2, for 0 ≤ t ≤2.
Find d2y/dx2 in terms of t.
Can I have the full workings also please?
Answers
Answer:
y''=(4-3t)/[16 t^3 (2-t)^(3/2)]
Step-by-step explanation:
x = t², y = (2 - t)^1/2
dy/dx=dy/dt×dt/dx by chain rule
dy/dt=1/2 (2-t)^(1/2-1) × (-1)
dy/dt=-1/2 (2-t)^(-1/2)
dy/dt=-1/[2(2-t)^(1/2) ]
dx/dt=2t
dy/dx=-1/[2(2-t)^(1/2) ] × 1/[2t]
dy/dx=-1/[4t (2-t)^(1/2) ]
We need to find the second derivative now.
That is we calculate d/dt(dy/dx in terms of t) then divide by derivative of x in terms of t).
dy/dx=-1/[4t (2-t)^(1/2) ]
Let's find derivative of this with respect to t.
d/dt(dy/dx)=
[0[4t (2-t)^(1/2)]-(-1)(4(2-t)^(1/2)+-4t(1/2)(2-t)^(-1/2))]/ [4t (2-t)^(1/2) ]^2
Let's simplify
d/dt(dy/dx)=
[(4(2-t)^(1/2)+-4t(1/2)(2-t)^(-1/2))]/ [4t (2-t)^(1/2) ]^2
Continuing to simplify
Apply the power in the denominator
d/dt(dy/dx)=
[(4(2-t)^(1/2)+-4t(1/2)(2-t)^(-1/2))]/ [16t^2 (2-t) ]
Multiply by (2-t)^(1/2)/(2-t)^(1/2):
d/dt(dy/dx)=
[(4(2-t)+-4t(1/2)]/ [16t^2 (2-t)^(3/2)]
Distribute/multiply:
d/dt(dy/dx)=
[(8-4t+-2t)]/ [16t^2 (2-t)^(3/2)]
Combine like terms:
d/dt(dy/dx)=
[(8-6t)]/ [16t^2 (2-t)^(3/2)]
Reducing fraction by dividing top and bottom by 2:
d/dt(dy/dx)=
[(4-3t)]/ [8t^2 (2-t)^(3/2)]
Now finally the d^2 y/dx^2 in terms of t is
d/dt(dy/dx) ÷ dx/dt=
[(4-3t)]/ [8t^2 (2-t)^(3/2)] ÷ 2t
d/dt(dy/dx) ÷ dx/dt=
[(4-3t)]/ [8t^2 (2-t)^(3/2)] × 1/( 2t)
d/dt(dy/dx) ÷ dx/dt=
[(4-3t)]/ [16t^3 (2-t)^(3/2)]
Or!!!!!!
x = t², y = (2 - t)^1/2
Since t>0, then t=sqrt(x) or x^(1/2).
Make this substitution into the equation explicitly solved for y:
y = (2 - x^1/2)^1/2
Differentiate:
y' =(1/2) (2 - x^1/2)^(-1/2) × -1/2x^(-1/2)
y'=-1/4(2 - x^1/2)^(-1/2)x^(-1/2)
y'=-1/4(2x-x^3/2)^(-1/2)
Differentiate:
y''=1/8(2x-x^3/2)^(-3/2)×(2-3/2x^1/2)
y''=(2-3/2x^1/2)/[8 (2x-x^3/2)^(3/2)]
Replace x with t^2
y''=(2-3/2t)/[8 (2t^2-t^3)^(3/2)]
Multiply top and bottom by 2
y''=(4-3t)/[16 (2t^2-t^3)^(3/2)]
Factor out t^2 inside the 3/2 power factor:
y''=(4-3t)/[16 (t^2)^(3/2) (2-t)^(3/2)]
y''=(4-3t)/[16 t^3 (2-t)^(3/2)]
What type of conic section is the following equation?
5x^2-y=12
Answers
Answer:
The conic section for the equation 5x^2 - y = 12 is parabola
A line with slope 3 intersects a line with slope 5 at the point (10, 15). What is the distance between the x-intercepts of these two lines?
Answers
Answer:
2
y = 3x-15
y=5x-35
x1=5
x2=7
distance between = 7-5 = 2
Step-by-step explanation:
please find y and round to the nearest tenth
Answers
The length of a rectangle is 10 m more than its breadth. If the perimeter of rectangle is 80 m, find the dimensions of the rectangle.
Answers
if you like my answer then please mark me as brainliest
Solve for m g=4cm-3cm
Answers
Answer:
g/c =m
Step-by-step explanation:
g=4cm-3cm
Combine like terms
g = 1cm
g =cm
Divide by c
g/c = cm/c
g/c =m
which of the following is a tinomial
Answers
Good luck.
30 Points cuz I need help ASAP
Answers
Answer:
the answer is option 1
Step-by-step explanation:
the negative angle => a quarter round angle (clockwise) = ¼ x ( -360°) = -90°
and
the positive angle => a full round angle + 270° = (360°)+270°
= 630°
Answer:
correct answer is -90 and 630
Step-by-step explanation:
Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answers
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
cho x,y thuộc n thoả mãn x hia 3 dư 1,y chia 3 dư 2.hỏi x.y chia 3 có số dư bằng bao nhiêu
Answers
Answer:
2
Step-by-step explanation:
x÷3 dư 1-->x=3a+1
y÷3 dư 2-->y=3b+2
x×y=(3a+1)×(3b+2)
=9ab+6a+3b+2
Mà 9ab, 6a, 3b chia hết cho 3, 2 chia 3 dư 1
==>x×y chia 3 dư 2
What is a linear system?
Answers
Answer:
Linear systems are systems of equations in which the variables are never multiplied with each other but only with constants and then summed up
If the blue radius below is perpendicular to the chord AC which is. 14 units long, what is the length of the segment AB?
Answers
Answer:
C. 7 units
Step-by-step explanation:
The given parameters are;
The length of the chord of the circle, [tex]\overline{AC}[/tex] = 14 units
The orientation of the radius and the chord = The radius is perpendicular to the chord
We have in ΔAOC, [tex]\overline{AO}[/tex] = [tex]\overline{OC}[/tex] = The radius of the circle
[tex]\overline{OB}[/tex] ≅ [tex]\overline{OB}[/tex] by reflexive property
The angle at point B = 90° by angle formed by the radius which is perpendiclar to the chord [tex]\overline{AC}[/tex]
ΔAOB and ΔCOB are right triangles (triangles having one 90° angle)
[tex]\overline{AO}[/tex] and [tex]\overline{OC}[/tex] are hypotenuse sides of ΔAOB and ΔCOB respectively and [tex]\overline{OB}[/tex] is a leg to ΔAOB and ΔCOB
Therefore;
ΔAOB ≅ ΔCOB, by Hypotenuse Leg rule of congruency
Therefore;
[tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] by Congruent Parts of Congruent Triangles are Congruent, CPCTC
[tex]\overline{AB}[/tex] = [tex]\overline{BC}[/tex] by definition of congruency
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] by segment addition postulate
∴ [tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AB}[/tex] + [tex]\overline{AB}[/tex] = 2 × [tex]\overline{AB}[/tex]
∴ [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex]/2
[tex]\overline{AB}[/tex] = 14/2 = 7
[tex]\overline{AB}[/tex] = 7 units.
Answer:
7 units
Step-by-step explanation:
. Ram solved 2/7 part of an exercise while Shyam solved 1/5 of it. Who solved greater part and by how much?
fast please
Answers
Step-by-step explanation:
LCM of 7 and 5 is 35
now will make the denominator equal,
10+7/35
So, Ram's work = 10/35
Shyam's work = 7/35
so
Ram > Shyam
hope it helps
Out of a sample of 327 Americans, 245 said they had no interest in professional soccer.
(Data simulated from Carey & Kereslidze, 2007) A 95% confidence interval for the
proportion of Americans who have no interest in professional soccer is 0.70 to 0.80.
Suppose that another sample of 784 Americans was taken and asked the same question.
How would the width of the new confidence interval compare to the width of the
confidence interval based on the 327 women in the armed forces?
The width of the confidence interval based on the 784 women would be narrower than the
confidence interval based on the 327 women.
The width of the confidence interval based on the 784 women would be wider than the
confidence interval based on the 327 women.
The width of the confidence interval based on the 784 women would be the same as the
confidence interval based on the 327 women.
O No answer text provided.
Answers
Answer:
The width of the confidence interval based on the 784 women would be narrower than the confidence interval based on the 327 women.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
From this, we have that the margin of error, and also the width, is inversely proportional to the sample size, that is, a larger sample size leads to a smaller margin of error and a narrower interval.
How would the width of the new confidence interval compare to the width of the confidence interval based on the 327 women in the armed forces?
New interval: 784
Old interval: 327
Sample size increased, so the new interval will be narrower, and the correct answer is:
The width of the confidence interval based on the 784 women would be narrower than the confidence interval based on the 327 women.
Tính : 2020^3-1/2020+2021
Answers
Answer:
2020³-1/4041
Step-by-step explanation:
A recipe for 4 servings requires salt and pepper to be added in the ratio of 2:3. If the recipe is adjusted from 4 to 8 servings, what is the ratio of salt and pepper that must now be added
Answers
Answer:
Is this a trick question ???
Why would the ratio of salt to pepper change if you doubled the recipe?
The amount of salt and pepper would double, but not the ratio...
the answer should be 2:3
Step-by-step explanation:
If m
Please Help!!!!!!!!!!!!
Answers
Answer:
45 degrees
Step-by-step explanation:
the 2 angles are supplementary (add up to 180 degrees)
180-135=45
if you can type 55 words in 20 seconds how long would it take to type 1,007 words
Answers
Answer:
2769.25Secound...........
(12, 9, 4) What is the area of the parallelogram shown below?
Answers
area of the parallelogram is: b x h
12 x 4 = 48 (d)
multiply
12/18×10/18
lesson name fraction.
find me out this question for answer
Answers
Hope it’s helps
The graph below shows the solution to which system of inequalities
Helpppp
Answers
Answer:
Step-by-step explanation:
(a + b)2 = 1a2 + 2ab + 1b2
(a + b)3 = 1a3 + 3a2b + 3ab2 + 1b3
How are binomial expansions related to Pascal’s triangle?
Answers
The Pascal triangle terms and binomial are related by the binomial theorem fomrula:
The row of the Pascal triangle is the same as
where n is the same as the row of the Pascal triangle.
For example,
.
is the same as the 2nd row of the Pascal triangle.
.
Also know the leading coefficient and last term degree will be the nth row of the Pascal triangle.
The first term, a will be 1 less than the previous terms and the second term, b will be 1 more than the previous terms. For example, look at
.
Another example is
.
The third row of Pascal Triangle
.
.
Pascal's triangle provides a systematic way to determine the coefficients of binomial expansions, making it a valuable tool in algebra and combinatorics.
Binomial expansions are directly related to Pascal's triangle.
Pascal's triangle is a triangular arrangement of numbers in which each number is the sum of the two numbers directly above it. The first and last numbers in each row of Pascal's triangle are always 1.
The coefficients of the terms in a binomial expansion correspond to the numbers in Pascal's triangle. Each row of Pascal's triangle represents the coefficients of the corresponding power of the binomial.
For example, in the expansion of (a + b)², the coefficients are 1, 2, and 1. These coefficients can be found in the third row of Pascal's triangle: 1, 2, 1. Similarly, in the expansion of (a + b)³, the coefficients are 1, 3, 3, and 1, which can be found in the fourth row of Pascal's triangle: 1, 3, 3, 1.
In summary, Pascal's triangle provides a systematic way to determine the coefficients of binomial expansions, making it a valuable tool in algebra and combinatorics.
Learn more about Pascal's triangle here;
https://brainly.com/question/29549939
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