Answers
the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.
multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.
so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5 <----- notice, current coefficient times 3 divided by 4+1.
anyhow, with that out of the way, lemme proceed in this one.
[tex]\bf ~~~~~~~~\textit{binomial theorem expansion} \\\\ \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^n(ax)^0\\\\ 2&+\frac{(1)(n)}{1}\to n&(1)^{n-1}(ax)^1\\\\ 3&+\frac{n\cdot (n-1)}{2}&(1)^{n-2}(ax)^2 \end{array}[/tex]
so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.
so then, we know that the expanded 2nd term is 24x therefore
[tex]\bf n(1)^{n-1}(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}[/tex]
we also know that the expanded 3rd term is 240x², therefore we can say that
[tex]\bf \cfrac{n(n-1)}{2}~~(1)^{n-2}(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \\\\\\ \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \\\\\\ a^2n^2-a^2n=480[/tex]
but but but, we know what "n" equals to, recall above, so let's do some quick substitution
[tex]\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \\\\\\ a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \\\\\\ -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft[/tex]
Related Questions
LMK ASAP...... 10 POINTS
Answers
Answer: The correct answer is 15 according to my work that I have done.
Step-by-step explanation:
* Here is all the all information you'll need just in case.
* Hopefully this helps:) Mark me the brainliest:)!!
∞ 234483279c20∞
Answer:
The correct answer is option 3
arc length = 7.5π
Step-by-step explanation:
It is given a circle with central angle ADC = 45° and radius = 30 cm
To find the length of arc ABC
From the figure we can see that the central angle of arc ABC = 45°
Therefore the arc length = (45/360) * Circumference
To find the circumference
Circumference = 2πr = 2 * π * 30 = 60π
To find the arc length
Arc ABC = (45/360) * 60π= 7.5π
Therefore arc length = 7.5π
The correct answer is option 3
Expand to write an equivalent expression: -1/4(-8+12y)
Answers
2-3y is the answer u used distributive property to expand it
Answer:
Step-by-step explanation:
An someone please help.
Answers
This is a special right triangle with 3 sides that are 5, 12, 13. You should remember this triangle.
[tex] {13}^{2} = {x}^{2} + {12}^{2} \\ {x}^{2} = {13}^{2} - {12}^{2} \\ x = \sqrt{ {13}^{2} - {12}^{2} } = \sqrt{169 - 144} = \sqrt{25} = 5[/tex]
What does alabama have that most students would like to have
Answers
4 a’s and only 1 b :)
4 is a and only 1 b , your welcome
Function k has a parent function. The table shows some ordered pairs that belong to k.
Answers
Answer:
C
Step-by-step explanation:
In the table -1 and 1 are equal to 5, which is also shown in C.
Since k is a transformed function, a graph that shows the parent function of k is: C. graph C.
Generally speaking, a function can be stretched by multiplying it with the absolute value of a numerical value that is either greater than 1 or less than -1.
Additionally, you should multiply the x-variable with the shrink or stretch factor when compressing (shrinking) or stretching a function horizontally.
Since the numbers 1 and -1 both yield the same output value, it ultimately implies that the graph of the parent function must be a parabola and a quadratic function;
As x decreases from -1, k(x) would increase.
As x increases from 1, k(x) would increase.
Missing information:
Function k has a parent function. The table shows some ordered pairs that belong to k.
Which graph shows the parent function of k?
The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers.
Answers
ANSWER
[tex]4,8,14[/tex]
EXPLANATION
Let the first number be
[tex]x[/tex]
Then the second number will be
[tex]2x[/tex]
and the third number is
[tex]2x + 6[/tex]
The sum of these numbers is 26.
This implies that;
[tex]x + 2x + (2x + 6) = 26[/tex]
Group similar terms;
[tex]x + 2x + 2x = 26 - 6[/tex]
Simplify;
[tex]5x = 20[/tex]
Divide both sides by 5
[tex]x = \frac{20}{5} [/tex]
This gives us;
[tex]x = 4[/tex]
The numbers are:
[tex]4,8,14[/tex]
What is the measure of angle x? Enter your answer in the box. x = ° Two perpendicular lines intersected by a third line, which goes from upper left to lower right. The angle formed on the left side of the figure by the diagonal line and the vertical line is labeled 42 degrees, and the angle formed on the right side of the figure by the diagonal line and the horizontal line is labeled x.
Answers
Two perpendicular lines make right angles which equal 90 degrees.
X = 90 - 42 = 48 degrees.
John wrote 1/5 of a paper in 1/4 of an hour how long did it take him to write an entire paper?\
Answers
Answer:
2 hours and 5 minutes.
Step-by-step explanation:
1 hour and 15 minutes. A quarter of an hour is 15 minutes. A full paper would be 5/5. So you would take 15x5 which would give you 75 minutes or an hour and 15 minutes
If SS= 162 from a sample of 15 data, find s^2
Answers
Answer:
11.57
Step-by-step explanation:
We have a simple formula to solve this:
[tex]s^2=\frac{SS}{n-1}[/tex]
where
SS is sum of squares
s^2 is the variance, and
n is the number of data points
We are given all the info to find out s^2. Hence,
[tex]s^2=\frac{SS}{n-1}\\s^2=\frac{162}{15-1}\\s^2=\frac{162}{14}=11.57[/tex]
The function k(x) = (g x h)(x) is graphed below, where g is an exponential function and h is a linear function. If h(x) = x + 1, which option below give the formula for g? h(x) = 2x h(x) = –2x h(x) = –2–x h(x) = 2–x
Answers
Answer:
The graph of your question is attached in the picture below.
g(x) = 2^(-x)
Step-by-step explanation:
First of all, we use a graphing tool to plot each of the equations.
If we multiply in the plotter each graph, we can easily see which is the correct option.
h(x) =x+1
g(x) = 2^-x
Answer:
h(x)=-2^-x
Step-by-step explanation:
if the radius of a circle is 15 units abs the center of the circle is (-3,2), what is the equation of the circle?
Answers
Answer:
[tex]\large\boxed{(x+3)^2+(y-2)^2=225}[/tex]
Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have r = 15 and the center (-3, 2). Substitute:
[tex](x-(-3))^2+(y-2)^2=15^2\\\\(x+3)^2+(y-2)^2=225[/tex]
the perimeter of a parallelogram is 72 meters. the width of the parallelogram is 4 meters less than it's length. Find the length and the width of the parallelogram
Answers
Answer:
Length is 18 meters and width is 14 meters
Step-by-step explanation:
You can solve for the length by using the perimeter formula.
P = 2l + 2w.
You know P = 72. You also know the length is l and the width is w = l - 4.
72 = 2l + 2(l - 4)
72 = 2l + 2l - 8
72 = 4l - 8
72 = 4l
18 = l
This means the width which is 4 meters less is 18 - 4 = 14.
(f(x) = 0.5x2 - 2) + (g(x) = 8x3 + 2)
Answers
Answer:
Final answer is [tex]f(x)+g(x)=0.5x^2+8x^3[/tex]
Step-by-step explanation:
Given functions are [tex]f\left(x\right)=0.5x^2-2[/tex] and [tex]g(x)=8x^3+2[/tex]
Now we need to add both functions:
[tex]f(x)+g(x)[/tex]
[tex]=(0.5x^2-2)+(8x^3+2)[/tex]
[tex]=0.5x^2-2+8x^3+2[/tex]
[tex]=0.5x^2+8x^3-2+2[/tex]
combine like terms -2 and +2
[tex]=0.5x^2+8x^3[/tex]
Hence final answer is [tex]f(x)+g(x)=0.5x^2+8x^3[/tex]
Answer:
[tex] f ( x ) + g ( x ) = 8 x^3 + 0.5 x ^2 [/tex]
Step-by-step explanation:
We are given the following two functions and we are to find their sum:
[tex] f ( x ) = 0.5 x ^ 2 - 2 [/tex]
[tex] g ( x ) = 8 x ^ 3 + 2 [/tex]
Adding the two given functions to get:
[tex] f ( x ) + g ( x ) = 0.5 x ^ 2 - 2 + 8 x ^ 3 + 2 [/tex]
Rearranging them to solve further:
[tex]f(x)+g(x) =8x^3+0.5x^2+2-2[/tex]
So finally we get:
[tex]f(x)+g(x) =8x^3+0.5x^2[/tex]
Esta es una bebida amarga.
sweet
yellow
bitter
salty
Answers
Answer:
Step-by-step explanation:
It's not math, but the answer is BITTER. (i used google translate)
Write and solve an equation to answer the question,
"5 is 5% of what number w?"
An equation is blank =0.05 blank .
The solution is w= blank.
Answers
The mathematical representation of '5 is 5% of what number?' is 5 = 0.05w. To solve for w, we divide 5 by 0.05, which gives us a value of w=100.
Explanation:To solve the question, '5 is 5% of what number w?', we can set up the equation as 5 = 0.05w. This equation represents the statement '5 is 5% of some number w' in mathematical terms. To find the value of w, we divide both sides of the equation by 0.05. The calculation goes like this:
Set up the equation: 5 = 0.05wDivide both sides by 0.05: w = 5 / 0.05Perform the division to find the value of w: w=100Learn more about Math Percentage here:
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The equation to find the number for which 5 is 5% is: 5 = 0.05w. The solution to the equation is w = 100.
To write and solve the equation that represents the given statement, we can let 'w' represent the unknown number.
The equation is:
5 = 0.05w
Solving for w, we divide both sides by 0.05:
w = 5 / 0.05
w = 100
Therefore, the solution to the equation is w = 100. This means that 5 is 5% of 100.
oof IDK anymore look above at the picture
Answers
Answer:
V=120 in^3
Step-by-step explanation:
Height x Width x Length
Drawing A Red Tile From A Bag And Then Drawing A Green Tile After Replacing The First Tile. Dependent Or Independent?
Answers
Answer:
Independent
Step-by-step explanation:
with replacement the total number of tiles will always remain the same,i.e the sample size will not be changed. so the events are independent.
Drawing a red tile from a bag and a green tile after replacing the first tile are independent events because the composition of the bag remains unchanged, meaning the probability of drawing the green tile remains constant.
When drawing a red tile from a bag and then drawing a green tile after replacing the first tile, the two events are considered independent. The outcome of drawing the green tile does not depend on the outcome of drawing the red tile. This is because when the first tile is replaced, the composition of the tiles in the bag remains unchanged, resulting in the probability of drawing a green tile being the same regardless of the previous draw. This is known as sampling with replacement.
If, however, the first tile was not replaced, the events would then be dependent, because the removal of the red tile would alter the composition of the bag, affecting the probability of drawing a green tile on the second draw. This is referred to as sampling without replacement. An example of dependent events is a scenario where if a bag contains four blue and three white marbles, and a marble is drawn and not replaced, the probability of drawing a marble of a particular color would change for the second draw.
what is the experimental probability of rolling a sum of 7 or 11?
Answers
Answer:
1/6
Step-by-step explanation:
The sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6.
Now I need help with this one please I’m really bad at math
Answers
y = -10
Hope this helped
rewrite 3 x 6/8 as the product of a unit fraction and a whole number
Answers
3/1×6/8=3/1×3/4=9/4=2 1/4
Solve 2,401 = 76 – 2x.
Answers
Subtract 2,401 from both sides.
0 = 76 - 2401 - 2x
0 = -2325 - 2x
Add 2x on both sides.
2x = -2325
Divide both sides by 2.
x = -2325 / 2
x = -1162.5
There is the answer.
Please consider marking this answer as Brainliest to help me advance.
Answer:
its 1.
Step-by-step explanation:
PLEASE HELP MEH I REALLY NEED HELP
Answers
Answer:
find A PATTERN
Step-by-step explanation:
FIND A PATTERN IN THE NUMBERS
Answer:
The answer is 53
Step-by-step explanation:
Which of the following values in the set below will make the equation 5x + 6 = 6 true? (Only input the number.) {0, 1, 2, 3, 4} Numerical Answers Expected! Answer for Blank 1:
Answers
Answer:
0Step-by-step explanation:
Put the values of x from the set {0, 1, 2, 3, 4} to the euation 5x + 6 = 6 and check it:
for x = 0:
5(0) + 6 = 6
0 + 6 = 6
6 = 6 TRUE
for x = 1:
5(1) + 6 = 6
5 + 6 = 6
11 = 6 FALSE
for x = 2:
5(2) + 6 = 6
10 + 6 = 6
16 = 6 FALSE
for x = 3:
5(3) + 6 = 6
15 + 6 = 6
21 = 6 FALSE
for x = 4:
5(4) + 6 = 6
20 + 6 = 6
26 = 6 FALSE
A triangle has an area of 80 yd2
and a height of 10 yd
How long is the base of the triangle?
Enter your answer in the box.
Answers
Answer:
The base is 16
Step-by-step explanation:
Answer:
8 yd²
Step-by-step explanation:
A right triangle has:
three sides with the same length
two sides that are parallel
at least two congruent sides
two sides that are perpendicular
I think that the answer is that two sides are perpendicular but I am not very sure and would like to know
Answers
Answer:
An isosceles right triangle has 2 congruent sides.
Factor 16w^4+16w^2-140
Answers
Find the Greatest Common Factor (GCF)
GCF = 4
Factor out the GCF. (Write the GCF first, then in parenthesis, divide each term by the GCF)
4(16w^4/4 + 16w^2/4 - 140/4)
Simplify each term in parenthesis
4(4w^4 + 4w^2 - 35)
Split the second term in 4w^4 + 4w^2 - 35 into two terms
4(4w^4 + 14w^2 - 10w^2 - 35)
Factor out common terms in the first two terms, then in the last two terms.
4(2w^2(2w^2 + 7) - 5(2w^2 + 7))
Factor out the common term 2w^2 + 7
= 4(2w^2 + 7)(2w^2 - 5)
Please help with this normal distribution problem
Answers
900 = 750 + 2*75. In other words, 900 is 2 standard deviations away from the mean. Similarly, 975 is 3 standard deviations from the mean. So
[tex]P(900<X<975)=P(2<Z<3)[/tex
where [tex]X[/tex] is the random variable for the lifespan of a light bulb with the given normal distribution, and [tex]Z=\dfrac{X-750}{75}[/tex] with the standard normal distribution.
We get
[tex]P(2<Z<3)\approx0.0214=2.14\%[/tex]
If you don't have a calculator/lookup table available, you can invoke the empirical rule, the one that says
[tex]\begin{cases}P(-1<Z<1)\approx68\%\\P(-2<Z<2)\approx95\%\\P(-3<Z<3)\approx99.7\%\end{cases}[/tex]
The normal distribution is symmetric about its mean, so we also know
[tex]\begin{cases}P(0<Z<1)\approx34\%\\P(0<Z<2)\approx47.5\%\\P(0<Z<3)\approx49.85\%\end{cases}[/tex]
Then
[tex]P(2<Z<3)=P(0<Z<3)-P(0<Z<2)\approx2.35\%[/tex]
Answer:
0.021
Step-by-step explanation:
One way in which to approach this problem solution is to use a calculator that has statistical distribution functions built in. My old TI-83Plus has the function "normalcdf," which does the job nicely.
Typing in normalcdf(900,975,750,75) results in the probability 0.021 that a light bulb chosen at random will last between 900 and 975 hours.
Using a table of z-scores would be a good alternative approach. Note that the z-score corresponding to 750 hours is 0; that for 900 is +2; and that for 975 is +3. Find the area under the standard normal curve to the left of 975 (z = 3) and that to the left of 900 (z = 2), and then subtract the two results. It will be 0.021, as before.
a store increased its prices on computers by 12%. If p represents the regular price of computers, what expression could be used to find the new prices of computers?
Answers
Answer:ayy but imma rapper follow me on souncloud kid ice pvt
Step-by-step explanation:
To find the new prices of computers after a 12% increase, use the expression p + 0.12p or 1.12p.
Explanation:To find the new prices of computers after a 12% increase, you can use the expression p + 0.12p. This expression represents the regular price p plus 12% of p. Simplifying this expression, we get 1.12p as the new prices of computers.
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which of the statements is true?
A) the sum of two irrational numbers is always irrational.
b) the product if two irrational numbers is sometimes rational.
c) the profuct of a rational number and an irrational number is sometimes rational.
d) the sum of two rational numbers is sometimes irrational
Answers
Answer: the answer is B beacuase The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational. "The product of two irrational numbers is SOMETIMES irrational."
The sum of two irrational numbers is always irrational is true. Option A is correct.
Given that,
To determine the statements that is true from the given statements.
In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.
What are irrational numbers?An irrational number is a type of real number which cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.
Here,
A) the sum of two irrational numbers is always irrational.
True,
b) the product if two irrational numbers is sometimes rational.
False
c) the product of a rational number and an irrational number is sometimes rational.
False
d) the sum of two rational numbers is sometimes irrational.
False
Thus, the only option that is true is the sum of two irrational numbers is always irrational. Option A is correct.
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What is the volume of the square pyramid with base edges 16m and height 24m?
Answers
Answer:
192
Step-by-step explanation:
1/2 of 24 times 16=192