Answer:
[tex]{x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 [/tex]
Step-by-step explanation:
This too follows the as same process as
https://brainly.com/question/27201053recall binomial theorem,
[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]
Given binomial:
(x+8)⁵comparing it to (a+b)ⁿ , we acquire:
[tex]a \implies x[/tex][tex]b\implies 8[/tex][tex]n\implies 5[/tex]Now substitute:
[tex] \displaystyle (x +8 {)}^{5} = \sum _{k = 0} ^{5} \binom{n}{k} {a}^{5- k} {b}^{k} [/tex]
To convert the summation into a sum, substitute the values from k=0 to k=5 into the expression which yields
[tex] \displaystyle (x + 8{)}^{5} = \binom{5}{0} {x}^{5 - 0} \cdot {8}^{0} + \binom{5}{1} {x}^{5 - 1} \cdot {8}^{1} + \binom{5}{2} {x}^{5 - 2} \cdot {8}^{2} + \binom{5}{3} {x}^{5 - 3} \cdot {8}^{3} + \binom{5}{4} {x}^{5- 4} \cdot {8}^{4} + \binom{5}{5} {x}^{5 - 5} \cdot {8}^{5} \\ \implies(x + 8 {)}^{5} = \binom{5}{0} {x}^{5} \cdot 1 + \binom{5}{1} {x}^{4} \cdot {8} + \binom{5}{2} {x}^{3} \cdot 64+ \binom{5}{3} {x}^{2} \cdot 512 + \binom{6}{4} {x}^{1} \cdot 4096+ \binom{5}{5} {x}^{0} \cdot 32768\\ \implies(x + 8{)}^{5} = 1 \cdot {x}^{5 } \cdot 1 + 5\cdot{x}^{4} \cdot {8} + 10 \cdot {x}^{3} \cdot 64+ 10 \cdot {x}^{2} \cdot 512 + 5 \cdot{x}^{1} \cdot 4096+ 1 \cdot {x}^{0} \cdot 32768 \\ \implies \boxed{ (x + 8 {)}^{5} = {x}^{5} + 40{x}^{4} + 640{x}^{3} + 5120 {x}^{2} + 20480{x}^{}+ 32768 }[/tex]
and we're done!
The enrollment at Allenton High School is expected to decrease by 5% each year.
There are currently 720 students at the high school. The following function can be used to approximate the
number of students who will be enrolled at Allenton High School in tyears from now.
ald) = 720(1 – 0.05)
A. In how many years will the high school have approximately 450 students?
Round your solution to the nearest hundredth of a year. Show your work.
Answer:
around 8 or 9 years
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST
Answer:
y=2x+b
Step-by-step explanation:
4/9 x 5/6 simplest form
5/6 x 4/9 = 10/27 as a fraction form. The work for 5/6 times 4/9 as a fraction provides more insight of how to find what is 5/6 times 4/9 in fraction form and the different variations of such problems.
help me please I will mark as brainlist
Answer:
[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]
Step-by-step explanation:
If we simplify that fraction, we get
[tex] \frac{ \alpha + \beta + \gamma }{ \alpha \beta \gamma } [/tex]
Keep that in mind.
If y, a ,b are zeroes of the cubic polynomial, then that means
[tex](x - \alpha )(x - \beta )(x - \gamma )[/tex]
make up the polynomial.
Notice that leading xoeffeicent will be 1, so the roots will multiply to
[tex] - d[/tex]
so
[tex] \alpha \beta \gamma = - d[/tex]
which gives us
[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]
Proof:
Consider the function
[tex](x - 2)(x - 3)(x - 5)[/tex]
The roots are 2, 3, 5.
D is -30 so we get
Using the value,
[tex] \frac{2 + 3 + 5}{ 30} = \frac{1}{3} [/tex]
If we use the orginal equation, we get
[tex] \frac{1}{6} + \frac{1}{10} + \frac{1}{15} = \frac{10}{30} = \frac{1}{3} [/tex]
Answer:
Hey,mate
Notice that leading xoeffeicent will be 1, so the roots will multiply to
The roots are 2, 3, 5.
[tex]\sqrt{2} \sqrt{3} \sqrt{5}[/tex]
D is -30
the half life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount . The half-life of the radioactive gas radon is approximately 3.8 days. The initial amount of radon used in an experiment is 75 grams. if N represents the number of grams of radon remaining t days after the start of the experiment,
a. Write an equation that gives N in terms of t.
b. How much gas radon approximately remains after 3.8 days?
c. approximately when will the amount of radon remaining be 10 grams?
Using an exponential function, it is found that:
a) [tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
b) 37.5 grams of the gas remains after 3.8 days.
c) The amount remaining will be of 10 grams after approximately 11 days.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.Item a:
We start with 75 grams, and then work with a half-life of 3.8 days, hence the amount after t daus is given by:
[tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
Item b:
This is N when t = 3.8, hence:
[tex]N(t) = 75(0.5)^{\frac{3.8}{3.8}} = 37.5[/tex]
37.5 grams of the gas remains after 3.8 days.
Item c:
This is t for which N(t) = 10, hence:
[tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
[tex]10 = 75(0.5)^{\frac{t}{3.8}}[/tex]
[tex](0.5)^{\frac{t}{3.8}} = \frac{10}{75}[/tex]
[tex]\log{(0.5)^{\frac{t}{3.8}}} = \log{\frac{10}{75}}[/tex]
[tex]\frac{t}{3.8}\log{0.5} = \log{\frac{10}{75}}[/tex]
[tex]t = 3.8\frac{\log{\frac{10}{75}}}{\log{0.5}}[/tex]
[tex]t \approx 11[/tex]
The amount remaining will be of 10 grams after approximately 11 days.
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solve- cbb to work it out
➝ Hypotenuse of triangle ( a ) = 21.63 mm
➝ Hypotenuse of triangle ( b ) = 150 mm
➝ Hypotenuse of triangle ( c ) = 111.80 mm
[tex] \quad\rule{300pt}{1.5pt}\quad[/tex]
Solution:We have to find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.
Pythagoras theorem states that :" In a right angled triangle, the square of hypotenuse side is equal to the sum of square of other two sides "
[tex] \qquad \bull \:{\pmb{\mathfrak{ h^2 = b^2 + p^2}}}[/tex]
And we have to convert the answer to the units indicated in red i.e, in mm.
Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula
For triangle ( a )[tex] :\implies\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{b^2 + p^2}}[/tex]
[tex] :\implies\qquad \sf{h=\sqrt{ (12)^2 + (18)^2 }}[/tex]
[tex] :\implies\qquad \sf{ h= \sqrt{144 + 324}}[/tex]
[tex] :\implies\qquad \sf{ h = \sqrt{468}}[/tex]
[tex] :\implies\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}}[/tex]
For triangle ( b )[tex] :\implies\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex] :\implies\qquad \sf{h =\sqrt{b^2 + p^2} }[/tex]
[tex] :\implies\qquad \sf{ h = \sqrt{(90)^2+(120)^2}}[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{8100+14400}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{22500}}[/tex]
[tex] :\implies\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} }[/tex]
For triangle ( c )[tex] :\implies\qquad \sf{h^2 = b^2 + p^2 }[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{b^2 + p^2}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{(100)^2)+(50)^2}}[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{10000+2500}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{12500}}[/tex]
[tex] :\implies\qquad \underline{\underline{\pmb{\sf{h = 111.80mm}}} }[/tex]
Hypotenuse of triangle ( a ) = 21.63 mm
Hypotenuse of triangle ( b ) = 150 mm
Hypotenuse of triangle ( c ) = 111.80 mm
Explanation :find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.
[tex]h^2 = b^2 + p^2[/tex]
And we have to convert the answer to the units indicated in red i.e, in mm.
Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula
[tex]For \: \: triangle ( a )
\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex]\qquad \sf{ h =\sqrt{b^2 + p^2}}[/tex][tex]\qquad \sf{h=\sqrt{ (12)^2 + (18)^2 }}[/tex][tex]\qquad\sf{h=\sqrt{ (12)^2 + (18)^2 }} \\ \\ \qquad \sf{ h= \sqrt{144 + 324}} \\ \\ \qquad \sf{ h = \sqrt{468}}
\\ \\\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}} \\ \\ For \: \: triangle ( b ) \qquad \sf{ h^2 = b^2 + p^2} \\ \\ \qquad \sf{h =\sqrt{b^2 + p^2} } \\ \\ \qquad \sf{ h = \sqrt{(90)^2+(120)^2}} \\ \\ \qquad \sf{ h=\sqrt{8100+14400}} \\ \\
\qquad \sf{ h =\sqrt{22500}} \\ \\\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} } \\ \\ For \: \: triangle ( c ) \qquad \sf{h^2 = b^2 + p^2 } \\ \\ \qquad \sf{ h=\sqrt{b^2 + p^2}} \\ \\\qquad\sf{ h=\sqrt{(100)^2)+(50)^2}} \\ \\\qquad\sf{ h=\sqrt{10000+2500}} \\ \\ \qquad \sf{ h =\sqrt{12500}} \\ \\
\qquad\underline{\underline{\pmb{\sf{h = 111.80mm}}} } [/tex]
Jocelyn is pregnant and needs to eat at least 500 more calories a day than usual. when buying groceries one day with a
budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150
calories each. the bananas cost $0. 35 each and the granola bars cost $2. 50 each.
Indicate whether the two functions are equal. If the two functions are not equal, then give an element of the domain on which the two functions have different values
The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
How to interpret the function?From the complete information, it should be noted that the function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
Also, f(x) = x³ and g(x) = |x|³ are not equal. This is because both functions are not equal for x < 0. This can be illustrated when x = -1. In this case, f(x) = -1 and g(x) = 1.
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The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
What is the equality of the two functions?Two functions are equal if they have the same domain and codomain and their values are the same for all elements of the domain.
The function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
Also, f(x) = x³ and g(x) = |x|³ are not equal.
This is because both functions are not equal for x < 0.
This can be illustrated when x = -1. In this case, f(x) = -1 and g(x) = 1.
Hence, the function f(x) = x² and g(x) = |x|² are the same since they both give a positive value.
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A square with side length s has an area of 324 square centimeters. This equation shows the area of the square ^{s^2}is 324
Answer:
the side s is 18
Step-by-step explanation:
s=?
Area of square(A)=324
Now,
A=s²
324=s²
√(324)=s
s=18
More help please! IF YOU DON'T KNOW THE ANSWER THEN DO NOT ANSWER!
Answer:
8/3 < 8/2
D
Step-by-step explanation:
8/3 = 2.67
8/2 = 4
So, when fractions have equivalent (same) numerators, the one with the lesser denominator is the greater fraction.
There is more left if 8 is divided by 2 than when it is divided by 3
[Answer]8/3 < 8/2
[Answer] D
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
ABCD is an irregular quadrilateral. The sum of all the interior angles is 360 degrees. What is the measure of angle D?
A. 60°
B. 120°
C. 180°
D. Need more information
please hurry! first CORRECT answer gets brainliest! :)
Answer:
D. Need more informationStep-by-step explanation:
The given information is not sufficient to determine each angle measure since the quadrilateral is irregular.
It would be good to see the picture at least.
Possible options are A or B but we can't confirm without additional detals, option C can't be a correct choice as 180° represents a straight line.
Help if you understand thanks
Step-by-step explanation:
Table A represents an arithmetic sequence with a common difference d=+7.5
so for x=4, it's y³+7.5=25+7.5=32.5
for x=5, it's y⁴+7.5=32.5+7.5=40
Table B represents a geometric sequence with a common ratio r=4, so you're essentially multiplying by 4.
for x=4, y⁴=y³×4=160×4=640
for x=5, y⁵=y⁴×4=640×4=2560
solve pls brainliest
Answer:
63
Step-by-step explanation:
Multiply each side by 9
4y=252
Divide by 4
y=63
Answer:
y= 63
Step-by-step explanation:
simplify 35x-35
over 14x-49
Answer: Distributive property a(b+c) = ab + ac
-5(7)x + 7(7) = -35x + 49 (D)
Evaluate the expression 120n+160,500120n+160,500 when n=32n=32.
Answer: The answer should be 164,340.
what is the slope of line AB
Answer:
2,3
Step-by-step explanation:
you count up 2,then count over three
The ratio of the measures of the three angles in a triangle is 15:8:13. Find the measure of the three angles.
Answer: 75, 40, 65
Step-by-step explanation:
Let the angles measure 15x, 8x, and 13x.
Since the sum of the angles of a triangle is 180 degrees,
15x+8x+13x=180, meaning that x=5.
So, the angles are 15(5)=75 degrees, 8(5)=40 degrees, and 13(5)=65 degrees.
It’s a 4 digit number. The tens are double the ones. The thousands are double the tens. The sum of the digit is 19
URGENT
Mr. Wilson bought a bag of birdseed and put half of it in his bird feeder. He split the other half equally among his 4 pet birds. How much of the bag did each pet bird get?
Answer:
each pet bird got 1/8 of the bag of birdseed
Step-by-step explanation:
the easiest way to do this is to divide the bag into eighths. if you divide the bag into eighths, 4/8 of the bag, being half, goes into the bird feeder. the other 4/8 of the bag is divided among Mr. Wilson's four pet birds, leaving each bird to get 1/4 of the bag when split evenly.
hope this helps
A ________ is a set of points that extends infinitely in both directions.
Answer:
line
Step-by-step explanation:
A line is a set of points that extends infinitely in both directions.
A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is23ft ft?
Answer:
Step-by-step explanation:
Simply put, it is similar to finding the area of a circle.
Therefore, a=pi*r^2
a=pi*23^2
a=529pi
a=1661.9 ft^2
An equilateral triangle has an area of 50 units 2. What is the length of each side?
Answer:
Length of each side of equilateral Traingle is 10.75 unitsStep-by-step explanation:
Given that area of an equilateral traingle 50 square units.
Let the length of side of equilateral traingle be 'x' units. To calculate length of each side we will use the formula of area of equilateral traingle:
[tex] \: \: { \underline { \boxed{\pmb { \sf{ \purple {Area_{(equilateral \: traingle)} = \dfrac{\sqrt 3}{4} \times (Side)^2}} }}}} \\ [/tex]
By substituting the values in above formula:
[tex]~[/tex]
[tex] : \implies \sf \: \: 50 = \dfrac{ \sqrt{3} }{4} \times {(x)}^{2} \\ \\ \\ : \implies \sf \: \: {(x)}^{2} = \dfrac{50 \times 4}{ \sqrt{3} } \\ \\ \\ : \implies \sf \: \: {(x)}^{2} = \dfrac{200}{ \sqrt{3} } \\ \\ \\ : \implies \sf \: \: x = \sqrt{ \dfrac{200}{ \sqrt{3} } } \\ \\ \\ : \implies \: \: { \boxed{\pmb{ \frak{ x = 10.75 \: units }}}}\\ \\ \\ [/tex]
Hence, Length of each side of equilateral Traingle is 10.75 unitsthe measures of the angles in a triangle are in a ratio 1:5:6. find the measures of the angles
Answer:
The required angles are 15, 75 and 90
Step-by-step explanation:
1x + 5x+ 6x = 180
or 12x = 180
180 ÷ 12 = 15
hence,
15, 75, 90.
The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount. The half-life of the radioactive gas radon is approximately 2.8 days. The initial amount of radon used in an experiment is 74 grams. If N represents the number of grams of radon remaining t days after the start of the experiment,
Answer:
N = 74(1/2)^(t/2.8)
Step-by-step explanation:
The exponential function expressing a half-life relation can be written ...
amount = (initial amount) × (1/2)^(t/(half-life))
For the numbers given in this problem, this is ...
N = 74(1/2)^(t/2.8)
__
Some folks like to express these relations in the form ...
N = 74e^(-kt)
In this form, the value of k is ...
k = ln(2)/(half-life) ≈ 0.693147/2.8 ≈ 0.24755
N = 74e^(-0.24755t)
line d has a slope of 7/3. line e is perpendicular to line d. what is the slope of line e?
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
Here we have the number:-
[tex]\boxed{\frac{7}{3}}[/tex]
Flop it over:-
[tex]\boxed{\frac{3}{7} }\longleftarrow\sf{the~numerator~and~denominator~switch~places}[/tex]
Change its sign:-
[tex]\boxed{-\frac{3}{7}}[/tex]
Hence, the slope of line e is:-
[tex]\bigstar{\boxed{\pmb{Slope=-\frac{3}{7}}}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Convert km into cm
10 points available
The leg lengths of a right triangle are 14 in and 26 in. What is the length of the missing side?
Answer:
29.5
Step-by-step explanation:
14sq + 26sq = 872
sq root of 872 is 29.5
Find the side labeled x.
Answer:
4√3
Step-by-step explanation:
Hello!
This is a 30° 60° 90° because it has a 90° angle, a 30° angle, and the missing angle is 60° (sum of angles in a triangle is 180°). This triangle has special properties.
In a 30°-60°-90° triangle, the leg opposite 30° is always half the hypotenuse.
This means that the hypotenuse would be 2 times 4, or 8.
The leg opposite to 60° in a right triangle of this sort is the length of a leg multiplied by √3.
So the measure of x is 4√3.
An image is attached for your reference.
The value of side labeled x using Trigonometric ratio is [tex]{4}{\sqrt 3}[/tex].unit.
Given:
Angle = 30
Perpendicular or opposite side= 4
Using Trigonometric ratio
tan 30 = Opposite side / Adjacent side
Substituting Opposite side= 4 and Adjacent side = 4 in above ratio
So, tan 30 = 4 / x
As, the value of tan 30 = [tex]\dfrac{1}{\sqrt 3}[/tex] then
tan 30 = 4 / x
[tex]\dfrac{1}{\sqrt 3}[/tex] = [tex]\dfrac{4}{x}[/tex]
solving for x
x = [tex]{4}{\sqrt 3}[/tex]
Thus, the value of x is [tex]{4}{\sqrt 3}[/tex].
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It is now 11:15 A.M. What time will it be in three quarters of an hour?
A) noon
B) 11:45 A.M.
C) 11:45 P.M.
D) midnigh
Answer:
Ur mom
Step-by-step explanation:
Ur mom JK here's the answer 11:45 A.M. because 15 + 15 + 15 = 45 15 is a quarter so yeah Bois is 11:45 A.M Good luck
A lifeguard fills a pool with water at a constant rate. After 1/2 hour, 1/3 of the pool is filled.
At this rate, what fraction of the pool is filled per hour?
A. 1/6 of the pool
B. 1/3 of the pool
C. 1/2 of the pool
D. 2/3 of the pool
Answer:
D
Step-by-step explanation:
1/2 hour -> 1/3 pool
multiply this by 2
1 hour -> 2/3 pool
so D 2/3 pool
The fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.
What is a Constant Rate?A constant rate can be described as a quantity that changes steadlity over time.
The rate that the pool gets filled is given as:
1/2 hr = 1/3 of the water that would be filled in the pool
1 hr would be: 1/3 × 2 = 2/3
Therefore, the fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.
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