The expression in the 6th term in the binomial expression is [tex]265781250y^6[/tex]
How to determine the expression in the sixth term?The expression is given as:
(5y + 3)^10
The above expression is a binomial expression, and the xth term can be represented using:
[tex]^nC_x (a)^x * (b)^{n-x}[/tex]
So, we have:
[tex]^{10}C_6 * (5y)^6 * (3)^4[/tex]
Evaluate the combination expression
[tex]210 * (5y)^6 * (3)^4[/tex]
Evaluate the exponents
[tex]210 * 15625y^6 * 81[/tex]
Evaluate the product
[tex]265781250y^6[/tex]
Hence, the expression in the 6th term is [tex]265781250y^6[/tex]
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Solve for x.
X=?
4x+4 4x -32
Step-by-step explanation:
4x-4x=-32-4
X=28
Is the answer
Answer:
No solution
Step-by-step explanation:
As the slopes are same and y-intercepts are different, we can conclude this system of equations has no solution.
Determine each segment length in right triangle ABC
The length of BC= 7√2 and BD = 7.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given:
AD= 7, AC= 14
In Δ BDC
cos 45 = B/ H
1/√2 = 7/ BC
BC= 7√2
In Δ BDC
sin 45 = P/H
1/√2= BD / 7√2
BD = 7
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Write the ratio 12:16:8 in simplest form
Answer:
[tex]\huge\boxed{\bf\: 3:4:2}[/tex]
Step-by-step explanation:
In the given ratio, [tex]12:16:8[/tex], we can see that all the 3 numbers in ratio are multiples of 4. Hence the lowest common multiple (LCM) of the given ratio = 4.
Now, let's divide the 3 numbers by 4.
[tex]12:16:8\\= \frac{12}{4}:\frac{16}{4}:\frac{8}{4}\\=\boxed{\bf\: 3:4:2}[/tex]
This ratio cannot be further simplified as they don't have any common multiples except for 1.
So, the simplified ratio = [tex]\boxed{\bf\: 3:4:2}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
I will give brainliest to whoever gives me the correct answer once I figure out how
In a company which services air-conditioner units, the revenue,
$r, is given by the equation r = 20x, where x is the number of
units serviced. The operating cost, $c, is given by the equation
c= 3600 + 4x.
The profit, $P, is given by the expression, r — c.
(a) Find a formula for P in terms of x only.
(b) For each of the following cases, find the value of x if
(i) the revenue earned is twice that of the cost,
(ii)the profit earned is $292 more than one third of the revenue
earned.
Answer:
p(x) = 16x -3600600 units417 unitsStep-by-step explanation:
The problem statement gives expressions and relations for revenue, cost, and profit. Substitute and simplify or solve, as appropriate.
__
(a)Given: r(x) = 20x; c(x) = 3600+4x; p(x) = r(x) -c(x)
The formula for p(x) is ...
p(x) = (20x) -(3600 +4x) . . . . substitute for r(x) and c(x)
p(x) = 16x -3600 . . . . . . . . simplify
__
(b-i)r(x) = 2·c(x) . . . . given relation for revenue and cost
20x = 2(3600 +4x) . . . . substitute for each
12x = 7200 . . . . . . . simplify and subtract 8x
x = 600 . . . . . . . divide by 12
Revenue is twice the cost when x = 600 units.
__
(b-ii)p(x) = 292 +1/3r(x) . . . . given relation for profit and revenue
16x -3600 = 292 +1/3(20x) . . . . . substitute for each
28/3x = 3892 . . . . . . . . add 3600 -20/3x
x = 417 . . . . . . . . multiply by 3/28
Profit is $292 more than 1/3 the revenue earned for 417 units.
The coordinates of a parallelogram are given segment AB is parallel to the x-axis determine the values for a,b,c,d
Answer:
a=3 d=1 b and c cant be solved
Step-by-step explanation:
because segment AB is parallel to x axis . So the slope of ABco is 0. So the y value is congruent
a=3 d=1
We know AB=CO b+2=8-C
we can only find ad, but we could not get b,c
PLS HELP PLS
How many days were less than 84°?
Answer:
D
Step-by-step explanation:
the number of days for 80 - 82 is 7 and the number of days for 82-84 is 9. Those are the only temperatures below 84 degrees, so you add them and get 16 :)
From previous experience, the owner of a Apple orchard knows that the mean weight of a gala Apple is 140 grams. This year there has been more precipitation than usual and the owner believes the weights of the apples will be heavier than usual. The owner takes a random sample of 30 apples and records their weights. What is the appropriate inference procedure?
The appropriate inference procedure is the t test for μdiff.
What is the t test?The t test is used to compare the means of two groups. It is a very important tool that can be used in inferential statistics.
Since it shows whether the means of two groups are significantly different, we can say that, the appropriate inference procedure is the t test for μdiff.
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Mathew sells half the books in his library. After
he does this, he buys 6 more books. Now he has
102 books. How many books did he have to start
with?
pleaseeeee help ill give u brainliest
The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $250 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following.
C=250n+6500
Answer the following questions.
(a)
What is the total cost of transporting 11 tons?
$?
(b)
If the total cost is $11,750, how many tons is the company transporting?
? tons
Answer:
(a) C = $9250
(b) n = 21 tons
Step-by-step explanation:
(a) 11 tons being transported, so n = 11.
∴ C = 250 (11) + 650
C = $9250
(b) C = $11,750
∴ 11750 = 250n + 6500
250n = 5250
n = 21 tons
Hope this helps!
Given the equations and the graph below, how many solutions are there to the system of equations?
Explain your answer.
Answer:
One, since the lines are not parallel (you can tell by either the graph, or the coefficient of the x term, called "slope", and it's (3;4)
A builder is developing a neighborhood of one-bedroom and two-bedroom houses. the builder wants to build 12 houses and can use as many as 88 total
windows. the one-bedroom houses need 6 windows and the two-bedroom houses need 9 windows.
part a
write and solve a system of equations to represent the situation. let 2 represent the number of one-bedroom houses. let y represent the number of two-
bedroom houses. round your answers to the nearest hundredth, if necessary.
Builder can build 7 one bedroom houses and 5 two bedroom houses.
What is consistent Equation?
A linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.
Let x represents the number of one-bedroom houses and y represents the number of two bedroom houses.
According to Question,
Total number of houses is 12 i.e. x + y = 12..........(i)
Total we have 88 windows in which 6 windows can be use in one bedroom house and 9 windows can be used in two bedroom house so,
6x + 9y = 88 ..................(ii)
From Equation (i) and (ii), we get
x = 7 and y = 5
Thus, Builder can build 7 one bedroom houses and 5 two bedroom houses.
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The longest length of a sail on Jessica's sailboat is 12v40 feet long. Which number is equivalent to this length?
O 24140
O 4840
O 247/10
O 48V/10
Answer:48V/10
Step-by-step explanation:
I got it right from Khan Academy
Which fraction and decimal are equivalent to 10^-3
Answer:
1/1000, 0.001
1/1000
Convert the negative exponent of base 10 into decimal: move to the left thrice
=0.001
if 1 yard = 3 feet and 1 mile = 5.280 feet how many yards are there in 2 miles .
Answer:
3520
Step-by-step explanation:
Because 3 feet are equal to a yard and 1760 yards are in one mile
So.. just add 1760+1760 and thats the equivalent of 2 miles
PLEASE HELP
Select the correct answer.
A six-sided fair die and an eight-sided fair die are rolled together. What is the probability of getting numbers whose sum is a multiple of 3?
A. 1/18
B. 1/4
C. 1/3
D. 4/9
E. 2/3
Answer:
C. 1/3
Step-by-step explanation:
there are 48 possible outcomes, and out of those 16 of them have a sum of 3.
16/48
simplify
1/3
100 members in a band, 12 members play the flute. What percentage of the band plays the flute?
Whoever answers first i'll mark brainlist
please make sure it's right!
Investments increase exponentially by
26% every 3 years. If you start with a
$2,000 investment, how much money would you have after 45 years?
would you have after 45 years?
First, complete the equation:
Future Amount = 2,000 (1 + [?])
Enter
The amount of money I would have after 45 years with an exponential increase is $64,060.18.
What is the future value of $2000?The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = Present value R = interest rate N = number of years = 45 / 3 = 15 years$2000 x (1.26)^15 = $64,060.18
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wierd circles i dont like using pi please help
A complete graph of the polynomial function f is provided. Use your knowledge of the domain, range, behavior at each x intercept, end behavior, symmetry, local and global extreme values, and intervals of increasing and decreasing to select the best choice of the polynomial function, f.
The graph represents a polynomial graph, and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²
How to determine the equation?From the graph, we have the following observations:
The graph has a turning point at x = 2The graph changes the factor of its direction at x = -5This means that the graph has a multiplicity of 2 at x = 2 and a multiplicity of 3 at x = -5
So, we have:
f(x) = a(x + 5)³(x - 2)²
The curve is inverted,
This means that a < 0
Assume a = -1.
Then, we have:
f(x) = -(x + 5)³(x - 2)²
Hence, the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²
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PLEASE HELP MODULE 7
The difference between a temperate coniferous forest and a taiga forest is a temperate coniferous forest receive a good amount of rainfall.
What is a temperate coniferous forest ?Temperate coniferous forest is a terrestrial biome that is found in coastal regions that have warm summers and cool winters. They are also found in montane areas.
What is a taiga forest?A taiga forest is characterised by cold, harsh climate with a low rate of rainfall and snow. They are characterized by coniferous forests.
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solve the inequality 1/2b+2≤8
1/2b+2≤8
1/2b≤6
b≤12
Any number less than or equal to 12 can solve the equation.
Answer
[tex]b\leq 12[/tex]
Step-by-step explanation
You would subtract two from the eight and that would get you six, and the reciprocal of 1/2 is two so technically you would multiply the 6 by two and that gets you 12.
Hope this helps any!
The two expressions below have the same value when rounded to the nearest hundredth. log subscript 5 baseline b. log subscript 9 baseline 48 what is the approximate value of log b to the nearest hundredth?
The approximate value of log b to the nearest hundredth is 1.23
Laws of logarithmGiven the following logarithmic expressions
loog(5)b and log(9)48
Determine the value of log(9) 48
log(9)48 = 1.762
Equate log(5) b to 1.762 to log(5)b to determine the value of b
log(5)b = 1.762
b = 5^1.762
b = 17.044
log b = log 17.044 = 1.232
Hence the approximate value of log b to the nearest hundredth is 1.23
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Answer:
B = 1.232
Step-by-step explanation:
Just did it
Help me with this question please
Answer:
∠A≅∠X AB≅XZ
∠B≅∠Z AC≅XY
∠C≅∠Y BC≅ZY
ΔABC≅ΔZYX
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
Please awnser my other question
Answer:
S = (-6, -1)
T = (-7, 4)
U = (-6, 9)
V = (-4, 4)
3[(x^3 -7x+1) - (x+4)]
О А. 3х³ - 24х-9
О B. х-8х-3
0 С. 3x²-5x-6
O D. 3x²-6x+15
Answer:
A
Step-by-step explanation:
You have to simplify the brackets in turn.
3 times x^3- 7x+1 = 3x^3- 21x+ 3
then do 3 times x + 4= 3x + 12
you then add them all together, if they have a power add them, if they just have an x add them, and if they are just a number add them.
So it goes to 3x^3- 24x - 9,
this is because 3x^3 cant be added/ subtracted by anything, -24x is made from -21x- 3x, and -9 is made from 3 - + 12, so this means 3 - 12 = -9.
I hope this helps, have a lovely day.
Find mQTS⌢, m∠RQS and mQS⌢.
If the measure of the angle ∠RQT is 125°. Then the measure of the angles ∠RQS and ∠SQT will be 44° and 81°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
If the measure of the angle ∠RQT is 125°. Then the measure of the angles ∠RQS and ∠SQT will be
Then we have
∠RQS + ∠SQT = 125°
(3x - 10)° + (4x + 9)° = 125°
7x - 1 = 125°
7x = 126°
x = 18°
Then the measure of the angle ∠RQS will be
∠RQS = 3 × 18 - 10
∠RQS = 44°
Then the measure of the angle ∠SQT will be
∠SQT = 4 × 18 + 9
∠SQT = 81°
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Please solve this in a few mins! :)
Answer:
The answer is greater than or equal to 15 which is the third answer.
What is the area of the figure? Show your work.
Answer:
50m^2
Step-by-step explanation:
cut the shape into half. Now you should have a rectangle and a right triangle. Then do 5•7=35 so 35m for the rectangle. Now do the triangle! 10-7=3 so the base is 3 so do 3•5=15m so add them together 15m+35m=50m^2
ALSO IF YOU NEED TO KNOW THE ANGLE X IS: 60*
Hope this helps! ;-)
