The binomial expansion of (2+3x)^5 - (2 - 3x)^5 is 480x + 2160x^3 + 486x^5
Concept: Binomial expansion is to expand and write the terms which are equal to the natural number exponent of the sum or difference of two terms.
For two terms x and y the binomial expansion to the power of n is (x + y)n = nC0 0 xn y0 + nC1 1 xn - 1 y1 + nC2 2 xn-2 y2 + nC3.
Binomial expansion of (2+3x)^5 =32+240x+720x^2+1080x^3+810x^4+243x^5
Binomial expansion of (2-3x)^5 = 32-240x+720x^2-1080x^3+810x^4-243x^5
Combining both the expansions,=32+240x+720x^2+1080x^3+810x^4+243x^5 - (32-240x+720x^2-1080x^3+810x^4-243x^5)
= 32+240x+720x^2+1080x^3+810x^4+243x^5 - 32+ 240x - 720x^2 +1080x^3 -810x^4 +243x^5
=480x + 2160x^3 + 486x^5
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The given equation is either linear or equivalent to a linear equation. Solve the equation. (If there is no solution, enter NO SOLUTION. If all real numbers are solutions, enter REALS.)
(t − 7)2 = (t + 7)2 − 112
t =
Answer:
No solution
Step-by-step explanation:
Question 3, please help. Very urgent and due soon!
Answer:
A = 5, B = 9, C = 6
Step-by-step explanation:
let me know if you want an explanation :))
Help I have no idea to do this!! I’m stuck!
Answer: 7
Step-by-step explanation:
[tex]A \cap C[/tex] denotes the intersection of A and C, or in other words, how many elements are shared between them.
The number of elements is 2 + 5 = 7
Which expression is equivalent to...
Answer:
A is correct yes
Step-by-step explanation:
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The price of admission at a movie theater is $6 for an adult and $4 for a child. In one day, the movie theater sold 80 tickets and made $420. How many adults and how many children bought tickets to the movie theater that day?
x + y = 80,
6x + 4y = 420
Which is a solution of the system of equations, and what does it represent?
(20, 60); 20 adult tickets and 60 child tickets
(30, 50); 30 adult tickets and 50 child tickets
(40, 40); 40 adult tickets and 40 child tickets
(50, 30); 50 adult tickets and 30
Last option: (50, 30); 50 adult tickets and 30 child tickets
What is Linear Equation?A linear equation is an equation in which the highest power of the variable is always 1.
We have the system of equations:
x + y = 80
6x + 4y = 420
We will use elimination method to solve it:
Multiply the first equation by -6 and then add the equations:
- 6x - 6y = -480
6x + 4y = 420
We get:
-2y = -60
After dividing both sides by -2 we get:
y = 30
then plugging 30 in place of y into the original first equation we get:
x+30=80
Then subtracting 30 from both sides we get:
x = 50
The solution to the system is (50, 30)
Then notice the second equation 6x+4y=420 clear indicates that x represents the tickets for adults since the price for adults $6 is the coefficient of the x-term, while the price for children which is $4 is attached as coefficient in front of the y.
Thus, x=50 means there were sold 50 adult tickets. And y=30 that there were sold 30 child tickets.
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Answer:
( 50, 30)
Step-by-step explanation:
The average car sold from Dealership A is $25,700. If the sales person receives 1.5% commission on price of car, how much commission is made on average per car sold?
Answer:
$385.50
Step-by-step explanation:
The amount of commission is found by multiplying the commission rate by the value of the sale.
1.5% × $25,700 = $385.50
A commission of $385.50 is made on an average car sold.
What is the value of the expression 24 + 3²? What is the value of the expression 24 + 3² ?
Answer:
33
Step-by-step explanation:
3² = 3.3 = 9 => 24 + 9 = 33
Which pair of angles are vertical angles?
Answer:
Vertical angles are angles opposite of each other. hope it helps
How much would it cost to buy a piece of candy for 50 cents plus tax
Answer:
it depends on which state your in or in your even in the us usually it is either 6% or 4% some times more or less % so im going to do both
50*0.06=53
50*0.04=52
Hope This Helps!!!
Find the nature of the graph of the function y = 9x4 + 8x - 2 using end
behavior.
the end behavior is:
as x ⇒ ∞, f(x) ⇒∞as x ⇒- ∞, f(x) ⇒∞What is the end behavior of the function?
If we have a polynomial of even degree, then the end behavior in both ends is the same one.
Particularly, in these cases (even degree) we only need to look at the leading coefficient. If it is positive, then as x tends to infinity and negative infinity, the function tends to infinity.
In this case, the polynomial is:
y = 9x⁴ + 8x - 2
Notice that the degree is 4, even, and the leading coefficient is 9 (positive).
Then the end behavior is:
as x ⇒ ∞, f(x) ⇒∞as x ⇒- ∞, f(x) ⇒∞If you want to learn more about end behaviors:
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Which expression is equivalent to...
Answer:
p^2/r
Step-by-step explanation:
so I have shown every work in the picture attached
please let me know if this doesn't help
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: a = -1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
For a function f(x) = y,
x represents the value ( x - coordinate ) at which the function has a value y.
[tex]\qquad \tt \rightarrow \: f(x) = a {x}^{2} + 2[/tex]
for point (-1 , 1) to satisfy the equation, we have to calculate the value of a
[tex]\qquad \tt \rightarrow \: f( - 1) = a( - 1) {}^{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: 1 = a + 2[/tex]
[tex]\qquad \tt \rightarrow \: a = 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: a = - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Substitute -1 into x
Substitute 1 into y
f(x)= a (-1) ^2+2=1
a=-1
Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been transformed to produce figure 2.
Answer:
0 and -6
(0,-6)
Step-by-step explanation:
Can't really explain, but this is a guess on the actual question.
If
5 , 3 = 28
9 , 1 = 810
8 , 7 = 115
6 , 2 = 48
then
7 , 5 = ?
Answer:
212
Step-by-step explanation:
Simple addition and subtraction is to be used here.
5, 3 = 28
5-3 = 2 , 5+3 = 8
9 , 1 = 810
9-1 = 8 , 9+1 = 10
8 , 7 = 115
8-7= 1 , 8+7 = 15
6 , 2 = 48
6-2 = 4 , 6+2 = 8
7 , 5 = 212
7-5 = 2 , 7+5 = 12
Answer:
212
Step-by-step explanation:
Rule
Subtract the 2nd number from the first to obtain the first digit(s) of the answer.Add the 2nd number to the 1st to obtain the last digit(s) of the answer.5 - 3 = 2
5 + 3 = 8
Therefore: 28
9 - 1 = 8
9 + 1 = 10
Therefore: 810
8 - 7 = 1
8 + 7 = 15
Therefore: 115
6 - 2 = 4
6 + 2 = 8
Therefore: 48
7 - 5 = 2
7 + 5 = 12
Therefore: 212
Find limit (x / 3x+2) as x approach 1
Answer:
x/ 3x + 2
x approach 1
1/3 (1) + 2
1/ 5.
&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = square numbers E = even numbers Complete the Venn diagram. E, S 4 2,6 8, 10, 12 E & = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } S = square numbers E = even numbers Complete the Venn diagram . E , S 4 2,6 8 , 10 , 12 E
The remaining elements if Venn diagram is S= { 4, 9}
What is Venn diagram?A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.
Given:
E = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }
S = square numbers
E = even numbers
Element in set S= { 4, 9}
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Generate the ordered pairs for y = x2 − 4 using x = −2, −1, 0, 1 and 2. Identify the corresponding graph.
The ordered pairs are ( -2,0),( -1,-3),( 0,-4),(1,-3),(-2,0).
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
The ordered pairs will be calculated as:-
y = x² − 4
At x = -2
y = ( -2)² - 4 = 4 - 4 = 0
At x = -1
y = (-1)² - 4 = -3
At x = 0
Y = 0² - 4 = -4
At x = 1
Y = 1 ² - 4 = -3
At x = 2
Y = (2)² - 4 = 0
Therefore ordered pairs are ( -2,0),( -1,-3),( 0,-4),(1,-3),(-2,0).
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Find the slope of the curve y=2/x at x=a.
Answer:
We are given:- y=2/xWe need to find the slope of the curve at x=a.Step-by-step explanation:
Solution,
We use the slope formula, setting x=a :
[tex] \displaystyle{{{{ \lim_{h \to0}}}} \frac{ \frac{2}{x + h} - \frac{2}{x} }{h} = \lim_{h \to0} \frac{ \frac{2}{a + h} - \frac{2}{a} }{h} }[/tex]
[tex] \displaystyle{ \lim_{h \to0} \frac{ \frac{2a - 2(a + h)}{a(a + h)} }{h} = \displaystyle{ \lim_{h \to0} \frac{2a - 2(a + h)}{ha(a + h)} }}[/tex]
[tex] \displaystyle{ \lim_{h \to0} \frac{2a - 2a - 2h}{ha(a + h)} = \displaystyle{ \lim_{h \to0} \frac{ - 2h}{ha(a + h)} }}[/tex]
[tex] \displaystyle{ \lim_{h \to0} \frac{ - 2}{a(a + h)} = - \frac{ 2}{ {a}^{2} } }[/tex]
Therefore, The slope of the curve y=2/x at x=a is -2/a^2.
Find the numeral preceding and succeeding each of the following numerals. Use T as the digit for 10.
a. TTO eleven
b. 100000 nine
c. 222 three
The numeral preceding and succeeding each of the following numerals.
Now, what happens when you add 1 or subtract 1 from 100 in the familiar base 10.
Adding adds 1 to the unit digit.
Subtracting 1 gives 99 because 9 is the largest digit in base 10.
So A. 100 base 8
The largest digit in base 8 is 7, so
..., 77, 100, 101,...
B. 10000 base 7
What is the largest digit in base 7?
The largest digit in base 7 is 6, so
..., 6666, 10000, 10001, ...
Next what happens when you add 1 to 509 in base 10. 9 is the largest digit in base 9, so adding 1 makes the units digit 0, and you carry a 1 to the next digit to the left:
509 + 1 = 510.
C. 305 base 6
5 is the largest digit in base 6, so
..., 304, 305, 310, ...
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Which choices are equivalent to the expression below? Check all that apply. √8 × √8
A. √ 8
B. 8
C. 64
D. 8
E. 16
F. √64
Answer:
the answers are B and F since √8 x √8 = √64 which simplifies to 8.
Migdalia is a consultant. She works 3 days a week in the company's headquarters and 2
week at a production site.When she works at the company headquarters, she takes a bus
from work. When she goes to production sites, she uses her car and travels 52 ms
cast for using the bus is $48.00 for 10 one-way trips. The cost of using her car she
30 per mile Migdalia budgets $50 per week for travel expenses to and from work whether or not she has set aside enough money.
Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip
How to find the expenses and know if it's enough?She works 3 days in a week in the headquarter and 2 days a week at the production site.
When she works at the company headquarters, she takes a bus to and from work. The cost for using the bus is $48.00 for 10 one-way trips.
Therefore,
each one way trip = 48 / 10 = $4.8
To and from the headquarters = 4.8 × 2 = $9.6
Hence,
Therefore,
three days cost = 9.6 × 3 = $28.8
The cost of using her car she estimates at 30 cent per mile. When she goes to production sites, she uses her car and travels 52 miles per day. Therefore,
cost of travelling to production site in a week = 2 × (52 × 0.3) = $31.2
Hence,
cost of expenses per week = 31.2 + 28.8 = $60
Since she has set aside only $50 for the trip, she hasn't set aside enough money for the trip
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NEED HELP ASAP WILL MARK BRAINLIEST!
Answer:
log_{b} (5b) = 2.609
Given that:
log_{b} (3) = 1.099
log_{b} (5) = 1.609
Evaluating with that:
[tex]\sf log_b (5b) = log_b\left(5\right)+log_b\left(b\right)[/tex]
[tex]= \sf 1.609 + 1[/tex]
[tex]= \sf 2.609[/tex]
Rule Used:
[tex]\rm \log _a\left(xy\right)=\log _a\left(x\right)+\log _a\left(y\right)[/tex]
Find the solutions to the equation below. check all that apply. x^2-2x-15=0
The student did not make any mistake, the solution is correct. Then the correct option is A.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A student perform the following steps to find the solution of the equation x² – 2x – 15 = 0.
The factor of the equation will be
Step 1 : x² – 2x – 15 = (x – 5)(x + 3)
Step 2 : (x – 5) = 0 and (x + 3) = 0
Step 3 : x = 5 and – 3
The student did not make any mistake, the solution is correct.
Then the correct option is A.
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Find the domain and range
Answer:
Domain: (-∞, ∞)
Range: [-2, ∞)
Step-by-step explanation:
The domain of any parabola is (-∞, ∞)
The range of this parabola is [-2, ∞) because the vertex is at (-2, -2).
By selling a table for sh.56, gain is as much as percent as its cost in dollars. What is the cost price? By selling a table for sh.56 , gain is as much as percent as its cost in dollars . What is the cost price ?
The cost price of the table is $40.
What is Gain ?Gain is the amount gain by selling the product at a higher price than its cost.
Let the cost of the table is $ x
The percentage gain is x% (as given in the question)
Cost price = ?
It is known that
Step 1 : Gain = ( selling Price - Cost Price) * 100 / Cost Price
Selling price = 56
Cost Price = $ x
Therefore substituting the value
x = (56 - x) * 100 / x
x² = 5600 - 100x
x² +100x -5600 = 0
Step 2 : Factorizing
x² + 140x - 40 x -5600 = 0
x( x+14 ) -40( x +14) = 0
( x - 40)(x +14) = 0
x = $40
Therefore the cost price of the table is $40.
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Evaluate and reduce:
solve for x: 5x-4y=24
Answer:
x=4y+24/5
Step-by-step explanation:
add 4y
Divide by 5
Find the y-intercept.
(2x + 1)(x + 7).
(x + 3)(x + 4)
y =
([?],
all three would be pretty nice
Answer:
(0, 7/12)
Step-by-step explanation:
to find the y intercept we equate x to 0.
hence,
f(0) = 7/12
the coordinate is (0, 7/12)
Answer:
[tex](0,\frac{7}{12})[/tex]
Step-by-step explanation:
In order to find the y-intercept of an equation, simply plug in 0 for x, as that's where the y-axis is.
[tex]\frac{(2(0)+1)(0+7)}{((0)+3)((0)+4)}[/tex]
Simplify:
[tex]\frac{7}{(3)(4)}=\frac{7}{14}[/tex]
Therefore, the y-intercept for the equation is:
[tex]\frac{7}{14}[/tex]
Basically look at the picture I don’t even know what to say
Answer:
C
Step-by-step explanation:
x = [tex]\frac{2}{3}[/tex] πr³ ( multiply both sides by 3 to clear the fraction )
3x = 2πr³ ( divide both sides by 2π )
[tex]\frac{3x}{2\pi }[/tex] = r³ ( take cube root of both sides )
[tex]\sqrt[3]{\frac{3x}{2\pi } }[/tex] = r
Answer:
[tex]r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]
Step-by-step explanation:
This question make look scary, but don't judge its book by its cover.
[tex]x=\frac{2}{3} \pi r^{3} \\\frac{2}{3} \pi r^{3}=x\\r^{3} =x / \frac{2\pi }{3} \\r^{3} =x*\frac{3}{2\pi } \\r^{3} =\frac{3x}{2\pi } \\r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]
A line / passes through point (-2, 5) and has the same y-intercept as
the line y-3x-4. What is the equation for the line /?
I'm assuming you meant to write y = 3x-4
We know that the y-intercept of the given line is (0,-4), so we need to find the equation of the line passing through (-2,5) and (0,-4).
The slope is
[tex]\frac{-4-5}{0-(-2)}=-\frac{9}{2}[/tex]
So, this means the equation is [tex]\boxed{y=-\frac{9}{2}x-4}[/tex]
