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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need help with this please
The values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
Given the equation of x as the function of t is
x= 5 cos t
similarly, the equation of y as the function of t is
y= 3 sin t
At t=3 the value of x will be
x (at t=3) = 5 cos 3= 5(-0.989)= -4.95
At t=3 the value of y will be
y (at t=3) = 3 sin 3= 3(0.141)= 0.423
The derivative of the function of x with respect to t will be
dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t
at t=3 the value of dx/dt will be
dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71
The derivative of the function of y with respect to t will be
dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t
at t=3 the value of dy/dt will be
dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97
The tangent slope is dy/dx which can be calculated by
dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t= (-3/5) cot t
at t=3 the value of tangent slope will be
dy/dx (at t=3) = (-3/5) cot 3= 4.21
The speed at t=3 will be
speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]
= √(dx/dt)²+(dy/dt)²
at t=3
= √(0.71)²+(-2.97)²
= √9.325
= 3.05 unit/sec
Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
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Use the point-slope formula to write an equation of the line that passes through (4,10) and has a slope of m= 3. Write the
answer in slope-intercept form (if possible).
The equation of the line is
An expression is shown below:
4ck2 + 10k2 − 16ck − 40k
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Part A:
The greatest common factor is 2k
2k(2ck + 5k - 8c - 20)
Part B:
factor by grouping
2k (k(2c + 5) - 4(2c + 5))2k(k - 4)(2c + 5)2k(k - 4)(2c + 5) is the final factored form
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms which ones should he check
Step-by-step explanation:
please attach a picture for us to see the choices
1 x 1 x 99 x 100 hat is the awnser
Question 1
The total length of a hiking trail in the mountains is 8 miles. If Dale and his son completed 4/5 of the trail yesterday, how many feet did they hike?
42,240 feet
22,528 feet
11,264 feet
33,792 feet
Answer:
33, 792
Step-by-step explanation:
first convert the 8 miles to feet because our answers are in feet.
1 mile= 5280 feet
therefore 8 miles= 5280×8
= 42240
Dale and son covered 4/5 of the 42240 feet
= 4/5×42240
= 33,782 feet
Solve for u. -5/6u = 15
Answer:
u = -18
Step-by-step explanation:
[tex]\frac{-5u}{6} =15[/tex]
Multiply both sides by 6.
-5u = 15 × 6
-5u = 90
Divide both sides by -5.
u = -18
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°. Find m∠G. Round your answer to the nearest tenth.
The value of m∠G = 48.6° .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°
m∠G = ?
well, using the law of cosines,
GH ² = 9² + 11² - 2(9)(11) cos65°
f = 10.88 ft
now, using the law of sines,
sinG/9 = sin65°/10.88
m∠G = 48.6°
Therefore the value of m∠G = 48.6° .
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For the function y= -2+5 sim {pi/12(x-2)}, what is the minimum value
The function has a local minima at ( 20 , -7 )
What is a Function ?Function is a mathematical statement formed when two algebraic expression are equated by an equal sign.
The expression given is
y = -2 +5sin ( (π/12) (x-2))
the minima of the given expression will be when
the sine term = -1
as the lowest value sin can have is -1
y = -2 +5 * (-1)
y = -7
The sin ( (π/12) (x-2)) = -1
(π/12) (x-2) = 3π /2
On solving this
x = 20
Therefore the function has a local minima at ( 20 , -7 )
It can also be confirmed form the graph attached with the answer.
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An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. If (h) represents hours, how much will the mechanic charge if they worked 10 hours in one day?
$450
$400
$550
None of these choices are correct.
Answer:
$800
Step-by-step explanation:
per hour $40×10hours=$400
$400÷$50=8 times initial fee
8×$50=$400 total initial fee
$400hours fee+$400 initial fee=$800 total payment
given the following pyramid identify the L, P, and B then find the surface area
Answer:
slant length (l) = 7.5 m
perimeter of base P = 40 m
area of base B = 100 m^2
Surface Area = 250 m^2
Step-by-step explanation:
Surface area of a pyramid formula
1/2Pl + B
1/2 (40)(7.5) + 100
150 + 100 = 250 square meters
What is another way to write the equation 7/8x3/4=-6
Another way to write the equation is 7x + 54 = 0
How to rewrite the equationGiven the equation;
[tex]\frac{7}{8}x + \frac{3}{4} = -6[/tex]
Find the LCM on the left side, which is 8
[tex]\frac{7x + 6}{8} = -6[/tex]
Cross multiply
[tex]7x + 6 = -6[/tex] × [tex]8[/tex]
[tex]7x + 6 = -48[/tex]
Collect like terms
[tex]7x = -48 - 6[/tex]
[tex]7x = -54[/tex]
Take all to one side
[tex]7x + 54 = 0[/tex]
Thus, another way to write the equation is 7x + 54 = 0
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Kerry has a job that pays $1,954 biweekly. How much is withheld annually for Social Security?
$82.07
$41.03
$2,113.77
$88.91
$177.81
Answer:
hi
Step-by-step explanation:
no
What is the solution to the equation 7(a-10)=13-2(2a+3)?
26
O a=11
O a=7
89
O a = 11
O a=621
Answer:
[tex]a = 7[/tex]
Step-by-step explanation:
[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]
What are the measures of ∠1 and ∠2? Show your work or explain your answers.
Answer:
angle 1 is 105degrees and angle 2 is 75degrees
Step-by-step explanation:
The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.
The points (0, -8) and (10, 2) represent the endpoints of a diameter of a circle. Which of the following represents the equation of this circle?
Answer:
(x-5)²+(y+2)²=200.
Step-by-step explanation:
1) using the given coordinates it is possible to calculate
- the centre of the given circle:
[tex]x_0=\frac{10+0}{2}=5; \ y_0=\frac{2-8}{2}=-2;[/tex]
- the radius of the given circle:
[tex]r=\sqrt{(10-0)^2+(2+8)^2} =\sqrt{200} ;[/tex]
2) finally, the required equation (common form is (x-x₀)²+(y-y₀)²=r²):
(x-5)²+(y+2)²=200.
If A=P+I make the subject as P
Answer:
[tex]P = A - I[/tex]
Step-by-step explanation:
A = P + I (Given)[tex]\implies P = A - I[/tex]identify the percentage in 15 is 25% of 60
Answer:
25%
Step-by-step explanation:
In the sentence "15 is 25% of 60.", 25% is the percentage.
15 is the partial amount and 60 is the total amount.
15/60 = .25
convert a decimal to a percentage by multiplying by 100
.25 × 100 = 25
Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.
15/60 is 25%
Given: A = { -1,5,6} B = {-1,2,3,4,6,8} Find the union of sets A and B.
Step-by-step explanation:
{-1,2,3,4,5,6,8} is the answer
❗️URGENT❗️
Chase has won 80% of the 30 football video games he has played with his brother, Jacob. If Chase and Jacob continue to play the video game, how many more games in a row goes Chase have to win to achieve an 85% win percentage?
Answer:
10
Step-by-step explanation:
24/30 = 0.8
24+x/30+x =0.85
10=x
If you want more clarification just ask
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
We can write the total number game won by Chase as -
w = 80% of 30
w = 80/100 x 30
w = 4/5 x 30
w = 24
Assume that he wins {x} games after winning 24 games to achieve 85% win percentage. Now, we can write that out of (30 + x) number of games played, Chase won (24 + x) games to achieve 85% win percentage. So, we can write that -
(24 + x)/(30 + x) = 85/100
(24 + x)/(30 + x) = 0.85
(24 + x) = 0.85(30 + x)
24 + x = 25.5 + 0.85x
0.15x = 1.5
x = 10
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
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Prove Triangle ABC is congruent to Triangle CDA.
The triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
What is the similarity?If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
In the given triangles we can see that:-
Angle BAC is congruent to Angle DCA Angle B and Angle D are congruent.The two triangles are sharing common side which is AC.Therefore we can see that the triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
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A paramedic maintains a time card for hours she works on the rescue squad. How many hours did she work per week ?
39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:
We can write a mixed fraction in a fraction:
6 1/2 = 13/2
8 1/2 = 33/2
7 3/4 = 31/4
8 1/12 = 97/12
8 5/12 = 101/12
Adding all the fractions:
[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]
[tex]=23+\dfrac{64}{4}[/tex]
= 39 hours
Thus, 39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
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there are 1,500 pupils in school , 0.6 are boys how many pupils are girls
Answer:
1491 girls (99.4 percent)
Step-by-step explanation:
explanation is in the attached picture
Which statements are true about the ordered pair (-1,-4) and the system of equations? x-y=3 and 7x-y=-3
Answer:
when (-1, -4) is substituted into the first equation it's true
when (-1, -4) is substituted into the second equation it's true
the ordered pair (-1, -4) is a solution to the systems of equation
Step-by-step explanation:
original equation
x-y=3
multiply both sides by 7
7x-7y = 21
add 7y to both sides
7x=7y + 21
substitute into second equation
(7y+21)-y=-3
simplify
6y+21=-3
subtract 21 from both sides
6y=-24
y=-4
substitute y into original equation
x-(-4) = 3
cancel out negative signs
x+4=3
subtract -4 from both sides
x=-1
If 13 metres of a uniform iron rod weights 23.4 kg then what will be the weight of 6 metres of the same rod?
Answer:
Solution:
Here,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]
Weight of 13 m of rod=23.4 kg
Weight of 1 m of rod=23.4/13 kg
[less length,less weight]
Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg
[more length,more weight]
Thus,the weight of 6 m of rod is 10.8 kg.
Alternative method:
Let,the required weight be x kg.
Then,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]
We know that,
More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).
So,using the rule of direct proportion;
i.e. Ratio of length=Ratio of weight
[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]
[tex] \rm{13x = 6 \times 23.4}[/tex]
[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]
[tex] \therefore{x = 10.8}[/tex]
Thus,the weight of 6 m long iron rod is 10.8 kg.
The legs of a 90-45-45 triangle are 3 and 7. What is the hypotenuse?
Answer:
The hypotenuse is [tex]\sqrt{58}[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2 + 7^2 = c^2
9 + 49 = c^2
58 = c^2
Taking the square root of each side
[tex]\sqrt{58} = \sqrt{c^2}[/tex]
[tex]\sqrt{58} =c[/tex]
Evaluate each expression for r=9 n t=14 enter in your numerical answer
Answer:
1764
Step-by-step explanation:
[tex]from \: the \: question \: rt {}^{2} \\ were \: r =9 \\ and \: t = 14 \\ rt {}^{2} = 9 \times (14) {}^{2} = 9 \times 196 = 1764[/tex]
Hii!
__________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ \leftharpoonup[/tex]
1764
[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]
Stick in the values: 9 for r and 14 for t, and simplify.
[tex]\twoheadrightarrow\sf 9\cdot14^2}[/tex]
[tex]\bullet[/tex] Square 14 first
[tex]\twoheadrightarrow\sf 9\cdot196}[/tex]
[tex]\bullet[/tex] Multiply the numbers
[tex]\twoheadrightarrow\sf 1764}[/tex]
[tex]\bullet[/tex] Great job! We found the answer
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
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Find the value of c that makes the expression a perfect square trinomial. x2 + 9 4 x + c
A) 9/16
B) 9/64
C) 81/16
D) 81/64
The value of c is 81/64 for the expression a perfect square trinomial.
What is an Expression?An expression can be defined as a mathematical statement that consists of variables, constants and mathematical operators simultaneously.
It is given that an expression
x² +9/4x +c is a perfect square polynomial
c =?
(a+b)² = a² +2ab+b²
2ab = 9/4
b = 9/8
c = b² = 81/64
Therefore the value of c is 81/64 for the expression a perfect square trinomial.
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The probability that the number of students who will take the mathematics exam is 40 out of 50. What is the expressed as a percentage
Answer:
I think it's 80%
Step-by-step explanation:
Method 1: (40/50)*100 = 80%
Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%
Bob has decided to make his move to his new house easier, so he is going to rent a truck to get it all moved in one trip. He is looking at two truck rental companies. U-Haul rents a 32 ft truck for $19.95 plus 49 cents per mile driven. The formula to calculate the cost with U-Haul is C = 19.95 + 0.49x, where x represents the number of miles driven. Penske rents a truck for 69 cents per mile but has no extra fees. The formula to calculate costs for Penske is C = 0.69x, where x represents miles driven. How many miles indicate that the cost of renting a truck from U-Haul is equal to the cost of renting a truck from Penske?
