Answer:
(i) [tex]64+192 x^2+240 x^4+160x^6[/tex]
(ii) 1072
Step-by-step explanation:
Part (i)
Using Binomial series formula:
[tex](2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3[/tex]
[tex]=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6[/tex]
[tex]=64+192 x^2+240 x^4+160x^6[/tex]
Part (ii)
[tex](1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})[/tex]
[tex]=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}[/tex]
[tex](2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)[/tex]
[tex]=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...[/tex]
There is no need to keep expanding since the remaining will include the variable.
Therefore, the term independent of x = 64 - 1152 + 2160 = 1072
Is ABSE- ATES? If so, identify the similarity postulate or theorem that
applies.
Joe collects toy cars and marbles. Whenever he collects 4 cars, he also collects 12 marbles. How many marbles does he collect after collecting 20 cars? What rule is being used?
Answer; 60
Step-by-step explanation:
solution:
here,
4 cars = 12 marbles
1 car = 12/4. = 3 marbles
then,
20 cars = 3(20) marbles
= 60 marbles
We can make this into a fraction 4/12 = 20/x
Then, we will solve for x
4x = 240 cross multiply
x = 60
Joe collects 60 marbles after collecting 20 cars.
The Multiplicative Inverse Property is being used.
Express √12+√27 in the form n√3, where n is an integer.
Answer:
5sqroot3
Step-by-step explanation:
see image.
An integer is just a whole positive or negative (positive in this case) number that's not a fraction or decimal or mixed number. In the answer that is the 5.
To simplify a radical, look for a factor that is a perfect square. Radicals and multiplying are very friendly to each other and you can separate the "radicand" (the inside number) into factors inside the radical also into separate radicals to simplify. See image
how many one third cup servings are in 16 cups
The volume of a right cone is 252pi units^3. If its height is 21 units, find its radius.
Based on the calculations, the radius of this right cone is equal to 6 units.
Given the following data:
Volume of cone = [tex]252\pi \;units^3[/tex]Height of cone = 21 units.How to calculate the volume of a cone.Mathematically, the volume of a cone is given by this formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where:
h is the height.r is the radius.Making r the subject of formula, we have:
[tex]r=\sqrt{\frac{3V}{\pi h} } \\\\[/tex]
Substituting the given parameters into the formula, we have;
[tex]r=\sqrt{\frac{3\times 252\pi}{\pi \times 21} } \\\\r=\sqrt{\frac{756}{21} }\\\\r=\sqrt{36}[/tex]
r = 6 units.
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If 10% of your paycheck was withheld for federal income taxes and another 6% for state income taxes, how much would your net (or take-home) pay be?
Your net income/take-home would be 84.6 percent of the gross amount.
What is net income?Your net income is the amount of money left after payroll deductions in the form of taxes and other charges on the gross amount of your paycheck.
If we deduct federal and state taxes, 10 percent and 6 percent respectively, we would charge 10 percent and 6 percent of 100 and have 84.6 percent of your original(gross) income left.
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If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores
that fall between 54.3 and 63.5?
A 34
B 47.5
C 68
D 95
Answer:
A
Step-by-step explanation:
If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores
that fall between 54.3 and 63.5?
What is the area, in square inches, of the isosceles trapezoid below?
What the line measures
Factor each completely.one zero has been given
f(x)=x^3-4x+16;-2
F(x) = X^4+ 2x^-13x^2 -10x + 40;2
F(x)=x^3-3x^2-13x+15;-3
F(x)=x^4-8x^3+19x^2-12x;3
The polynomials in factored form are listed below:
f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716) f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)f(x) = (x + 3) · (x - 5) · (x - 1)f(x) = (x - 4) · (x - 3) · (x - 1) · xHow to factor polynomialsIn this question we must factor polynomials as there are both numerical and analytical methods. Mathematically speaking, factoring polynomials is represented by the following formula:
[tex]\sum^{n}_{i = 0} \,c_{i}\cdot x^{i} = \prod^{n}_{i=1}(x-r_{i})[/tex], [tex]\forall\,x, r_{i}\in \mathbb{C}[/tex] (1)
Where:
[tex]c_{i}[/tex] - [tex]i[/tex]-th Coefficient[tex]r_{i}[/tex] - [tex]i[/tex]-th RootRegarding fourth order polynomials we can solve them by Ferrari's method and third order polynomials by Descartes' method. Then, the solutions of each polynomials are given below:
Polynomial 1 ([tex]f(x) = x^{3}-4\cdot x +16[/tex])f(x) = (x - 4) · (x - 3) · (x - 1) · x
Polynomial 2 ([tex]f(x) = x^{4}+2\cdot x^{3}-13\cdot x^{2}-10\cdot x + 40[/tex])f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)
Polynomial 3 ([tex]f(x) = x^{3}-3\cdot x^{2}-13\cdot x +15[/tex])f(x) = (x + 3) · (x - 5) · (x - 1)
Polynomial 4 ([tex]f(x) = x^{4}-8\cdot x^{3}+19\cdot x^{2}-12\cdot x[/tex])f(x) = (x - 4) · (x - 3) · (x - 1) · x
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Choose the correct graph of the function y=√x-3
Answer:
C. where the start point is on (3,0) and goes up and to the right
Step-by-step explanation:
y= √x−3
Swap sides so that all variable terms are on the left hand side.
√x−3 =y
Square both sides of the equation.
x−3=y^2
Add 3 to both sides of the equation.
x−3−(−3)=y^2 −(−3)
Subtracting −3 from itself leaves 0.
x=y^2 −(−3)
Subtract −3 from y^2.
x=y^2 +3
For each pair of real numbers show that the first number is a factor of the second number?
Need help ASAP!!
Answer:
[tex]\red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}}[/tex]
Answer:
Putanginaaaaaaaaaaaaaaaaaaaaa
A group of people are fundraising, and each person raises a certain amount of money for every mile they walk. Each person's fundraising is represented below using d for the dollars that person raises and w for the miles that person walks. Select all the representations that can be described by the equation d = 2w.
Answer:
B, C, EStep-by-step explanation:
According to coordinates on the graphs and numbers in the tables we have the following relationship:
A) d = 1/2wB) d = 2wC) d = 2wD) d is not proportional with w since 12/6 ≠ 18/10 ≠ 20/12E) d = 2wAs we see B, C and E have same relationship, matching the target.
Step-by-step explanation:
hope it's help you this answer
Find the greatest possible number of consecutive zeros at the end of the product of three positive integers if the sum of these three integers equals 939.
Answer:
I think its 5 consecutive zeros.
Step-by-step explanation:
This would be a guess but I think you would need two numbers in the hundreds that also have 2 parts of which have a product of a number ending in 0, like 4 and 5.
So my guess would be
400 * 500 * 39
= 7800000
What is the volume of this cone? Use 3.14 for π and round your answer to the nearest tenth.
In your answer, give the volume of the cone rounded to the nearest tenth, and then explain how you calculated it.
Answer:
volume = 33.5 in³
Step-by-step explanation:
Formula:
[tex]\sf volume \ of \ a \ cone=\dfrac13\pi r^2h[/tex]
Given:
r = 2 inh = 8 inπ = 3.14Substituting the given values into the formula:
[tex]\sf \implies volume=\dfrac13 \times 3.14 \times 2^2 \times 8[/tex]
[tex]=\dfrac13 \times 3.14 \times 4 \times 8[/tex]
[tex]\sf =33.49333333...[/tex]
[tex]\sf =33.5 \ in^3 \ (nearest \ tenth)[/tex]
A store receives a shipment of boxes of tea. The total mass shipment is 6kg.
-each box has a mass of 0.040 kg.
-boxes of green tea make up 18% of the shipment.
How many boxes of green tea were in the shipment?
A. 7
B. 27
C. 58
D. 108
See the picture below and answer for 50 points and brainliest
Answer:
Non-linear equations:
[tex]y=x^2 +2x-3[/tex]
[tex]3y=2^x[/tex]
Step-by-step explanation:
Linear equation: y = mx + b
Therefore, a linear equation has 2 variables that have no exponents.
So the non-linear equations are:
[tex]y=x^2 +2x-3[/tex] (this is a quadratic equation - polynomial with degree 2)
[tex]3y=2^x[/tex] (this is an exponential equation)
The length is :____meters and the width is____meters.
Answer:
Length = 42, Width = 14
Step-by-step explanation:
Say width = x
3x + x = 56
4x = 56
x = 14
14 x 3 = 42.
Answer:
width = 7
length = 21
Step-by-step explanation:
x + 3x = 56/2
4x = 28
x = 7
Answer the Both (a) and (b) . And show the method too. I will make Brainelist + 50 points
#a
4p-6pq+9q-64p-3(2pq+3q-2)#b
That be x and y
So
x+y=15--(1)2x+4y=64--(2)So
from eq(1)
x=15-y--(3)Put in second one
2(15-y)+4y=6430-2y+4y=642y=34y=17Put in third one
x=15-17x=-2Take it positive
x=2Answer:
(a) (i) Factorize [tex]\sf 4p-6pq+9q-6[/tex]
Rewrite by swapping the order of the first two terms:
⇒ -6pq + 4p + 9q - 6
Factorize the first two terms and the last two terms separately:
⇒ -2p(3q - 2) + 3(3q - 2)
Factor out the common term (3q - 2):
⇒ (3q - 2)(-2p + 3)
(ii)
Square of the binomial: [tex](a+b)^2=a^2+2ab+b^2[/tex]
Rewrite [tex]9.9[/tex] as [tex]10 - 0.1[/tex]
Therefore, [tex]a = 10[/tex] and [tex]b = -0.1[/tex]
Also, remember that multiplying a number by 0.1 is the same as dividing it by 10. (when dividing a decimal number by 10, simply move the decimal point 1 place to the left).
[tex]\begin{aligned}\implies 9.9^2 & =(10-0.1)^2\\ & =10^2-2 \cdot 10 \cdot 0.1+0.1^2\\& = 100-\dfrac{2 \cdot 10}{10}+\dfrac{0.1}{10}\\& =100-2+0.01\\ & =98 + 0.01\\ & = 98.01\end{aligned}[/tex]
(b) (i)
Let x = number of motor bicycles
Let y = number of cars
Given:
There are 15 vehicles of two types⇒ x + y = 15
Given:
The number of tires in all vehicles is 64⇒ 2x + 4y = 64
(ii) Rewrite x + y = 15 to make x the subject:
⇒ x = 15 - y
Substitute into 2x + 4y = 64 and solve for y:
⇒ 2(15 - y) + 4y = 64
⇒ 30 - 2y + 4y = 64
⇒ 30 + 2y = 64
⇒ 2y = 34
⇒ y = 17 cars
Substitute found value of y into x = 15 - y to find x:
⇒ x = 15 - 17 = -2 motorbikes
**There must be an error in the question, as with the given information, the number of motorbikes is -2, which is impossible.**
Here are the possible combinations of number of motorbikes (M) and number of cars (C) whose sum of tires is 64. As you can see, there is no combination that sums to 15 vehicles:
0 M + 16 C = 16 vehicles
2 M + 15 C = 17 vehicles
4 M + 14 C = 18 vehicles
6 M + 13 C = 19 vehicles
8 M + 12 C = 20 vehicles
10 M + 11 C = 21 vehicles
12 M + 10 C = 22 vehicles
14 M + 9 C = 23 vehicles
16 M + 8 C = 24 vehicles
18 M + 7 C = 25 vehicles
20 M + 6 C = 26 vehicles
22 M + 5 C = 27 vehicles
24 M + 4 C = 28 vehicles
26 M + 3 C = 29 vehicles
28 M + 2 C = 30 vehicles
30 M + 1 C = 31 vehicles
32 M + 0 C = 32 vehicles
Data Analysis 7th grade math
Laura kept a record of the number of minutes she spent at the gym this week.
Day Minutes
Monday 60
Tuesday 70
Wednesday 62
Thursday ?
How many minutes should she spend at the gym on Thursday in order to average 65 minutes a day for four days.
________ Minutes
she spends 68 minutes at the gym on Thursday in order to average 65 minutes a day for four days.
What is Average?The mean (also known as the arithmetic mean, which varies from the geometric mean) of a dataset is calculated as the sum of all values divided by the total number of values. This measure of central tendency is usually referred to as the "average".
Granted, Laura recorded how long she spent at the gym each day this week.
Let "x" represent the time she spent working out on Thursday.
Since,
Average = (sum of values)/ count of values
Thus, in our case
Average = (60 +70 +62 +x)/4
average is 65 minutes a day for four days.
65 = 192 +x)/4
192 +x = 260
x = 260-192
x = 68
Therefore, she spends 68 minutes at the gym on Thursday in order to average 65 minutes a day for four days.
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Whcih choice best describes the group this shape belongs in, based on the kinds of sides and angles it has? Angela chose A as the correct answer. How did she get that answer?
The shape in the figure has 6 sides
The choice that describes the group the shape belongs to is (a) parallel sides, acute angles
How to determine the group of the shape?From the figure, we have the following highlights
The shape has 6 sidesThe direct opposite sides are equalThe direct opposite sides are parallelThe measure of angles between adjacent sides are less than 90 degrees i.e. acute anglesThe above highlight mean that:
The shape belongs to parallel sides, acute angles group of shapes
Hence, Angela's conclusion is correct
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May someone please help me with this?
Answer:
Step-by-step explanation:
First, calculate the angle of FDE (assume it as α) by:
[tex]EF=\frac{\alpha}{360}\times(2\pi)(DE) \rightarrow 2\pi = \frac{\alpha}{360}(2\pi)(6)[/tex]
[tex]\alpha=60^{0}[/tex]
So, use this angle to calculate the area of FDE (unshaded region):
[tex]A_{US}=\frac{\alpha}{360}\times(\pi)(DE)^{2}=\frac{60}{360}(\pi)(6^{2})=6\pi[/tex]
So, the shaded region can be determined by:
[tex]A_{S}=A-A_{US}=\pi(DE)^{2}-6\pi=36\pi-6\pi=30\pi=\frac{60}{2}\pi[/tex]
can someone pls answer the UNANSWERED questions. (the ones that dont have the blue dot on them) WILL MARK BRAINLIEST
Answer:
7.B
9.A
Step-by-step explanation:
Gcf of 24 and 36
is 12
a^2 and a is a
180-50
=130
acute mean less than 90 degrees
180-89=41
89 and 41 are acute
1 is also wrong
Answer:
7. B 2·2·3·a
9. B 41°
Step-by-step explanation:
You want the greatest common factor of 24a² and 36ab, and you want the smallest integer-valued angle in an acute triangle with one angle 50 degrees.
7. GCFThe factors of 24a² are 2·2·2·3·a·a.
The factors of 36ab are 2·2·3·3·a·b.
The factors these lists have in common are 2·2·3·a, matching choice B.
9. AnglesIf one angle of a triangle is 50°, the sum of the other two angles must be ...
180° -50° = 130° . . . . . . sum of angles B and C
One of these angles will be the smallest it can be only if the other is the largest it can be. The largest integer acute angle is 89°, so the smaller angle will be ...
130° -89° = 41°
The smallest possible angle in the acute triangle is 41°.
__
Additional comment
8. A dodecagon has 12 lines of symmetry, 6 through opposite vertices, and 6 through opposite sides. The correct choice for 8 is A.
<95141404393>
CHOICES -> TRUE OR FALSE
Answer:
1.True
2.false
3.True
4.True
5.false
6.false
7.false
8.True
9.True
10.false
Step-by-step explanation:
10,000cm^2=1m^2
Find the value of the expression 1/2x + 3 if x = 12
Step-by-step explanation:
please mark me as brainlest
A school's principal wanted to give a special 'Good Luck' pencil for each student in the fifth grade. If there are 105 kids in the fifth grade, and there are 12 pencils in each box, how many boxes will he need to buy?
Find the volume. Please help! Thanks!
hehe
Volume of a Square Pyramid: 1/3 x length x width x height
Length = 2
Width = 2
Height = 3
Volume = 1/3 x 2 x 2 x 3
Volume = 1/3 x 4 x 3
Volume = 1/3 x 12
Volume = 4
Volume = 4 cm^3
Hope this helps!
Consider the rectangle with width 4 ft and length 18 ft, write a ratio of the length to the width.
Answer: 18:4
Step-by-step explanation:
Ez
Answer:
9 : 2
Step-by-step explanation:
length : Width = 18 : 4
[tex]\sf = \dfrac{18 \ \div \ 2}{4 \ \div \ 2}\\\\=\dfrac{9}{2}[/tex]
= 9 : 2
Find the equation of the line that passes through points a and B. A(1 ,7) B(-3,-1)
Answer:
well i wrote it in paper nothing to explain it's ez
I need help with this
Answer:
The correct answer is B: 3 cubic feet.
Step-by-step explanation:
If you want to find the volume of a rectangular prism, you need to know the length, width, and height. The first rectangular prism is a cube with a length of 3 feet, so the volume of the figure would be [tex]3^{3}=27 ft^{3}[/tex]. The second rectangular prism has a length of 3 feet, a width of 2 feet, and a height of 4 feet, so the volume of the prism would be 3 × 2 × 4 = [tex]24 ft^{3}[/tex]. Now that you know the 2 volumes, you need to subtract the volumes in order to find the difference, which is 27 - 24 = 3 [tex]ft^{3}[/tex].