Explanation:
A direct proportion is of the form y = kx
To find k, pick any row to divide the y over x value
k = y/x = 20/10 = 2k = y/x = 24/12 = 2k = y/x = 42/21 = 2k = y/x = 44/22 = 2No matter which row you go for, the constant of proportionality is 2. Meaning that we double the x value to get to y.
Therefore, we go from y = kx to y = 2x
i) Find the first 4 terms in the expansion of
[tex](2 + x ^{2})^{6}[/tex]
in ascending powers of x.
ii) Find the term independent of x in the expansion of
[tex](2 + x ^{2})^{6}(1 - \frac{3}{x {}^{2} } ) {}^{2} [/tex]
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
Solve and will mark brainliest
Answer:
24 degrees
Step-by-step explanation:
24 degrees because
angle a is 24 degrees
and since its the middles and main angle
24 degrees is the answer
29. An acting improvisation class divides into 6 teams that each have at
most 4 students.
a. Write and solve an inequality to represent the number of students
in the class.
b. Each team has at least two students. Could there be 20 students in
the class? Explain why or why not.
The inequality that represent the number of students in the class is x ≤ 24. They could be 20 students
What is an inequality?
An inequality is an expression that shows the non equal comparison of two or more numbers and variables.
Let x represent the number of students in the class, hence:
x ≤ 6(4)
x ≤ 24
If each team has at least 2 students:
x ≥ 6(2)
x ≥ 12 and x ≤ 24
The inequality that represent the number of students in the class is x ≤ 24. They could be 20 students
Find out more on inequality at: https://brainly.com/question/24372553
In a certain triangle, two of the sides have measures of 13 and 16. If the triangle is isosceles, then which of the following could be the measure of the third side?
A. 3
B. 29
C. 13
D. 32
PLEASEEE help! I think it's A or B
Answer:
Choice C.
An isosceles triangle always has two sides of the same length.
what shape is this will give brainliest and all that
Answer:
that is a Trapezoid
Step-by-step explanation:
it has two lines that are parallel and two lines that are not. crd. MathGeek99
Answer:
I believe it is a Quadrilateral
Step-by-step explanation:
It's a quadrilateral because of how many sides it has and other stuff
A Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 532 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 95% confidence level.
Answer:
En la Imagen adjunta
Step-by-step explanation:
Toca Para Abrir Imagen
Espero haberte ayudado si es así dame Corona
f(x) = x^1/2 is continuous for all x but not differentiable at x=0. is it True or False?
Answer:
it's true because the x=0 and that why it must be true FX may be the some I would say it's true
Find measure of <1. (The figure may not be drawn to scale)
Answer:
t = 55
Step-by-step explanation:
The figure is a straight line and the sum of angles that make a straight line is 180 degrees
90 + t+ 35 = 180
125+t = 180
Subtract 125 from each side
125 +t-125 = 180-125
t = 180-125
t = 55
Hey! Does can anyone help me with this? Thank you!
Answer:
=x^3/4
Step-by-step explanation:
(x^1/2)(x^1/4)
same base
1/2+1/4
=3/4
=x^3/4
Read the sentence. Patriots, people who supported freedom from England, were especially angry when British soldiers overtook their homes. What type of phrase is people who supported freedom from England?
Appositive
Fragment
Participial
Prepositional
Answer: Fragment.
Step-by-step explanation:
A Fragment phrase can be defined as a sentence that resembles a sentence but lacks delivering a complete idea. This sentence serves as a dependent clause in a sentence.
The given sentence is an example of a fragment phrase or sentence. Though the phrase appears to be a sentence but it lacks complete idea because we don't know about which 'people' is it talking about.
Perimeter of following rectangle mixed number in simplest form 1 1/3 ft 5/8 ft
Answer: 3 11/12
Step-by-step explanation:
1 1/3 * 2 = 2 2/3
5/8 * 2 = 1 1/4
2 2/3 + 1 1/4 = 3 11/12
Please helpppppppppppppp <3
Answer:
Part 1: -10, -5, 0, 8 Part 2: -3/2, -15%, 0.80, 143%, 2 1/4
Step-by-step explanation:
Part 1: The lower the number, the lower the temperature
Part 2: Convert the fractions into decimals
2 1/4 = 2.25
-15% = -0.15
143% = 1.43
-3/2 = -1.5
0.80 = 0.80
The order from least to greatest is -3/2, -15%, 0.80, 143%, 2 1/4
Hope this helps :)
Among all rectangles that have a perimeter of 188, find the dimensions of the one whose area is largest.
-1 (1 + 7x) - 6(-7 -x) = 36
Answer: x = 5
Step-by-step explanation:
If you need to solve for x,
Given:
-1 (1 + 7x) - 6(-7 -x) = 36
Distribute:
-1 - 7x + 42 + 6x = 36
Combine like terms:
- x + 41 = 36
Subtract 41 from both sides of the equation:
- x = -5
Divide both sides by -1:
x = 5
A rectangular prism has a base area of 17 cm², and a height of 5 centimeters. What is the volume of the prism?
Answer:
85cm^3
Step-by-step explanation:
Volume = Base Area * Height
17*5=85
PLEASE HELP PLEASE I WILL GIVE BRAINLIEST
Answer:
QUESTION:1:TYLERCOMPLETELY FILLED THE BOX SHOWN BELOW WITH UNIT,CUBES WITH NO GAPS OR OVERLAPS.HE THEN VOUNTED THE NUMBER OF CUBES THAT HE USED TO FILL THE BOX WHAT TYPE OF MESUREMENT IS REPRESENTED BY THE NUMBER OF CUBES TYLER COUNTED?(5.MD.3)A.AREA B.HEIGHT C.VOLUME D.PERIMETER The CORRECT OPTION :C.VOLUMEStep-by-step explanation:
pls brainlest me thank you
One natural number is 4 more than another one. The product of the two numbers is three times the square of the lesser
number. Find the numbers.
Answer:
2 and 6
Step-by-step explanation:
find the greatest factor of 29g5h4 19g3h5
Answer:
gh1
Step-by-step explanation:
19 is prime and 29 is not divisible by 19 therefore 1g is the highest. 5 and 3 are both prime so again, 1h and finally, 5 is a prime number so gh1 is the greatest factor
How could you demonstrate that the force of gravity acting on an object is proportional to the mass of the object?
Answer:
F = mg
Step-by-step explanation:
g is the constant of proportionality and force is the product of mass and the acceleration due to gravity
f is directly proportional to m, therefore, f = mg
how do I write this out? Expand to write an equivalent expression…
1/2(-4x + 2y)
Answer:
-2x + y
Step-by-step explanation:
This is distributive property, so multiply the terms inside the parentheses by 1/2.
1/2 (-4x) = -2x
1/2(2y) = y
-2x + y
How far could the Apostle Paul walk in 4.5 hours if he walked an average of 4.3 kilometers per hour?
Answer 19.35 km
Step-by-step explanation:
We are looking for the Distance that Apostle Paul walked in 4.5 Hours!
I will be using the formula Distance=rate*time 1)
We DONT know the distance so I'll leave it as variable "D".
We know his rate of walking is 4.3 km/h, and we know he walked for a total of 4.5 hours.
Set up the following equation. D=4.3*4.5 2)
Simplify the equation above: D=19.35
Find simple interest
Principal=rs 4000
Time :2
rate of interest :10%
Step-by-step explanation:
please mark me as brainlest
Step-by-step explanation:
Simple Interest is calculated using the following formula: SI = P × R × T/100, where P = Principal , T is time and r is interest rate.
So , by the values given
Principal :-rs 4000
Time :-2
rate of interest :- 10%
[tex] \frac{p \times r \times t}{100} [/tex]
[tex] \frac{4000 \times 10 \times 2}{100} [/tex]
[tex] = 800 \: rs[/tex]
A kite with diagonals is shown. It has side lengths of 13, 13, 37, and 37. The length from the left point to the middle point is 12, and the distance from the right point to the middle point is 12.
The figure is a kite. What is the length of the kite’s longer diagonal?
5 units
35 units
40 units
48 units
Step-by-step explanation:
we have to solve 2 right-angled triangles via Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle).
one triangle is 37, 12 and the longer part of the long diagonal.
the second triangle is 13, 12 and the shorter part of the long diagonal.
the whole diagonal is then the sum of both parts.
37² = 12² + longer part²
1369 = 144 + longer part²
longer part² = 1225
longer part = 35
13² = 12² + short part²
169 = 144 + short part²
25 = short part²
short part = 5
so, the total diagonal is 35 + 5 = 40 units.
The length of the longer diagonal obtained using Pythagorean theorem is 40 units
What is the Pythagorean theorem?The Pythagorean theorem is a fundamental geometric relationship that states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the other two sides (the legs). Mathematically, we get
c² = a² + b²
Where a and b are the lengths of the legs and c is the length of the hypotenuse side of the right triangle.
The diagonals of a kite are perpendicular to each other
The diagonal that is bisected in a kite is the shorter diagonal
The lengths from the left point to the middle and the distance from the right point to the middle are both 12, which indicates that the diagonal from left to right of the kite is bisected, which is the shorter diagonal. Therefore;
The length of the shorter diagonal is; 12 + 12 = 24
Therefore, the longer diagonal forms two right triangles to the left and two right triangles to the right
The hypotenuse length of the right triangles are 37 and 13, while the leg common to both right triangles on each side is half the length of the shorter diagonal, or 12
The Pythagorean theorem indicates that we get;
Length of the longer diagonal = √(13² - 12²) + √(37² - 12²) = 40
The length of the longer diagonal is 40 units
Learn more on Pythagorean theorem here: https://brainly.com/question/30276548
#SPJ2
Which number is a common multiple of 2 and 4?
A) 14
B) 24
C) 26
D) 34
LAST QUESTION MORE POINTS LETS TAKE IT TO 100!
Answer: B) 24
Step-by-step explanation:
All of these are multiples of 2 since they are all even numbers, so we will look to see which is a multiple of four.
Multiples of four are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, etc.
I bolded and underlined 24 because it is in the list of options. B) 24 is a common multiple of 2 and 4.
24 / 2 = 12
24 / 4 = 6
A mother invests $7000 in a bank account at the time of her daughter's birth. The interest is 18) compounded quarterly at a rate of 8%. What will be the value of the daughter's account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period?
well, from birth to your twentieth birthday that'll just be 20 years, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=7000\left(1+\frac{0.08}{4}\right)^{4\cdot 20}\implies A=7000(1.02)^{80}\implies A\approx 34128.07[/tex]
Which of the following is a right triangle?
70°
60
30*
249
459
128
90°
45°
/60°
60°
55
559
Triangle A
Triangle e
Triangle C
Triangle D
A. Triangle C
B. Triangle D
C. Triangle A
D. Triangle B
SUBMIT
Answer:
Triangle C
Step-by-step explanation:
Triangle C contains a 90° angle.
Answer:
Triangle C
Step-by-step explanation:
The right triangle has one side that is 90° the other two sides have to add up to 90° (45 + 45= 90)
If the difference of 3 / 4 and 1 / 6 of a number is 7, find the number and also verify your answer.
Harry is scuba diving off the coast of Australia. When he is ready to come back to the surface, he rises 12 meters at a safe speed. He climbs 15 centimeters every second. How many seconds will it take him to reach the surface?
Find the surface area of the cube.
[tex]\rightarrow[/tex] Side(a) of the cube = [tex]\sf{\frac{1}{3}ft}[/tex].
To Find:-[tex]\rightarrow[/tex] Surface Area of the cube with side [tex]\sf{\frac{1}{3}ft.}[/tex]
Formula Used:-[tex]\rightarrow[/tex] Surface area of cube = [tex]\sf{6a^2}[/tex]
Solution:-[tex]\rightarrow[/tex] Surface area of cube = [tex]\sf{6a^2}[/tex] (putting the value of a from the above given)
[tex]\rightarrow[/tex] [tex]\sf{=\:6×(\frac{1}{3})^2}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\:6×\frac{1}{9}}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\:\frac{6}{9}}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\:\frac{2}{3}ft^2}[/tex]
Therefore, surface area of the given square = [tex]\sf{=\:\frac{2}{3}ft^2}[/tex]
__________________________________
Hope it helps you:)
Answer:
Step-by-step explanation:
there are 6 square faces of a cube.
if side=x
surface area=6x²
=6(1/3)²
=6/9
=2/3 square foot
EXPLAIN AND SOLVE THE EQUATION
Answer:
1st answer: 61000+(X-1) x 700
2nd answer: 64500
Step-by-step explanation:
Since it says the population increases linearly, which means by the same amount, it is an arithmetic progression. So the formula to find a term in arithmetic progression is [tex]T_{n}[/tex]=a + ( n - 1 ) x d , where a is the first term, n is number of terms, and d is common difference. So now just put the values in the equation, where 61000 is a, x is n and d is 700. To find second answer put 6 in place of n as it says from 2003 to 2009 which is 6 years later.