By the binomial theorem,
[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]
where
[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]
is the so-called binomial coefficient.
The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have
[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]
but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]
Which of the binomials below is a factor of this trinomial? x2+12x+31
A. x+4 B.x-2 C. x+2 D. x-4
(x+4) is a factor of this trinomial given , Option A is the right answer.
What is a Factor ?A factor is a number o expression that completely divides the number or the expression and the remainder is equal to zero.
The given trinomial is
x² +12x+32
x² + 8x +4x +32
x(x+8)+4 (x+8)
(x+8)(x+4)
From the given option Option A (x+4) is the right answer.
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The domain of the function
Step-by-step explanation:
[-5, 4] because it is an empty circle, meaning less than
The distance between points A and B is 15. The coordinates of point A are (1, 18) and the
coordinates of B are (13, z). Solve for the two values of z. Show your work to prove your
answer.
Answer:
9 and 27
Step-by-step explanation:
let me know if you want an explanation
What value of a make the equation 14-a=19-12
[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]
Answer:
7
Step-by-step explanation:
14-a=19-12
14-a=7
14-7=a
7=a
Combine like terms
the number of sides of regular polygon if the measure of its interior angle is 150 degree
Answer:
12 sides
Explanation:
[tex]\sf interior \ angle = \dfrac{(n-2) \times 180}{n} \quad (where \ n \ denotes\ number \ of \ sides)[/tex]
Solving Steps:
[tex]\sf \dfrac{(n-2) \times 180}{n} = 150[/tex]
[tex]\sf (n-2) \times 180} = 150n[/tex]
[tex]\sf 180n-360 = 150n[/tex]
[tex]\sf 180n-150n = 360[/tex]
[tex]\sf 30n = 360[/tex]
[tex]\sf n = 12[/tex]
The area of a rectangle, A = l • w is represented by the expression 24x^6y^15. Which could be the dimensions of the rectangle?
After calculating the value, l & w could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
Calculation:The inquiry relates to the laws of indices
where, [tex]x^{a} * x^{b}=x^{a+b}[/tex]
Provided the query, A= [tex]24x^{6}y^{15}[/tex]
[tex]2* 12[/tex] might be used to calculate the length and width of 24.
Hence,
[tex]x^{6}=x^{5} * x^{1} =x^{5+1}[/tex]
& [tex]y^{15}= y^{8} * y^{7} =y^{8+7}[/tex]
So, it can be written as,
A=l * w
⇒ [tex]24x^{6}y^{15}[/tex] = [tex]2x^{5}y^{8}[/tex] * [tex]12xy^{7}[/tex]
Therefore, it is concluded that the dimensions of the rectangle could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
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Complete the statements about the cross sections of cylinders and cones.
The cross section parallel to the base of a cone is a
The cross section parallel to the base of a cylinder is a
The cross section perpendicular to the base of a cone is a
The cross section perpendicular to the base of a cylinder is a
The cross-section parallel to the base of a cone is a circle
The cross-section parallel to the base of a cylinder is a circle
The cross-section perpendicular to the base of a cone is a triangle
The cross-section perpendicular to the base of a cylinder is a rectangle
If 5 men or 10 women can complete any work in 50 days. Than in how many days 8 men and 4 women complete that whole work?
Firstly, let’s assume the the whole capacity the work requires is 1.
Then, let’s see how 1 man can do in 50 days: 1/5.
Further, let’s see how 1 man can do in 1 day : 1/(5×50) = 1/250.
Similarly, let’s see how 1 woman can do in 1 day: 1/(10×50) = 1/500.
Now, we have 8 men, and they can do 8*1/250 in 1 day, which is 4/125.
Besides, we have 4 women, and they can do 4×1/500 in 1 day, which is 1/125.
Therefore, all people we have can do 4/125 + 1/125 of the work in 1 day, which is 1/25.
As a result, the work takes 1/(1/25)= 25 days.
Help me with steps please!
Answer:
18, 36, 54
Step-by-step explanation:
Find the least common multiple of 6 and 9:
Multiples of 6: 6, 12, 18, ......
Multiples of 9: 9, 18, 27, ......
We see that 18 is the least common multiple of 6 and 9.
Additional multiples of 18 are 36 and 54.
If an integer is divisible by 6 and by 9 , then the integer must be divisible by 54.
How to estimate an integer which is divisible by 6 and by 9?Consider the statement as a contradiction.
The assertion exists that any natural number divisible by 6 and 9 exists also divisible by 54.
Let us consider divisible to mean that the outcome of the division of the number and 54 provides another natural number. We can take the prime factors of 6 and 9 which are {2,3} and {3,3}. We can consider that the product [tex]$2 \times 3 \times 3=18$[/tex] exists a number that exists divisible by 6 and 9 but exists not divisible by 54. Another instance exists the product of [tex]$2 \times 2 \times 3 \times 3=36$[/tex] which exists also not divisible by 54.
Therefore, the correct answer is option e) 54.
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Betty has the option of using three types of tables in her coffee shop:
square tables with a side length of 36 inches
rectangular tables 20 inches wide and 73 inches long
round (circular) tables with a diameter of 42 inches.
Which type of table has the largest area?
a.)
Square tables
b.)
Rectangular tables
c.)
Round tables
d.)
The tables all have the same area.
Answer:
The rectangular table
Step-by-step explanation:
Square table: 36*36=1296
Rectangular table: 20*42=1460 [tex]in^{2}[/tex]
Circular table: [tex]\pi * 21^{2}[/tex]≅1384
If the inequality contains < symbol, then graph the equation using a _______________ line.
Answer:
broken line
Step-by-step explanation:
for the graph of an inequality with < or > use a broken line
-----------------------------------
for the graph of an inequality with ≤ or ≥ use a solid line
Laurel has an area in her yard that is in the shape of a parallelogram. It has a base of 30 feet and a height of 22 feet. She wants to cover this area with wildflower seeds. She finds out that 1 ounce of seeds covers 125 square feet of ground. How many ounces of seeds does she need to cover this area?
Answer:
Laurel has to cover this area with 2.64 ounces of seeds.
Step-by-step explanation:
Given
Base of Parallelogram = 30ft
Height of Parallelogram = 22ft
Area of Parallelogram = 1/2*base*height
Therefore, Area of Parallelogram = 1/2*30*22
= 330sq. ft
Given
One ounce of seed covers 125 sq. ft
Hence, No. of ounces needed to cover 330 sq. ft= 330/125
= 2.64
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What is the range of the function y=-x² +1?
Oys-1
Oy2-1
Oyst
y21
The range of the function is
[tex]y \leqslant 1[/tex]
what is the explict formula for this sequence 5, 10, 20, 40, 80, 160, ...
Step-by-step explanation:
as we see in the sequence, each term is twice of the previous term.
we mark the Nth as a(N), then:
a(N)=2a(N-1)
Answer:
[tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
10 ÷ 5 = 20 ÷ 10 = 40 ÷ 20 = 80 ÷ 40 = 2
this indicates the sequence is geometric with explicit formula
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 5 and r = 2 , then
[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]
Martin uses of a gallon of paint to cover of a wall. What is the unit rate at which Martin paints in walls per gallon?
The unit rate at which Martin paints in walls per gallon is 1 7/25 walls per gallon
Unit rateUnit rate of paint per gallon = Quantity of wall / gallon of paint
= 4/5 ÷ 5/8
= 4/5 × 8/5
= (4 × 8) / (5 × 5)
= 32/25
= 1 7/25 walls per gallon
Complete question:
Martin uses 5/8 of a gallon of paint to cover4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon
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)If 18th February, 2030 falls on Monday then what will be the day on 18th February, 2040
Who ever answers this quickly with explanation I will make then brainliest
The Saturday will be the day on 18th February 2040 if 18th February 2030 falls on Monday
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
18th February 2030 falls on Monday
To find what will be the day on 18th February 2040
Calculate the expression:
= Given date + Month code + (difference between years) + Numbe of leap year
Leap year = difference between years/4
= (2040-2030)/4
= 10/4 = 2.5 ≈2
= 18 + 3 + (2040-2030) + 2
= 33
Divide 33 by 7 the remainder will be 5
Day code = given day code + remainder
= 1 + 5
= 6 (saturday from the table attahced)
Thus, Saturday will be the day on 18th February 2040 if 18th February 2030 falls on Monday.
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Find the Value of log10 (0.0001). Rescue me!
Let's see
[tex]\boxed{\sf log_aa=1}[/tex]
Now
[tex]\\ \rm\Rrightarrow log_{10}0.0001)[/tex]
[tex]\\ \rm\Rrightarrow log_{10}10^{-4}[/tex]
[tex]\\ \rm\Rrightarrow -4log_{10}10[/tex]
[tex]\\ \rm\Rrightarrow -4[/tex]
Answer:
This has already been answered correctly, but I'll add an additional perspective. The log of (0.0001 to the base 10 is -4.
Step-by-step explanation:
log(base 10) says give us an exponent, x, that would be required to make [tex]10^{x}[/tex] equal to a specified number, in this case 0.0001.
[tex]10^{0}[/tex] = 1
[tex]10^{1}[/tex] = 10
[tex]10^{-1}[/tex] = 0.1
[tex]10^{-2}[/tex] = 0.01
[tex]10^{-4}[/tex] = 0.0001
The log of (0.0001) to the base 10 is -4.
What is the solution set for Ix+3| =5?
S-8 and s-8
s=-2 and s=2
s=-8 and s=2
s = 2 and s= 8
if 9^x=25, what does 3^x equal?
Answer:
[tex]3^x=5[/tex]
Step-by-step explanation:
Given:
[tex]9^x=25[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^x=25[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2x}=25[/tex]
Apply the same exponent rule:
[tex]\implies (3^x)^2=25[/tex]
Square root both sides:
[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]
[tex]\implies 3^x=5[/tex]
Jacob traveled 171 miles in 3.8 hours. He wants to know how many miles he traveled in one hour, so he set up this problem:
171 divided by 3.8
Jacob started by multiplying the divisor and the dividend by 10. This is the new problem:
1710 divided by 38
Use long division to find the quotient.
0.45
4.5
45
450
The answer is 45
------------------------------------------------------------
Make "t" subject by algebra:-
s=ut+at2
Function h is a transformation of the parent exponential function. Which statement is true about this function? h(x)=2^x-5
A function assigns the values. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
Function h is a transformation of the parent exponential function. Which statement is true about this function? h(x) = 2^(x-5)
As x approaches negative infinity, h(r) approaches negative infinity.
As x approaches positive infinity, h(t) approaches 0.
As x approaches positive Infinity, h(t) approaches positive infinity.
As x approaches negative infinity, h(a) approaches positive infinity.
The graph of the function is given below, as it can be observed that as x approaches positive Infinity, h(t) approaches positive infinity.
Hence, the correct option is C.
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work out the size of angle x
Answer:
x =83
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
x+43 = 126
Subtract 43 from each side
x = 126 -43
x =83
Let's take this problem step by step:
For the angle adjacent to the exterior angle of 126°:
⇒ exterior angle plus the that angle is equal to 180 degrees
⇒ since it is on a straight line
[tex]126 + that_.angle=180\\\rm \hookrightarrow that.angle=180-126\\\rm \hookrightarrow that.angle=54[/tex]
The sum of all the angles in a triangle is: 180°
[tex]that.angle+43+x=180\\\rm \hookrightarrow 54+43+x=180\\\rm \hookrightarrow 97+x=180\\\rm \hookrightarrowx=83[/tex]
The size of angle x is 83°
Answer: 83°
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The probability of a drawing a blue marble from a box of 18 marbles is 2/3. How many green marbles should be added to the box in order to reduce the probability to 1/2?
Answer:
6 green marbles should be added.
Step-by-step explanation:
If the probability of drawing a blue marble from 18 marbles is 2/3 then there are 12 blue marbles because 18 times 2/3 is 12. This means that to reduce this probability to 1/2 you need to add 6 more marbles to the total amount to get it to 24. Now the probability of getting a blue marble is 12/24 which is 1/2.
The sides of a triangle are 5, 12 and 13 inches long. what is the angle between the 2 shortest sides?
a. 30
b. 45
c. 60
d. 90
e. 120
Answer: 90 degrees
Step-by-step explanation:
The hypotenuse is opposite the right angle, which is created by the two shortest sides.
A state offers specialty license plates that contain 5 numbers followed by 2 letters. License plates are assigned randomly. All license plates are equally likely. Find the number of possible license plates that can be issued using this system.
The number of possible license plates that can be issued using this system is 67600000.
What is Combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.
Here, number plate contains 5 numbers and 2 letters
Total possible number (0-9) = 10
Total possible letters (A-Z) = 26
Possible number plates which contains 5 numbers and 2 letters are
¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ²⁶C₁ X ²⁶C₁
10 X 10 X 10 X 10 X 10 X 26 X 26
10⁵ X 26²
676 X 10⁵
67600000
Thus, the number of possible license plates that can be issued using this system is 67600000.
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Will bought a new skateboard that was on sale. The original price of the skateboard was $60. The store had marked it down by 20 percent, and Will had a 25 percent off coupon as well.
We conclude that after the discount and the coupon, Will paid $36 for the skateboard.
How much did Will pay for the skateboard?We know that the original price was $60, and two discounts were applied. One of 20% and other of 25%.
Then the amount that he paid is given by:
P = $60*(1 - 20%/100%)*(1 - 25%/100%)
P = $60*(0.8)*(0.75) = $36
We conclude that after the discount and the coupon, Will paid $36 for the skateboard.
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Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours
Step-by-step explanation:
im sorry but im not sure about this question
Answer:
334.488 miles
Step-by-step explanation:
You don't have a specific request on what I should answer, if it was distance then here's your answer
1/3 · (-3x + 4y - 5z)
(1/3 Is A Fraction)
(Write Explanation)
The value of expression is -(x- 4y/3 + 5z/3)
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.
Given:
1/3 · (-3x + 4y - 5z)
= 1/3(-3x) + 1/3 *4y + 1/3* (-5z)
= -x +4/3*y -5/3 *z
=-(x- 4y/3 + 5z/3)
Hence, 1/3 · (-3x + 4y - 5z)= -(x- 4y/3 + 5z/3)
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A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids.
A hexagon is shown. The hexagon is comprised of 2 congruent isosceles trapezoids. The bases of the trapezoid have lengths of 5 and 8. The height of the trapezoid is 3.
The volume of the prism is 234 cubic units. What is the height of the prism?
3 units
4 units
6 units
8 units
Answer:
the answer is 4 units im pretty sure
Step-by-step explanation:
The height of the prism is 6 units.
The correct option is C.
What is a prism?A prism is a polyhedron in three dimensions with two identical ends.
To find the height of the prism, we need to use the formula for the volume of a prism, which is:
Volume = Base area x Height
Since the prism has two congruent hexagonal bases, we can find the base area by adding the areas of the two congruent isosceles trapezoids.
The area of an isosceles trapezoid is given by the formula:
Area = ((b1 + b2) / 2) x h
where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.
In this case, the two parallel bases have lengths of 5 and 8, and the height of each trapezoid is 3, so the area of one trapezoid is:
Area = ((5 + 8) / 2) x 3 = 19.5 square units
The base area of the prism is then:
Base area = 2 x 19.5 = 39 square units
We are given that the volume of the prism is 234 cubic units, so we can use the formula for the volume of a prism to find the height:
Volume = Base area x Height
234 = 39 x Height
Height = 6 units
Therefore, the height of the prism is 6 units.
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