Answer:
1, 6, 15, 20, 15, 6, 1
Step-by-step explanation:
The binomial expansion of (p + q)⁶ gives 1, 6, 15, 20, 15, 6, 1.
There is always one more extra term for each power;
(p + q)⁰ = 1
(p + q)¹ = 1 1
(p + q)² = 1 2 1
(p + q)³ = 1 3 3 1
(p + q)⁴ = 1 4 6 4 1
(p + q)⁵ = 1 5 10 10 5 1
(p + q)⁶ = 1 6 15 20 15 6 1
The above is a paschal triangle and which shows the coefficients of the expanded terms to their power.
Answer: B: 1, 6, 15, 20, 15, 6, 1
Name a pair of numbers which would represent the slopes of perpendicular lines.
-7/8 + 1/4
pleasee help!!
Answer:
-5/8
Step-by-step explanation:
make them common denominatiers
(1/4)2 = 2/8
-7/8+2/8 = -5/8
Consider the function f(x) = 2 * (x - 20) ^ 2 - 3 What is the value of f(29) ?
Answer:
f(29) = - [tex]\frac{9}{290}[/tex]
Step-by-step explanation:
Step 1: substitute f(29) into the equation.
f(29) = 2(29 - 20)²⁻³
29 replaces x.
Step 2: simplify the exponent
f(29) = 2(29 - 20)⁻¹
2-3 is -1, so the exponent is -1
Step 3: distribute the exponent to the parentheses
f(29) = 2([tex]\frac{1}{29}[/tex] - [tex]\frac{1}{20}[/tex])
Since the exponent is a negative one, basically make it a fraction with the base as the denominator and the exponent as a numerator. I don't know too much about negative exponents, but this is how to factor in a -1.
Step 4: Distribute.
f(29) = [tex]\frac{2}{29} -\frac{2}{20}[/tex]
Step 5: Simplify before finding a common denominator (2/20 cancels out)
f(29) = 2/29 - 1/10
Step 6: Find a common denominator (290)
f(29) = [tex]\frac{20}{290}[/tex] - [tex]\frac{29}{290}[/tex]
Step 7: Simplify
f(29) = - [tex]\frac{9}{290}[/tex]
TBH I'm not sure this is correct, but I hope this helps =)
Binomial expansion
(x+3)^3
Answer:
x ^3 + 9 x^ 2 + 27 x + 27
Step-by-step explanation:
Answer:
x+9
Step-by-step explanation:
square the 3 and keep the x
The number of students in a chess club decreased from 40 to 19. What is the percent decrease? Round your answer to the nearest percent. The percent decrease is %.
Answer:
i think its 20
Step-by-step explanation:
Answer:
46
Step-by-step explanation:
Amount of change = Greater Value − Lesser Value
= 24 − 13 Substitute values.
= 11 Subtract.
Find the percent decrease. Round to the nearest percent.
Percent Change =
Amount of Change
Original Amount
=
11
24
Substitute values.
≈ 0.458 Divide.
= 46% Write as a percent and round.
The percent decrease is 46%.
. A train travels at 75 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?
Answer:
The domain is time (t) and the range is distance (d).
Step-by-step explanation:
I TOOK THE Test
The time (t) is the domain and range is distance (d)
What are range and domain?The word domain refers to a set of possible input values, on the other hand range refers to the set of possible output value.
How can I locate the domain?Allow x to be an independent variable in the function y is equal to fx, and y is a reliant variable. A value for x is said to be in the domain of a function f if it successfully allows the production of a numerical result y using another value for x.
A train travels at 75 miles per hour.
An equation can be written that compares the time (t) with the distance
here, time (t) is independent value and distance (d) is dependent value which is dependent on time (t).
The domain is time (t) and the range is distance (d).
Learn more about domain and range here:
https://brainly.com/question/30133157
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Sally prepaid
11/
the price of a ticket to a concert. The amount she prepaid was $15.
What was the total price of the ticket?
pls help
Answer: option c
good luck
Answer:
Step-by-step explanation:
30
Find m_ABD and mZCBD given m ABC = 77º. A (3x + 22) D 16 (5x - 17) B C mZ ABD |° and mZCBD
Answer:
∠ ABD = 49°, ∠ CBD = 28°
Step-by-step explanation:
∠ ABD + ∠ CBD = ∠ ABC , substitute values
3x + 22 + 5x - 17 = 77 , that is
8x + 5 = 77 ( subtract 5 from both sides )
8x = 72 ( divide both sides by 8 )
x = 9
Thus
∠ ABD = 3x + 22 = 3(9) + 22 = 27 + 22 = 49°
∠ CBD = 5x - 17 = 5(9) - 17 = 45 - 17 = 28°
A new amusement park ride that last one minute can have up to 1,200 Riders per hour. How many riders can ride per minute.
Pls help
Answer:
20
Step-by-step explanation:
1 hour = 60 minutes
1200 riders = 60 minutes: divide by sixty to set equal to 1
20 riders = 1 minute
Just divide 1,200 by 60 because there are 60 minutes in 1 hour.
Just think about it this way: If you eat 1 banana a minute, you eat 60 bananas an hour. The amusement park ride goes around once a minute. In one hour it goes around 60 times. Each time it carries the same amount of people.
1,200 divided by 60 is...
20!
The ride can carry 20 riders each ride, and each ride lasts a minute.
what is an equation of the line that passes through the points (-6,2)
and (-6,6)
(14 POINTS!) Based On the information in the table, is the cost of the apples proportional to the weight of apples ?
Answer:
yes it is proportional, if you subtract 3.76 from 5.64 you get 1.88 then add 1.88 to each number to make sure it's right.
Answer:
The statement of whether the cost is proportional to the cost and weight of apples is: yes, it is proportional.
Step-by-step explanation:
From what I can find out from the graph, I would firstly likely want to see if there is a constant between each pound and cost. Meaning, I would want to see if there is a rule that is used throughout the table.
From what I had found out, the rule of this table is:
(x = pounds of apples)
(y = cost of apples)
y = 1.88x
This means that in order to get the 'y' value, also known as the cost of apples, we must multiply 1.88 to the 'x' values, pounds of apples.
This can be found by:
First, dividing 3.76 to 2, your quotient is: 1.88
[tex]\frac{3.76}{2}=1.88[/tex]
Then we need to see if this applies to the other terms as well by multiplying 1.88 to each 'x'
y = 1.88x
y = 1.88(3) = 5.64
y = 1.88(4) = 7.52
y = 1.88(5) = 9.4
You get the same vaule, which means that this is proportional to the table provided.
PLEASE HELP!! its due in 20 minutes and i dont get this
Answer:
Please see below :)
Step-by-step explanation:
The slope is just what's in front of the x!
So:
1.) slope = -1/4
2.) slope = undefined
3.) slope = -9
4.) slope = 9/2
Hope this helps!
Answer:
1. -1/4
2. undefined
3. zero
4. 6/5
Step-by-step explanation:
PLEASE HELP! :)
A restaurant owner was experimenting with the taste of her homestyle lemon
drink. She started with 60 litres of water. She removed 15 litres of the water and
replaced it with 15 litres of pure lemon juice.
After thoroughly stirring the new mixture, she discovered that it was too
“lemony”. So she removed 10 litres of the new mixture and replaced it with 10
litres of water. She thoroughly stirred the mixture and concluded that the new
mixture was just right.
Determine the ratio of pure lemon juice to water in the final 60 litre mixture.
Answer:
Lemon juice / water = 12,5 / 47,5 or 26,31 %
Step-by-step explanation:
First step:
We got 60 liters. of water and we replace 15 liters. of water and add 15 liters of lemon juice, then our mixture is:
60 lts. of mixture ⇒ with 45 lts. is water and 15 lts. is lemon juice
The proportion of the mixture
each liter of the mixture is 0,75 lts. of water and 0,25 of lemon juice
2 step
Removing 10 lts. of mixture implies
10 lts of mixture means 7,5 lts. of water and 2,5 lts. of lemon juice
then we have
50 lts. of mixture with (45 - 7,5 = 37,5 lts.) of water and (15 - 2,5 = 12,5 ) lts. of lemon juice
third step
Addind 10 lts. of water:
60 lts. of mixture with ( 37,5 + 10 = 47,5) lts. of water and 12,5 lts. of lemon juice
Final mixture is
60 lts. of mixture with 47,5 lts. of water and 12,5 lts. of lemon juice
Proportion
Lemon juice / water = 12,5 / 47,5 or 26,32 %
can anyone plz help with this
HELP PLEASSEEE QUICKLYY IM BEGGING
Train A and Train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 4h. Train B reaches station B after 3 1/2 h. Station A and Station B are 562.5 mi apart. What is the rate of the trains?
Find the distance between the two points in simplest radical form.
(-6,0) and (-3,-4)
Answer:
Answer:
5
Step-by-step explanation:
Answer:
I beleave the awnser is √74
Please give me brainlyist :)
Step-by-step explanation: Also if I am wrong please tell me
What is the equation of the line that passes through the point (6,6) and has a slope of 5/3
Answer:
The answer is
[tex] \huge y = \frac{5}{3} x - 4[/tex]
Step-by-step explanation:
To find an equation of a line given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)\\[/tex]
where
m is the slope
( x1 , y1) is the point
From the question the point is (6,6) and slope 5/3
We have
[tex]y - 6 = \frac{5}{3} (x - 6) \\ y - 6 = \frac{5}{3} x - 10 \\ y = \frac{5}{3} x - 10 + 6 \\ [/tex]
We have the final answer as
[tex]y = \frac{5}{3} x - 4 \\ [/tex]
Hope this helps you
If f() = 3 -3 and g(x) = 3x2 + x - 6, find (f+ g)(x).
O A. 3x?- 1x-3
B. 3x2 + x - 3
C. 4x2 - 9
D. 3x2 + x - 9
LMN is a right triangle.
A. True
B. False
Answer:
A: True
Step-by-step explanation:
58z-8=56z+11
What’s z
Answer:
z=19/2
Step-by-step explanation:
Below, you are given the 2012 value of a product and the rate at which the value is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year. (Let t = 12 represent 2012.) 2012 Value Rate $48,000 $2200 decrease per year
Answer:
[tex]y = 48000 - 2200x[/tex] --- equation
[tex]y = 37000[/tex] --- value at 5th year
Step-by-step explanation:
Given
[tex]Value = \$48000[/tex]
[tex]Rate = \$2200[/tex] decrease
Required
Determine the linear equation
Determine the value at the 5th year
Represent years with x.
If the rate in 1 year is 2200,
in x years, it'll be 2200x (decrement)
So, the value (y) at x years is.
[tex]y = 48000 - 2200x[/tex]
The value at the 5th year is when x = 5.
So, we have:
[tex]y = 48000 - 2200 * 5[/tex]
[tex]y = 48000 - 11000[/tex]
[tex]y = 37000[/tex]
anyone know this !! I'll brainlist u
Answer:
Step-by-step explanation:
Number of days = y
Number of weeks = x
1 week = 7days
Formula = 7x = y
13 weeks = 7(13) = 91 days
29 weeks = 7(29) = 203 days
7.5 weeks = 7(7.5) = 52.5 days
Please answer thank you :D
Answer:
You could type 360 words in 12 minutes
Step-by-step explanation:
150/5=30
12*30=360
The triangles are similar. Find the missing length x.
Answer:
36
Step-by-step explanation:
If the triangles have similar sides, any increase or decrease in side length is in equal number. This means equal ratio. How?
Let the common factor of decrease in side OD to AP be, z
[tex]\frac{30}{20} = z[/tex]
And, the common factor of decrease in side DT to PN be, z
[tex]\frac{x}{24} = z[/tex]
So, [tex]z = z[/tex]
[tex]\frac{30}{20} = \frac{x}{24}[/tex]
[tex]\frac{30}{20}[/tex] × [tex]24[/tex] = [tex]{x}[/tex]
Therefore,
[tex]{x}[/tex] = [tex]\frac{3}{2}[/tex] × [tex]24[/tex]
= [tex]3[/tex] × [tex]12[/tex]
= [tex]36[/tex]
What is 10.0239808 Rounded to the nearest one-hundredth of one percent?
Answer:
10.02
Step-by-step explanation:
Brian needs to buy some pencils bread I had a pack of 12 pencils for 298 when we has a pack of a pack of 18 pencils for 499 find the unit price for each brand then state which brand is the better by based on the unit price we want your answers to the nearest sent
Answer:
The pack of 12 pencils for 298 is better as it has a lower unit price.
Step-by-step explanation:
To be able to find the answer, you have to calculate the unit price for each brand by dividing the price of the pack by the number of pencils in the pack.
-298/12=24.83
-499/18=27.72
According to this, the answer is that the pack of 12 pencils for 298 is better as it has a lower unit price.
WILL GIVE Brainlist and thanks. Give reasons if possible
Help I’m actually stuck
Answer:
a is 64 b 125 c 36
Step-by-step
so you do 2 times 2 times 2 = 8 because there is a 3 so you multiply it by it self how ever many times the number above it says so after you do that its the same for the other number so they are both 8 so 8 times 8 is 64
NEED HELPP!! WILL GIVE 60 POINTS AND BRAINILY TO THE BEST ANSWER!!!
Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?
a) 45 degrees
b) 60 degrees
c) 120 degrees
d) 135 degrees
d) 135°
Step-by-step explanation:x ; y =supplementary =>
=> x + y = 180
x = 3y
replace x
3y + y = 180
4y = 180
y = 180 : 4
y = 45°
x = 3y
x = 3×45°
x = 135°
Good luck !
Answer:
D
Step-by-step explanation:
Supplementary angle: sum equals 180 degrees cannot be a straight line(180 degrees).
Y.3 + X = 180
A.
45/3 = 15
45 + 15 = 60
B.
60/3 = 20
60 + 20 = 80
C.
120/3 = 40
120 + 40 = 160
D.
135/3 = 45
135 + 45 = 180
h(t) = t + 2 + 3; Find h(6)
h(6) = 11
Step-by-step explanation:Hi there !
h(t) = t + 2 + 3
= t + 5
replace t = 6
h(6) = 6 + 5
= 11
Good luck !
Find the percent decrease. Round to the nearest percent.
From 94°F to 70°F
The percent decrease is%
Answer:
-25.53%
Step-by-step explanation: