Answer:
x= -2
TO MUCH STEPS
The value of nCn - 1 + nCn - 2 is
(a) n/2
(b) n(n + 1)/2
(c) n(n-1)/2
(d) (n + 1)²/2
Step-by-step explanation:
We have,
[tex]\displaystyle\sf{\,^{n}C_{n-1}+\,^{n}C_{n-2}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n!}{(n-1)!(n-(n-1))!}+\dfrac{n!}{(n-2)!(n-(n-2))!}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n!}{(n-1)!(n-n+1)!}+\dfrac{n!}{(n-2)!(n-n+2)!}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n!}{(n-1)!(1)!}+\dfrac{n!}{(n-2)!(2)!}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n(n-1)!}{(n-1)!(1)!}+\dfrac{n(n-1)(n-2)!}{(n-2)!(2)!}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n}{1}+\dfrac{n(n-1)}{2}}[/tex]
[tex]\displaystyle\sf{=n+\dfrac{n^2-n}{2}}[/tex]
[tex]\displaystyle\sf{=\dfrac{2n+n^2-n}{2}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n^2+n}{2}}[/tex]
[tex]\displaystyle\sf{=\dfrac{n(n+1)}{2}}[/tex]
Using the combination formula, it is found that the value of the expression is given by:
(b) n(n + 1)/2
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
[tex]C_{n, n-1} = \frac{n!}{(n-1)!(n - n + 1)!} = \frac{n(n-1)!}{(n-1)!} = n[/tex]
[tex]C_{n, n-2} = \frac{n!}{(n-2)!(n - n + 2)!} = \frac{n(n-1)(n-2)!}{(n-2)!2!} = \frac{n(n-1)}{2}[/tex]
Then, adding these values:
[tex]n + \frac{n(n-1)}{2} = \frac{2n + n^2 - n}{2} = \frac{n(n + 1)}{2}[/tex]
Hence option b is correct.
More can be learned about the combination formula at https://brainly.com/question/25821700
Write the equation of the line that passes through the
point (2, -1) and has a slope of —3.
Answer:
y = -3x + 5
Step-by-step explanation:
y = -3x + b
-1 = -3(2) + b
-1 = -6 + b
5 = b
y-6= -3(x-1) use integers A B C
y=-3x+9 this should be the answer you are looking for
A.) How many seats are in the 20th row
B.) Which row contains 36 seats
Write the equation of a line, in slope-intercept form, that has a slope of m=9 and passes through the point (4, 31) .
Enter your answer in the box, without spaces.
Answer:
[tex]\sf y=9x-5[/tex]
Step-by-step explanation:
[tex]\begin{aligned}&\sf y-y_1=m(x-x_1) \\&\sf y-31=9(x-4) \\&\sf y-31=9x-36 \\&\sf y=9x-36+31 \\&\boxed{\sf y=9x-5} \end{aligned} [/tex]
Question makes no sense to me, can someone help?
Answer:
-1 or -0.5
Step-by-step explanation:
f(x) is a common phrase you will see a lot in more advanced math.
Think of it as saying "Function of X". So, when you see f(-1), that means the function of x=-1.
So, when it's asking what value X is in f(-1), remember that that number is the x value.
I say COULD BE -0.5 if it means what y is when x = -1. This is if AND ONLY IF you have a check button to see if -1 is right or the wrong answer. I doubt it is, but I want you to be successful in your work.
I hope this helps :)
If I had seventeen 1/3s of pizza how many full pizzas could I make and how many thirds would be left over?
Pls hurry !!!!!! I will mark BRAINLIEST
Explain how to add integers that have like signs (all + or all -).
Answer:
Step-by-step explanation:
If there is two - signs you make it a positive
Answer:
Step-by-step explanation:
To add integers having the same sign, keep the same sign and add the absolute value of each number. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite.
Solve x please!!!!!!!
Answer:
X=7
Step-by-step explanation:
These are supplementary angles. So they measure to 180º. 180º-95º=85º. 85º-10= 84º. 84º÷12x= 7.
Answer:
12x+1°+95°=180° (int angles)
12x+96°=180°
12x=180°-96°
=84°
x=84÷12
=7
Emilio compra 3,6 kg de manzanas a 1,45 euros el kilo ¿Cuánto pagara por las manzanas?
Answer:
Emilio compra kg De manzanas a euros el kilo cuanto pagara por Las manzanas
Answer:
emilio compra de manzanas a euros el kilo cuanta pagara por las manzanas
Employees of landscaping companies built a retaining wall. They used brick to make the top 2/3 of the wall.
250 POINTS
Part A: What is the height of the brick proportion of the wall? Write an equation
Part B: Estimate the area of the whole retaining wall. A= LxW
For part c you need a equation
Part C: What is the area of the whole retaining wall? Write an equation to show your work. Compare your answer to your estimate to see whether your answer is reasonable
Answer with Step-by-step explanation:
a) 2 3/4 ÷ 3 = 11/12 feet
11/12 + 11/12 = 1 5/6
Or, you could write an algebraic equation:
2 3/4 ÷ 3 = x. (3x = 2 3/4)
x = 11/12
The height of the brick proportion of the wall is 1 5/6
b)
You know that 8 x 2 is 16. Well, you already know that the whole total of fractions, multiplied together, would probably be less that 1 and less than 1/2.
So, your rounded answer should be 16. Or 16 1/2
c)
Area = 8 1/2 x 2 3/4.
Use Distributive Property to solve the area.
(8 x 2) + (3/4 x 1/2) = x
8 x 2 = 16
3/4 x 1/2 = 3/8
16 + 3/8 = 16 3/8
x = 16 3/8
I think my answer is reasonable because I estimated 16, and 1/2. 3/8 is close to 1/2. That's why my answer is reasonable.
-kiniwih426
PLEASEE HELP
In the diagram below, AB and CB each have a length of 5 centimeters. If m<A=6(x-3) and m<C=4(x+1), determine the value of each angle of the triangle.
Considering that angles A and C are equal, and the sum of the internal angles of a triangle is 180º, we have that:
The measure of angle A is of: 48º.
The measure of angle B is of: 84º.
The measure of angle C is of: 48º.
-----------------------------
Segments AC and CB have the same length, thus, angles A and C have the same measure, and then:[tex]6(x - 3) = 4(x + 1)[/tex]
[tex]6x - 18 = 4x + 4[/tex]
[tex]2x = 22[/tex]
[tex]x = \frac{22}{2}[/tex]
[tex]x = 11[/tex]
[tex]6(11 - 3) = 6(8) = 48[/tex]
The measure of angle A is of: 48º.
The measure of angle C is of: 48º.
The sum of the internal angles of a triangle is of 180º, and this is used to find the measure of angle B.
[tex]mA + mB + mC = 180[/tex]
[tex]2(48) + mB = 180[/tex]
[tex]mB = 84[/tex]
The measure of angle B is of: 84º.
A similar problem is given at https://brainly.com/question/13216436
HELP PLEASE I NEED TO GET THIS DONE
Answer:
3x^2
Step-by-step explanation:
Factor 3x^4
3 * x * x * x * x
Factor 15x^3
3 * 5 * x * x * x
Factor 21x^2
3 * 7 * x * x
Common factor is
3 * x * x
Simplify:
3x^2
3x to the power of 2
Kevin and Randy Muise have a jar containing 68 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $8.00. How many of each
type of coin do they have?
The jar contains
quarters
9514 1404 393
Answer:
23 quarters45 nickelsStep-by-step explanation:
Let q represent the number of quarters. Then the number of nickels is 68-q, and the number of cents in the jar is ...
25q +5(68 -q) = 800
20q +340 = 800 . . . . simplify
20q = 460 . . . . . . . . subtract 340
q = 23 . . . . . . . . . . . divide by 20; this is the number of quarters
68-q = 45 . . . . . . . find the number of nickels
The jar contains 23 quarters and 45 nickels.
convert $2.40 into cents
Answer: 240¢
Step-by-step explanation:
100¢ in a dollar.
$2.40 * 100 = 240
240¢
Find the coordinates of Cafter a 90° clockwise rotation
around the origin.
(0, -6)
6
(-6,0)
0
(-6, -6)
(6, 6)
Answer:
(0,-6)
Step-by-step explanation:here the answer
Use a factor tree to find the GCF of 32 and 80.
Answer:
GCF of 32 and 80 is 16
Step-by-step explanation:
factors of 32 = 1, 2, 4, 8, 16, 32
factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
what area of a rectangular cloth is (x²+7xy +12y²)m². Find the length and the width of the rectangular cloth
please help me
[tex]( {x}^{2} + 7xy + 12 {y}^{2} ) {m}^{2} [/tex]
What is the equation of a line through point (-12,20) that is perpendicular to the line
with equation y=-6x + 4?
Find the slope of the perpendicular line
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.
⇒ if the slope of one of the lines = - 6
then the slope of the perpendicular line (m) = ¹/₆
Determine the equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 20 = ¹/₆ (x - (-12))
∴ y - 20 = ¹/₆ (x + 12)
We can also write the equation in the slope-intercept form (y=mx+c) like the equation in the question by making y the subject of the equation and expanding the bracket to simplify:
since y - 20 = ¹/₆ (x + 12)
y - 20 = ¹/₆x + 2
y = ¹/₆x + 22
∴ the slope-intercept equation of the perpendicular line is y = ¹/₆ x + 22.
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
There are 16 students sitting on the bleachers and 21 students sitting on the floor. What is
the ratio of the number of students sitting on the floor to the total number of students?
Answer:16:21
Step-by-step explanation:
The graph of F(x) shown below, resembles the graph of G(x) = x2 but it has been charged somewhat. which of the following could be the equation of F(x)? Please help!!! I’m stuck!!! Thanks!!!!!
Answer:
es la a espero que te ayude corona
what is the equation for the quadratic formula?
sara estimates that they will sell approximately 400 pizzas next week. About how much tomato sacue and cheese should she order to be prepared for next week? Show your work clearly. Write an equation that relates t
Answer:
5/9-2/12=?
9x8=72
5x8=40
12x6=72
2x6=12
40/72 - 12/72 = 28/72
28/4=7
72/4=18
28/72=7/18
Samuel wants to ride his bicycle 32.4 miles this week. He has already ridden 18 miles.
If he rides for 4 more days, write and solve an equation which can be used to
determine 2, the average number of miles he would have to ride each day to meet his
goal.
Equation:
Answer: 2=
Submit Answer
Answer:
equation: 4x + 18 = 32.4
answer: x = 3.6
Step-by-step explanation:
What is the value of W in this exterior angle therom
Answer:
I think it is 60w2+2640w−11520
Step-by-step explanation:
pls brailiest
Which are the coordinates of Jefferson High School's Parking Lot B?
(-4, 3)
(-4,-3)
(-3,-4)
(-3, 4)
Answer:
(-3,4)
Step-by-step explanation:
the point is on -3 on the x-axis and 4 on the y-axis
Answer:(-3,4)
Step-by-step explanation:took the test and got right
help me due in 15 minutes! - giving brainly if correct and WORK IS SHOWN
please answer both if possible!
Answer:
both questions are same i think
look at the photo i have sent
Pleaseee help meee I’m desprateeee
help me, please. I need it quick
Answer:
Perimeter : 8
Step-by-step explanation: 2 times 4= 8
