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Answer:A

Step-by-step explanation:

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

[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

Answer:

-1, 0, 1/2, 1, 4/3

Step-by-step explanation:

8x² - 24 = 8 (x² - 3)

Answer:

9

Step-by-step explanation:

Answer: x=2 because for any y value the x value is always 2.

Step-by-step explanation:

[tex] \green{\large\underline{\sf{Solution-}}}[/tex]

Given pair of linear equations are

[tex]\rm :\longmapsto\:0.4x + 0.3y = 1.7 \\ \\ \rm :\longmapsto\:0.7x - 0.2y = 0.8[/tex]

can be rewritten as on multiply by 10,

[tex]\rm :\longmapsto\:4x + 3y = 17 - - - - (1)\\ \\ \rm :\longmapsto\:7x - 2y = 8 - - - - - (2)[/tex]

[tex]\rm :\longmapsto\:2y = 7x - 8[/tex]

[tex]\rm\implies \:\boxed{\tt{ y = \frac{7x - 8}{2}}} - - - - (3) [/tex]

On substituting the value of y in equation (1), we get

[tex]\rm :\longmapsto\:4x + 3\bigg( \dfrac{7x - 8}{2} \bigg) = 17[/tex]

[tex]\rm :\longmapsto\:\dfrac{8x + 21x - 24}{2} = 17[/tex]

[tex]\rm :\longmapsto\:29x - 24 = 34[/tex]

[tex]\rm :\longmapsto\:29x = 34 + 24[/tex]

[tex]\rm :\longmapsto\:29x = 58[/tex]

[tex]\bf\implies \:x = 2 - - - - (4)[/tex]

On substituting x = 2 in equation (3), we get

[tex]\rm :\longmapsto\:y = \dfrac{7 \times 2 - 8}{2} [/tex]

[tex]\rm :\longmapsto\:y = \dfrac{14 - 8}{2} [/tex]

[tex]\rm :\longmapsto\:y = \dfrac{6}{2} [/tex]

[tex]\bf\implies \:y = 3[/tex]

So, we get

[tex]\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\bf{x = 2} \\ \\ &\bf{y = 3} \end{cases}\end{gathered}\end{gathered}[/tex]

From equation (1),

[tex]\rm :\longmapsto\:0.4x + 0.3y = 1.7[/tex]

On substituting the value of x and y, we get

[tex]\rm :\longmapsto\:0.4(2) + 0.3(3) = 1.7[/tex]

[tex]\rm :\longmapsto\:0.8 + 0.9 = 1.7[/tex]

[tex]\rm :\longmapsto\:1.7 = 1.7[/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

To solve systems using Method of Substitution, follow this procedure:

1. Select one equation and solve it for one of its variables.

2. In the other equation, substitute the value of one variable evaluated in step 1 to reduced the equation to one variable.

3. Solve the equation to get the value of this variable

4. Substitute the value found in to first equation involving both variables and solve for the other variable.

Answer:

x=81

z=99

y=68

Step-by-step explanation:

63+36=99

180-99=81

x=81

Angles in a triangle sum to 180

180-81=99

z=99

Angles on a line sum to 180

99+13=112

180-112=68

y=68

Angles in a triangle sum to 180

Step-by-step explanation:

1. The rabbit would be hopping at 3 feet per second.

You would first:

1. Divide each sides by 2

This would result into 3 = 1.

2. Given, 6 = 2.

If we said feet (6) = x and 2 (seconds) = y,

x = y or

feet = second (6 = 2).

Answer:

By using the formula, Parts /whole = percent/100, ⇒ 25/ 50 × 100 = 50%. So, 50 % of 50 is 25 proportion.

Answer:

C(90) = 15.35

Step-by-step explanation:

Given the function, C(n) = 0.06n + 9.95:

where C = total cost of texting plan

n = number of texts sent in a month

9.95 = flat fee

To find C(90):

Substitute 90 as the input, n,  for the function:

C(90) = 0.06n + 9.95

C(90) = 0.06(90) + 9.95

C(90) = 5.40 + 9.95

C(90) = 15.35

C(90) represents the cost of sending 90 texts in a month is $15.35.

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Rise = -4

Run = 3

Rise/run = -4/3

Answer:

-4/3

Step-by-step explanation:

Rise: 4

Run:3

And, this is negative because any line slanted downward right (pointing to the left) indicates it is negative.

Answer:

The x-axis

Step-by-step explanation:

This line means, the line going through [tex](1, 0)[/tex] with [tex]m=0[/tex] means there is a flat line(m=0, 0 slope) with a y-value of [tex]0[/tex] from the point given.

So, the line is [tex]y=0[/tex], i.e. the x-axis.

So, graph the x-axis and we're done!

Answer:

a^(4/15)

Step-by-step explanation:

rules of indices:

WHEN MULTIPLYING POWERS WITH THE SAME BASE YOU ADD THE POWERS

a^(1/5) × a^(2/3) = a^(1/5 + 2/3)

a^(13/15)

WHEN DIVIDING POWERS WITH THE SAME BASE YOU SUBTRACT THE POWERS

a^(13/15) / a^(3/5) = a^(13/15 - 3/5)

a^(4/15)

NOTE: YOU HAVE TO FOLLOW BODMAS RULE IN THE QUESTION.. AND PLEASE LOOK OUT FOR THE POWERS WITH THE SAME BASE. IF BASE IS DIFFERENT YOU CANNOT SIMPLIFY...

g(x)=1/5x² is the equation for blue graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The equation of the red quadratic graph is f(x)=x²

This is the parent quadratic function or the base of the quadratic functions.

This red quadratic graph has been dilated by a certain scale factor  to obtain the blue graph.

Recall that, when the scale factor is a fraction, such that 0<k<1 the graph is stretched horizontally.

The dilated graph then becomes wider than the parent function.

From the given function equations, the possible value of k can only be k=1/5

Therefore the blue graph has equation g(x)=1/5x²

Hence, g(x)=1/5x² is the equation for blue graph.

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Answer:

a) w=6

b) a=3

c) c=7

Step-by-step explanation:

[tex]3w+6=4w[/tex]

[tex]\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}[/tex]

[tex]3w+6-6=4w-6[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]3w=4w-6[/tex]

[tex]\mathrm{Subtract\:}4w\mathrm{\:from\:both\:sides}[/tex]

[tex]3w-4w=4w-6-4w[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-w=-6[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-w}{-1}=\frac{-6}{-1}[/tex]

[tex]w=6[/tex]

___________________________________________

[tex]a+18=7a[/tex]

[tex]\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}[/tex]

[tex]a+18-18=7a-18[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]a=7a-18[/tex]

[tex]\mathrm{Subtract\:}7a\mathrm{\:from\:both\:sides}[/tex]

[tex]a-7a=7a-18-7a[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-6a=-18[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-6[/tex]

[tex]\frac{-6a}{-6}=\frac{-18}{-6}[/tex]

[tex]a=3[/tex]

Answer:

No

Step-by-step explanation:

Unit rate consists of at least one 1. the unit rate for this would be 1 slice for $1.25

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Step-by-step explanation:

(7 x 10^*13) (3.39 x 10^*5)

= 23.73 × 10¹⁸

=2.373 × 10¹⁹

Hello there!

(7x10^13)(3.39x10^5)

70,000,000,000,000

339,000

2.373x10^19

Hope this helps!

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[tex](: GraceRosalia :)[/tex]

Answer:

1.75

Step-by-step explanation:

you divide 7 by 4

7÷4= 1.75

The value to be added to both sides of the equation to make the left side a perfect square trinomial is; -36.

To make the equation x2 – 12x = 1 look similar to the completing the square kind of expression where the left hand side of the equation becomes a perfect square, we must do the following;

In this scenario, the term (x² - 12x) can be rewritten as; (x - 6)² - 36.

This so because the expansion of (x - 6)² becomes;

Therefore, there's a need to subtract 36 from both sides of the equation so that the equation x2 – 12x = 1 is retained.

Therefore, the value to be added to both sides of the equation to make the left side a perfect square trinomial is; -36.

Read more;

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Answer:

you are correct

because when you add and calculate All the answers you will know it is correct

Answer:

this property is commutative property

Answer:

Commutative

Step-by-step explanation:

Answer:

169 I think?

Step-by-step explanation:

if you look at images of number rows 169 is the only one in it with the others

Answer:

wait I will give the answer in 2 minutes

Step-by-step explanation

Answer:

13.5%

Step-by-step explanation:

Answer:

Typical transactions include ATM withdrawals, debit card payments, and e-transfers.

Answer:

8x + 10 = AC

Step-by-step explanation:

AB + BC = AC

6x + 1 + 2x + 9 = AC

8x + 10 = AC