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Genrish500 [490]

3 years ago

12

Find the value of x. A. 22.5 B.40 C.45 D.95

1 answer:

Troyanec [42]3 years ago

4 0

Answer:

x = 22.5

Step-by-step explanation:

The tangent- secant angle x is half the difference of the measures of the intercepted arcs, that is

$\frac{1}{2}$ (4x + 5 - 50 ) = x ( multiply both sides by 2 )

4x - 45 = 2x ( subtract 2x from both sides )

2x - 45 = 0 ( add 45 to both sides )

2x = 45 ( divide both sides by 2 )

x = 22.5

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If f(x) = |x| + 9 and g(x) = –6, which describes the range of (f + g)(x)?

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Read 2 more answers

A teacher places n seats to form the back row of a classroom layout. Each successive row contains two fewer seats than the prece

Alex_Xolod [135]

Answer:

The number of seat when n is odd $S_n=\frac{n^2+2n+1}{4}$

The number of seat when n is even $S_n=\frac{n^2+2n}{4}$

Step-by-step explanation:

Given that, each successive row contains two fewer seats than the preceding row.

Formula:

The sum n terms of an A.P series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{n}{2}[a+l]$

a = first term of the series.

d= common difference.

n= number of term

l= last term

$n^{th}$ term of a A.P series is

$T_n=a+(n-1)d$

n is odd:

n,n-2,n-4,........,5,3,1

Or we can write 1,3,5,.....,n-4,n-2,n

Here a= 1 and d = second term- first term = 3-1=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=1 and d=2

$n=1+(t-1)2$

⇒(t-1)2=n-1

$\Rightarrow t-1=\frac{n-1}{2}$

$\Rightarrow t = \frac{n-1}{2}+1$

$\Rightarrow t = \frac{n-1+2}{2}$

$\Rightarrow t = \frac{n+1}{2}$

Last term l= n,, the number of term $=\frac{ n+1}2$ , First term = 1

Total number of seat

$S_n=\frac{\frac{n+1}{2}}{2}[1+n}]$

$=\frac{{n+1}}{4}[1+n}]$

$=\frac{(1+n)^2}{4}$

$=\frac{n^2+2n+1}{4}$

n is even:

n,n-2,n-4,.......,4,2

Or we can write

2,4,.......,n-4,n-2,n

Here a= 2 and d = second term- first term = 4-2=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=2 and d=2

$n=2+(t-1)2$

⇒(t-1)2=n-2

$\Rightarrow t-1=\frac{n-2}{2}$

$\Rightarrow t = \frac{n-2}{2}+1$

$\Rightarrow t = \frac{n-2+2}{2}$

$\Rightarrow t = \frac{n}{2}$

Last term l= n, the number of term $=\frac n2$ , First term = 2

Total number of seat

$S_n=\frac{\frac{n}{2}}{2}[2+n}]$

$=\frac{{n}}{4}[2+n}]$

$=\frac{n(2+n)}{4}$

$=\frac{n^2+2n}{4}$

4 0

3 years ago

What is the area of the figure below

jek_recluse [69]

Answer:

Option A

Step-by-step explanation:

Area of the composite figure = Area of ΔABH + Area of BCGH + Area of ΔDEF

Area of ΔABH = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(6)(8-5)$

= 9 in²

Area of the trapezoid = $\frac{1}{2}(CG+BH)(\text{Distance between these lines})$

= $\frac{1}{2}(6+4)(5)$

= 25 in²

Area of ΔDEF = $\frac{1}{2}(8)(6)$

= 24 in²

Therefore, area of the given figure = 9 + 25 + 24

= 58 in²

Option A will be the correct option.

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Answer: 5/4

Step-by-step explanation:

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