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3 years ago

Reduce then calculate 7/8 x 4/15 x 3/7 = ? Can you help?

1 answer:

8 0

since this is a multiplication, all the numerators are just factors of the product numerator and all denominators are just factors of the product denominator, so we can simply reorder them some, without changing the product.

$\bf \cfrac{7}{8}\times \cfrac{4}{15}\times \cfrac{3}{7}\implies \cfrac{7}{7}\times \cfrac{4}{8}\times \cfrac{3}{15}\implies \cfrac{1}{1}\times \cfrac{1}{2}\times \cfrac{1}{5}\implies \cfrac{1\cdot 1\cdot 1}{1\cdot 2\cdot 5}\implies \cfrac{1}{10}$

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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

Find the discriminant and determine the nature of the roots to the quadratic equation

Katen [24]

№17
$x^{2} +6x-7=0 \\ D=6 ^{2} -4*(-7)=36+28=64=8 ^{2} \\ \\ x_{1} = \frac{-6+8}{2} =1 \\ \\ x_{2} = \frac{-6-8}{2} =-7$
Answer: x₁ = 1
   x₂ = - 7

№18
$2 x^{2} -3x+4=3 \\ 2 x^{2} -3x+4-3=0 \\ 2 x^{2} -3x+1=0 \\ \\ D= -3 ^{2} -4*2=9-8=1 \\ \\ x_{1} = \frac{3+1}{2*2} = \frac{4}{4} =1 \\ \\ x_{2} = \frac{3-1}{2*2} = \frac{2}{4} =0.5$
Answer: x₁ = 1
     x₂ = 0,5.

№19
$2 x^{2} -4x-5=0 \\ D=-4 ^{2} -4*2*(-5)=16+40=56 \\ \\ x_{1}= \frac{4+ \sqrt{56} }{2*2} = \frac{4}{4} + \sqrt{ \frac{56}{16} } =1+ \sqrt{3.5} \\ \\ x_{2} = \frac{4- \sqrt{56} }{2*2} = \frac{4}{4} - \sqrt{ \frac{56}{16} } =1- \sqrt{3.5} 
$
Answer: x₁ = 1 + √3.5
     x₂ = 1 - √3.5

3 0

4 years ago

I need help with #3

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

divide nine by .74 and that's your answer

7 0

3 years ago

Read 2 more answers

SOMEONE PLS HELP ME ON ALL THESE ASAP!!!!!

natulia [17]

Answer:

4Q a). angle1=55°

angle2=23°

angle3=63°

angle4=125°

5Q. x=35°

6Q. y=15°

8Q. C. 28°

9Q. Yes, they are congruent by S.S.S. congruence

10Q. A.A.S.

11Q. S.S.S.

12Q. Not possible

13Q. S.A.S.

14Q. S.S.S.

15Q. 66°

16Q. 24°

I hope it will be useful.

Step-by-step explanation:

7Q. angle1=angle3 (Alternate Interior Angles)

angle2=angle4 (A.I.A.)

angleXWZ=angleXYZ (opposite angles of a parallelogram)

By A.A.A. congruence criteria, they are congruent.

8Q. Hint: Make the diagram first!

AngleC is halved since M is the mid-point.

angleA=angleB (Property of an isosceles triangle)

which implies, angleAMC=angleBMC=90°

Thus, CM is perpendicular to AB.

I hope it will be useful.

7 0

3 years ago

Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.

frutty [35]

Answer:

(x - 5) (x - 7)

Step-by-step explanation:

To factor this trinomial, you must split the middle term (-12x) into two terms that can be added to get -12x, and multiplied to get 35:

$x^2$ - 12x + 35

$x^2$ -7x - 5x + 35

Group:

( $x^2$ -7x) (-5x + 35)

Take out the GCF (Greatest Common Factor):

x(x - 7) -5(x - 7)

(x - 5) (x - 7)

4 0

3 years ago

Read 2 more answers