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just olya [345]
3 years ago
7

A) Rationalise the denominator of a,b,c

Mathematics
1 answer:
Evgesh-ka [11]3 years ago
7 0

Answer:

See below

Step-by-step explanation:

a)

\frac{20}{ \sqrt{10} }  =  \frac{20 \sqrt{10} }{ \sqrt{10} \times  \sqrt{10}  }  =  \frac{20 \sqrt{10} }{10}  = 2 \sqrt{10}

b)

\frac{ \sqrt{2} }{2 \sqrt{5} - 1 }  \\  \\  = \frac{ \sqrt{2}  \times (2 \sqrt{5}  + 1 )}{(2 \sqrt{5} - 1)(2 \sqrt{5}  + 1) }  \\  \\ = \frac{ \sqrt{2}  \times 2 \sqrt{5}  + \sqrt{2}  \times 1 }{(2 \sqrt{5} ) ^{2} - (1)^{2}}  \\  \\ = \frac{ 2 \sqrt{10}  + \sqrt{2}}{20  - 1}  \\  \\ = \frac{ 2 \sqrt{10}  + \sqrt{2}}{19}  \\  \\ equating \: it \: with \:  \\ \frac{ a  + \sqrt{b}}{c}  \\  \\ a = 2 \sqrt{10}  \\  \\ b = 2 \\  \\ c = 19

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Liula [17]

We know that y = x^2 is a parabola, concave up, with vertex in the origin (0,0)

So, we may use three horizontal lines for our purpose: any horizontal line above the x axis will intersect the parabola twice. The x axis itself intersects the parabola once on the vertex, while any horizontal line below the x axis won't intercept the parabola.

Here's the examples:

  • The horizontal line y = 4 intercepts the parabola twice: the system y = x^2,\ y = 4 is solved by x^2=4 \implies x = \pm 2
  • The horizontal line y=0 intercepts the parabola only once: the system is y=x^2,\ y=0 which yields x^2=0\implies x=0 which is a repeated solution
  • The horizontal line y=-5 intercepts the parabola only once: the system is y=x^2,\ y=-5 which yields x^2=-5 which is impossible, because a squared number can't be negative.
5 0
3 years ago
The cloth shop has announced a reduction in price by 25%. How many shirts priced at Rs 28 should buy to avail a total reduction
Drupady [299]

Answer:

At least 6 shirts should be brought to avail a total reduction of Rs 40.

Step-by-step explanation:

The marked price of each shirt = Rs 28

Discount offered = 25%

So, 25% of marked price  28 = \frac{25}{100}  \times 28 = 7

⇒Reduction on each shirt is Rs 7

Now, total amount reduction needed = Rs 40

So, number of shirts purchased = \frac{\textrm{Total reduction needed}}{\textrm{Reduction on each shirt}}

= 40  Rs /7  Rs  =  5. 71  ≈  6

So, at least 6 shirts should be brought to avail a total reduction of Rs 40.

5 0
3 years ago
How to find b with (4a-b) + (4b-a) = 180
Sunny_sXe [5.5K]

Answer:

just simplify it ...

Step-by-step explanation:

  1. 4a-b+4b-a=180
  2. 3a+3b=180
  3. 3(a+b)=180
  4. both sides divide by 3
  5. a+b =60
  6. b=60-a
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3 years ago
A gumball machine has 260 red gumballs. If the red gumballs are 50% of the total number of gumballs, how many gumballs are in th
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3 years ago
Between the time Iko woke up and lunchtime, tue temperature rose by 11 degrees. Then by the time he went to bed, the temperature
Ierofanga [76]

Answer:

T_b=(x-3)\textdegree

Step-by-step explanation:

let x° be temperature when he woke up. Given that the temperature rose  by 11° then later dropped by 14°. Also let T_b be temperature at time she went to bed.

-We add the temperature rise and subtract the temperature drop to find temperature at time she goes to bed.

-The temperature relative to time of waking up can be expressed as:

T_b=x\textdegree\pm\bigtriangleup T\textdegree\\\\T_b=x\textdegree+11\textdegree-14\textdegree\\\\T_b=(x-3)\textdegree

Hence, the temperature relative to the time Iko woke up is (x-3)°

4 0
3 years ago
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