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Komok [63]
2 years ago
10

In triangle PQR, find the measure of angle Q. P= 64 degrees Q= X R= 2x

Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
4 0

Answer:

38.667°

Step-by-step explanation:

the total sum of 3 angles in a triangle is 180

in triangle PQR this means:

P+Q+R = 180

so:

64+x+2x=180

64+3x=180

3x=116

x=116/3=38.667

So Q=X=38.667

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If lim x-> infinity ((x^2)/(x+1)-ax-b)=0 find the value of a and b
MAXImum [283]

We have

\dfrac{x^2}{x+1}=\dfrac{(x+1)^2-2(x+1)+1}{x+1}=(x+1)-2+\dfrac1{x+1}=x-1+\dfrac1{x+1}

So

\displaystyle\lim_{x\to\infty}\left(\frac{x^2}{x+1}-ax-b\right)=\lim_{x\to\infty}\left(x-1+\frac1{x+1}-ax-b\right)=0

The rational term vanishes as <em>x</em> gets arbitrarily large, so we can ignore that term, leaving us with

\displaystyle\lim_{x\to\infty}\left((1-a)x-(1+b)\right)=0

and this happens if <em>a</em> = 1 and <em>b</em> = -1.

To confirm, we have

\displaystyle\lim_{x\to\infty}\left(\frac{x^2}{x+1}-x+1\right)=\lim_{x\to\infty}\frac{x^2-(x-1)(x+1)}{x+1}=\lim_{x\to\infty}\frac1{x+1}=0

as required.

3 0
2 years ago
The product (x-10) (x + 2)​
Karolina [17]

Answer :

To find the product of (x + 8)(x – 10)

We know that

(x + a)(x + b) = x2 + (a + b)x + ab

In the expression (x + 8)(x – 10)

a = 8

b = -10

a + b = 8- 10 = -2

ab = 8 × (-10) = – 80

Substitute the values in the above equation

(x + 8)(x – 10) = x2 + (8 – 10)x + 8 × (-10)

(x + 8)(x – 10) = x2 – 2x – 80.

Thank you !

8 0
2 years ago
- How many females represented in the Venn diagram below are right-handed?
Wewaii [24]

Answer:

You did not include the Venn diagram

Step-by-step explanation:

3 0
2 years ago
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPP
Sergeu [11.5K]

Answer:

2. y=9x

3. 180*9 = 1620

Step-by-step explanation:

2. y = mx+b, so find the slop efirst

lacampanella avatar

so take the first two points you got

lacampanella avatar

(2,18) and (5,45),

lacampanella avatar

(45-18)/(5-2) = 9

lacampanella avatar

then use (2,18)

lacampanella avatar

18= 9*2+b

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so b=0

3. y = 9x

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4 0
2 years ago
The employees of a firm that manufactures insulation are being tested for indications of asbestos in their lungs. The firm is re
balandron [24]

Answer:

0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.

Step-by-step explanation:

For each employee, there are only two possible outcomes. Either they test positive, or they do not. The probability of an employee testing positive is independent of any other employee, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

40% of the employees have positive indications of asbestos in their lungs

This means that p = 0.4

Find the probability that fifteen employees must be tested in order to find three positives.

2 during the first 14(given by P(X = 2) when n = 14).

The 15th is positive, with 0.4 probability. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{14,2}.(0.4)^{2}.(0.6)^{12} = 0.0317

0.0317*0.4 = 0.013.

0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.

7 0
2 years ago
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