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IgorLugansk [536]
2 years ago
9

For all values of x, x² + 6x - 2 = (x+p)² + q Find the value of p and the value of q.

Mathematics
1 answer:
Vlad [161]2 years ago
3 0

Step-by-step explanation:

{x}^{2}  + 6x - 2 =  {x}^{2}  + 2px +  {p}^{2}  + q

2p = 6

{p}^{2}  + q =   - 2

p = 3

{3}^{2}  + q =  - 2

q =  - 11

p=3, q=-11

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What does the point (1994, 400) on the graph represent?
yuradex [85]

Answer: There are 400 tadpoles in the year 1994.

This is because any point is of the form (x,y) where in this case

x = year number

y = tadpole population number

So (x,y) = (1994, 400) means x = 1994 and y = 400 pair up together.

In short, the year x = 1994 corresponds to the population of y = 400 tadpoles.

From the years 1990 to 1992, the population is increasing since the curve goes upward when moving from left to right. Then from 1992 to 1993, the population decreases hitting its lowest point in that specific region. From 1993 to 1997, the population increases before it decreases again from 1997 to 1999.

5 0
3 years ago
James is 60 years old. His age is 8 years more than twice Maggie's age. How old is Maggie?
kow [346]

Answer:26

Step-by-step explanation:

60-8=52

52•2=26

4 0
3 years ago
Read 2 more answers
The weekly amount spent by a small company for in-state travel has approximately a normal distribution with mean $1450 and stand
Llana [10]

Answer:

0.0903

Step-by-step explanation:

Given that :

The mean = 1450

The standard deviation = 220

sample mean = 1560

P(X > 1560) = P( Z > \dfrac{x - \mu}{\sigma})

P(X > 1560) = P(Z > \dfrac{1560 - 1450}{220})

P(X > 1560) = P(Z > \dfrac{110}{220})

P(X> 1560) = P(Z > 0.5)

P(X> 1560) = 1 - P(Z < 0.5)

From the z tables;

P(X> 1560) = 1 - 0.6915

P(X> 1560) = 0.3085

Let consider the given number of weeks = 52

Mean \mu_x = np = 52 × 0.3085 = 16.042

The standard deviation =  \sqrt {n \time p (1-p)}

The standard deviation = \sqrt {52 \times 0.3085 (1-0.3085)}

The standard deviation = 3.3306

Let Y be a random variable that proceeds in a binomial distribution, which denotes the number of weeks in a year that exceeds $1560.

Then;

Pr ( Y > 20) = P( z > 20)

Pr ( Y > 20) = P(Z > \dfrac{20.5 - 16.042}{3.3306})

Pr ( Y > 20) = P(Z >1 .338)

From z tables

P(Y > 20) \simeq 0.0903

7 0
3 years ago
What do 110°, 250°, and -470° angles have in common?
Nadusha1986 [10]
They are all larger than 90 degrees, and in a triangle they would all be obtuse angles.
4 0
3 years ago
Read 2 more answers
Suponhamos que temos x casos confirmados de coronavírus e y casos suspeitos. A - Se triplicar os casos confirmados e cair a meta
aleksandr82 [10.1K]

Answer:

[3x + (y/2)]

Step-by-step explanation:

English Translation

Suppose we have x confirmed cases of coronavirus and y suspected cases. A - If the confirmed cases triple and half of the suspects fall, we will have the following expression to represent the total number of cases:

Solution

Number of confirmed cases = x

Number of suspected cases = y

Number of confirmed cases triples and becomes 3x

Half of the suspected cases fall and becomes (y/2)

Total number of cases then becomes

[3x + (y/2)]

In Portugese/Em português

Número de casos confirmados = x

Número de casos suspeitos = y

O número de casos confirmados triplica e se torna 3x

Metade dos casos suspeitos cai e se torna (y / 2)

O número total de casos passa a ser

[3x + (y / 2)]

Hope this Helps!!!

Espero que isto ajude!!!

8 0
2 years ago
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