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3 years ago

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Find the vertex of the parabola?

1 answer:

omeli [17]3 years ago

7 0

The vertex of the parabola $y=ax^2+bx+c$ has coordinates

$x_v=-\dfrac{b}{2a}$

and

$y_v=ax_v^2+bx_v+c.$

In your case, for the parabola $y=x^2-4x+6$ the vertex has coordinates

$x_v=-\dfrac{-4}{2\cdot1}=2$

and

$y_v=2^2-4\cdot 2+6=4-8+6=2.$

Therefore, point (2,2) is the vertex of the parabola.

Answer: correct choice is B

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Which of the points A(−6, 2), B(0, 0), C(4, −2), D(−12, 6), E(−10, 10) belong to the graph of direct variation y=− 1 2 x?

vovangra [49]

ANSWER

B(0, 0),

EXPLANATION

The given points are A(−6, 2), B(0, 0), C(4, −2), D(−12, 6), E(−10, 10).

The equation of the direction variation is

$y = - 12x$

The point that belongs the graph of the direct variation must satisfy the variation equation.

Note that the graph of direct variation equation passes through the origin therefore the point (0,0) satisfies it.

0=-12(0)

0=0

This is true

The other points do not satisfy this variation equation, hence they do not lie on its graph

5 0

4 years ago

What the answer in simplest form, seven divided by ten times one divided by one hundred and five

IRISSAK [1]

The answer is 1.5 i think

3 0

3 years ago

Assume that X is normally distributed with a mean of 20 and a standard deviation of 2. Determine the following. (a) P(X 24) (b)

Tems11 [23]

Answer:

a) P( X < 24 ) = 0.9772

b) P ( X > 18 ) =0.8413

c) P ( 14 < X < 26) = 0.9973

d) P ( 14 < X < 26) = 0.9973

e) P ( 16 < X < 20) = 0.4772

f) P ( 20 < X < 26) = 0.4987

Step-by-step explanation:

Given:

- Mean of the distribution u = 20

- standard deviation sigma = 2

Find:

a. P ( X < 24 )

b. P ( X > 18 )

c. P ( 18 < X < 22 )

d. P ( 14 < X < 26 )

e. P ( 16 < X < 20 )

f. P ( 20 < X < 26 )

Solution:

- We will declare a random variable X that follows a normal distribution

X ~ N ( 20 , 2 )

- After defining our variable X follows a normal distribution. We can compute the probabilities as follows:

a) P ( X < 24 ) ?

- Compute the Z-score value as follows:

Z = (24 - 20) / 2 = 2

- Now use the Z-score tables and look for z = 2:

P( X < 24 ) = P ( Z < 2) = 0.9772

b) P ( X > 18 ) ?

- Compute the Z-score values as follows:

Z = (18 - 20) / 2 = -1

- Now use the Z-score tables and look for Z = -1:

P ( X > 18 ) = P ( Z > -1) = 0.8413

c) P ( 18 < X < 22) ?

- Compute the Z-score values as follows:

Z = (18 - 20) / 2 = -1

Z = (22 - 20) / 2 = 1

- Now use the Z-score tables and look for z = -1 and z = 1:

P ( 18 < X < 22) = P ( -1 < Z < 1) = 0.6827

d) P ( 14 < X < 26) ?

- Compute the Z-score values as follows:

Z = (14 - 20) / 2 = -3

Z = (26 - 20) / 2 = 3

- Now use the Z-score tables and look for z = -3 and z = 3:

P ( 14 < X < 26) = P ( -3 < Z < 3) = 0.9973

e) P ( 16 < X < 20) ?

- Compute the Z-score values as follows:

Z = (16 - 20) / 2 = -2

Z = (20 - 20) / 2 = 0

- Now use the Z-score tables and look for z = -2 and z = 0:

P ( 16 < X < 20) = P ( -2 < Z < 0) = 0.4772

f) P ( 20 < X < 26) ?

- Compute the Z-score values as follows:

Z = (26 - 20) / 2 = 3

Z = (20 - 20) / 2 = 0

- Now use the Z-score tables and look for z = 0 and z = 3:

P ( 20 < X < 26) = P ( 0 < Z < 3) = 0.4987

8 0

3 years ago

Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.

egoroff_w [7]

Answer:

r = (ab)/(a+b)

Step-by-step explanation:

Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).

Using the Pythagorean theorem, we can write the relation ...

((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2

a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2

-4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab

r = ab/(a+b) . . . . . . . . . divide by the coefficient of r

The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).

_____

The graph in the second attachment shows a trapezoid with the radius calculated as above.

6 0

4 years ago

This is the pond in a shape of a prism, it is completely full of water. Colin uses a pump to empty the pond. The level goes down

AnnZ [28]

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

water. Colin uses a pump to empty the pond. The level goes

down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = $\frac{1}{2}$ × (sum of sides)× height

= $\frac{1}{2}$ × (0.6 + 1.4)× 2

= $\frac{1}{2}$ × (2)× 2

= 2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

= 2 m² × 1 m

= 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = $\frac{1}{100} m$ = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

= 2 m² × 0.8 m

= 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

= 2 m³ - 1.6 m³

= 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in $\frac{30}{0.4}$ = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

5 0

3 years ago