The angle with measure between 0 and

A parabola y=1/2x^2-4x+21 can you help me find the vertex form of this parabola please and thank you :)

ale4655 [162]

Ok
First factor out the first 2 terms as follows:-

y = 1/2(x^2 - 8x) + 21

Now complete the square on x^2 - 8x:-

y = 1/2[ (x - 4)^2 - 16] + 21

y = 1/2(x - 4)^2 - 8 + 21

y = 1/2(x - 4)^2 + 13 Answer

3 0

3 years ago

PLS ANSWER ITS URGENT

matrenka [14]

Answer:

The length of the ramp must be at least 14.71 feet

Step-by-step explanation:

Given

$BC = 2.3ft$

$\theta = 9^\circ$

See attachment for complete figure

Required

Length of the ramp (z)

To do this, we consider sin of angle A ( $\theta$ ).

So, we have:

$sin\theta = \frac{Opposite}{Hypotenuse}$

This gives:

$sin(9)= \frac{2.3}{z}$

Make z the subject

$z= \frac{2.3}{sin(9)}$

$z = \frac{2.3}{0.1564}$

$z = 14.71 ft$

The length of the ramp must be at least 14.71 feet

6 0

3 years ago

A study has demonstrated that the more television a person watches, the lower that person’s level of physical fitness. However,

ad-work [718]

Answer:

Option D

Step-by-step explanation:

The most valid conclusion here is that the fact that running on a treadmill allows for a greater physical fitness with the television watching deterring the effect of the exercise. In as much as he only watches TV when running, it is not enough to conclude that TV can cause less physical fitness for Pablo.

7 0

3 years ago

6. Number of passengers who arrive at the platform in an Amtrack train station for the 2 pm train on a Saturday is a random vari

Aleks04 [339]

Answer:

99.7%

Step-by-step explanation:

Mean number of passengers (μ) = 180 passengers

Standard deviation (σ) = 20 passengers

The number of standard deviation from the mean for the lower and upper bounds of the 120 to 240 passengers intervals are:

$L = \frac{180-120}{20} =3\\U = \frac{240-180}{20} =3$

Therefore, all of the data is within 3 standard deviations from the mean. According to the empirical rule, 99.7% of the data is within 3 standard deviations from the mean. Therefore, we can assert with a 99.7% probability that there will be between 120 and 240 passengers.

4 0

3 years ago

Basic Computation: Testing M1 2 M2 A random sample of 49 measurements from a population with population standard deviation 3 had

Elenna [48]

Answer:

The sample statistics follows a standard normal distribution since the sample size are large enough.

Step-by-step explanation:

Given that:

First population:

Sample size $n_1$ = 49