As the equation is already in 'rectangular form), to work out the vertex, we can just compare this equation to that of the standard parabola y = x^2, and in particular, consider how it has been translated:

the (x+3) part moves the graph the the left 3 (i.e in the negative direction), while the +7 moves the graph up 7.

So as the vertex of the simple parabola y = x^2 is (0,0), the vertex of this graph is just (-3,7).

Note that the -2 at the front doesn't impact this vertex - this -2 just changes the 'scale' of the parabola (i.e makes it more narrow, and also turns it upside down as it's a negative number).

6 0

4 years ago

I need help with this is dont really understand it

user100 [1]

Answer:

y = 10x + 6.

Step-by-step explanation:

y = mx + c

Here the slope m = 10 and c = 6 ( the y-intercept)

It's 6 because the point (0, 6) lies on the y-axis (where x = 0).

7 0

3 years ago

What is the equation 6^2=36 in logarithmic

liq [111]

$log_{6}(36) = 2$

7 0

3 years ago

A drone builder states in their terms of conditions that the battery for their foldable drone will last for more than 4 hours of

ExtremeBDS [4]

Answer:

The manufacturer's claim is not supported

Step-by-step explanation:

The time duration the battery of the foldable drone is said to last, μ = 4 hours

The number of drones that were tested, n = 10 drones

The sample mean, $\overline x$ = 4.2 hours

The standard deviation, s = 0.4 hours

The hypothesis test level of significance = 0.5

The null hypothesis, H₀; μ = 4

The alternative hypothesis, Hₐ; μ ≠ 4

The test statistic is given as follows;

$t=\dfrac{\bar{x}-\mu }{\dfrac{s }{\sqrt{n}}}$

We get;

$The \ test \ statistic, \ t =\dfrac{4.2 - 4}{\dfrac{0.4}{\sqrt{10} } } \approx 1.58113883008$

Therefore, the test statistic, t ≈ 1.58

The degrees of freedom, d. f. = n - 1

For n = 10, we have;

The degrees of freedom, d. f. = 10 - 1 = 9

From the t-table at 0.5 level of significance, the critical-t = 0.7

Given that the test statistic is larger than the critical-t, we reject the null hypothesis and there is enough statistical evidence to suggest that the manufacturer claim is not supported and that the mean is not 4 hours as claimed.

7 0

3 years ago