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4 years ago

Identify the vertex and the axis of symmetry of the parabola. HELP PLEASE!!!

Mathematics

1 answer:

jeka944 years ago

8 0

We know that the graph goes in units of 1.

We know that the roots are -1 and 4. (Just assume it's accurate and not off by 0.0000000001.)

We can set it up as an equation: -1(x+1)(x-4) = y (I added -1 because there are two parabolas that go through those points on the x-axis, and since this parabola is facing down, I must add a negative a value.

Then multiply (F.O.I.L. - First, Outer, Inner, Last)

x^2 -4x + x - 4 = -(x^2 - 3x - 4) = -x^2 + 3x + 4

Then using -(b/2a) solve for vertex: -(3/-2) = 3/2

Plug 3/2 back into the equation.

-(3/2)^2 + 3(3/2) + 4 = -9/4 + (9/2) + 4 = 25/4

The vertex would be: (3/2, 25/4)

Axis of symmetry would be: x = 3/2

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Find the value of f. What can you do to Both Sides?f - ⅔ = ¼

Thepotemich [5.8K]

Answer:

11/12

Step-by-step explanation:

<h2><u>Value of F </u></h2>

to find the value of f , we need to move the -2/3 to the other side of the equal sign.

$f - \frac{2}{3} = \frac{1}{4}$

<u><em>Note </em></u>: is you move a number from one side of the equal sign to the other, this changes the sign of the number ( eg , -2/3 becomes +2/3)

$f = \frac{1}{4} + \frac{2}{3}$

f = $\frac{11}{12}$

<h3><u>hence the value of f is 11/12 </u></h3>

7 0

3 years ago

PLEASE HELP 30 POINTS.

Nookie1986 [14]

Answer:

Step-by-step explanation:

Note that the four input values, {3,4,6,11}, are all unique. Each has exactly one y value associated with it. This is an important criterion when we're deciding whether a relation is a function or not.

Suppose that we added one more input and its associated output:

{3,4,4,6,11}

If it happened that different values of y were associated with the two 4's, then we know immediatel that this relation is not a function.

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4 years ago

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. State the h

Soloha48 [4]

Answer:

Null hypothesis: $\mu \leq 60$

Alternative hypothesis: $\mu > 60$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33$

Step-by-step explanation:

Data given and notation

$\bar X=67$ represent the sample mean

$s=12$ represent the population standard deviation for the sample

$n=16$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 60, the system of hypothesis would be:

Null hypothesis: $\mu \leq 60$

Alternative hypothesis: $\mu > 60$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33$

4 0

3 years ago

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goblinko [34]

Reflected across the x-axis, the function becomes

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Of the choices offered, the best seems to be ...

... b. the car immediately begins to accelerate at the same rate it had previously decelerated.

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3 years ago

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Afina-wow [57]

Answer:

MG = 56

Step-by-step explanation:

The triangles EML and EGF are similar thus the ratios of corresponding sides are equal, that is

$\frac{EM}{EG}$ = $\frac{EL}{EF}$ , and substituting values