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aivan3 [116]
3 years ago
8

Vertex of the graph of f(x) = x 2 + 2x - 15

Mathematics
1 answer:
Goshia [24]3 years ago
7 0
Try this explanation:1. This curve is parabola; its equation is y=ax²+bx+c2. Using the formula for 'x' of vertex (x₀=-b/(2a)): x₀=-2/(2*1)=-1.3. If to substitute known x₀ into the equation of the given parabola it is possible to find y₀: y₀=x₀²+2x₀-15=1-2-15=-16.
answer: (-1;-16)

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a market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the
enot [183]

Answer and explanation:

Answer:

Two sample t test

Explanation:

The test that could be used here is the two sample t test. The two sample t test compares two groups to ascertain if there is an average significant different between the two groups being compared, also making sure the result of difference is not random. For instance to test the above example, the two sample t test compares the group before they watch the commercial with the group after the commercial to know if there is a significant difference between the two groups.

4 0
3 years ago
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7 0
3 years ago
L onUURS allu ueposits in transit in the are added to the bank statement balancedeposits to 75. l of the following are reasons t
ycow [4]
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6 0
3 years ago
What are the roots of the polynomial equation x3 - 6x = 3x2 - 8? Use a graphing calculator and a system of equations.
makkiz [27]

Answer:

d : 4, 1, -2.

Step-by-step explanation:

There's no need for a calculator in my opinion because we can use the rational root theorem which states that the equations of this form:

\sum_{i=0}^{n} a_{i}x^i = 0 = a_{0} + a_{1}x + a_2x^2 + ... + a_nx^n = 0\\ a_i \in \mathbb{Z}

Have rational roots, than the roots are of the form: \frac{k \cdot a_o}{p \cdot a_n}, \ where \ k, p \in \mathbb{Z}.

Rewriting the equation we have:

x^3 - 3x^2 -6x + 8 = 0\\By \ our\ previous \ claim \ x \in D_8 \ where \ D_n \ the \ set \ of \ divisors \ of \ n.\\D_8 = \{\pm 1, \pm 2, \pm 4, \pm 8\} \\We \ plug \ in \ some \ number from \ D_8.\\Letting \ x = -2;\\(-2)^3 -3(-2)^2 -6(-2) + 8 = 0 \ \ \ Thus \ x+2 \ is \ a \ factor.\\We \ can \ now \ simplify \ the \ eq. \ using \ Polynomial \ Long \ Division.

x^3 -3x^2 -6x + 8 = (x+2)(Q(x))\\To \ find \ Q \ we \ divide \ the \ original \ equation \ by \ x + 2; which \ yields:\\Q(x) = x^2 - 5x + 4.\\So \ we \ can \ use \ the \ quadratic \ formula \ to \ find \ the \ roots:\\x = 4,x = 1. \\Thus \ x \in \{-2, 1, 4\}. \ \ These \ are \ all \ the \ roots.

5 0
4 years ago
Alanah is picking up two friends to go to a concert. She drives from her house to pick up Mia, then she drives to pick up Teresa
Ksivusya [100]

Answer:

Total distance = 30.3 units

Step-by-step explanation:

Coordinates for the location of Alanah, Mia, Teresa and Arena are,

Alanah → (2, 8)

Mia → (8, 16)

Teresa → (8, 2)

Arena → (14, 4)

Distance between two points (x_1,y_1) and (x_2,y_2) is given by the formula,

d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

Distance between Alanah and Mia = \sqrt{(16-8)^2+(8-2)^2}

                                                          = \sqrt{100}

                                                          = 10 units

Distance between Mia and Teresa = \sqrt{(16-2)^2+(8-8)^2}

                                                          = 14 units

Distance between Teresa and Arena = \sqrt{(4-2)^2+(14-8)^2}

                                                              = \sqrt{40}

                                                              = 6.3 units

Total distance of Alanah's trip to Arena = 10 + 14 + 6.3

                                                                  = 30.3 units

3 0
3 years ago
Read 2 more answers
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