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krek1111 [17]
3 years ago
10

What is the vertex of the graph of the following equation? y = x^2 + 2x-3

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
6 0

Answer:

vertex = (- 1, - 4 )

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = - \frac{b}{2a}

y = x² + 2x - 3 ← is in standard form

with a = 1, b = 2 , then

x = - \frac{2}{2} = - 1

Substitute x = - 1 into the equation for corresponding value of y

y = (- 1)² + 2(- 1) - 3 = 1 - 2 - 3 = - 4

vertex = (- 1, - 4 )

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Find the area of each trapezoid, rhombus, or kite.
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Answer:

15 is the area

Step-by-step explanation:

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3 years ago
Use substitution to solve the<br> following system of equations.<br> - 4y - 5x = 30 AND x= y + 3
IRISSAK [1]

Answer:

The solution to the system of equations is y = -5 and x = -2.

Step-by-step explanation:

The question tells us to use substitution to solve the system.  This means that the given value for x (in terms of y) should be substituted into the other equation.  This is modeled below:

-4y - 5x = 30

-4y - 5(y+3) = 30

Next, we should use the distributive property to simplify the left side of the equation.

-4y -5y - 15 = 30

The next step is to combine like terms on the left side of the equation.

-9y - 15 = 30

Then, we can add 15 to both sides of the equation.

-9y = 45

Finally, we can divide both sides of the equation by -9.

y = -5

To find the value for x, we substitute in the value we just found for y into either of our original equations.

x = y + 3

x = -5 + 3

x = -2

Therefore, the correct answer is y = -5 and x = -2.

Hope this helps!

3 0
3 years ago
A manager of a grocery store wants to determine if consumers are spending
ololo11 [35]

Answer:

1. The error in the assumption is taking the sample mean, \bar x, as being equal to the population mean, μ

2. To correct the error, the manager will need to generate the confidence interval based on the population standard deviation on the acceptable values of the mean using the following relation;

CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}

Step-by-step explanation:

We note that from the central limit theorem as the size of the sample, n, becomes more and more larger, the mean of the sample, \bar x, approaches that of the population mean, μ, therefore as the grocery store manager uses the sample mean as the population mean's point estimate an error will be observed based on the size of the sample compared to the population, where the difference between the two means (the population mean and the sample mean) is \left | \bar{x} - \mu \right |

1. The error in the assumption is taking the sample mean, \bar x, as being equal to the population mean, μ

2. To correct the error, the manager will need to generate the confidence interval based on the population standard deviation on the acceptable values of the mean using the following relation;

CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}

Where:

σ = Population standard deviation = $30

z = z value at 95% confidence level = 1.96

\bar x = Sample mean $160

n = Sample size = 10

Plugging in the values, we have;

$141.4 < \bar x < $178.6

Hence the expected value of the mean should be between $141.4 and $178.6.

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3 years ago
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MaRussiya [10]
80X3 PLUS 2x3 that is awnser

                                                                                                                                 
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Answer:

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Step-by-step explanation:

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