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Darya [45]
3 years ago
7

BRAINLIESTTT ASAP! PLEASE HELP ME :)

Mathematics
2 answers:
Masja [62]3 years ago
7 0

Answer:

Here's what I get  

Step-by-step explanation:

1. Graph the parabola

(a) Create a table containing a few values of x and y

I chose the following points:

\begin{array}{rr}\mathbf{x} & \mathbf{f(x)}\\-3 & 0\\-2 & -3 \\-1 & -4\\0 & -3\\1 & 0 \\2 & 3\\\end{array}

(b) Plot your points

Draw dots at the coordinates of each point ( Fig. 1).

(c) Draw the graph

Draw a smooth line through the points.

Extend your line smoothly to the edge of the plot area (Fig. 2).

2. Label the intercepts and vertex

The x-intercepts are at (-3, 0) and (1, 0).

The y-intercept is at (0, -3).

The vertex is at (-1, -4).

See Fig.3 for the labels.

3. Axis of symmetry

The axis of symmetry is a vertical line that passes through the vertex and divides the graph into mirror- image halves.

The vertex is at (-1, -4), so the vertex is a straight line passing through (-1, -4) and (-1, 0). It is the dashed black line in Fig. 4

Scrat [10]3 years ago
4 0

x-intercepts: (-3,0), (1,0)

work:

0 = x^2 + 2x - 3

quadratic equation: x = -2 +√(2^(2) - 4 × 1(-3)) / (2 × 1) = 1

quadratic equation: x = -2 -√(2^(2) - 4 × 1(-3)) / (2 × 1) = -3

(x,y) --) (-3,0), (1,0)

y-intercept: (0,-3)

work:

y = (0)^2 + 2(0) - 3

y = -3

(x,y) --) (0,-3)

vertex: (-1,-4)

work:

xv = -( b / (2a) )

a = 1, b = 2, c = -3

xv = -( 2 / (2×1) )

xv = -1

yv = (-1)^2 + 2(-1) - 3

yv = -4

(x,y) --) (-1,-4)

axis of symmetry: -1

work:

a = 1 in the x^(2) + 2ax + a^(2)

x^(2) + 2x + 1^(2) = (x + 1)^(2)

(x + 1)^(2) - 3 - 1^(2)

y = (x + 1)^(2) - 4

y + 4 = (x - 1)^(2)

put in standard form --) 4 × 1/4( y -( -4 ) ) = ( x -( -1) )^(2)

(h,k) = (-1,-4); p = 1/4

in parabola form expression: 4p( y - k ) = ( x - h )^(2) and is symmetric around the y-axis at -1.

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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
avanturin [10]

The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".

The given inequality is -3(2x - 5) < 5(2 - x)

We need to simplify the inequality.

<h3>What is inequality?</h3>

In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)

⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]

Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)

⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]

Now, - 6x + 15 < 10 - 5x

By subtracting 15 from both sides, we get

- 6x < -5 - 5x

By adding 5x to both sides, we get - x < - 5

The coefficient of x is -1. So, divide both sides by -1

Then we get x > 5

Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".

To learn more about inequalities visit:

brainly.com/question/20383699.

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5 0
2 years ago
Please help me with this math problem.
ladessa [460]

Answer:

-6v < -3; v> -0.5

Step-by-step explanation:

We have to find a number let say x

Given that:

-6v < x  ........... eq1

v> - 0.5 ...........  eq2

By taking equation 1

-6v < x

Dividing both sides by -6

(inequality will be inverted because of negative sign)

-6/-6 v > x/-6

v > x/-6  .........eq3

Now comparing eq2 and eq3 we get:

x/-6 = -0.5

Multiplying both sides by -6

x = -0.5 * -6

x = -3

So it will give:

-6v < -3; v> -0.5

I hope it will help you!

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