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Bezzdna [24]
3 years ago
7

9

Mathematics
1 answer:
SashulF [63]3 years ago
7 0

Answer:

n = -5

Step-by-step explanation:

Given

Digit = 0.000025

Required

Rewrite using scientific notation, then find n

Digit = 0.000025

Express as fraction

Digit =\frac{25}{1000000}

This can be splitted to

Digit = 25 * 10^{-6}

The first number must be between 1 and 10; hence, 25 can be expressed as 2..5 * 10

Digit = 2.5 * 10* 10^{-6}

Apply law of indices

Digit = 2.5 * 10^{1-6}

Digit = 2.5 * 10^{-5}

Comparing n, the given options

n = -5

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Find the vertex point, axis of symmetry, x-intercepts, and y-intercept of the
Bond [772]

Answer:

1) Vertex point (-1.5,-20.25)

2) axis of symmetry: x=-1.5

3) x-intercepts: (-6,0) and (3,0)

4) y-intercept: (0,18)

5) Graph in attachment.

Step-by-step explanation:

1) The given parabola has equation:

y =  {x}^{2}  + 3x - 18

We need to complete the square.

y =  {x}^{2}  + 3x + {1.5}^{2}   -  {1.5}^{2} - 18

y = ( {x + 1.5)}^{2}  - 20. 25

This function is in the vertex form:

y = a( {x - h)}^{2}  + k

where (h,k) is the vertex, x=h is the axis of symmetry.

By comparing our equation to the general vertex form:

The vertex point is (-1.5,-20.25)

2) The axis of symmetry divides the parabola into two congruent halves.

Since this is a vertical parabola, the axis of symmetry occuring at x=h is a vertical line.

The axis of symmetry is x=-1.5

3) Y-INTERCEPT.

The y-intercept is the point where the graph cross the y-axis.

At this point, the value of x is zero.

To find the y-intercept, we substitute x=0 in the equation of the parabola and simplify.

when x=0,

y =  {(0)}^{2}  + 3(0) - 18 =  - 18

The y-intercept is (0,-18).

4) X-INTERCEPT

The x-intercepts are the points where the graph touches or intersect the x-axis.

To find the x-intercept, we substitute y=0.

( {x + 1.5)}^{2}  - 20.25 = 0

Add 20.25 to both sides;

( {x + 1.5)}^{2}   =  20.25

Take square root.

(x + 1.5)=  \pm \sqrt{20.25}

x =   - 1.5\pm 4.5

x =   - 1.5 -  4.5 \:  \:  or \:  \: x =  - 1.5 + 4.5

x =  - 6 \: or \: x = 3

The x-intercepts are(-6,0) and (3,0).

4) GRAPH

To graph this function, we can use transformation.

To graph the function,

y =  {(x + 1.5)}^{2}  - 20.25

We shift the parent quadratic function 1.5 units left and 20.25 units down.

See attachment for graph.

5 0
2 years ago
Why x^2=16 and x^2=-16 do not have the same solution
77julia77 [94]

Step-by-step explanation:

x^2 = 16

x = ±4

x^2 = -16

x = -

as a negative number cannot be squareroot

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