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Liono4ka [1.6K]
3 years ago
5

Caissa can download a maximum of 1000 megabytes (MB) of songs or movies to her smartphone each month. The file size of each movi

e is 85 MB, and the file size of each song is 4 MB. Write an inequality that represents the number of movies (M) and songs (S) that Caissa can download each month.
Mathematics
1 answer:
Firdavs [7]3 years ago
7 0

Answer:

85M + 4S <u><</u> 1000

Step-by-step explanation:

An inequality represents an expression that can have different values as long as the value is within the range given.  In this case, the number of songs and movies that Caissa can download can not exceed 1000 MB.  Since each move is 85 MB and each song is 4 MB, then any combination of these two files combined must not be larger than 1000 MB.  Using the variable (M) for movies and (S) for songs, we can set up an expression 85M + 4S to represent the number of movies times 85 for each movie and the number of songs times 4 for each song.  Since the total can be no greater than 1000, the expression would be less than or equal to (<u><)</u> 1000 MB.

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

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2) axis of symmetry: x=-1.5

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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.

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