Mr. Brettler is hanging up a 5-foot tall rectangular welcome sign in the gym. He has drawn a sketch on a coordinate grid.

Mathematics

1 answer:

zepelin [54]3 years ago

8 0

Answer:

(9,2) and (-6,2).

Step-by-step explanation:

Rectangular Coordinates

The lower vertices of a rectangular welcome sign in Mr. Brettler's gym are (9,-3) and (-6,-3).

Note these two vertices are 3 units below the x-axis. We know the sign is 5-foot tall, so the y-coordinates of the two upper vertices should be -3+5=2.

The upper vertices of the sign on the grid are (9,2) and (-6,2).

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Simplify completely: 8x+4/x^3+23÷4x^2-10x-6/9-x^2

Helen [10]

Answer:

The simplified form is: $-x^2-2x+\frac{4}{x^3}+\frac{23}{4x^2}-\frac{2}{3}$

Step-by-step explanation:

To simplify the expression given we, need to open the brackets, and if there is power term. Then we need to group all the like terms and then arrange in the descending order of powers of the given expression.

Now the expression that is given to us is:

$8x+\frac{4}{x^3}+\frac{23}{4x^2}-10x-\frac{6}{9}-x^2$

Here we will simplify it by grouping the like terms, as follows:

$8x+\frac{4}{x^3}+\frac{23}{4x^2}-10x-\frac{6}{9}-x^2\\=-x^2+8x-10x+\frac{4}{x^3}+\frac{23}{4x^2}-\frac{6}{9}=-x^2-2x+\frac{4}{x^3}+\frac{23}{4x^2}-\frac{2}{3}$