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3 years ago

(7q3r2 + 5qr2 + 23q) + (−5qr2 − qr² − 11q − 4q3r2) adding polynomials horizontally

Mathematics

1 answer:

zysi [14]3 years ago

5 0

You can remove the parentheses:-

= 7q^3r^2 + 5qr^2 + 23q + −5qr^2 − qr^2 − 11q − 4q^3r^2 ( because there is + outside)

Bring like terms together

= 7q^3r^2 − 4q^3r^2 + 5qr^2 − 5qr^2 − qr^2 + 23q − 11q

= 3q^3r^2 - qr^2 + 12q answer

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Amanda uses a rectangular canvas for a panting. The length is 6x-3 centimeters The width is 2x+6 centimeters,and is 4/5of the le

julia-pushkina [17]

Answer:

15 cm by 12 cm.

Step-by-step explanation:

Given:

Amanda uses a rectangular canvas for a panting.

The length is $6x-3$ centimeters.

The width is $2x+6$ centimeters, and is 4/5 of the length .

Question asked:

.What are the dimensions of the canvas ?

Solution:

As given that the width is $\frac{4}{5}$ of the length.

$2x+6=\frac{4}{5} (6x-3)\\ \\ 2x+6=\frac{4}{5}\times6x-\frac{4}{5}\times3\\ \\ 2x+6=\frac{24x}{5} -\frac{12}{5} \\ \\$

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$2x+6+\frac{12}{5} =\frac{24x}{5} -\frac{12}{5}+\frac{12}{5}\\ \\ 2x+\frac{42}{5} =\frac{24x}{5}$

Subtracting both sides by $2x$

$2x-2x+\frac{42}{5} =\frac{24x}{5} -2x\\ \\ \frac{42}{5} =\frac{24x-10x}{5} \\ \\ \frac{42}{5} =\frac{14x}{5} \\ \\$

By cross multiplication:-

$5\times14x=5\times42\\ \\ 70x=210\\ \\$

By diving both sides by 70

$x=3$

Now, substituting the value:-

The length = $6x-3$ cm

= $6\times3-3=18-3=15\ cm$

The width = $2x+6$ cm

= $2\times3+6=6+6=12\ cm$

Thus, length and width of canvas are 15 cm and 12 cm.

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