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3 years ago

Evaluate 3b−2a−9 a=12 and b=7

Mathematics

2 answers:

Artemon [7]3 years ago

8 0

The answer is 12. Substitute a for 12 and b for 7 in the equation. Multiply first, then add/subtract from left to right

Lemur [1.5K]3 years ago

4 0

First you would replace "b" with "7" and then "a" with "12"

You would have 3(7) - 2(12) - 9

Next step would be combining 3 and 7, also combine 2 and 12

You would have 21 - 2 x 12 - 9

Multiply 2 and 12 (24) and put back in equation

Then you would end up with 21 - 24 - 9

Subtract all that and you end up with -12

Answer: -12

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Part 1) $A=36(\pi-2)\ cm^2$

Part 2) $P=6(\pi+2\sqrt{2})\ cm$

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

Part 1) Find the area

we know that

The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle

$A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)$

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substitute

$A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)\\A=(36\pi-72)\ cm^2$

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$A=36(\pi-2)\ cm^2$

Part 2) Find the perimeter

The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle

The circumference of a quarter of circle is equal to

$C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r$

substitute the given values

$C=\frac{1}{2}\pi (12)\\C=6\pi\ cm$

Applying the Pythagorean Theorem

The hypotenuse of right triangle is equal to

$AC=\sqrt{12^2+12^2}\\AC=\sqrt{288}\ cm$

simplify

$AC=12\sqrt{2}\ cm$

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$P=(6\pi+12\sqrt{2})\ cm$

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Factor 6

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