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Thepotemich [5.8K]
2 years ago
7

What notes do I use on the first side then the 2nd side?

Mathematics
1 answer:
Vinil7 [7]2 years ago
7 0

Answer:

I would use either a dotted half note for the first measure (equivalent to 3 beats), or use a half note and a quarter note. In the second measure I would use a half note.

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Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
melamori03 [73]

Answer:

6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs AB=3, BC=4, and AC=5. The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base b and height h is given by A=\frac{1}{2}bh. Therefore, the area of this right triangle is:

A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}

The other triangle is a bit trickier. Triangle \triangle ADC is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

A=\sqrt{s(s-a)(s-b)(s-c)}, where a, b, and c are three sides of the triangle and s is the semi-perimeter (s=\frac{a+b+c}{2}).

The semi-perimeter, s, is:

s=\frac{5+5+4}{2}=\frac{14}{2}=7

Therefore, the area of the isosceles triangle is:

A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}

Thus, the area of the quadrilateral is:

6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}

4 0
3 years ago
Find ( f - g)(x).<br><br> f (x) = -2x2 - 2x - 3 and g(x) = 3x2 - 4x - 4
Kruka [31]

Answer:

\large\boxed{(f-g)(x)=-5x^2+2x+1}

Step-by-step explanation:

(f-g)(x)=f(x)-g(x)\\\\\text{We have}\ f(x)=-2x^2-2x-3\ \text{and}\ g(x)=3x^2-4x-4.\\\\\text{Substitute:}\\\\(f-g)(x)=(-2x^2-2x-3)-(3x^2-4x-4)\\\\(f-g)(x)=-2x^2-2x-3-3x^2+4x+4\qquad\text{combine like terms}\\\\(f-g)(x)=(-2x^2-3x^2)+(-2x+4x)+(-3+4)\\\\(f-g)(x)=-5x^2+2x+1

3 0
3 years ago
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