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Allisa [31]
3 years ago
7

If a change dispenser contains 32 coins consisting of

Mathematics
1 answer:
swat323 years ago
6 0
<h3>Answer:  19 dimes</h3>

=================================================

Work Shown:

d = number of dimes

q = 32-d = number of quarters

$5.15 = 515 cents

10d+25q = 515

10d+25(32-d) = 515

10d+800-25d = 515

-15d+800 = 515

-15d = 515-800

-15d = -285

d = -285/(-15)

d = 19

There are 19 dimes. You can stop here if you want.

q = 32-d = 32-19 = 13

There are 13 quarters

-------------------------------

Check:

1 dime = 10 cents

19 dimes = 19*10 = 190 cents

1 quarter = 25 cents

13 quarters = 13*25 = 325 cents

total value = 190 cents + 325 cents = 515 cents = $5.15

The answer is confirmed.

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Given WXYZ is a rhombus.
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Answer:

Diagonal of rhombus bisect the angles of it.

Step-by-step explanation:

Given: WXYZ is a rhombus.

To prove: WY bisects Angle ZWX and Angle XYZ.  ZX bisects Angle WZY and Angle YXW.

In rhombus WXYZ, WY is a diagonal.

In triangle WXY and triangle WZY,

WX=WZ        (sides of rhombus are equal)

XY=ZY        (sides of rhombus are equal)

WY=WY       (Common side)

By SSS postulate,

\triangle WXY\cong \triangle WZY

\angle WYX\cong \angle WYZ       (CPCTC)

\angle XWY\cong \angle ZWY       (CPCTC)

Hence prove, that WY bisects Angle ZWX and Angle XYZ.

Similarly,

In rhombus WXYZ, ZX is a diagonal.

In triangle WXZ and triangle YXZ,

WX=YX        (sides of rhombus are equal)

XZ=XZ         (Common side)

WZ=YZ        (sides of rhombus are equal)

By SSS postulate,

\triangle WXZ\cong \triangle YXZ

\angle WZX\cong \angle YZX       (CPCTC)

\angle WXZ\cong \angle YXZ       (CPCTC)

Hence prove, that ZX bisects Angle WZY and Angle YXW.

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