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3 years ago

Sue has $2.20 in dimes and nickels. If she has 13 more dimes than nickels, how many of each coin does she have?

1 answer:

4 0

10d+5n=220
divide both sides by 5
2d+n=44

d=13+n
sub 13+n for d in other equatin

2(13+n)+n=44
26+2n+n=44
26+3n=44
minus 26 both sides
3n=18
divide both sides by 3
n=6
sub back

d=13+n
d=13+6
d=19

19 dimes
6 nickles

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Experimentally verify sum of three angles of an triangle is 180⁰.

svetlana [45]

Draw line a through points A and B. Draw line b through point C and parallel to line a.

Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'.

It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees.

Thus <)ABC + <)BCA + <)CAB = 180 degrees.

Lemma

If ABCD is a quadrilateral and <)CAB = <)DCA then AB and DC are parallel.

Proof

Assume to the contrary that AB and DC are not parallel.

Draw a line trough A and B and draw a line trough D and C.

These lines are not parallel so they cross at one point. Call this point E.

Notice that <)AEC is greater than 0.

Since <)CAB = <)DCA, <)CAE + <)ACE = 180 degrees.

Hence <)AEC + <)CAE + <)ACE is greater than 180 degrees.

Contradiction. This completes the proof.

Definition

Two Triangles ABC and A'B'C' are congruent if and only if

|AB| = |A'B'|, |AC| = |A'C'|, |BC| = |B'C'| and,

<)ABC = <)A'B'C', <)BCA = <)B'C'A', <)CAB = <)C'A'B'.

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3 years ago

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trapecia [35]

<h2>Answer:</h2><h2>D. 4b + 6</h2><h2 /><h2>Hope this helps!!</h2>

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3 years ago

Read 2 more answers

Match the information on the left with the appropriate equation on the right.

solmaris [256]

Answer:

Step-by-step explanation:

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y = mx + b

If slope 'm' = 1 and y-intercept 'b' = -3

Equation of the line will be,

y = x - 3

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y - y' = m(x - x')

If the slope 'm' = 1 and point is (-1, 2),

The the equation of the line will be,

y - 2 = 1(x + 1)

y = x + 1 + 2

y = x + 3

x - y = -3

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$y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$

If this line passes through (-2, 3) and (-3, 4),

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