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3 years ago

PLEASE HELP ME ASAP!! I had trouble with this and it is now over due

Mathematics

1 answer:

erica [24]3 years ago

3 0

Answer:

Shira: x = 8

Samuel: m = 0

Step-by-step explanation:

Shira's mistake was that she subtracted 2 from both sides instead of adding to on both sides.

Correct Solving:

2x - 2 = 14

Add 2 to both sides;

2x = 16

Divide both sides by 2;

x = 8

Samuel's mistake was that when he distributed -2 to 8m and 8 he put the wrong sign for -2 * 8.

Correct Solving:

-2(8m + 8) = -16

Distribute;

-16m - 16 = -16

Add 16 to both sides;

-16m = 0

Divide both sides by -16;

m = 0

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3 years ago

The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

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3 years ago

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saul85 [17]

Answer: If Shelly reads 25 pages a day for 5 days she will finish her book

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125/25=5

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