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4 years ago

Answer questions below ASAP 5-1/2x=5/8x+2

1 answer:

5 0

Answer: x = 8/3 ; or, write as: 2 2/3; or, write as, 2.66666667 .
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Explanation:
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Given: 5 − 1/2 x = 5/8 x + 2 ;
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Change the 1/2 x to "4/8 x" ;
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Since "1/2" = "(1*4)/(2*4)" = "(4/8)"; and rewrite:
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→ 5 − (4/8)x = (5/8)x + 2 ;
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Subtract "5"; and add "(5/8)x" to EACH side of the equation:
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5 − (4/8)x − 5 + (5/8)x = (5/8)x + 2 − 5 + (5/8)x ;
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to get:
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(1/8) x = (10/8)x − 3
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Multiply the entire equation (BOTH SIDES) by "8"; to get rid of the fraction:
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8 * { (1/8) x = (10/8)x − 3 };
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to get:
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x = 10x − 24 ;
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Subtract "x" ; and add "24" ; to EACH side of the equation:
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→ x − x + 24 = 10x − 24  − x + 24 ;
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to get:
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→ 24 = 9x ; ↔ 9x = 24 ;
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  → Divide EACH side of the equation by "9" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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  → 9x / 9 = 24 / 9 ;
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  → x = 24/9 = (24÷3)/ (9÷3) = 8/3
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→ x = 8/3 ; or, write as: 2 2/3; or, write as, 2.66666667.
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Answer:

See explanation

Step-by-step explanation:

Theorem 1: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

Theorem 2: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

1. Start point: By the 1st theorem,

$x^2=25\cdot (49-25)=25\cdot 24=5^2\cdot 2^2\cdot 6\Rightarrow x=5\cdot 2\cdot \sqrt{6}=10\sqrt{6}.$

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$x^2=40\cdot (40+5)=4\cdot 5\cdot 2\cdot 9\cdot 5\Rightarrow x=2\cdot 5\cdot 3\cdot \sqrt{2}=30\sqrt{2}.$

3. West point from the previous: By the 2nd theorem,

$x^2=(32-20)\cdot 32=4\cdot 3\cdot 16\cdot 2\Rightarrow x=2\cdot 4\cdot \sqrt{6}=8\sqrt{6}.$

4. West point from the previous: By the 1st theorem,

$9^2=x\cdot 15\Rightarrow x=\dfrac{81}{15}=\dfrac{27}{5}=5.4.$

5. West point from the previous: By the 2nd theorem,

$10^2=8\cdot (8+x)\Rightarrow 8+x=12.5,\ x=4.5.$

6. North point from the previous: By the 1st theorem,

$x^2=48\cdot 6=6\cdot 4\cdot 2\cdot 6\Rightarrow x=6\cdot 2\cdot \sqrt{2}=12\sqrt{2}.$

7. East point from the previous: By the 2nd theorem,

$x^2=22.5\cdot 30=225\cdot 3\Rightarrow x=15\sqrt{3}.$

8. North point from the previous: By the 1st theorem,

$x^2=7.5\cdot 36=270\Rightarrow x=3\sqrt{30}.$

8. West point from the previous: By the 2nd theorem,

$x^2=12.5\cdot (12.5+13.5)=12.5\cdot 26=25\cdot 13\Rightarrow x=5\sqrt{13}.$

9. North point from the previous: By the 1st theorem,

$12^2=x\cdot 30\Rightarrow x=\dfrac{144}{30}=4.8.$

101. East point from the previous: By the 1st theorem,

$6^2=1.6\cdot (x-1.6)\Rightarrow x-1.6=22.5,\ x=24.1.$

11. East point from the previous: By the 2nd theorem,

$20^2=32\cdot (32-x)\Rightarrow 32-x=12.5,\ x=19.5.$

12. South-east point from the previous: By the 2nd theorem,

$18^2=x\cdot 21.6\Rightarrow x=15.$

13. North point=The end.

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Answer:

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Step-by-step explanation:

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4 years ago

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3 years ago