Write the equation. Don’t simplify.

Mathematics

1 answer:

skad [1K]3 years ago

7 0

$(8 {}^{3} ) + p$

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If the sum of the legs of a right triangle is 49 inches and the hypotenuse is 41 inches, find the length of the other two sides

german

The length of one leg is x inches.
The sum of the legs is 49 inches, so the length of the other leg is 49-x inches.
The length of the hypotenuse is 41 inches.

Use the Pythagorean theorem:
$(\hbox{one leg})^2 + (\hbox{the other leg})^2=(\hbox{hypotenuse})^2 \\ x^2+(49-x)^2=41^2 \\
x^2+2401-98x+x^2=1681 \\
2x^2-98x+2401=1681 \ \ \ |-1681 \\
2x^2-98x+720=0 \\ \\
a=2 \\ b=-98 \\ c=720 \\ b^2-4ac=(-98)^2-4 \times 2 \times 720=9604-5760=3844 \\ \\
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-98) \pm \sqrt{3844}}{2 \times 2}=\frac{98 \pm 62}{4} \\
x=\frac{98-62}{4} \ \lor \ x=\frac{98+62}{4} \\
x=\frac{36}{4} \ \lor \ x=\frac{160}{4} \\
x=9 \ \lor \ x=40$

$
49-x=49-9 \ \lor \ 49-x=49-40 \\
49-x=40 \ \lor \ 49-x=9$

The lengths of the legs are 9 inches and 40 inches.

4 0

4 years ago

Solve using the Elimination method.<br> 6x+2y=28<br> 2x-y=8

amid [387]

6x + 2y = 28 - Answer: y = 14 - 3x

2x - y = 8 - Answer: y = -8 + 2x

I hope that helped you! :)

5 0

4 years ago

Find the next five terms 512 256 128 64

Alborosie

The pattern is dividing by 2.

512, 256, 128, 64

512/2 = 256, 256/2 = 128, 128/2 = 64

64/2 = 32, 32/2 = 16, 16/2 = 8, 8/2 = 4, 4/2 = 2, ...

6 0

3 years ago

Help with this please

sp2606 [1]

Answer:

4,5,6.

Step-by-step explanation:

This is the answer because these 3 x values are the one's where the y value is less than one, and another name for y is f(x). Hope this helped!

8 0

3 years ago

Some money was invested at 12% interested for 2 years. If the interest was $21, how much was invested?

astra-53 [7]

Answer:

$87.5 was invested

Step-by-step explanation:

10.5 is 12% of 87.5, so if the money was in the bank for 2 years, we would have to do 10.5*2 which is 21, and that's how much money was gained from the investment.

6 0

3 years ago