3 years ago

For what values of is the quadratic function f (c)=22 – 20 – 24 positivie

Mathematics

1 answer:

Gennadij [26K]3 years ago

6 0

Answer:

5485/45

Step-by-step explanation:

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Find two numbers whose difference is 13 and whose squares when added is 449.

alex41 [277]

X, y - the numbers

$x-y=13 \\
x^2+y^2=449 \\ \\
\hbox{solve the first equation for x:} \\
x-y=13 \\
x=13+y \\ \\
\hbox{substitute the result for x in the second equation:} \\
(13+y)^2+y^2=449 \\
169+26y+y^2+y^2=449 \\
2y^2+26y+169-449=0 \\
2y^2+26y-280=0 \ \ \ \ \ \ \ \ \ \ \ |\div 2 \\
y^2+13y-140=0 \\
y^2+20y-7y-140=0 \\
y(y+20)-7(y+20)=0 \\
(y-7)(y+20)=0 \\
y-7=0 \ \lor \ y+20=0 \\
y=7 \ \lor \ y=-20$

$x=13+y \\ \Downarrow \\ \hbox{for } y=7: \\
x=13+7 \\
x=20 \\ \\
\hbox{for } y=-20: \\
x=13-20 \\
x=-7 \\ \\
(x,y)=(20,7) \hbox{ or } (x,y)=(-7,-20)$

The numbers are 20 and 7 or -7 and -20.

6 0

3 years ago

What is the height of an iscocles trapizoid, if the lengths of its bases are 5m and 11m and the length of a leg is 4m?

dsp73

Answer:

x=√5

Step-by-step explanation:

Use the pythagorean theorem