HELP ASAP!

Mathematics

2 answers:

alexgriva [62]3 years ago

5 0

Answer:

You answer is C. 70 degrees.

Step-by-step explanation:

Since you have the two other Interior values, you know that when you add them (40+30), and then subtract it from 180, you will find that the other Interior angle is 110 degrees.

Now, an interior and exterior angle must add up to 180 degrees to be a correct angle. Since you know that the interior one is 110, you can figure out that the exterior angle will be 70 degrees.

110+x=180

110+70= 180

180=180

Checks out!

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Hope it helps!

vesna_86 [32]3 years ago

4 0

Interior angles in any triangle sum up to 180 so 180-(30+40)=110
So the exterior angles equals 180-110= 70

70 is the final answer i hope it helps and good luck

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Please help! A-level maths.

astra-53 [7]

$x+y=k\implies y=k-x$

Substitute this into the parabolic equation,

$k-x=6-(x-3)^2\implies x^2-7x+(k+3)=0$

We're told the line $x+y=k$ intersects $C$ twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know

$(-7)^2-4(k+3)=49-4(k+3)>0\implies k$

We can tell from the quadratic equation that $C$ has its vertex at the point (3, 6). Also, note that

$-1\le\sin t\le1\implies3\le3+2\sin t\le5\implies3\le x\le5$

and

$-1\le\cos2t\le1\implies2\le4+2\cos2t\le6\implies2\le y\le6$

so the furthest to the right that $C$ extends is the point (5, 2). The line $x+y=k$ passes through this point for $2+5=k\implies k=7$ . For any value of $k$ , the line $x+y=k$ passes through $C$ either only once, or not at all.