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3 years ago

All the answers please on paper and work

Mathematics

1 answer:

REY [17]3 years ago

7 0

1)
8² + 15² = 17²
64 + 225 = 289
This is true, so the triangle is a right triangle.

2)
4² + 12² = 13²
16 + 144 = 169
This is false, so the triangle is not a right triangle.

3)
20² + 21² = 27²
400 + 441 = 729
This is false, so the triangle is not a right triangle.

4)
28² + 45² = 53²
784 + 2,025 = 2,809
This is true, so the triangle is a right triangle.

You might be interested in

Is 2 (x-y) and 2x-2y equivalent

MArishka [77]

Answer:

yes

Step-by-step explanation:

2(x-y) you distribute the 2 to whats inside the parenthesis

2x-2y

4 0

3 years ago

PLEASE WILL MARK BRANLIEST AND IS WORTH 20POINTS!!!!!

svlad2 [7]

Answer:

(3,-2)

Step-by-step explanation:

Part A:

1) Isolate x in x - y = 5

x = y + 5

2) Substitute that x into 4x+y=10

4(y + 5) + y = 10

4y + 20 + y = 10

5y = 10-20

5y = -10

y = -2

3) Use y to solve for x:

x = -2 + 5

x = 3

Part B:

Verify using results from Part A

3 - (-2) = 5

4(3) + (-2) = 12 - 2 = 10

Part C:

Just graph the equations and see where they intersect, which is exactly (3,-2). We got that in Part A and B

3 0

4 years ago

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.