1. Let the sides of a triangle be a, b and c.
Assume c is the largest side.
The maximum angle measure in an acute triangle can be 90°. In such a case we would have
Now forget about side c, and open the angle between a and b just a little bit. Now clearly
is larger that
because the "new c" is larger than the old one.
2. So for 3 numbers to be the lengths of the sides of an acute triangle, the sum of the squares of the 2 smaller numbers must be at most equal to the square of the largest number but not more.
Check:
A. 4^2+5^2=16+25=41<49
B. 5^2+7^2=25+49=74>64
C. 6^2+7^2=36+49=85<100
D. 7^2+9^2=49+81=130<144
3. Correct answer: only B
3.2
Step-by-step explanation:
The Image attached below.
The given fraction is .
Step 1: Write the numerator inside.and denominator outside.
Step 2: If we multiply a number 5 by 3 we get 15. Write 3 in the quotient place.
Step 3: Now subtract 15 from 16, we get 1
Step 4: Place a decimal point after 3 and give one zero after 1, we get 10.
Step 5: Now multiply 5 by 2, we get 10.
Step 6: Subtract 10 from 10, the remainder is 0.
Step 7: The decimal is 3.2.
Answer:
A)-1
Step-by-step explanation:
3x-5≥4x-3
3x-4x≥-3+5
-x≥2
x≤-2
(-infinity,-2]
-1 x
-2,-3,-5 ✓
First we calculate the slope (which is called "m".
Slope = m = (Y2 -Y1) ÷ (X2 -X1)
m = (-8 -1) / (5 -2) = -9 / 3 = -3
We next fill in this equation: b = y -mx
We know m = -3 and we can choose a point (2, 1) to calculate "b"
b = 1 --3 * 2 b = 7
Putting this into y = mx +b
y = -3x +7