Well, let's check if your inequality is true. We have to add the 3 scores up and divide them by 3 to know the average.

73 + 81 + 86 = 240
240 / 3 = 80

80%

That's true, now let's check 101.

73 + 81 + 101 = 255
255 / 3 = 85

85%

That's true.

Your inequality is correct.

5 0

3 years ago

Cost A=0.6489<br><br> take the inverse cosine of both sides

Stolb23 [73]

I am not quite sure what the question asks for,
But this is what i assume it wants:

Cos A= 0.6489
In this given one, we basically find the size of the angle A
we do cosine inverse on both sides to get the size of the angle A
$cos^{-1}$ : It looks like this in the calculator
$cos^{-1}$ × cos A= $cos^{-1}$ (0.6489)
( $cos^{-1}$ and cos cancels out)
A= $cos^{-1}$ (0.6489)
A=49.54°
check:
cos 49.54=0.6489 (its right!)

6 0

3 years ago

zhuklara [117]

Step-by-step answer:

Given:

A triangle

Perimeter = 60 cm

longest side = 4* shortest side (x)

Solution:

longest side = 4x

shortest side = x

third (intermediate side = 60 -x -4x = 60-5x

The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle. Hence

x + y > 4x

x + 60-5x > 4x

60 - 4x > 4x

8x < 60

x < 60/8 = 7.5, or

x < 7.5

Therefore to form a triangle, x (shortest side) must be less than 7.5 cm.

Examine the options: both 7 and 5 are both less than 7.5 cm.

40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.

Now also examine cases where 4x is NOT the longest side, in which case we need

4x>=y

4x >= 60-5x

9x >=60

x >= 6.67

so x=5 will not qualify, because 4x will no longer be the longest side.

The only valid option is x=7 cm

The side lengths for x=7 and x=5 are, respectively,

(7, 25, 28)

5, 20, 35 (in which case, the longest side is no longer 4x=20, so eliminated)

7 0

3 years ago