Answer:
9% decrease
Step-by-step explanation:
Percentage Decrease = [ (Starting Value - Final Value) / |Starting Value| ] × 100
Answer:
E) Line 5
Step-by-step explanation:
Line 5 contains the first incorrect mathematical process
Process
x−5(x+1)>3x+2
−4x−5>3x+2
−7x−5>2
−7x>7
x<−1
Answer:
86°
Step-by-step explanation:
Given:
A = (6x + 10)°
B = (4x +30)°
Two angles are supplementary if they sum up to 180° ;
A + B = 180°
Now insert the parameters and solve;
6x + 10 + 4x +30 = 180
10x + 40 = 180
10x = 140
x = 14
So;
B = (4x +30)° = 4(14) + 30 = 86°
Answer:
Step-by-step explanation:
One
v^2 - 16
This formation is called the difference of squares. That's because there are 2 squares v^2 and 16. The key to this question is the minus sign.
The square root of v^2 = v
The square root of 16 = 4
You get (v + 4)(v - 4)
Let's see what happens when you expand it.
- v*v = v^2
- v*(-4) = - 4v
- v*(4) = 4v
- 4*-4 = - 16
Look what happens when you add these 4 terms together.
- v^2 - 4v + 4v - 16
- v^2 - 16
is what is left. The two middle terms cancel out.
Two
This one is a perfect square
w^2 + 16w + 64
(w + 8)(w + 8)
Notice both factors are the same. You might wonder how I new that.
w^2 is a perfect square so take the square root. .... v
64 is a perfect square so take the square root ..... 8
Now you have to work backwards to see if it is right.
- w*w = w^2
- w*8 = 8w
- 8*w = 8w
- 8^2 = 64
Adding you get w^2 + 16w + 64 which is what you started with.
<em>FIRST QUESTION:</em>
The slide is 21 ft long. You can imagine that this slide is actually the <u>hypotenuse</u> of a right angled triangle.
To get to the top of the slide you must climb up a vertical 9 foot ladder. You can imagine that this ladder is the <u>opposite</u> side of the right angled triangle.
Now, the distance between the bottom of the ladder and the bottom of the slide can be thought of as the <u>adjacent</u> side of this right angled triangle.
We know, thanks to Pythagoras that:
A²+O²=H²
A = Adjacent length = b
O = Opposite length
H = Hypotenuse
Therefore:
b²+9²=21²
b²=21²-9²
b²=360
b=√360=18.97 (2dp)
So the answer you are looking for is <u>19 feet</u> to the nearest tenth (answer: B).
<em>SECOND QUESTION:</em>
18²+24²=30² (Yes)
Therefore the answer to the second question is YES (answer: A).