Answer: 6/8, 12/16, 15/20, 18/24, are all equal
Step-by-step explanation:
Hello! 3x + 20 and 8x - 5 are equal. To find the value of "x", we should set up and solve an equation. It would be written like this:
3x + 20 = 8x - 5
First off, subtract 3x from both sides in order to get 20 = 5x - 5. Add 5 to both sides to get 25 = 5x. Now, divide each side by 5 to isolate the "x". 25/5 is 5. Now, let's plug in the value and see if it works. 3 * 5 is 15. 15 + 20 is 35. 8 * 5 is 40. 40 - 5 is 35. 35 = 35. There. x = 5.
Answer:
y = 25
Step-by-step explanation:
Given that the quantities are proportional then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 10 when x = 6
k = 
= 
= 
y = x ← equation of proportion
When x = 15, then
y = × 15 = 5 × 5 = 25
<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).
