Answer:
Alicia is 18years
Quentin is 14years
Rosalyn is 16years
Step-by-step explanation:
Let the age of Alicia be x
Let the age of Quentin be y
Let the age of Rosalyn be z
If the sum of the siblings’ ages, in years, is 48 then;
x+y+z = 48.... 1
If Rosalyn is two years older than Quentin then;
z =y+2 ..... 2
Also if Quentin is four years younger than Alicia then;
y = x-4 ... 3
From 3:
x = y+4 ... 4
Substitute 2 and 4 into 1 to have:
y+4+y+y+2 = 48
3y + 6= 48
3y = 48-6
3y= 42
y = 14
Since x= y+4
x = 14+4
x = 18
Since z = y+2
z = 14+2
z = 16year
This means that;
Alicia is 18years
Quentin is 14years
Rosalyn is 16years
Let the amount B pays be £x
So,
A pays £125
B pays £x
They pay in the ration 3:2
Therefore,
125/x = 3/2
Cross multiplying we get,
125 x 2 = 3x
3x = 250
x = £63.33
<u><em>Answer:</em></u>
Part a .............> x = 11
Part b .............> k = 57.2
Part c .............> y = 9.2
<u><em>Explanation:</em></u>
The three problems deal with inverse variation between two variables
An inverse variation relation between two variables means that when one of the variables increases, the other will decrease (and vice versa)
<u>Mathematically, an inverse variation relation is represented as follows:</u>

where x and y are the two variables and k is the constant of variation
<u><em>Now, let's check the givens:</em></u>
<u>Part a:</u>
We are given that y = 3 and k = 33
<u>Substitute in the original relation and solve for x as follows:</u>

<u>Part b:</u>
We are given that y = 11 and x = 5.2
<u>Substitute in the original relation and solve for k as follows:</u>

<u>Part c:</u>
We are given that x=7.8 and k=72
<u>Substitute in the original relation and solve for y as follows:</u>
to the nearest tenth
Hope this helps :)
Answer: the diagonal is 10 units
Step-by-step explanation:
The rectangle has 2 parallel and equal sides. Each of the 4 angles in a rectangle is 90°. Therefore, the diagonal of the rectangle divides it into 2 equal right angle triangles and the diagonal represents the hypotenuse of both right triangles.
To determine the length of the diagonal of the rectangle, d, , we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore
d² = 5² + (5√3)²
d² = 25 + 25×3 = 100
d = √100
d = 10 units