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Sonja [21]
3 years ago
7

Quentin is one third the age of his aunt. And 20% older than his sister. If Quentin's sister is 15 years old, how old is his aun

t?
Mathematics
2 answers:
s2008m [1.1K]3 years ago
7 0

Answer:

54

Step-by-step explanation:

Q is 20% older than his sister so 15+20%=18 and 18=1/3 aunts age

So 18x3=54

anastassius [24]3 years ago
5 0

Answer:

54

Step-by-step explanation:

20% of 15 is 3 so Quentin is 18 years old

If Quentin is one thrid his Aunt's age that means his aunt is three times older.

18 * 3 = 54

So his Aunt is 54 years old

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What is the equation of the line shown in the graph? (-3,1) (2,-4)
ki77a [65]

Answer:

x + y = -2

Step-by-step explanation:

The two primary equations to remember when dealing with graphing 2-variable equations are: ax + by = c (a & b are the x & y coefficients, respectively), and the other is y = mx + c (m = slope, x & y represent themselves). There is another equation to find the slope. If not already known, it's: ∆y/∆x {∆(aka Delta) = difference}. So, since that's all been established, we can proceed to calculate your question:

1) Find your slope: 1 - (-4) = 5 for your y-variable. And -3 - 2 = -5 for your x-variable. So your slope = 5/-5 = -1

2) Use the y = mx + c equation together with either set of (x,y) coordinates to get the equation 1 = (-1)(-3) + c. Which gives you c = -2

3) So, going back to the main equation to remember, the ax + by = c, use a one of your given sets of x,y coordinates and input your known values for x, y, & c to get: a(-3) + b(1) = (-2) and do the same with other set (these are just double-checks, coefficients are all equal to 1 anyways). So, you should arrive to the equation: x + y = -2

4 0
3 years ago
Factorise <img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class="lat
Amanda [17]

Answer:

a1= 1   q= −sinx  , dla |q| <1   , ta suma jest zbieżna  

 a1   1  

S=  

=  

 1 −q   1+sinx  

w mianowniku podobnie:   a1=1  ,  q= sinx  , dla  | sinx| <1

 1  

S=  

 1 −sinx  

i mamy równanie:

 

1  

1+sinx  

 

 

= tg2x

 

1  

1− sinx  

 

Step-by-step explanation:

5 0
2 years ago
What is 500000 and 60000000 as a decimal
Juliette [100K]

The only way to make a decimal out of either of those numbers is to write a decimal point with some zeros after it.

500,000  =  500,000.000

60,000,000  =  60,000,000.00000

etc.

3 0
3 years ago
Factor 2m^3-12m^2+18m completely
Nina [5.8K]

Answer:

The answer is A.

Step-by-step explanation:

Firstly, you have to take out the common terms for this expression. In this expression, the common terms ard 2 and m :

2 {m}^{3}  - 12 {m}^{2}  + 18m

= 2( {m}^{3}  - 6 {m}^{2}  + 9m)

= 2m( {m}^{2}  - 6m + 9)

Next you have to factorise the brackets :

{m}^{2}  - 6m + 9

=  {m}^{2}  - 3m - 3m + 9

= m(m - 3) - 3(m - 3)

= (m - 3)(m - 3)

=  {(m - 3)}^{2}

So the final answer is :

2m {(m - 2)}^{2}

6 0
3 years ago
Read 2 more answers
A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep
prohojiy [21]
The sketch of the parabola is attached below

We have the focus (a,b) = (2, -0.5)
The point P(x,y)
The directrix, c at y=-1.5

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; (2, -0.5) and (x,y).
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
\sqrt{ (x-a)^{2}+ (y-b)^{2} }

Step 2
Find the distance between the point P to the directrix c. It is a vertical distance between y and c, expressed as y-c

Step 3
The equation of parabola is then given as 
\sqrt{ (x-a)^{2}+ (y-b)^{2} }=y-c
(x-a)^{2}+ (y-b)^{2}= (y-c)^{2} ⇒ substituting a, b and c
(x-2)^{2}+ (y--0.5)^{2}  = (y--1.5)^{2}
(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}⇒Rearranging and making y the subject gives

y= \frac{ x^{2} }{2} -2x+1

7 0
3 years ago
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