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2 years ago

Felix is now six times as old as Debbie. In twelve years time Felix will be two times as old as Debbie. How old are they

Mathematics

1 answer:

Minchanka [31]2 years ago

6 0

Step-by-step explanation:

let debbie be x years

let felix be 6x years

in 12 years felix will be 2x older than debbie

do the calc

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4x + 8y=20<br> 3x+6y=15<br> solve this system of equations

laila [671]

4x=20-8y

x=5-2y now use this value of x in the second equation...

3(5-2y)+6y=15

15-6y+6y=15

15=15 This is true for any y or x value.

So there are infinitely many solutions as the two equations describe the same line.

5 0

3 years ago

Read 2 more answers

A friend claims that it will rain today with probability 30% and tomorrow with probability four times as great as today. Which o

alexgriva [62]

Answer:

The claim cannot be true because any probability is between 0 and 1

Step-by-step explanation:

Probability is a concept used to mathematically provide a measure or determine the possibility that an event will occur. However, due to the nature of upcoming events, it is almost impossible to predict some events with absolute certainty, therefore, the chance of an event can be predicted based on the likelihood of the event occurring with probability values ranging from 0 to 1 or 0% to 100%. Where a value of 0 or 0% shows that it is certain that the event will not occur, while 1 or 100% indicates that it absolutely certain that an event will occur.

6 0

3 years ago

Suppose that the functions r and a are defined for all real numbers x as follows. r(x)=2x-1 S(x)=5x write the expressions for (r

NeTakaya

$\boxed{(r-s)(x)=-3x-1} \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x} \\ \\ \boxed{(r+s)(-2)=-15}$

<h2>Explanation:</h2>

In this exercise, we have the following functions:

$r(x)=2x-1 \\ \\ s(x)=5x$

And they are defined for all real numbers x. So we have to write the following expressions:

First expression:

$(r-s)(x)$

That is, we subtract s(x) from r(x):

$(r-s)(x)=2x-1-5x \\ \\ Combine \ like \ terms: \\ \\ (r-s)(x)=(2x-5x)-1 \\ \\ \boxed{(r-s)(x)=-3x-1}$

Second expression:

$(r\cdot s)(x)$

That is, we get the product of s(x) and r(x):

$(r\cdot s)(x)=(2x-1)(5x) \\ \\ By \ distributive \ property: \\ \\ (r\cdot s)(x)=(2x)(5x)-(1)(5x) \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x}$

Third expression:

Here we need to evaluate:

$(r+s)(-2)$

First of all, we find the sum of functions r(x) and s(x):

$(r+s)(x)=2x-1+5x \\ \\ Combine \ like \ terms: \\ \\ (r+s)(x)=(2x+5x)-1 \\ \\ (r+s)(x)=7x-1$

Finally, substituting x = -2:

$(r+s)(-2)=7(-2)-1 \\ \\ (r+s)(-2)=-14-1 \\ \\ \boxed{(r+s)(-2)=-15}$

<h2>Learn more: </h2>

Parabola: brainly.com/question/12178203

#LearnWithBrainly

5 0

3 years ago

Terrell wants to Drive his car at a speed of 50 miles per hour for 2.75 hours. His car has a fuel efficiency of 25 miles per gal

Oduvanchick [21]

HI there! To find the number of gallons he needs for travel, the first step we need to do is find the number of miles he'll travel, by multiplying speed by time. 50 * 2.75 is 137.5. Terrell will travel 137.5 miles in 2.75 hours. There are 25 miles in a gallon. Now, let's divide the number by 25 to get the number of gallons. 137.5 / 25 = 5.5. There. Terrell will need 5.5 gallons of gas for his journey.

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3 years ago

Read 2 more answers

g 1.32 Two points on a sphere of radius 3 are given as P1(3,0,30) and P2(3,45,45): (a) Find the position vectors of P1 and P2. (

Rama09 [41]

Answer:

a) P.V of is OP₁ = [ 1.5i + 0j + 2.6k ], P.V of is OP₂ = [ 1.5i + 1.5j + 2.12k ]

b) Vector connecting P₁ to P₂ is [ 0i + 1.5j + 0.48k ]

c) cylindrical coordinates are (1.5, π/2, 0.48)

Step-by-step explanation:

Given that;

r = 3

P₁ ( 3, 0°, 30° ), P₂ ( 3, 45°, 45° )

P.V of P₁

x = rcos∅sin∅ = 3(cos0°) ( sin30°) = (3 × 1 × 0.5) = 1.5

y = rsin∅sin∅ = 3(sin0°) (sin30°) = (3 × 0 × 0.5) = 0

z = rcos∅ = 3(cos30°) = ( 3 × 0.866) = 2.6

∴ P.V of is OP₁ = [ 1.5i + 0j + 2.6k ]

P.V of P₂

x = rcos∅sin∅ = 3(cos45°) ( sin45°) = (3 × 0.7071 × 0.7071) = 1.5

y = rsin∅sin∅ = 3(sin45°) (sin45°) = (3 × 0.7071 × 0.7071) = 1.5

z = rcos∅ = 3(cos45°) = ( 3 × 0.7071) = 2.12

∴ P.V of is OP₂ = [ 1.5i + 1.5j + 2.12k ]

Vector connecting P₁ to P₂ is given by

OP₂ - OP₁ = [ 1.5i + 1.5j + 2.12k ] - [ 1.5i + 0j + 2.6k ]

= [ 0i + 1.5j + 0.48k ]

P₁P₂ → = [ 0i + 1.5j + 0.48k ] = [ 1.5j + 0.48k ]

so in a cylindrical coordinate, it should be

r = √(o² + 1.5²) = 1.5

∅ = tan⁻¹[y/π] = π/2

z = 0.48

cylindrical coordinates are (1.5, π/2, 0.48)

5 0

3 years ago

Felix is now six times as old as Debbie. In twelve years time Felix will be two times as old as Debbie. How old are they​

Felix is now six times as old as Debbie. In twelve years time Felix will be two times as old as Debbie. How old are they