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2 years ago

The sum of two numbers is 21.The second is 6 times the first number .work out the two numbers

Mathematics

2 answers:

antiseptic1488 [7]2 years ago

5 0

Answer:

Step-by-step explanation:

$n-first\ number\\\text{the second number is 6 times the first number}\\6n-second\ number\\\\\text{the sum is 21:}\\\\n+6n=21\\7n=21\qquad\text{divide both sides by 7}\\\boxed{n=3}\\\\6n=6(3)\\\boxed{6n=18}$

Nimfa-mama [501]2 years ago

4 0

Answer:

Sum of the two numbers is 21 and Second number is six times the first number

x+6x = 21

7x = 21

x = 21/7

x = 3

substitute x value in 6x to find second number,

= 6x

= 6*3

= 18

Therefore first number is 3 and second number is 18

Step-by-step explanation:

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What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

aalyn [17]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

in this problem we have

the point $(5,12)$ is on the line of direct variation

Find the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

the equation is

$y=\frac{12}{5}x$

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

case A) point $(0,0)$

$x=0\ y=0$

Substitute the value of x and y in the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is true

therefore

the point $(0,0)$ is on the line of direct variation

case B) point $(2.5,6)$

$x=2.5\ y=6$

Substitute the value of x and y in the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is true

therefore

the point $(2.5,6)$ is on the line of direct variation

case C) point $(3,10)$

$x=3\ y=10$

Substitute the value of x and y in the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not true

therefore

the point $(3,10)$ is not on the line of direct variation

case D) point $(7.5,18)$

$x=7.5\ y=18$

Substitute the value of x and y in the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is true

therefore

the point $(7.5,18)$ is on the line of direct variation

case E) point $(12.5,24)$

$x=12.5\ y=24$

Substitute the value of x and y in the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not true

therefore

the point $(12.5,24)$ is not on the line of direct variation

case F) point $(15,36)$

$x=15\ y=36$

Substitute the value of x and y in the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is true

therefore

the point $(15,36)$ is on the line of direct variation

therefore

the answer is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

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