The sum of a number and two is equal to negative seven. Translate this sentence to an equation and then find the number.

Mathematics

1 answer:

dimaraw [331]2 years ago

8 0

Answer: -9

Step-by-step explanation:

Given

The sum of a number and two is equal to negative 7

Suppose x is that number

$\therefore x+2=-7\\\text{add -2 both sides}\\\Rightarrow x+2-2=-7-2\\\Rightarrow x=-9$

So, the number is $-9$ .

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Answer:

$\huge\boxed{(2,\ 3);\ (-1,\ 6)}$

Step-by-step explanation:

$f(x)=x^2-2x+3\to y=x^2-2x+3\\f(x)=-x+5\to y=-x+5\\\\\left\{\begin{array}{ccc}y=x^2-2x+3&(1)\\y=-x+5&(2)\end{array}\right$

substitute (1) to (2):

$x^2-2x+3=-x+5$ add x to both sides

$x^2-2x+x+3=-x+x+5$

$x^2-x+3=5$ subtract 5 from both sides

$x^2-x+3-5=5-5$

$x^2-x-2=0\\\\x^2+x-2x-2=0\\\\x(x+1)-2(x+1)=0\\\\(x+1)(x-2)=0\iff x+1=0\ \vee\ x-2=0\\\\\boxed{x=-1\ \vee\ x=2}$

substitute the values of x to (2):

$x=-1\\\\y=-(-1)+5=1+5=6\\\\\huge\boxed{(-1,\ 6)}\\\\x=2\\\\y=-2+5=3\\\\\huge\boxed{(2,\ 3)}$

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The population of a town can be modeled by P= 22,000 + 125t, where P represents the population and the t represents the number o

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