The sum of two numbers is 48. The larger number is 7 less than four times the smaller number. Find the numbers.

2 answers:

7 0

Answer: x = 37 and y = 11

Explanation:

Let x be the bigger number
Let y be the smaller number

x + y = 48

But x is 7 less 4 times the smaller number.

=> x = 4y - 7
Substitute this value of x:

4y - 7 + y = 48
5y = 48 + 7
5y = 55
y = 11

Substitute the value of y in to the equation:

x + 11 = 48
x = 48 - 11
x = 37

Therefore, x = 37 and y = 11

scoundrel [369]3 years ago

5 0

Answer:

Larger number = 37

Smaller Number = 11

Step-by-step explanation:

Lets take x as the bigger number and y as the smaller number

x + y = 48

What do we know?

The larger number is 7 less than four times the smaller number

so 4y - 7 = x

Lets replace the equation obove with x

4y - 7 + y = 48

5y - 7 = 48

5y = 48 + 7

y = 55/5

y = 11

Then multiply 11 by 4 11 times 4 = 44 and subtract by 7 44 - 7 = 37

To recheck add 37 to 11 and u should get 48

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The graph of the function showing the path of a soccer ball thrown by a goalie in a video game, f(x) = –0.05x2 + 2.5x + 5.2, is

Tju [1.3M]

Answer:

The correct option is 4.

Step-by-step explanation:

The given function is

$f(x)=-0.05x^2+2.5x+5.2$

Where f(x) is height of the ball and x is the distance.

It is a polynomial function with degree 2. All polynomial functions are defined for all real numbers, therefore the mathematical domain of the function is all real numbers.

$-\infty$

Factorize the given function.

$f(x)=-0.05(x^2-50x-104)$

$f(x)=-0.05(x^2-52x+2x-104)$

$f(x)=-0.05(x(x-52)+2(x-52))$

$f(x) = -0.05 (x - 52) (x + 2)$

Put f(x)=0 to find the x intercepts.

$0 = -0.05 (x - 52) (x + 2)$

Equate each factor equal to 0.

$x=52,-2$

Therefore at x=52 and -2, the graph of f(x) intersects x-axis. Before x=-2 and after x=52 the values of f(x) is negative. Height cannot be negative, therefore reasonable domain is lie between -2 to 52.

Distance cannot be negative, therefore the reasonable domain must be positive.

$0\leq x\leq 52$