A square has an area of 144m^2 What is the length of each side?

In principle when a function f(x) varies directly with x it suggests that any changes in x results in the equivalent changes in f(x). If we have two variables, i.e. y representing f(x) and x representing itself, any increment/decrement in x will result to the same increment/decrement in y by a factor a, thus we can say that y = ax, implying y and x have the same ratio.

In the given question we know that $f(x) = 45$ when $x=9$ , which translates as

$f(x=9) = 45$

This tells us that $f(x)$ varies by a factor (lets call it) $a$ for a given value of $x$ .

To find this factor we can just divide 45 with 9 which gives: $\frac{45}{9} = 5$

Thus the factor $a$ here is $a=5$ which finally tells us that

$f(x) = 5x$ Eqn (1) our original function.

Since we now know our function we can plug in the value for $x=3$ and solve for $f(x=3)$ as follow:

$f(x=3)= 5*3$

$f(x=3) = 15$

$f(3) = 15$

Looking at the given options in the question we can conclude that the correct answer is Option C = 15

3 0

3 years ago

If DGH ~ DEF, Find the value of X

DIA [1.3K]

Answer:

$x=25$

Step-by-step explanation:

we know that

DGH ~ DEF ---> given problem

Remember that

If two triangles are similar, then the rtio of its corresponding sides is proportional and its corresponding angles are congruent

so

$\frac{DG}{DE}=\frac{GH}{EF}$

substitute the given values

$\frac{52}{91}=\frac{x+3}{2x-1}$

$(2x-1)52=(x+3)91\\104x-52=91x+273\\104x-91x=273+52\\13x=325\\x=25$

4 0

3 years ago

Sin(20)=x/670 ????????

mash [69]

Answer:

229.2

Step-by-step explanation:

Remark

There's a lot in this question. The x is not just any x. It is defined and limited by its relationship with the sine function.

The Sin is defined as Opposite over Hypotenuse in a right triangle. The 670 is the Hypotenuse. You know that by the definition of Sine.

So one thing you should always keep in mind: the x because of where it is in the definition, will always be smaller than the Hypotenuse. So you should get a value less than 670.

Formula

Just as you have it

Sin(20) = x / 670

Solution

Multiply both sides by 570

670 * sin(20) = x

sin(20) = 0.3420

x = 670 * 0.3420

x = 229.2

6 0

2 years ago