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3 years ago

Melinda has shown that a function, f(x), increases by 4 for every unit in the domain. What does this prove?

Mathematics

2 answers:

inn [45]3 years ago

5 0

It proves The function f(x) is an arithmetic sequence.

loris [4]3 years ago

5 0

Answer:-The function f(x) is an arithmetic sequence.

Explanation:-

Let $a_1$ be the initial value

According to the question

$a_2=a_1+4$

$a_3=a_2+4\\\Rightarrow\ a_3=(a_1+4)+4\\\Rightarrow\ a_3=a_1+4+4\\\Rightarrow\ a_3=a_1+2(4)\\\Rightarrow\ a_3=a_1+2\times4\\\Rightarrow\ a_3=a_1+(3-1)4$ and so on

Thus, we can write a formula for the term n of an arithmetic sequence in the form:

$a_n=a_1+(n-1)4$

where, n=1,2,3,4,....

4= common difference

Therefore, the function f(x) is an arithmetic sequence.

An arithmetic sequence is a sequence of numbers in which each term increases or decreases by a constant number.

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(2 − 3)(1 − ) − (3 − )(3 + )

Lostsunrise [7]

Answer:

your equation is wrong!! the answer is $10$

Step-by-step explanation:

the correct order of the equation is:

$(2-3)(-1)-(-3)(3)$

first, solve in the parentheses from left to right:

$(2-3)(-1)-(-3)(3)=\\(-1)(-1)-(-3)(3)=\\1-(-3)(3)=\\$

If we have 2 negative signs then we will change them to positive :

$1-(-3)(3)=\\1+3(3)\\$

now we have an equation with parentheses, we will multiply $3(3)\\$ because the parentheses go first.

$1+3(3)=\\1+9=10$

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2 years ago

Help me solve it please

snow_tiger [21]

Answer:

$\fbox{\begin{minipage}{5.8 em}x =5.97 cm\end{minipage}}$

Step-by-step explanation:

(1) As definition, the area ( $A$ ) of a circle is calculated by:

$A = \pi$ x $r^{2}$ with $r$ is radius of circle.

(2) The relation between radius ( $r$ ) and diameter ( $d_{1}$ ) of a circle is:

$d_{1}$ = 2 x $r$

(3) Applying the Pythagorean theorem for a square with sides of length $x$ ,

the relation between side $x$ and diagonal $d_{2}$ is:

$x^{2} +x^{2} = d^{2} \\or\\2x^{2} = d^{2}$

=> The diagonal ( $d_{2}$ ) of that square is calculated by:

$d_{2}$ = $x\sqrt{2}$

(4) The square fits exactly inside a circle, with each of its vertices being on the circumference of the circle.

Applying the theorem of inscribed angle in a circle, the measure of arc BD is twice as the measure of inscribed angle BAD.

In other words, the measure of arc AC = 2 x 90 = 180 deg, or half of circle.

It means that the diagonal BD is coincide with a diameter of circle.

=> $d_{1} = d_{2}$

or $2$ x $r$ = $x\sqrt{2}$

or $r$ = $x\frac{\sqrt{2} }{2}$

Substitute $r$ back into original formula used for calculating the area of circle:

=> A = $\pi$ x $(x\frac{\sqrt{2}}{2})^{2}$ = $\pi$ x $\frac{x^{2}}{2}$

=> $x^{2} = A$ x $\frac{2}{\pi }$

=> $x = \sqrt{A}$ x $\sqrt{\frac{2}{\pi } }$ = $\sqrt{56}$ x $\sqrt{\frac{2}{\pi } }$ = 5.97 cm

Hope this helps!

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