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3 years ago

Tell whether the relation is a function. Explain

Mathematics

1 answer:

stira [4]3 years ago

4 0

This relationship is a function because each input has its own output is that makes sense

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Solve The Complex Number System<br><br><img src="https://tex.z-dn.net/?f=x%5E%7B3%7D-125%3D0" id="TexFormula1" title="x^{3}-125=

Ganezh [65]

$\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2)~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-125=0\implies x^3-5^3=0\implies (x-5)(x^2+5x+5^2)=0 \\\\[-0.35em] ~\dotfill\\\\ x-5=0\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula}$

$\bf \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{+25} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-5\pm\sqrt{5^2-4(1)(25)}}{2(1)}\implies x=\cfrac{-5\pm\sqrt{25-100}}{2} \\\\\\ x=\cfrac{-5\pm\sqrt{-75}}{2}~~ \begin{cases} 75=&3\cdot 5\cdot 5\\ &3\cdot 5^2 \end{cases}\implies x=\cfrac{-5\pm\sqrt{-3\cdot 5^2}}{2}$

$\bf x=\cfrac{-5\pm 5\sqrt{-3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1\cdot 3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1}\cdot \sqrt{3}}{2} \\\\\\ x=\cfrac{-5\pm 5i\sqrt{3}}{2}\implies \boxed{x= \begin{cases} \frac{-5+ 5i\sqrt{3}}{2}\\\\ \frac{-5-5i\sqrt{3}}{2} \end{cases}}$

6 0

3 years ago

What subset of real numbers does 18.5 inches belong to?

Julli [10]

Answer:

The correct answer is rational.

Step-by-step explanation:

The diameter of the tree belongs to the subset of rational numbers.

Natural numbers are the numbers 1, 2, 3 4, etc. Since 18.5 has a fractional/decimal component, it is not considered a natural number. Whole numbers include all of the natural numbers, as well as 0; therefore, 18.5 is not a whole number either.

Integers include all whole numbers as well as negative numbers, but the integer category still does not encompass numbers with a decimal component. For this reason, 18.5 is not an integer either.

Therefore, the only subset of numbers that 18.5 can fall under is rational numbers. A rational number is a number that can be represented as a fraction. 18.5 can be represented as 37/2 and is thus a rational number.

You can also refer to the infographic given in the question for further clarity on which subsets of numbers are more inclusive than others.

Hope this helps!

5 0

3 years ago

Given the coordinates below, what is the midpoint of AB?<br> A(-6, -10)<br> B(2,5)

madreJ [45]

Given :

$\:$

A(-6, -10)
B( 2, 5)

$\:$

$\gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}$

$\:$

Let's solve by using midpoint formula :

$\:$

$\bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}$

$\:$

$\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}$

$\:$

$\: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}$

$\:$

$\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}$

$\: \:$

$\underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓$

Hope Helps! :)

6 0

2 years ago

Complete the number sentence to solve. Enter the answer in simplest form. Four students share 6 granola bars equally. How many g

nata0808 [166]

Answer:

1.5 bars of granola per student

Step-by-step explanation:

Number of students = 4

Number of granola bars = 6

Four students share 6 granola bars equally.

Each student gets = 6 ÷ 4

= 1 1/2

= 1.5 bars of granola per student

Each student's share is 1.5 granola bars.

3 0

3 years ago

How do this problem?

Naily [24]

1/5(3x - 0.5) + 1/6= x/5 + 0.5
change decimals to fractions (0.5=1/2)

1/5(3x - 1/2) + 1/6= x/5 + 1/2
multiply 1/5 by each term in parentheses

(1/5*3x) + (1/5*-1/2) + 1/6= x/5 + 1/2
multiply within parentheses

3x/5 - 1/10 + 1/6= x/5 + 1/2

need a common denominator; all denominators go into 30

18x/30 - 3/30 + 5/30= 6x/30 + 15/30
combine like terms

18x/30 + 2/30= 6x/30 + 15/30
subtract 6x/30 from both sides

12x/30 + 2/30= 15/30
subtract 2/30 from both sides

12x/30= 13/30
multiply both sides by 30 to eliminate fractions

(12x/30)(30)= (13/30)(30)
12x= 13
divide both sides by 12

x= 13/12 or 1.083333

ANSWER: x= 13/12 or 1.083333

Hope this helps! :)

7 0

3 years ago

Read 2 more answers