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3 years ago

7

Which of the following relations is a function?

1 answer:

djyliett [7]3 years ago

7 0

Answer & Step-by-step explanation:

The definition of a function is that every input, x, must have only one output, y. So, for every x value, there should be only one y value with it. If you have two x values that are the same and have different y values, then that is not a function. The only answer that showcases this is letter D.

<em>1 → 2</em>

<em>2 → 3</em>

<em>3 → 4</em>

<em>4 → 5</em>

In this function, every input has one output and each x value is different.

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Of the girls on the Alden Middle School soccer team, % also play on a travel team. How many of the girls on the middle school te

Wewaii [24]

Answer:

The question is incomplete, so I looked for similar ones and found:

<em>Of the 25 girls on the Alden Middle School soccer team, 40% also play on a travel team. How many of the girls on the middle school team also play on a travel team? </em>

we can solve this the following way:

25 girls on the soccer team x 40% that play on a travel team = 10 girls form the soccer team that play on a travel team

we can also multiply (25 girls x 40) / 100 = 10 girls

we can check our work by:

10 girls / 40% = 25 girls in total

8 0

3 years ago

F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

<u>Given function</u>:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find <em>a</em>, compare the coefficients of x³:

$\implies a=3$

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find <em>c</em>, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

<u>Zero Product Property</u>

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

1 year ago

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Elden [556K]

Answer:

The Answer is 2

Step-by-step explanation:

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Answer:

2nd option is the answer

Step-by-step explanation:

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Answer:

the answer is b

Step-by-step explanation:

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3 years ago