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Alekssandra [29.7K]

2 years ago

6

What is the x-coordinate of the vertex of the parabola whose equation is y = 3x² + 9x?

1 answer:

saveliy_v [14]2 years ago

3 0

Answer: -3/2

Step-by-step explanation:

The axis of symmetry, and thus the x-coordinate of the vertex, is given by $x=-\frac{b}{2a}$

So, the answer is $x=-\frac{9}{2(3)}=\boxed{-\frac{3}{2}}$

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Find the perimeter of the triangle with vertices (−2,2), (0,4), and (1,−2). the perimeter is . round to the nearest hundredth.

mina [271]

The answer is about 12.5 (when rounded to the nearest 10th).

This can be found using the distance formula between each point. One distance is 5, one is $\sqrt{2}$ and one is $\sqrt{37}$ . Added together gives you the answer above.

4 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

Write an equation in slope-intercept form given the point and the slope. Then graph the equation.

liq [111]

Answer:

y=-3/4x+5.5

Step-by-step explanation:

5 0

3 years ago

Find x<br><br> plz help!!!!!!!!

kompoz [17]

<span>'x' can be anything. There's no information here to say that it must be
one thing or another. You can't find 'x', because there is no equation.

You can probably simplify the fraction by doing some factoring, but there's
no way to tell a value for 'x'. As long as 'x' is not -4, it can be anything, and
its value determines the value of the fraction.</span>

7 0

4 years ago

Read 2 more answers

Find the area of the following shape. You must show all work to receive credit.

almond37 [142]

Answer:

10

Step-by-step explanation:

Hope this helps!

Brainliest pls

Have a great day!

4 0

3 years ago