A. f(x) =1/2 (4,000)^x

CR 3

enyata [817]

Answer:

A. positive -positive = positive

5 0

3 years ago

F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2) 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:

Given function:

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

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 a, compare the coefficients of x³:

$\implies a=3$

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

$\implies 2a+b=-2$

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

$\implies b=-8$

To find c, 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:

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

Zero Product Property

$\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

How to do this question plz answer me step by step plzz plz

Firdavs [7]

Answer:

24.99 cm

Step-by-step explanation:

We are provided with the radius of the circle so we can use that to solve for the circumference(perimeter) of the circle. The formula to solve for the circumference is 2*pi*r.

2*pi*7 = 14pi = 43.98 cm

Although this is the circumference of the entire circle... To solve for the circumference of a quarter-circle we must find the quarter of that:

43.98 * 1/4 = 10.99 cm

We are already provided with the other two sides, which are both equal to 7 cm since they are radii.

Perimeter = 10.99 +7 + 7 = 24.99 cm

Hope this helps!

8 0

3 years ago

yolanda makes 3 sweaters a day. she sews 6 buttons onto each sweaters she makes. how many buttons will she sew in 3 day

KengaRu [80]

Yolanda will sew 54 buttons in 3 days.

If she sews 3 sweaters a day then, by the end of each day she will have 18. After three days she will have 54.

hope this helps and have an awesome day !

4 0

3 years ago

of the 200 seniors graduating, 50 took an art class while in highschool and 99 were in the band . Only 30 of the students who to

elena-s [515]

Answer:

69 or 71, read below for details.

Step-by-step explanation:

This is unfinished, but I'll answer to my best ability.

200 seniors graduated

99 in band

30 students in art were NOT in band.

I assume the question here is either how many students were in band and art, which would be 69 as 99 - 30 = 69.

If the question is how many students didn't take any electives, the answer is 200 - 99 - 30 = 71.

Message me if you have any questions/clarifications.

8 0

4 years ago