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2 years ago

Consider the quadratic function f(x)= 9x^2+30x+25=0

Mathematics

1 answer:

Alchen [17]2 years ago

4 0

Answer:

D) 0

There is 1 real solution.

Step-by-step explanation:

Hi there!

$f(x)= 9x^2+30x+25=0$

This is written in standard form:

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

This means:

a=9

b=30

c=25

The discriminant states:

$D=b^2-4ac$

If D>0, there are 2 real solutions.

If D=0, there is 1 real solution.

If D<0, there are 2 complex solutions.

Plug in the values:

$D=30^2-4(9)(25)\\D=0$

Therefore, there is 1 real solution.

I hope this helps!

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A rental car company offers a rental package for a mid-size car.

skelet666 [1.2K]

Answer:

$y=45x+40$

Step-by-step explanation:

Let

x -----> the number of days

y ----> the total cost in dollars,

we know that

The equation of a linear function in slope intercept form is equal to

$y=mx+b$

where

m is the slope o rate of the linear equation

b is the y-coordinate of the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem we have

The slope is equal to the rental cost per day

$m=45\frac{\$}{day}$

When the number of days is equal to zero (x=0) the total cost is equal to $40 (administrative fee for the cleaning and maintenance of the car)

The y-intercept is the point (0,40)

$b=\$40$

substitute the values

$y=45x+40$

8 0

2 years ago

A charter airline finds that on its Saturday flights from Philadelphia to London, all 120 seats will be sold if the ticket price

Nataliya [291]

Answer:

a) $P=3(120-s)+200$

b) $215 \leq P \leq 290$

Step-by-step explanation:

For this case we can use a linear model to solve the problem.

s) Create an equation to express the increase on the price tickets and the number of seats sold

$s$ number of seats, if w analyze the info given the number of seats after increase the price is given by $120-s$ .

And let P the price for the ticket. So after the increase in ticket price the expression for the increase is P-200.

We have an additional info, for each increase of $3 the number of setas decrease 1. And the equation that gives to us the price change in terms of the increase of price is:

$P-200=3(120-s)$

So then our linear equation is given by:

$P=3(120-s)+200$

b) Over a certain period, the number of seats sold for this flight ranged between 90 and 115. What was the corresponding range of ticket prices?

So for this case we just need to replace the limits into the linear equation and see what we got:

$P_L=3(120-90)+200=290$

$P_U=3(120-115)+200=215$

So the corresponding range of ticket prices is:

$215 \leq P \leq 290$

4 0

2 years ago

If y varies inversely with x, and y=-5 when x=20, find X when y-4.

larisa [96]

Answer:

x=-25

Step-by-step explanation:

looked it up

4 0

2 years ago

What are the real roots of 2x^3+9x^2+4x-15=0

klemol [59]

Well, luckily it is apparent that (x-1) is a root because when x=1 the equation is equal to zero. So we can divide the equation by that factor to find the other roots.

(2x^3+9x^2+4x-15)/(x-1)
2x^2 r 11x^2+4x-15
11x r 15x-15
15 r 0

(x-1)(2x^2+11x+15)=0

(x-1)(2x^2+6x+5x+15)=0

(x-1)(2x(x+3)+5(x+3))=0

(x-1)(2x+5)(x+3)=0

So the roots are x= -3, -2.5, 1

8 0

3 years ago

Find variable values for two variables in an equation

never [62]

Simplifying

2x + 3y = 12

Solving

2x + 3y = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3y' to each side of the equation.

2x + 3y + -3y = 12 + -3y

Combine like terms: 3y + -3y = 0

2x + 0 = 12 + -3y

2x = 12 + -3y

Divide each side by '2'.

x = 6 + -1.5y

Simplifying

x = 6 + -1.5y

5 0

2 years ago