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2 years ago

At which x value will f(x)=3x+3 exceed g(x)=3x+10

Mathematics

2 answers:

Artyom0805 [142]2 years ago

7 0

There are no x value that allows f(x) to exceed g(x). f(x) is parallel to g(x) and it will always be 7 less than g(x).

Anvisha [2.4K]2 years ago

3 0

We write an inequality:

$f(x) > g(x)$

$3^x + 3 > 3x + 10$

$3^x > 3x + 7$

This equation cannot be solved using trivial methods found in high-school classes, so we resort to graphical examination. $3x+7$ is a linear function while $3^x$ is an exponential one (with limit zero as $x$ approaches $- \infty$ ). We see that $3^x = 3x+7$ at approximately $x=2.4$ and $x=-2.3$ .

Indeed, using a computer algebra system such as the ones on modern TI calculators and on many internet sites gives equality at $x=2.42, -2.31$ . By observing our graph, we see that $f(x) > g(x)$ when $x > 2.42$ or $x < -2.31$ .

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n the graph below determine how many real solutions the quadratic function has, and state them, if applicable. List solutions in

IRINA_888 [86]

Answer:

There are no real solutions.

Step-by-step explanation:

There are 3 options.

2 real solutions: This happens if in the graph, each arm intersects the x-axis, this means that there are two different values of x such that the equation:

a*x^2 + b*x + c

is equal to zero.

Another way to see this, is if the determinant:

b^2 - 4*a*c

is larger than zero.

1 real solution: This happens when the vertex of the graph intersects the x-axis. This means that there is a single value of x such that:

a*x^2 + b*x + c

is equal to zero.

Another way to see this is if the determinant:

b^2 - 4*a*c

is larger equal zero.

No real solution: if in the graph we can not see any intersection of the x-axis, then we do not have real solutions (only complex ones).

Another way to see this is if the determinant:

b^2 - 4*a*c

is smaller than zero.

Now that we know this, let's look at the graph.

We can see that the vertex is below the x-axis, and the arms of the graph go downwards. So the arms will never intersect the x-axis (and neither the vertex).

So the graph does not intersect the x-axis at any point, which means that there are no real solutions for the quadratic equation.

The correct answer would be "none"

3 0

2 years ago

The circumference of a standard bowling ball is about 27 in. To the nearest unit, how many square inches is the surface area of

Sidana [21]

The surface area of a sphere is $S=4 \pi r^{2}$ where r is the radius;
The circumference is $2 \pi r=27 in$ so that $r= \frac{27}{2 \pi }=4.5 in$ using this value we can evaluate the surface area of 1 ball as:
$S=4 \pi r^{2} =4 \pi (4.5)^{2} =254.3 in^{2}$
For 100 ball you get: $100*254.3=25430 in^{2}$

4 0

2 years ago

write the slope-intercept form of the line with a slope of 2 and a y-intercept of -4. include your work in your final answer.

IgorLugansk [536]

I cant really show you how to graph this but i can try to explain it. you would make a 4 quadrant graph and do rise over run.
1)start by making the graph
2) on the line of the graph marked Y is where you would put -4
3) From -4, you would go up (rise) by 2 and go over to the right 1 where you end is the slop