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3 years ago

At how many points does the graph of the function below intersect the x-axis?

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

6 0

Setting y=0, we can solve the quadratic equation or factor the polynomial to
(5x-1)•(5x-1) = 0
(5x-1)^2 = 0
5x-1=0
x=1/5 or 0.2
So there is only one root and the function intersects the x-axis at only one point.
The answer is B. 1.

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icang [17]

Answer:

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3 years ago

If x+a is a factor of 2x²+2ax+5x+10,find a.

vazorg [7]

If $x+a$ is a factor of the polynomial, it means that $-a$ is a root of the polynomial.

In fact, if a polynomial $p(x)$ has a root $x_0$ (i.e. $p(x_0)=0$ ), then the polynomial is divisible by $(x-x_0)$

In your case, you know that the polynomial is divisible by $(x+a)=(x-(-a))$ , so $-a$ is a solution.

Let's evaluate $p(-a)$ and set it to zero:

$2(-a)^2+2a(-a)+5(-a)+10 = 0 \iff 2a^2-2a^2-5a+10=0 \iff -5a+10 = 0 \iff a = 2$

We can check the answer: if $a=2$ the polynomial becomes

$2x^2+2(2)x+5x+10 = 2x^2+9x+10$

And we're claiming that $-a=-2$ is a root of this polynomial:

$2(-2)^2+9(-2)+10 = 2\cdot 4 - 18 + 10 = 0$

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3 years ago

Isaac is making sandwiches for a group of friends. He needs 3 ounces of meat for each sandwich.

lidiya [134]

Answer:

Part A: x=3

Part B: 6oz

3x=18

Step-by-step explanation:

Part A-

So, he needs 3 oz for each sandwich.

This gives us 3 for the equation.

The question says that we need an equation for this.

If we need an equation, we could write something like

x=3

There's really not anything else that we could write here.

Part B-

We now have something that we need to write.

He has 18 oz for sandwiches.

Each sandwich needs 3 oz.

So, we can write something like 3x=18

Then we could solve the equation by dividing both sides by 3.

This will leave us with x=6

Hope this works!

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