All categories

4 years ago

The function F is defined by F(x)=x^2+3X-10

Mathematics

1 answer:

vesna_86 [32]4 years ago

7 0

Answer:

k = 13

smallest zero = -6

Step-by-step explanation:

f(x) is basically the function of x.

x could be any integer. f(x) is the solution of the function of x.

f(x) is defined as x² + 3x - 10

f(x) = x² + 3x - 10

Now, f(x+5) = x² + kx + 30

This statement here says that if the value of x is x+5, then the answer would be x² + kx + 30.

f(x) = x² + 3x - 10

f(x+5) = (x+5)² + 3(x+5) - 10

f(x+5) = x² + 10x + 25 + 3x + 15 - 10

f(x+5) = x² + 13x + 40 - 10

f(x+5) = x² + 13x + 30

x² + 13x + 30 = x² + kx + 30

hence, k = 13

Smallest zero = The smallest x value.

f(x+5) = x² + 13x + 30

Let's take f(x+5) = 0

x² + 13x + 30 = 0

which two numbers products give us 30 and add up to 13?

== 6 and 5

(x+6)(x+5) = 0

x+6 = 0

x = -6

x+5 = 0

x = -5

The two solutions are -6 and -5

The smallest out of these two is -6.

You might be interested in

JT = 5x+ 8 CT = 70, and CJ = 7x + 2 Find JT

defon

Answer:33

Step-by-step explanation: took one for the team

8 0

3 years ago

Alejandro uses the steps below to convert

dezoksy [38]

Answer:

The division was computed incorrectly.

Step-by-step explanation:

Given

Workings:

$\frac{5}{8}$ to percentage

$\frac{8}{5} = 1.6 = 160\%$

Required

Explain his error

The question says 5/8

Instead, Alejandro's working shows 8/5.

This working is done in an incorrect order and the correct solution is:

Let

$x = \frac{5}{8}$

Solve the fraction

$x = 0.625$

Multiply by 100%

$x = 0.625 * 100\%$

$x = 62.5\%$

Hence, option (a) is correct.

7 0

3 years ago

question; The chart below shows the number of tickets to the annual teachers vs. students basketball game. How many tickets did

Marianna [84]

31-40. C. 12 students sold that many, therefore it's the most.

5 0

3 years ago

A line joins the point

Harrizon [31]

Intersection of the first two lines:

$\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}$

Multiply the first equation by 4 and the second by 5:

$\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}$

Subtract the two equations:

$(20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1$

Plug this value for y in one of the equation, for example the first:

$5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1$

So, the first point of intersection is $(-1,-1)$

We can find the intersection of the other two lines in the same way: we start with

$\begin{cases}x=y\\x=3y+4\end{cases}$

Use the fact that x and y are the same to rewrite the second equation as

$x=3x+4 \iff 2x=-4 \iff x=-2$

And since x and y are the same, the second point is $(-2, -2)$

So, we're looking for a line passing through $(-1,-1)$ and $(-2, -2)$ . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be $y=x$