Anyone wanna help with the lesson proportional reasoning with percents it’s 12 questions

Consider the quadratic function f(x)=−x^2+x+30

yaroslaw [1]

Answer:

The smallest xx-intercept is $x = -5$

The largest xx-intercept is $x = 6$

The yy-intercept is $y = 30$ .

Step-by-step explanation:

Given a quadratic function in the following format:

$f(x) = ax^{2} + bx + c = 0, a \neq 0$

The x-values of the x-intercepts are $x_{1}, x_{2}$ , given by the following formulas.

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

We have that:

$f(x) = -x^{2} + x + 30$

This is not in the format above. I will multiply by (-1), so we have:

$f(x) = x^{2} - x - 30$

So, $a = 1, b = -1, c = -30$

$\bigtriangleup = b^{2} - 4ac = (-1)^{2} - 4*(1)*(-30) = 1 + 120 = 121$

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a} = \frac{-(-1) + \sqrt{121}}{2(1)} = \frac{12}{2} = 6$

$x_{2} = \frac{-b + \sqrt{\bigtriangleup}}{2*a} = \frac{-(-1) - \sqrt{121}}{2(1)} = \frac{-10}{2} = -5$

This means that

The smallest xx-intercept is $x = -5$

The largest xx-intercept is $x = 6$

The y-intercept is the value of f(x) when x = 0. So

$f(x)=−x^{2}+x+30$

$f(0) = 30$

The yy-intercept is $y = 30$ .

5 0

3 years ago

Which graph shows the linear inequality y < 2x – 4?

yuradex [85]

Answer:

Graph the line

y = 2 x − 4

After you have plotted the line, shade in the area to right of the line.

To help you to graph the line, two points are

( 0 , − 4 ) and ( 2, 0 )

Remember to make it a dashed line to indicate that it is not included.

Here is a how it should look:

5 0

3 years ago

Multiply x^1/3 times x^3/7

sladkih [1.3K]

$x^{\tfrac{1}{3}}\cdot x^{\tfrac{3}{7}}=\\\\
x^{\tfrac{1}{3}+\tfrac{3}{7}}=\\\\
x^{\tfrac{7}{21}+\tfrac{9}{21}}=\\\\
x^{\tfrac{16}{21}$

8 0

4 years ago

Which is the biggest number 2.07 2.24 2.4 2 2.04

Temka [501]

Among all these no., see the first no. that lies before or left side of decimal point, here... 2 is common so next check the no. After decimal... 2.0, 2.2, 2.4, 2 is considered as 2.0 and then we have 2.0... Let's not take 2.0s and let's take 2.2 and 2.4 which is greater than 2.0. Next see the second no. That comes after decimal We have 2.24 and 2.4 which can be taken as 2.40... The no.s after decimal, 24 is greater than 40 so 2.4 is greater...

3 0

4 years ago

42 students are going on a field trip and need to ride in a bus. Each bus can hold 4 students. How many buses will the students

Ivenika [448]

Answer:

11 buses

Step-by-step explanation:

Divide 42 by 4 to get 10 and a remainder of 2. The 2 students not on the bus need another bus so you need 10+1=11 buses

8 0

3 years ago