Question

PLEASE HELP!!!!

Lunna [17]

NOTES:

Given a quadratic function in standard format (y = ax² + bx + c), the direction of the parabola is as follows:

if "a" is positive, then opens UP
if "a" is negative, then opens DOWN

Given a quadratic function in standard format (y = ax² + bx + c), the vertex can be found as follows:

the Axis Of Symmetry (x-value) is: x = $\frac{-b}{2a}$
y-value is found by plugging in the AOS for "x" in the equation

****************************************************************************************

1) y = x² + 11x + 24

a = +1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-11}{2(1)}$ = $-\frac{11}{2}$

y = $(-\frac{11}{2})^{2}$ + 11 $(-\frac{11}{2} )$ + 24 = $-\frac{25}{4}$

vertex $(-\frac{11}{2}$ , $-\frac{25}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-3, 0) and (-8, 0), and y-intercept (0, 24)

******************************************************************************************

2) y = -x² - 6x - 8

a = -1 so the parabola opens DOWN

x = $\frac{-b}{2a}$ = $\frac{-(-6)}{2(-1)}$ = $\frac{6}{-2}$ = -3

y = -(-3)² - 6(-3) - 8 = -9 + 18 - 8 = 1

vertex (-3, 1) is in Quadrant 2 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-4, 0), and y-intercept (0, -8)

******************************************************************************************

3) y = x² - 2x + 3

a = 1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-(-2)}{2(1)}$ = $\frac{2}{2}$ = 1

y = (1)² - 2(1) + 3 = 1 - 2 + 3 = 2

vertex (1, 2) is in Quadrant 1 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 3), and its mirror image (2, 3). <em>There are no x-intercepts</em>

******************************************************************************************

4) y = x² + 4x + 4

a = 1 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-4}{2(1)}$ = -2

y = (-2)² + 4(-2) + 4 = 4 - 8 + 4 = 0

vertex (-2, 0) is in Quadrant 2 and is on the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 4), and its mirror image (-4, 4). <em>The x-intercept is the vertex.</em>

Compared to the other four graphs, this is most likely the equation for the rain gauge!

******************************************************************************************

5) y = 3x² + 21x + 30

a = +3 so the parabola opens UP

x = $\frac{-b}{2a}$ = $\frac{-21}{2(3)}$ = $-\frac{7}{2}$

y = 3 $(-\frac{7}{2})^{2}$ + 21 $(-\frac{7}{2} )$ + 30 = $-\frac{27}{4}$

vertex $(-\frac{7}{2}$ , $-\frac{27}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-5, 0), and y-intercept (0, 30)

*******************************************************************************************

4 0

3 years ago

Read 2 more answers

en una balansa de platillos esta equilibrada, en uno de los platillos hay una piedra, una pesa de un noveno kilogramos y la otra

Komok [63]

Se escribe una equacion y se resolve.

Vamos a usar x para representar el peso de la piedra.

En en platillo que tiene la piedra, el peso total es: x + 1/9 + 2/3

En el otro platillo: 1/2 + 1/3

La balanza esta equilibrada por eso los pesos en los platillos son iguales.

x + 1/9 + 2/3 = 1/2 + 1/3

x + 2/18 + 12/18 = 9/18 + 6/18

x + 14/18 = 15/18

x = 1/18

Respuesta: La piedra pesa un octavo de kilogramo.

3 0

3 years ago

Read 2 more answers

A car starts with a dull tank of gas. After driving around 5he city, 1/7 of the gas has been used. With the rest of the gas in t

Sati [7]

Answer:

$\frac{2}{7}$

Step-by-step explanation:

Given:

A car starts with a dull tank of gas

1/7 of the gas has been used around the city.

With the rest of the gas in the car, the car can travel to and from Ottawa three times.

Question asked:

What fractions of a tank of gas does each complete trip to Ottawa use?

Solution:

Fuel used around the city = $\frac{1}{7}$

Remaining fuel after driving around the city = 1 - $\frac{1}{7}$

= $\frac{7 - 1}{7} = \frac{6}{7}$

According to question:

As from the rest of the gas in the car that is $\frac{6}{7}$ , the car can complete 3 trip to Ottawa which means,

By unitary method:

The car can complete 3 trip by using = $\frac{6}{7}$ tank of gas.

The car can complete 1 trip by using = $\frac{6}{7} \div 3$

= $\frac{6}{7} \times\frac{1}{3}$

= $\frac{6}{21}$

= $\frac{2}{7}$ tank of gas

Thus, $\frac{2}{7}$ tank of gas used for each complete trip to Ottawa.

5 0

3 years ago

There are 1295 students attending a small university there are 714 woman in rolled what percentage of students are woman

MatroZZZ [7]

Answer:

Approximately 55% of enrolled students are women.

Step-by-step explanation:

To find the percentage of a given set of data, you need to divide the number of actual students by the total number of students. In this case, they are wanting the percentage of just women students at the university:

$\frac{women students}{total students} =\frac{714}{1295}$ x 100 = 55%

4 0

3 years ago

You roll a six-sided die. Find the probability of each of the following scenarios

romanna [79]

Answer:

a) $1/2$

b) $5/6$

c) $2/3$

Step-by-step explanation:

a)

Rolling a number greater than 3 means you can roll a 4, 5, or 6, which contains rolling a 6. So, the probability is $(1+1+1)/6=3/6=\boxed{1/2}$

b)

Rolling a number less than 5 means you can roll a 1, 2, 3, or 4, but because you could also roll an even number, so you could also roll a 6.

So, the probability is $(1+1+1+1+1)/6=\boxed{5/6}$

c)

Rolling a 4 or an odd number means you can roll a 1, 3, 5, or 4. So, the probability is $(1+1+1+1)/6=4/6=\boxed{2/3}$

6 0

2 years ago