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2 years ago

Y=−4(x+2) ^2 −1. Graph the equation

Mathematics

1 answer:

Kitty [74]2 years ago

3 0

Answer:

4x^2+15

Step-by-step explanation:

1. multiply whole parenthesis by power of 2

2. gets you 4(x^2+4)-1

3.Multply and it gets you 4x^2+16-1 so it would be 4x^2+15 for your answer

4. throw that into your calculator and make sure its not on radian mode and then press graph

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NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.

Oliga [24]

Answer:

$\displaystyle 1)48.2 \: \: \text{sec}$

$\rm \displaystyle 2)3021.6 \: m$

Step-by-step explanation:

<h3>Question-1:</h3>

so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

$\displaystyle - 4.9 {t}^{2} + 229t + 346 = 0$

to solve the equation can consider the quadratic formula given by

$\displaystyle x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 ac} }{2a}$

so let our a,b and c be -4.9,229 and 346 Thus substitute:

$\rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}$

remove parentheses:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}$

simplify square:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)}$

simplify multiplication:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8}$

simplify Substraction:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8}$

by simplifying we acquire:

$\displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5$

since time can't be negative

$\displaystyle t = 48.2$

hence,

at 48.2 seconds splashdown occurs

<h3>Question-2:</h3>

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

$\displaystyle x _{ \text{max}} = \frac{ - b}{2a}$

let a and b be -4.9 and 229 respectively thus substitute:

$\displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)}$

simplify which yields:

$\displaystyle t _{ \text{max}} = 23.4$

now plug in the maximum t to the function:

$\rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346$

simplify:

$\rm \displaystyle h(23.4) = 3021.6$

hence,

about 3021.6 meters high above sea-level the rocket gets at its peak?

5 0

2 years ago

WILL MARK BRAINLIEST!!!

butalik [34]

The distance between the horizontal legs be the distance between the 'x' values '-5' and '2'. 2+5=7 (It is +5 because the distance between -5 and 0 is 5*)
The distance between the horizontals is 7

Same with the vertical points, as the distance is 2. (1+1=2)

Considering that the pythagorean theorem is the a^2+b^2=c^2, and 'a' and 'b' are the sides, then you plug in '7' and '2', making the equation 7^2+2^2=c^2
49+4=c^2
53=c^2
c=sqrt(53)
Hope this helps.

4 0

2 years ago

Read 2 more answers

I'll mark you as the brainiest if you get this correct thx xxx This homework is due tomorrow thx sm for your help

Juli2301 [7.4K]

Answer:

7:21

Step-by-step explanation:

Lcm(9,12)=9*4=36 minutes later

That is

6:45+36min=7:21

6 0

3 years ago

Can somebody please help m eits 9th grade math im so confused !

prisoha [69]

Answer:

Option 3: (5, 1)

Step-by-step explanation:

There are several ways of solving for systems of linear equations, either through graphing, substitution, or elimination.

The graphing method is the easiest, as you only need to plot points on the graph using the y-intercepts and the slopes.

I will be demonstrating the graphing method.

Given the systems of linear equations:

Equation 1: y = x - 4

where the slope, m = 1, and y-intercept (0, -4).

Equation2: y = -x + 6

where the slope, m = -1, and y-intercept (0, 6).

The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b).

<h3>Graphing Instructions:</h3>

For Equation 1, plot the y-intercept, (0, -4) on the graph. Then use the slope, m = 1 (rise 1 unit, run 1 unit) to plot other points on the graph. Repeat this process until you have enough points to connect a line with.

Repeat these same procedures for graphing Equation 2, start by plotting its y-intercept at (0, 6), and its slope, m = -1 (down 1 unit, run 1 unit).

<h3>Solution: </h3>

The intersection of both lines occurs at point, (5, 1), which is solution to the given systems of linear equations. Therefore, the correct answer is the third option, (5, 1).

Attached is the screenshot of the graphed systems of linear equations, where it shows the point of intersection at (5, 1).

5 0

2 years ago

The sum of three consecutive integers is 48. What are the three numbers?

Alinara [238K]

What three consecutive integers have a sum of 48? Which means that the first number is 15, the second number is 15 + 1 and the third number is 15 + 2. Therefore, three consecutive integers that add up to 48 are 15, 16, and 17.

7 0

3 years ago