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insens350 [35]
2 years ago
5

Rewrite f(x) into vertex form by completing the square f(x)=−x2+8x+9​

Mathematics
1 answer:
GalinKa [24]2 years ago
3 0

Answer:

vertex  = ( 4  ,  25 )

Step-by-step explanation:

given a parabola in  standard form  y =  a x 2 + b x + c x ; a ≠ 0

then the x-coordinate of the vertex is

X vertex=-b/2a

y=-x2+8x+9 with a=-1 b=8 c=9

X vertex= -8/-2=4

substitute the value on the equation

Y vertex = -(4)squared+8(4)+9=25

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CAN SOMEBODY HELP ME PLEASE
Natasha_Volkova [10]

Answer:

  • vertex (3, -1)
  • y-intercept: (0, 8)
  • x-intercepts: (2, 0), (4, 0)

Step-by-step explanation:

You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.

__

<h3>Vertex</h3>

The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).

<h3>Y-intercept</h3>

The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).

<h3>X-intercepts</h3>

The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).

__

<em>Additional comment</em>

The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.

5 0
2 years ago
The first element in an arithmetic sequence is 2. Its twenty second is 14. Find the value of n so that a(n)=6
Aleks04 [339]

Answer:

<h2>n = 8</h2>

Step-by-step explanation:

Given the nth term of an arithmetic sequence to be Tn = a+(n-1)d

a = first term of the sequence

n = number of terms

d = common difference.

Given the first element a = 2 and 22nd to be 14

T22 = a+(22-1)d = 14

a+21d = 14

Substtuting a = 2 into the equation to get d

2+21d = 14

21d = 12

d = 12/21

d = 4/7

The nth term of the sequence given a = 2 and d = 4/7 will be expressed as;

Tn = 2+(n-1)4/7

Given Tn = 6

6 = 2+(n-1)4/7

6 = 2+4/7 n - 4/7

6-2+4/7 = 4/7 n

32/7=4/7 n

32 = 4n

n = 32/4

n = 8

8 0
3 years ago
Write the slope-intercept form of the equation that passes through the point (4,-6) and is parallel to the line y = -3/4x - 5
Karolina [17]

The equation that runs through the location (4,-6) has the slope-intercept form,  y=-\frac{3}{4}x-3 .

<h2>Formation of the equation</h2>

A line's equation written in the slope-intercept form:

y=mx+b

where m= slope & b= y-intercept

The slope of two parallel lines is equal.

Currently, we know the line's equation:

y=-\frac{3}{4} x-5

here, slope, m= -\frac{3}{4}

A line equation is created by adding the slope's value and the point's coordinates (4, -6):

-6=-\frac{3}{4}(4)+b

⇒ -6=-3 +b [adding 3 to both sides]

⇒-3=b

⇒b= -3

Hence the solution is  y=-\frac{3}{4}x-3 .

Learn more about slope-intercept form here:

brainly.com/question/9682526

#SPJ4

5 0
1 year ago
Plsss helpppppppppp if you do, you a cool guy or girl
STatiana [176]

9514 1404 393

Answer:

  • Tyler
  • 2 hundredths of a mile

Step-by-step explanation:

The graph is a little difficult to read, but we note that there are 6 grid lines between times that are 2 minutes apart. So, each grid line stands for 2/6 = 1/3 minute.

At the 1-mile mark, the graph crosses 1 grid line above 8 minutes, indicating it takes Tyler 8 1/3 minutes to run 1 mile.

Then in 10 minutes, Tyler will run ...

  distance = speed · time = 1 mile/(8 1/3 min) · 10 min

  = 1/(25/3)·10 = 10·3/25 = 30/25 = 1.2 . . . . miles

__

The equation tells you that Elena runs each mile in 8.5 minutes. To see how far she runs in 10 minutes, we can solve ...

  10 = 8.5x

  x = 10/8.5 ≈ 1.18 . . . . miles

So, Tyler runs farther in 10 minutes by a distance of ...

  1.20 -1.18 = 0.02 . . . . miles

8 0
3 years ago
The Old-Fashioned but Newfangled Candy Company wants to mix some of its $5.50 per pound Tropical Taffy, with 100 pounds of its $
mel-nik [20]

Answer:

50

Step-by-step explanation:

x= the number of pounds of the tropical taffy that should be used

You need to take the value of the Tropical Taffy + the value of the Passion Fruit taffy to = the value of Tropical Passion

value- price per pound times the number of pounds

Your equation is going to look like this-->

5.50x+6.25(100)=6(x+100)

5.50x+625=6x+600

-5.50x        -5.50x

625=0.5x+600

-600         -600

25=0.5x

50=x

Hope this helps!

5 0
3 years ago
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