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padilas [110]
2 years ago
13

determine the vertex and axis of symmetry for the following: f(x) = 2x to the power of 2 - 12x + 24 ?

Mathematics
1 answer:
Vikki [24]2 years ago
7 0

Answer:

vertex = (3,24)  Axis of symmetry = 3

Step-by-step explanation:

Use the vertex formula to find x: x=-b/2(a)

x= 12/2(2) = 3 (this is your axis of symmetry)

Substitute 3 for x in the equation to get y: y = 42

Once you have both x and y you have your vertex.

You might be interested in
2x+2y=16 , 6x+4y=38 what is the value of x
ra1l [238]
1st equation—x, substitute y: 
<span>3x + 2(x + 3) = 16 </span>
<span>3x + 2x + 6 = 16 </span>
<span>5x = 10 </span>
<span>x = 2 </span>

<span>y in the above equation: </span>
<span>= 2 + 3 </span>
<span>= 5 </span>

<span>Answer: x = 2, y = 5</span>
5 0
3 years ago
Please answer correctly and quickly all question
Papessa [141]

Answer:

4) c

6) a, b

7) a

8) b, c

10) I'm not sure but I believe it is C.

Step-by-step explanation:

5 0
3 years ago
A line passes through the points (-3,-4) and (6,2)
Zanzabum

Answer: x - int : (3,0)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = y2-y1/x2-x1

   = -4-2/-3-6

   =-6/-9

   = 2/3

y1 = 2

x1 =6

y - 2 = 2/3(x-6)  

x -int: when y = 0, what is x?

0-2 = 2/3(x-6)

-2 = 2/3x - 4

2 = 2/3x

x=3

~Hope this helps!~

5 0
1 year ago
What line is parallel to 2x+5y=6 that goes through (5,3)
Anna11 [10]

Answer:

4y = x - 17

Step-by-step explanation:

First off, in the equation given : 2x + 5y = 6 , make y the subject of the formula which will give y = \frac{-2x}{5} + \frac{6}{5}  which make the gradient, m, the coefficient of x = \frac{-2}{5}  . Since the line we're looking for is parallel to the one we were given, their respective gradients would be the same. (If they were perpendicular, the gradient of the new line would be a negative inverse of the given line)

Then you proceed to use the one-point formula : y - y₀ = m(x - x₀), where   y₀ = 3 and x₀ = 5 from the point it goes through (5, 3)

y - 3 = \frac{1}{4}(x - 5); y - 3 = \frac{x}{4} - \frac{5}{4};  y = \frac{x}{4} - \frac{5}{4} +3

y = \frac{x}{4} - \frac{17}{4};  y = \frac{x-17}{4}  ;   4y = x - 17

7 0
2 years ago
In a random sample of 1066 U.S. adults, 580 think that the U.S. government
alexandr402 [8]

Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the adults who think that the U.S. government is doing too little to protect the environment presently and the adults who think that the U.S. government is doing too little to protect the environment 10 years ago. The population proportions would be p1 and p2 respectively.

p1 - p2 = difference in the proportion of adults who think that the U.S. government is doing too little to protect the environment presently and the adults who think that the U.S. government is doing too little to protect the environment 10 years ago.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 ≠ p2

p1 - p2 ≠ 0

it is a two tailed test

Sample proportion = x/n

Where

x represents number of success

n represents number of samples

For the present,

x1 = 580

n1 = 1066

p1 = 580/1066 = 0.54

For 10 years ago,

x2 = 514

n2 = 1038

P2 = 514/1038 = 0.5

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (580 + 514)/(1066 + 1038) = 0.52

1 - pc = 1 - 0.52 = 0.48

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.54 - 0.5)/√(0.52)(0.48)(1/1066 + 1/1038) = 0.04/0.02178551744

z = 1.84

Since it is a two tailed test, the curve is symmetrical. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above the test z score in the right tail 1 - 0.967 = 0.033

We would double this area to include the area in the left tail of z = - 1.84 Thus

p = 0.033 × 2 = 0.066

Alpha = 0.1

Since alpha, 0.1 > p value 0.066, we would reject the null hypothesis.

Therefore, at a = 0.10, we can reject the

claim that the proportion of U.S. adults who think that the U.S. government

is doing too little to protect the environment has not changed.

4 0
3 years ago
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