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Gnom [1K]
3 years ago
10

Please help me with these questions

Mathematics
1 answer:
adoni [48]3 years ago
8 0
Number one is a number 2 is c number 3 is D number for is be number six is d
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15. Rewrite the given functions in
Lisa [10]

15. The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17. The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Step-by-step explanation:

Any quadratic function has:

1. A vertex form form f(x) = a(x - h)² + k, where (h , k) are the

   coordinates of its vertex point

2. A standard form g(x) = ax² + bx + c, where a , b , c are constant and

   a is the coefficient of x², b is the coefficient of x and c is the

    y-intercept

3. the x-coordinate of the vertex point h = \frac{-b}{2a} and

    k = f(h)

15.

∵ f(x) = x² + 8x - 10

∴ a = 1 and b = 8

∵ h = \frac{-b}{2a}

∴ h = \frac{-8}{2(1)}=-4

∴ h = -4

∵ k = f(h)

∴ k = f(-4)

- Substitute x by -4 in f(x)

∴ k = (-4)² + 8(-4) - 10

∴ k = 16 - 32 - 10

∴ k = -26

∴ f(x) = (x - -4)² + (-26)

∴ f(x) = (x + 4)² - 26

The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17.

∵ g(x) = (x + 3)² - 4

- Lets solve the power 2 of the bracket:

 (1st + 2nd)² = (1st)(1st) + 2(1st)(2nd) + (2nd)(2nd)

∵ (x + 3)² = (x)(x) + 2(x)(3) + (3)(3)

∴ (x + 3)² = x² + 6x + 9

∴ (x + 3)² - 4 = (x² + 6x + 9) - 4

∵ 9 - 4 = 5

∴ (x + 3)² - 4 = x² + 6x + 5

The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Learn more:

You can learn more about the vertex form of quadratic function in brainly.com/question/9390381

#LearnwithBrainly

4 0
3 years ago
A bag with 12 marbles has 3 red marbles and 5 yellow marbles. A marble is chosen from the bag at random. What is the probability
alexgriva [62]

Answer:

3/12 = 1/4

Step-by-step explanation:

There are 12 marbles in the bag.  If the marble drawn at random is red, it is one of the 3 red marbles.

The probability is "3 out of 12" = 3/12 which simplifies to 1/4.

7 0
3 years ago
Read 2 more answers
Find the ​slope-intercept form of the equation of the line that passes through the point P and makes angle with the positive ​x-
SIZIF [17.4K]

Answer:

The answer is "y= -x+7"

Step-by-step explanation:

If \bold{\theta = 135^{\circ}}

point: p=(2,5)

Formula:

\to m= \tan \theta \\\\\to (y-y_1)= m(x-x_1)

\to m= \tan \ 135^{\circ} =  -1\\\\\to x_1= 2\\\\\to y_1=5

Put the value in the above formula:

\to y- 5 = -1(x-2)\\\\\to y- 5 = -x+2\\\\\to x+y = 5+2\\\\\to x+y=7

\to y= -x+7

3 0
3 years ago
What value of n makes the equation true?
Naddik [55]

Answer:

n = 5.2.

Step-by-step explanation:

-20.8 = -4n

We divide both sides of the equation by -4:

-20.8 / -4 = -4n/-4

5.2 = n  (answer).

4 0
3 years ago
Read 2 more answers
Please help me (attachment)<br><br>PLease DO NOT FLAG it appilies to all the rules!
lara31 [8.8K]
9) 46
10) 4
11) 46
12) 5.8
13) 36
14) 34
15) 9
16) 56
5 0
1 year ago
Read 2 more answers
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