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Oliga [24]
2 years ago
8

A. Transform each quadratic function into standard form. Identify the constants h and k. - 1) y = x2 + 10x – 13 2) y = x2 - 6x +

5 3) y = x2 - 2x + 3 4) y = x2 – 3x + 16 5) y = x2 – 18x – 9 6) y = 2x2 – 3x + 4 7) y = 3x2 - 12x - 4 8) y = 2x2 - 8x - 22 9) y = 3x2 + 6x - 1 10) y = 9x2 + 18x + 4 - -​
Mathematics
1 answer:
BaLLatris [955]2 years ago
4 0

1. (-5,-12)

2. (3,-4)

To identify the constant H and K

- You need to write the given equation in vertex form

- Use complete the square method to write in vertex form

- The vertex form is

a  (x - h)  ^{2}  + k

- after writing the equation in the world storm you can see that there is a h and a k

- Pull the h and the k in into (h,k)

I can't do all of it so I'll do 2 for you and with explanations.

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The figures show the dimensions of a tennis court and a basketball court given in terms of the width in feet of the tennis court
Sholpan [36]

Answer:

a.  Perimeter of the tennis court = 6x + 12

Perimeter of the Basketball court = 7x + 36

b.  x + 24

c.  Length of the tennis court = 78 feet

Width of the tennis court = 36 feet

Length of the Basketball court = 94 feet

Width of the Basketball court = 50 feet

Step-by-step explanation:

a.  Perimeter of the rectangle = 2(length + width)

So, perimeter of the tennis court = 2[(2x + 6) + x]

= 2(3x + 6)

= 6x + 12

Perimeter of the Basketball court = 2[(3x - 14)+(\frac{1}{2}x + 32)]

= 6x - 28 + x + 64

= 7x + 36


b.  Perimeter of the Basketball court - perimeter of the tennis court

= (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24

So, perimeter of the basketball court is x + 24 feet greater than that of the tennis court


c.  It is given that the width of the tennis court = 36 feet

But, from the figure,

width of the tennis court = x

So, x = 36

Therefore, length of the tennis court = 2x + 6

= 2(36) + 6

= 72 + 6

= 78 feet

Width of the tennis court = x = 36 feet

Length of the basketball court = 3x - 14

= 3(36) - 14

= 108 - 14

= 94 feet

Width of the basketball court = \frac{1}{2} x+32

=\frac{1}{2} (36)+32

= 18 + 32

= 50 feet

7 0
3 years ago
if a > 0, b>0, show that f(x)= a(1-e^-bx) is everywhere increasing and everywhere concave down.
faltersainse [42]
If a > 0, b>0, show that f(x)= a(1-e^-bx)
4 0
3 years ago
A bag contains 7 red, 3 green, 4 blue, and 6 yellow marbles. Find the probability of randomly selecting a red marble three times
77julia77 [94]

Answer:

B

Step-by-step explanation:

8 0
3 years ago
Dave can complete a sales route by himself in 4 hours. James can do the same job in 5 hours. How long will it take them to do it
Alexeev081 [22]
We can solve this problem by calculating the individual rate of working and equate it to their total rate of working.

If Dave can complete a sales route in 4 hours, then his working rate is

\frac{1}{4}

Also, if James can do it in 5 hours, then his working rate is

\frac{1}{5}

Let
x
be the hours that both will use to complete the sales route,

Then rate at which both completes this task is
\frac{1}{x}


Meaning if we add their individual rates we should get

\frac{1}{x}

That is;

\frac{1}{4} + \frac{1}{5} = \frac{1}{x}

The LCM is
20x

So let us multiply through with the LCM.

20x \times \frac{1}{4} + 20x \times \frac{1}{5} =20x \times \frac{1}{x}

5x + 4x = 20

We simplify to get,

9x = 20

Dividing through by 9 gives;

x = \frac{20}{9}

x = 2\frac{1}{9}

Therefore the two will complete sales route in
2 \frac{1}{9}
hours.
3 0
3 years ago
Any 5 examples to explain the method of place value principle for converting a fraction to decimal
pogonyaev
Sorry !!!!!!!!!!!! But i can give u only 1.....
say, 10/3  u get 3.3333333.....  , by rounding using place value u get 3.33 .

8 0
3 years ago
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