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Elis [28]
2 years ago
7

Sue has 18 sweets.

Mathematics
1 answer:
babymother [125]2 years ago
3 0

Answer:

<h2>Sue : 13 - x  </h2><h2>Tony :  x/2 + 9</h2>

Step-by-step explanation:

<h3>                                                  Sue                  Tony </h3>

_________________________________________________

<u>initial number of sweets    </u>           |   18                   |      18

                                                       |                          |

<u>Sue gives Tony x sweets</u>              |   18 - x              |      18 + x

                                                       |                          |

<u>Sue ,eats 5 of her sweets. and </u>   |  18 - x - 5 =       |      (18 + x)/2 =

<u>Tony ,eats half of his sweets</u>        | 13 - x                |     9 + x/2

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1.) Determine the type of solutions for the function (Picture 1)
NNADVOKAT [17]

Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

7 0
2 years ago
45.3297 rounded to the nearest tenth would be?
Alex
45.3297 rounded to the nearest tenth is 45.3
3 is in the tenths place, so you look at the number to the right of it. If that number is 5 or more, you round up. If the number is 4 or less, you round down. So you round 45.3297 down to 45.3
5 0
3 years ago
Plz help its about volume of a rectangular prism
dusya [7]

Answer:

V = 7*4*1

V = 1*4*7

V = 4*7*1

Step-by-step explanation:

The volume is found by

V = l*w*h

V = 7*4*1

We can multiply in any order

8 0
2 years ago
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Divide 7 by 10 the write answer as a fraction
mash [69]

1/7

Step-by-step explanation:

3 0
2 years ago
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Given a 30-60-90 triangle with a long<br> leg of 9 in, determine the length of the<br> hypotenuse.
aniked [119]

Answer:

10.38 in

Step-by-step explanation:

Long side would be opposite to 60°.

Since, side opposite to 60° is root 3 upon 2 times of hypotenuse.

9 =  \frac{ \sqrt{3} }{2} \times hypotenuse \\  \\ hypotenuse =  \frac{9 \times 2}{ \sqrt{3} }  \\  =  \frac{18}{ \sqrt{3} }  =  \frac{18 \sqrt{3} }{3}  = 6 \sqrt{3}  = 6 \times 1.73 \\   \:  \:  \: \red{ \bold{hypotenuse = 10.38 \: in}}

8 0
3 years ago
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