1.)order the group of quadratic fractions from widest to narrowest graph.

y=3x^2;y=5x^2;y=7x^2
a.)y=3x^2;y=5x^2;y=7x^2
b.)y=7x^2;y=5x^2;y=3x^2
c.)y=3x^2;y=7x^2;y=5x^2***
d.)y=2x^2;y=7x^2;y=3x^2

2.)the area of a play ground is 234yd^2. the width of the playground is 5 yard longer than its length, find the length and the width of the playground.
a.)L=18 yards;W=13 yards
b.)L=13 yards;W=18 yards**
c.)L=18 yards;W=26 yards
d.)L=26 yards;W=18 yards

3.)what is the value of c so that x^2+8x+c is a perfect square trinomial?
a.)16
b.)34
c.)4***
d.)64

4.)what is the value of c so that x^2+17x+c is a perfect square trinomial?
a.)17/2
b.)289
c.)289/4
d.)289/2

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what about the last one ?

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1.)c.)y=3x^2;y=7x^2;y=5x^2

The quadratic fractions can be ordered from widest to narrowest graph by looking at the coefficients of the x^2 term. In this case, the widest graph would have the largest coefficient of x^2, so y=7x^2 would be the widest graph, followed by y=5x^2, and y=3x^2 as the narrowest.
So, the correct answer is c.)y=3x^2;y=7x^2;y=5x^2

2.)b.)L=13 yards;W=18 yards
Let the length of the playground be x.
Then, the width would be x+5.
The area of the playground is given by length multiplied by width:
x(x+5) = 234
x^2 + 5x - 234 = 0
Factoring or using the quadratic formula, we find that x = 13 or x = -18 (ignore negative value).
So, the length is 13 yards and the width is 13 + 5 = 18 yards.
The correct answer is b.)L=13 yards;W=18 yards.

3.)c.)4
To make the trinomial x^2+8x+c a perfect square trinomial, we need the coefficient of the x term to be twice the square root of c.
In this case, the coefficient of the x term is 8, so we want 2 times the square root of c to be 8.
Solving for c, we have:
2(sqrt(c)) = 8
sqrt(c) = 4
c = 4
So, the value of c is 4.
The correct answer is c.)4.

4.)c.)289/4
To make the trinomial x^2+17x+c a perfect square trinomial, we need the coefficient of the x term to be twice the square root of c.
In this case, the coefficient of the x term is 17, so we want 2 times the square root of c to be 17.
Solving for c, we have:
2(sqrt(c)) = 17
sqrt(c) = 17/2
c = (17/2)^2 = 289/4
So, the value of c is 289/4.
The correct answer is c.)289/4.

1.) To determine the order of the quadratic fractions from widest to narrowest graph, we need to compare the coefficients of the x^2 term. The coefficient represents the "stretching" or "narrowing" factor of the graph.

In this case, we have the following quadratic fractions:
y = 3x^2
y = 5x^2
y = 7x^2

Comparing the coefficients, we can see that the quadratic fractions are in the order of increasing coefficients: 3, 5, and 7. The wider the graph, the smaller the coefficient, and vice versa. Therefore, the correct answer is:

c.) y = 3x^2; y = 7x^2; y = 5x^2

2.) Let's assume the length of the playground is x yards. According to the problem, the width is 5 yards longer than the length, so the width would be (x + 5) yards.

The area of a rectangle is equal to its length multiplied by its width. We are given that the area is 234 yd^2, so we can set up the equation:

x * (x + 5) = 234

Expanding and rearranging the equation, we get:

x^2 + 5x = 234

To solve this quadratic equation, we can set it equal to zero:

x^2 + 5x - 234 = 0

Now we can factorize or use the quadratic formula to solve for x. After finding the solutions, we can check which combination of length and width satisfies the given conditions:

a.) L = 18 yards; W = 13 yards
b.) L = 13 yards; W = 18 yards**
c.) L = 18 yards; W = 26 yards
d.) L = 26 yards; W = 18 yards

Among the options, the one that satisfies the condition of the width being 5 yards longer than the length is option b:

Length (L) = 13 yards
Width (W) = 18 yards

3.) For a quadratic trinomial x^2 + 8x + c to be a perfect square trinomial, its middle term (8x) must be twice the product of the square root of the first and last terms (x * √c).

In this case, the first term is x^2, and the last term is c. So, doubling the product of x and √c gives us 2(x * √c) = 2x√c.

To make the middle term 8x, we need 8x = 2x√c. Canceling out x, we get:

8 = 2√c

Dividing both sides by 2, we find:

4 = √c

Squaring both sides, we get:

16 = c

Therefore, the correct answer is:

c.) 4

4.) Similar to the previous question, for the quadratic trinomial x^2 + 17x + c to be a perfect square trinomial, its middle term (17x) must be twice the product of the square root of the first and last terms (x * √c).

In this case, the first term is x^2, and the last term is c. So, doubling the product of x and √c gives us 2(x * √c) = 2x√c.

To make the middle term 17x, we need 17x = 2x√c. Canceling out x, we get:

17 = 2√c

Dividing both sides by 2, we find:

8.5 = √c

Squaring both sides, we get:

72.25 = c

Therefore, the correct answer is:

b.) 289

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