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3 years ago

The standard form of a quadratic function

2 answers:

8 0

Standard Form. The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

zmey [24]3 years ago

7 0

Answer:The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Step-by-step explanation:

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The length of the base of a rectangular prism is 9

Tatiana [17]

Answer:

The volume of the prism is 320 15/16 inches³.

Step-by-step explanation:

Given:

The length of the base of a rectangular prism is 9 7/8.

The width of the prism is 8 1/8.

And the height is 4 inches.

Now, to find the volume of the prism.

(Length) l = 9 7/8 = 79/8 inches.

(Width) w = 8 1/8 = 65/8 inches.

(Height) h = 4 inches.

So, by putting the formula to get the volume:

Volume = w×h×l.

$Volume=\frac{65}{8}\times 4\times \frac{79}{8}$

$Volume=320\frac{15}{16}$

Volume = 320 15/16 inches³.

Therefore, the volume of the prism is 320 15/16 inches³.

7 0

4 years ago

Becky made 4 quarts of chicken noodle soup in a big pot, then served 1 1/2-cup bowls of soup to 6 people. How much soup is left

bogdanovich [222]

Answer:

There are 7 cups of soup left in the pot

Step-by-step explanation:

Firstly, we need to know the number of cups of soup made.

Since 1 quarts = 4 cups, the number of cups her 4 quarts is would be 4 * 4 = 16 cups

Now she served 1.5( 1 1/2 = 1.5) to 6 people, her total servings is thus 6 * 1.5 = 9 cups

What is remaining is thus 16 cups - 9 cups = 7 cups

5 0

3 years ago

Read 2 more answers

Verify the following identity. <img src="https://tex.z-dn.net/?f=-%5Cfrac%7Bcos%283x%29%2Bcos%285x%29%7D%7Bsin%283x%29-

kogti [31]

Recall the angle sum identities:

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

cos(a - b) = cos(a) cos(b) + sin(a) sin(b)

sin(a + b) = sin(a) cos(b) + sin(b) cos(a)

sin(a - b) = sin(a) cos(b) - sin(b) cos(a)

Notice that adding the first two together, and subtract the last from the third, we get two more identities:

cos(a + b) + cos(a - b) = 2 cos(a) cos(b)

sin(a + b) + sin(a - b) = 2 sin(b) cos(a)

Let a = 4x and b = x. Then

cos(5x) + cos(3x) = 2 cos(4x) cos(x)

sin(5x) - sin(3x) = 2 sin(x) cos(4x)

Now,

$-\dfrac{\cos(3x)+\cos(5x)}{\sin(3x)-\sin(5x)}=\dfrac{\cos(5x)+\cos(3x)}{\sin(5x)-\sin(3x)}=\dfrac{2\cos(4x)\cos x}{2\sin x\cos(4x)}=\dfrac{\cos x}{\sin x}=\cot x$