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amid [387]
3 years ago
11

8 less than the product of eleven and a number c

Mathematics
2 answers:
4vir4ik [10]3 years ago
4 0
11c-8 11c is the product of both 11 and c, and the 8 less than the product is shown with -8
m_a_m_a [10]3 years ago
3 0
11c >8 that means 11 multiply a number by c is less than 8 so 11c is greater than 8
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Determine whether each of the following functions is even, odd, or neither even nor odd.
Illusion [34]

Answer:

A.) Even.

Step-by-step explanation:

If a function is an even function, then

F(-x) = f(x)

Also, if a function is an odd function, then, f(-x) = -f(x)

You are given the below function

f(x) = 1 + 3x^2 − x^4

Let x = 2

Substitute 2 for x in the function

F(x) = 1 + 3(2)^2 - (2)^4

F(x) = 1 + 3(4) - 16

F(x) = 1 + 12 - 16

F(x) = -3

Also, Substitute -2 for x in the function

F(x) = 1 + 3(-2)^2 - (-2)^4

F(x) = 1 + 3(4) - 16

F(x) = 1 + 12 - 16

F(x) = -3

Since f(-x) = f(x), we can conclude that

F(x) = 1 + 3x^2 - x^4 is even

5 0
3 years ago
What is the distance between -9 and 14 on a number line?
Mademuasel [1]

-9 to 0 is 9 and 0 to 14 is 14.

Total distance = 9 +14 = 23

6 0
3 years ago
The ideal width of a certain conveyor belt for a manufacturing plant is 50 in. an actual conveyor belt can vary from the ideal b
Nastasia [14]
50 + 7/32 = 50 7/32
50 - 7/32 = 49 25/32

answers are :
c.) 49 25/32 < = x < = 50 7/32
e.) |x - 50| < = 7/32
     

8 0
3 years ago
The tuition at a certain college was $29,793 last year and increased 5.3% from last year to the current year. How much is this y
SCORPION-xisa [38]

Answer:

the answer is 67

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the equation of a parabola with a directrix of y=2 and a focus point of 0,-2
KiRa [710]
Hope this helped. :)

Any point, <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> on the parabola satisfies the definition of parabola, so there are two distances to calculate:

<span>Distance between the point on the parabola to the focusDistance between the point on the parabola to the directrix</span>

To find the equation of the parabola, equate these two expressions and solve for <span><span>y0</span><span>y0</span></span> .

Find the equation of the parabola in the example above.

Distance between the point <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> and <span><span>(<span>a,b</span>)</span><span>(<span>a,b</span>)</span></span> :

<span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span><span>‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾</span>√</span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span></span>

Distance between point <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> and the line <span><span>y=c</span><span>y=c</span></span> :

<span><span><span>∣∣</span><span><span>y0</span>−c</span><span>∣∣</span></span><span>| <span><span>y0</span>−c</span> |</span></span>

(Here, the distance between the point and horizontal line is difference of their <span>yy</span> -coordinates.)

Equate the two expressions.

<span><span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span><span>‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾</span>√</span>=<span><span>∣∣</span><span><span>y0</span>−c</span><span>∣∣</span></span></span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span>=<span>| <span><span>y0</span>−c</span> |</span></span></span>

Square both sides.

<span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span>=<span><span>(<span><span>y0</span>−c</span>)</span>2</span></span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span>=<span><span>(<span><span>y0</span>−c</span>)</span>2</span></span></span>

Expand the expression in <span><span>y0</span><span>y0</span></span> on both sides and simplify.

<span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span><span>y0</span></span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span><span>y0</span></span></span>

This equation in <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> is true for all other values on the parabola and hence we can rewrite with <span><span>(<span>x,y</span>)</span><span>(<span>x,y</span>)</span></span> .

Therefore, the equation of the parabola with focus <span><span>(<span>a,b</span>)</span><span>(<span>a,b</span>)</span></span> and directrix <span><span>y=c</span><span>y=c</span></span> is

<span><span><span><span>(<span>x−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span>y</span></span>

3 0
3 years ago
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