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coldgirl [10]
2 years ago
14

Use the following function rule to find f(0). f(x)= -9 (3)^x f (0 ) =

Mathematics
1 answer:
AlladinOne [14]2 years ago
7 0

Step-by-step explanation:

<u>Substitute f(0) into the function:</u>

f(0) =  - 9(3)^{0}

<u>Include exponent:</u>

f(0) =  - 9(1)

<u>Multiply:</u>

f(0) =  - 9

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A quarterback throws a football to a teammate. The football is 6.5ft above the ground when it leaves the quarterback's hand. His
sergejj [24]

Answer:

y = - 16t² + 55.6t + 6

Step-by-step explanation:

Using y - y₀ = vt - 1/2gt² where g = 32 ft/s², and v the velocity of the football

So y = y₀ + vt - 1/2 × (32 ft/s²)t²

y = y₀ + vt - 16t² where y₀ = 6.5 ft

y = 6 + vt - 16t²

Now, when t = 3.5 s, that is the time the teammate catches the ball after the quarterback throws it, y = 5 ft. Substituting these into the equation, we have

5 = 6.5 + v(3.5 s) - 16(3.5 s)²

5 = 6.5 + 3.5v - 196

collecting like terms, we have

5 - 6.5 + 196 = 3.5v

194.5 = 3.5v

v = 194.5/3.5 = 55.57 ft/s ≅ 55.6 ft/s

So, substituting v into y, our quadratic model is

y = 6 + 55.6t - 16t²

re-arranging, we have

y = - 16t² + 55.6t + 6

6 0
3 years ago
In a recent 10-year period, the change in the number of visitors in the U.S. National parks was about -11,150,000. What was the
Trava [24]

Answer:

Mean = -1,115,000 per year.

Step-by-step explanation:

Mean = (Σx)/N

The mean is the sum of variables divided by the number of variables

Σx = sum of variable = change in number of visitors over a 10 year period = -11150000

N = number of variables = 10

Mean = (-11150000)/10

Mean = -1,115,000 per year.

Hope this Helps!!!

4 0
2 years ago
Can someone please help me factor and write the equations for these two problems ?
prisoha [69]

Answer:

Step-by-step explanation:

Asymptotes 3

g(x) = \frac{3x}{x^2-3x-10}

Factors of denominator will be,

x² - 3x - 10 = x² - 5x + 2x - 10

                 = x(x - 5) + 2(x - 5)

                 = (x + 2)(x - 5)

Therefore, factored form of g(x) will be,

g(x) = \frac{3x}{(x + 2)(x - 5)}

Asymptotes 4

h(x) = \frac{(x-5)}{x^{2} + 14x + 40}

      = \frac{x-5}{x^{2}+10x+4x+40}

      = \frac{x-5}{x(x+10)+4(x+10)}

      = \frac{x-5}{(x+10)(x+4)}

5 0
3 years ago
X^2 + Y^2 +ax + 2y + 3 = 0<br><br> What number is this equation the equation of a circle?
Sav [38]

Answer:

Eq: (x+a/2)²+(y+1)²=(a²-8)/4

Center: O(-a/2, -1)

Radius: r=0.5×sqrt(a²-8)

Mandatory: a>2×sqrt(2)

Step-by-step explanation:

The circle with center in O(xo,yo) and radius r has the equation:

(x-xo)²+(y-yo)²=r²

We have:

x²+y²+ax+2y+3=0

But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4

And

y²+2y+3=y²+2y+1+2=(y+1)²+2

Replacing, we get:

(x+a/2)²-a²/4+(y+1)²+2=0

(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4

By visual inspection we note that:

- center of circle: O(-a/2, -1)

- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)

6 0
3 years ago
Jennie makes quilts. She can make 7 quilts with 21 yards of material. How many yards of material would be required to make 12 qu
nlexa [21]
\frac{7}{21} = \frac{12}{yards}  \\  \\ 7*yards=21*12 \\  \\ 7yards=252 \\  \\ yards=36
4 0
3 years ago
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