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3 years ago

Use graphing technology to find the range of the function f(x)=x2 +6x+9

Mathematics

1 answer:

lbvjy [14]3 years ago

5 0

Answer:

See below.

Step-by-step explanation:

Refer to the graph.

The range of a graph is the span of y-values it covers.

From the graph, we can see that the span of y-values is all values greater than or equal to 0.

Therefore, our range is, in interval notation:

$[0,\infty)$

Note that we use brackets with the 0 because 0 is included in our range.

In set notation, this is:

$\{y|y\in\mathbb{R},y\geq 0\}$

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To get your car repaired at a certain dealership in Woodstock, the rate charged is $90 per hour worked on your car, plus a $50 d

kakasveta [241]

C- charge
H- hours
D- diagnostic fee

C= #H(90)+ D

C= 4.6(90)+50
=414+50
=$464

C-$800
H-?
D-50

C= #H(90)+50

800=H(90)+50

H(90)=800-50

H(90)=750

H(90)/90=750/90

H=750/90

H= 8.33333333

4 0

1 year ago

Plz help due 2morrow 14 and 15

lions [1.4K]

Answer:

14 length of the side is 3x-7

and 15 length of side is 2x+6

6 0

2 years ago

In step one do you found the volume (in cubic feet) of the main tank(359,006.67). The maximum density of killer whales per cubic

Luba_88 [7]

Answer:

4 killer whales

Step-by-step explanation:

The dimensional analysis is ...

(whales/ft³)(ft³/tank) = whales/tank

Putting the numbers with the units, we get ...

(1.1142·10^-5 whales/ft³)(3.5900667·10^5 ft³/tank) = 4.00005... whales/tank

The maximum number of killer whales allowed in the main show tank is 4.

6 0

2 years ago

Use the given transformation to evaluate the given integral, where r is the triangular region with vertices (0, 0), (8, 1), and

Jlenok [28]

We first obtain the equation of the lines bounding R.

For the line with points (0, 0) and (8, 1), the equation is given by:

$\frac{y}{x} = \frac{1}{8} \\ \\ \Rightarrow x=8y \\ \\ \Rightarrow8u+v=8(u+8v)=8u+64v \\ \\ \Rightarrow v=0$

For the line with points (0, 0) and (1, 8), the equation is given by:

$\frac{y}{x} = \frac{8}{1} \\ \\ \Rightarrow y=8x \\ \\ \Rightarrow u+8v=8(8u+v)=64u+8v \\ \\ \Rightarrow u=0$

For the line with points (8, 1) and (1, 8), the equation is given by:

$\frac{y-1}{x-8} = \frac{8-1}{1-8} = \frac{7}{-7} =-1 \\ \\ \Rightarrow y-1=-x+8 \\ \\ \Rightarrow y=-x+9 \\ \\ \Rightarrow u+8v=-8u-v+9 \\ \\ \Rightarrow u=1-v$

The Jacobian determinant is given by

$\left|\begin{array}{cc} \frac{\partial x}{\partial u} &\frac{\partial x}{\partial v}\\\frac{\partial y}{\partial u}&\frac{\partial y}{\partial v}\end{array}\right| = \left|\begin{array}{cc} 8 &1\\1&8\end{array}\right| \\ \\ =64-1=63$

The integrand x - 3y is transformed as 8u + v - 3(u + 8v) = 8u + v - 3u - 24v = 5u - 23v

Therefore, the integration is given by:

$63 \int\limits^1_0 \int\limits^{1}_0 {(5u-23v)} \, dudv =63 \int\limits^1_0\left[\frac{5}{2}u^2-23uv\right]^{1}_0 \\ \\ =63\int\limits^1_0(\frac{5}{2}-23v)dv=63\left[\frac{5}{2}v-\frac{23}{2}v^2\right]^1_0=63\left(\frac{5}{2}-\frac{23}{2}\right) \\ \\ =63(-9)=|-576|=576$

6 0

2 years ago

Factors of x3 – 9x2 + 5x – 45 by grouping

kati45 [8]

Important: Use the symbol "^" to denote exponentiation:

<span>x3 – 9x2 + 5x – 45 NO
</span><span>x^3 – 9x^2 + 5x – 45 YES

Look at the first 2 terms. They can be rewritten as x^2(x-9). Then look at the last 2 terms. They can be rewritten as 5(x-9). So, x-9 is the common factor here. Thus, the original expression becomes:

(x^2-5)(x-9).

Note that x^2-5 can be factored, so that the final 3 factors are:

(x-sqrt(5)), (x+sqrt(5)), (x-9).</span>

8 0

2 years ago