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3 years ago

Ricky bought a jacket for $52.00. If the sales tax is 9.5%, how much did he pay in total?

Mathematics

1 answer:

Firdavs [7]3 years ago

6 0

Multiply 52*.095=4.94 then add this to 52... $56.94

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The nearest hundred to 83,752,245 is?

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Answer:

83,752,000

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2 years ago

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What percentage of goldfish will have lengths between 4.6 inches and 9.4 inches? 34%

ella [17]

Answer:

95%

Step-by-step explanation:

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3 years ago

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Which statements about functions g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are true? Select all that apply.

Tanya [424]

Answer:

A and B

Step-by-step explanation:

We are given that

$g(x)=x^2-4x+3$

$g(x)=(x^2-2\times x\times 2+4)-4+3=(x-2)^2-1$

Compare with it

$y=(x-h)^2+k$

Where vertex=(h,k)

We get

Vertex of g=(2,-1)

$f(x)=x^2-4x=(x^2-2\times x\times 2+4)-4=(x-2)^2-4$

Vertex of f=(2,-4)

Equation of axis of symmetry=x-coordinate of vertex

Axis of symmetry of g

x=2

Axis of symmetry of f

x=2

Differentiate w.r.t x

$g'(x)=2x-4=0$

$2x-4=0\implies 2x=4$

$x=\frac{4}{2}=2$

$f'(x)=2x-4$

$2x-4=0\implies 2x=4$

$x=\frac{4}{2}=2$

$g''(x)=2>0$

$f''(x)=2>0$

f and g have both minima at x=2

Hence, option A and B are true.

8 0

4 years ago

The total number of seats in an auditorium is modeled by f(x) = 2x² - 12x, where x represents the number of rows of seats. How m

steposvetlana [31]

320 = 2x² - 12x as when there are an unknown number of rows there are 320 seats.
0 = 2x² - 12x - 320
0 = x² - 6x - 160
0 = (x - 16)(x + 10)
for this to = 0 one bracket must equal 0
therefore x = 16 or x = -10
not a negative number of rows.

Therefore must be 16.

3 0

4 years ago

Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^3, x = 2, and y = 1 about the y-axis.

vladimir1956 [14]

If you're using the shell method, the setup would be

$\displaystyle2\pi\int_1^2x(x^3-1)\,\mathrm dx$

Reasoning: consider just one shell (see the image below). The height of the shell is determined by the vertical distance between the curve $y=x^3$ and the line $y=1$ . The radius of each shell is determined by the value of $x$ , which can only range from 1 to 2 within the region of interest, and the height is determined exactly by $x^3-1$ at this $x$ . Multiply by $2\pi$ to get the surface area of this infinitesimally thin cylindrical shell, then integrate along the interval [1, 2] to get the volume.

We have

$\displaystyle2\pi\int_1^2x(x^3-1)\,\mathrm dx=2\pi\int_1^2(x^4-x)\,\mathrm dx=2\pi\left(\dfrac{x^5}5-\dfrac{x^2}2\right)\bigg|_1^2=\dfrac{47\pi}5$

4 0

4 years ago