MATHEMATICS HIGH SCHOOL

daniel is buhying a video game that costs 52.99. the sales tax is found by multiplying the cost of the video game by 0.07. how much is the sales tax for the video game? what is the total cost, including tax?

Answers

Answer 1

Answer:

Answer:

sales tax for video games:

52.99*0.07=3.7093

total cost, including tax?

52.99+3.7093=56.6993=56.7

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Answers

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A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is 950 ft2. If the length of the pool is 8 feet longer than the width, find the dimensions of the pool.

Answers

Answer:

$x \approx 21.080\,ft$ , $y = 29.080\,ft$

Step-by-step explanation:

The total area of the pool and the walkway is:

$(x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^(2)$

$(x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^(2)$

$x^(2) + 20\cdot x + 84\,ft^(2) = 950\,ft^(2)$

$x^(2) + 20\cdot x - 866\,ft^(2) = 0$

The roots of the second-order polynomial is:

$x_(1) \approx 21.080\,ft$ and $x_(2) \approx -41.081\,ft$

The only possible root is:

$x \approx 21.080\,ft$

The other dimension of the pool is:

$y = x + 8\,ft$

$y = 21.080\,ft + 8\,ft$

$y = 29.080\,ft$

The cubic parent function y=x^3 contains the point (2,8). If the function reflected over the x-axis and shifted right 6 units, what are the coordinates of the new point

Answers

Answer:

The new coordinate are (8,-8)

Step-by-step explanation:

Whenever a graph is reflected about the x-axis, positive y values become negative and vice versa. In this case positive y(8) becomes negative (-8). While the x values remain unchanged.

So the coordinates when moving by one unit will be (2,-8)

Shifting it 6units to the right increases the x values by six to give the new coordinates which is (8,-8)

What is the value of x in the equation 4x+8y=40 when y=0.8

Answers

inpus 0.8 for y
4x+8(0.8)=40
4x+6.4=40
minus 6.4 both sides
4x=33.6
divie both sides by 5
x=8.4

x=8.4 when y=0.8

4x+8y=40
4x + (8x.8)= 40
4x + 6.4 = 40
4x = 33.6
x = 8.4

A sprinkler mounted on the ground sends out a jet of water at a 30o angle to the horizontal. The water leaves the nozzle at a speed of 12 m/s. (a) How far does the water travel before it hits the ground?

Answers

Answer:

12.7m

Step-by-step explanation:

The equation for motion to be used to find how far the water travels is

xf = xi + Vix(t) + 1/2axt^2

xf = 0 + ViCos α(t) + 0

xf = ViCosα(t)

xf = 12 Cos 30°(t)

xf = (6√3)t

To find the total times we will use the vertical displacement equation

yf = yi + Viy(t) + 1/2ayt^2

0 = 0 + ViSinα(t) + (1/2 * (-9.8)t^2)

0 = 12Sin30°(t) - 4.9t^2

4.9t^2 = 12Sin30°(t)

4.9t^2 = 6t

Divide through by t

4.9t = 6

t = 6/4.9

t = 1.22secs

Put t = 1.22 into (6√3)t

xf = 6√3 * 1.22

xf = 12.7m

Which shows 54^2 − 46^2 being evaluated using the difference of squares method

Answers

We use the formula: a^2 - b^2 = (a - b )(a + b);
54^2 − 46^2 = (54 - 46)(54 + 46) = 8 x 100 = 800;

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