Gary wants to buy a video game with a price of $48 the game is marked as 50% off and the sales tax in his state is 4.5%

Leslie is currently 8 years older than her neighbor Bill. In 4 years she will be 2 times as old as Bill. Let x equal Bill's curr

Sauron [17]

8+x= 4x times 2 the times is multiplication

4 0

3 years ago

What is the measure of the hypotenuse?

SVETLANKA909090 [29]

Answer:

To find the hypotenuse you need to use the Pythagorean Theorem which is

a^2+b^2=c^2

Where a and b are your two sides and c is your diagonal line

So you want to plug the numbers in for the right variables

5^2+12^2=c^2

We want to find what c equals so we are first gonna simplify

25+144=c^2

we take 5^2=25, and 12^2=144, then we add them together 25+144=169

169=c^2 now you want to take 169 and square root it because the opposite of squaring is taking it by the root square

The square root of 169=13

Your hypotenuse is 13

Hope this helps ;)

4 0

3 years ago

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A group of rowdy teenagers near a wind turbine decide to place a pair of

Marrrta [24]

Answer:

a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is $y = 9 + 7* sin(\pi * t / 15 - \pi / 6)$

b) Hence the height of the shorts at exactly t = 10 minutes, to

the nearest tenth of a meter is 5.5 meters

Step-by-step explanation:

a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :

$x^2 + (y-yc)^2 = R^2$ ,

where

R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)

= 14 m / 2

= 7 m (radius of the circle)

Also, center of the circle will be at (0, 2 + R) i.e (0,9)

So, is the trajectory path equation to the circle

Let $x = 7* cos(w*t + \phi ) & y = 9 + 7* sin(w* t + \phi)$ be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t

At t= 10s, y = 16 m so we have,

$9 + 7 * sin(10* w + \phi) = 16$ ---------------(1)

Also, at t= 25s, y =2 m so we have,

$9 + 7* sin(25 * w +\phi) = 2$ --------------(2)

Solving we have, $10* w + \phi = \pi/2 & 25*w + \phi = 3*pi/2$

$15* w = \pi\\\\w = \pi/15 & \phi = \pi/2 - 10*\pi/15 = -\pi / 6$

Therefore $y = 9 + 7* sin(\pi * t / 15 - \pi / 6)$ is the instantaneous height of the pink short at time t ( in seconds)

b) At t= 10minutes = 10 * 60 s = 600s, we have,

$y = 9 + 7 * sin(\pi * 600/15 - \pi / 6)\\\\= 9 + 7 * sin(40* \pi - \pi / 6)$

= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)

5 0

2 years ago

2) Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95. How m

d1i1m1o1n [39]

Answer:

13 pencils.

Step-by-step explanation:

Let x be the pens and y be the pencils

Given:

Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95.

Total pens and pencils is 22

So, $x+y=22$ ----------------(1)

And he bought all utensils for $11.95. and each pen for 75 cents and pencils for 40 cents.

$0.75x+0.40y=11.95$ ------------(2)

solve equation 1 and equation 2 for x and y.

From equation 1.

$x+y=22$

$y=22-x$ ----------------(3)

put y value in equation 2.

$0.75x+0.4(22-x)=11.95$

$0.75x+0.4\times 22-0.4x=11.95$

$0.75x+8.8-0.4x=11.95$

$0.75x-0.4x=11.95-8.8$

$0.35x=3.15$

$x=\frac{3.15}{0.35}$

$x=9$

Now substitute x value in equation 3.

$y=22-9$

$y=13$

So, he buy 13 pencils.

5 0

3 years ago

Please choose the answer that describes the scientific notation for 5,098,000.. A. 5.098 × 75777. B. 5.098 × 108. C. 5.098 × 107

Sidana [21]

Standard form:
5,098,000

Scientific notation.
1) only 1 digit should be before the decimal point.
5.098000

2) only non-zero number must be part of the coefficient. the rest are included in the base of 10.

5.098 x 10^6 Choice D.

Exponent is the number of times the decimal moved from its original placement to its place after the 1st digit.

5 0

2 years ago

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