Write 3/2 using a fractional exponent.

Are the given lengths 24, 60, 66, sides of a right triangle?

GarryVolchara [31]

24+60=84>66

60+66=126>24

66+24=90>60

Therefore, the lengths are the sides of a triangle because the sum of lengths of two sides must be greater than the third side. All the sum of length of 2 sides are greater than the third side.

5 0

3 years ago

Read 2 more answers

Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?

masha68 [24]

Answer:

The Width of the garden will be 9 feet.

Step-by-step explanation:

Given:

Manny has wood =48 feet

Length of the garden = 15 feet

The equation which can be used .

We need to find the width of the garden.

Solution :

Now Length of the garden is given we will substitute in the given equation to find the width.

Now Using Subtraction property we will subtract both side by 30 we get;

Now Using Division Property we will divide both side by 2 we get;

Hence the Width of the garden will be 9 feet.

4 0

3 years ago

A buoy floating in the sea is bobbing in simple harmonic motion with period 2 seconds and amplitude 8 in. Its displacement d fro

Mrac [35]

Answer:

The equation of the displacement $d$ as a function of time $t$ is :

$d(t)=8sin(\pi t+\pi )$

Step-by-step explanation:

Generally , A simple harmonic wave is a sinusoidal function that is it can be expressed in simple $sin$ or $cos$ terms.

Thus,

$d(t) = Asin(wt+c)$

is the general form of displacement of a SHM.

where,

$d(t)$ is the displacement with respect to the mean position at any time $t$
$A$ is amplitude
$w$ is the natural frequency of oscillation ( $rads^{-1}$ )
$c$ is the phase angle which indicates the initial position of the object in SHM ( $rad$ )

given,

Time period ( $T$ ) = $2s$
$A=8$
The natural frequency ( $w$ ) and time period ( $T$ ) is :

$w=\frac{2\pi} {T}$

∴

$w$ = $\frac{2\pi }{2} = \pi$ $rads^{-1}$

∴

the equation :

⇒ $d(t)=8sin(\pi t+c)$ ------1

since $d=0$ when $t=o$ ,

⇒ $0=8sinc\\c=n\pi$ ------2

where n is an integer ;

⇒since the bouy immediately moves in the negative direction , $x$ must be negative or c must be an odd multiple of $\pi$ .

⇒ $d(t) = 8sin(\pi t+(2k+1)\pi )$ ------3

where k is also an integer ;

the least value of $k=0$ ;

thus ,

the equation is :

$d(t)=8sin(\pi t+\pi )$

7 0

3 years ago

Which point lies on the circle represented by the equation (x+5) + (y-9) = 8

olga_2 [115]

Answer:

(-5,9+√8)

Step-by-step explanation:

There are two ways in which you can find a point that lies in the circle. One of them is to do y the subject of the formula, and another one is to determine the center of the circumference, and with the information of the radius, you can sum this value upward or downward.

the general equation of a circle is:

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

with center at (h,k)

you have the following equation:

$(x+5)^2+(y-9)^2=8\\\\h=-5\\\\k=9\\\\r=\sqrt{8}$

Then, the center is (-5,9)

if you sum the value of the radius in one of the fourth directions (up, down, left, right), for example upward you have

$(-5,9+r)=(-5,9+\sqrt{8})$

Then, one point that lies in the circle is (-5,9+√8)

3 0

3 years ago

The residual plot for a data set is shown.

UNO [17]

The true statement about the residual plot is (a) The regression line is a good model because there is no pattern in the residuals.

<h3>How to interpret the residual plot?</h3>

For a residual plot to be considered a good model, the points on the plot must be at random and they must not follow a specific pattern

From the graph, we can see that the points are scattered

Hence, the true statement about the residual plot is (a)