Which ordered pairs in the form (x,y) are solutions to the equation 4x-5y=24?

A steel ball is dropped from a building’s roof and passes a window, taking 0.125 s to fall from the top to the bottom of the win

Anna35 [415]

Answer:

20.425 m

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

$s=ut+\frac{1}{2}at^2\\\Rightarrow u=\frac{s-\frac{1}{2}at^2}{t}\\\Rightarrow u=\frac{1.2-\frac{1}{2}\times 9.81\times 0.125^2}{0.125}\\\Rightarrow u=8.98\ m/s$

Now this will the final velocity when it reaches the top of the window

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{8.98^2-0^2}{2\times 9.81}\\\Rightarrow s=4.11\ m$

$v=u+at\\\Rightarrow v=8.98+9.81\times 0.125\\\Rightarrow v=10.21\ m/s$

If the upward flight is an exact reverse of the downward flight then the time taken while going down will be 1 second and going up will be 1 second.

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=10.21\times 1+\frac{1}{2}\times 9.81\times 1^2\\\Rightarrow s=15.115\ m$

Hence total height of the building is 4.11+1.2+15.115 = 20.425 m

4 0

4 years ago

jacks tent is shaped like an isosceles triangle. the height of the tent measures 7 feet and the diagonal side measures 9 feet. f

Maru [420]

Answer:

$8\sqrt{2}\ ft$

Step-by-step explanation:

see the attached figure to better understand the problem

Remember that

An isosceles triangle has two equal sides and two equal interior angles

In the isosceles triangle ABC

Applying the Pythagorean Theorem

Let

b ----> the length of the tents base

$9^2=7^2+(b/2)^2$

$(b/2)^2=9^2-7^2$

$(b^2/4)=32$

$b^2=128\\\\b=\sqrt{128}\ ft$

simplify

$b=8\sqrt{2}\ ft$

7 0

4 years ago

A student walks a distance of 3km in 20minutes. calculate his average speed

NNADVOKAT [17]

Answer:

9 Km/h

Step-by-step explanation:

Walking 3 Km for 20 minutes from the definition of speed, it's distance covered per unit time. Here, the distance covered is expressed per unit hour.

$Speed=\frac {distance}{time}$

Substituting 3.5 Km for distance and time for 20 minutes

To convert time into hours, we divide the minutes by 60 hence time=20/60=1/3 hours

$Speed=\frac {3 Km}{1/3 hours}=9 Km/h$

Therefore, the speed is 9 Km/h

4 0

3 years ago

7x+3x+3=4x+6 what is x

vovikov84 [41]

Answer:

x = 1/2

Step-by-step explanation:

Simplify the sides of the equation...

10x + 3 = 4x + 6

Subtract 3 from both sides...

10x = 4x + 3

Subtract 4x from both sides...

6x = 3

Divide by 6

x = 1/2

Thank me later :)

(or just give brainliest)

7 0

3 years ago

Read 2 more answers

Solve the equation x^2+17x+12=-3x^2 to the nearest tenth.

mote1985 [20]

Answer:

$x=-\frac{17}{8}+\frac{\sqrt{97} }{8}$ or $x=-\frac{17}{8}-\frac{\sqrt{97} }{8}$

Step-by-step explanation:

$x^2+17x+12=-3x^2$

Add $3x^2$ on both sides.

$x^2+17x+12+3x^2=-3x^2+3x^2$

$x^2+17x+12+3x^2=0$

Combine like terms;

$4x^2+17x+12=0$

Use the quadratic formula;

a=4

b=17

c=12

$x=\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}$

$x=\frac{-(17)\frac{+}{}\sqrt{(17)^2-4(4)(12)} }{2(4)}$

$x=\frac{-17\frac{+}{}\sqrt{289-192} }{8}$

$x=\frac{-17\frac{+}{}\sqrt{97} }{8}$

$x=-\frac{17}{8}+\frac{\sqrt{97} }{8}$ or $x=-\frac{17}{8}-\frac{\sqrt{97} }{8}$

6 0

3 years ago