51 is 85% of what number? A) 1.67 B) 51 C) 60 D) 43.35

Identify the lateral area and surface area of a regular square pyramid with base edge length 5 in. and slant height 9 in.

Galina-37 [17]

Note that a squared pyramid has a square base & 4 equal triangles.
To find the lateral the lateral area you calculate the area of the 4 equal triangles and to find the surface area (total Area) you add the area of the base:

Area of each triangle = side (5) x slant (9) and you divide by 2

==>Aera of 1 triangle = (9x5)/2 = 45/2 & for the 4 triangles

Lateral area = (45/2) x 4 = 90 in²

Now the base area (square) = 5 x 5= 25 in²

so the surface area = 90+25 = 115 in² (answer a)

7 0

3 years ago

A rocket is launched straight up from the ground with an initial velocity of 192 feet per second. The equation for the height of

Ivenika [448]

The equation for the height of the rocket at time t given

$h= -16t^2+192t$

We have to find the time t, when the rocket reaches 560 feet.

That means we have to find t when h = 560 ft. we will place 560 in the place of h to find t now.

$h= -16t^2+192t$

$560 = -16t^2+192t$

In the right side, we can check -16 is the common factor. So we will take out -16 from the rigbht side.

$560 = -16(t^2 - 12t)$

To get rid of -16 from the right side and move it to left side, we will divide both sides by -16.

$560/-16 = -16(t^2-12t)/-16$

$-35 = t^2 -12t$

Now we will move -35 to the righ side by adding 35 to both sides.

$-35+35 = t^2-12t+35$

$0 = t^2 -12t+35$

$t^2-12t+35 = 0$

We will factorize thee left side to find the values of t now. We need to find a pair of factors of 35 that by adding them we will get -12.

The pair of factors of 35 are -5 and -7 and by adding -5-7 we will get -12.

$t^2-12t+35 =0$

$(t-5)(t-7) =0$

So by using zero product property we will get

$t-5 =0$

$t-5+5 = 0+5$

$t=5$

Also $t-7 =0$

$t-7+7 = 0+7$

$t=7$

So we have got the rocket reaches at 560ft when t = 5 seconds and also when t = 7 seconds.

Now part b.

When the rocket completes its trajectory and hits the ground then the height or h = 0. So we will place h = 0 there in the equation.

$h= -16t^2+192t$

$0= -16t^2 + 192 t$

$0 = -16(t^2-12t)$

$-16(t^2-12t) = 0$

We will move -16 to the other side by dividing it to both sides.

$-16(t^2-12t)/-16 = 0/-16$

$t^2-12t = 0$

We will take out the common factor t from the left side. By taking out t we will get,

$t(t-12) = 0$

We will use zero product property now. By using that we will get,

$t = 0$

ans also $t-12 = 0$

$t-12+12 = 0+12$

$t = 12$

When the rocket completes its trajectory and hits the ground the time t can not be 0. When t =0, the rocket starts the trajectory.

So when the rocket completes its trajectory and hits the ground ,

then t = 12seconds.

So we have got the required answers.

6 0

3 years ago

Pleaseee helpp answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!

Alinara [238K]

So you have to add all the numbers to get the perimeter or the outside distance but it looks like t and s is there a few times so that’s were you have to simplify.
So here’s the answer simplified
4t+2s+w+v+x+u
Good luck!

8 0

3 years ago

1. Write an expression in simplest form for the area of the figure below: (answer pls)

san4es73 [151]

Answer:

(5x+6)(2x+5)-(2x+4)(x+8) simplified is 8x^2+17x-2

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Change 34.55% to a decimal

Jet001 [13]