I need a step by step explanation, please.

SSSSS [86.1K]

Answer:

AB = BC = 2√2

Step-by-step explanation:

Start by focusing on the 45 degree angle. The unknown AB is the side adjacent to this 45 degree angle, and the hypotenuse is known to be 4.

Thus,

cos 45 degrees = adj / hyp = AB / 4, or

AB = 4 cos 45 degrees = 4 (1 / √2) =

4 √2

----------- * --------- = 2√2

√2 √2

Since this is a 45-45-90 triangle, the two shorter sides are equal, and so BC = 2√2 also.

3 0

3 years ago

A rectangular prism has a base that is 5 cm by 7 cm and a height of 12 cm. If all dimensions are doubled, what happens to the vo

Delvig [45]

Answer:

volume becomes 8 times of original rectangular prism

Step-by-step explanation:

Given dimension of prism : 5 cm by 7 cm and a height of 12 cm

volume of prism is given by = length * width * height

thus volume of given prism = 5*7* 12 cubic cm = 420 cubic units.

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next given that all the dimensions are double

the new dimension are

width = 5*2 cm = 10 cm

length = 7*2 cm = 14 cm

height = 12*2 cm = 24 cm

Volume of new prism = 10*14*24 cubic cm = 3,360 cubic units.

3,360 = 8*420 (420 is volume of original cube)

Thus , volume becomes 8 times of old rectangular prism.

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it can be solved even if we do not have any dimension.

if x,y ,z care dimension of rectangular prism

then its volume = x*y*z cubic units

now if dimension are doubled then new dimensions are

2x,2y,2z

thus,

new volume = 2x*2y*2z cubic units = 8xyz cubic units

Thus , we see volume is 8 times of original cube.

3 0

3 years ago

Greenfield village is spread across 240 acres of land. Only 37% of the land is used for the exhibits, while the rest of the land

irinina [24]

88.8 acres are used for exhibits

Step-by-step explanation:

Given

Total area of Greenfield = 24 acres

Percentage of lad for exhibits = 37%

Now,

$Acres\ used\ for\ exhibits = 37\%\ of\ 240\\= \frac{37}{100} * 240\\=0.37*240\\=88.8\ acres$

Hence,

88.8 acres are used for exhibits

Keywords: Percentage, percent

Learn more about percentage at:

#LearnwithBrainly

6 0

3 years ago

A rock falls off a balcony. It’s height(in feet)is given by the formula f(x)= -16t^2+12.5t+150, where t is measured in seconds.

ELEN [110]

Answer: $3.47\ seconds$

Step-by-step explanation:

Given the following function:

$f(x)= -16t^2+12.5t+150$

You need to follow these steps in order to solve the exercise:

1. Substitute $f(x)=0$ :

$0= -16t^2+12.5t+150$

2. Now you need to apply the Quadratic formula. This is:

$x=t=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

In this case, you can identify that:

$a=-16\\b=12.5\\c=150$

Then, you can substitute these values into the formula:

$t=\frac{-12.5\±\sqrt{(12.5)^2-4(-16)(150)}}{2(-16)}$

3. Evaluating, you get:

$t_1=3.47\\\\t_2=-2.69$

4. You must choose the positive value. Then:

$t=3.47\ seconds$

7 0

4 years ago

An automobile depreciates by 20% per year. how soon will it be worth only half its original value? [hint: depreciation is like i

dimaraw [331]

1/2p=p (1-0.2)^t
1/2=(1-0.2)^t
1/2=(0.8)^t
Log (1/2)=t×log (0.8)
T=log(1÷2)÷log(0.8)
T=3.1 years

8 0

4 years ago