Find the surface area of the following figures 16 ft 13 ft 12ft 19ftPlease help me solve number 3! And if i got #2 incorrect, please help me fix that one too.

Answers

Answer 1

Answer:

Answer:

1192 ft²

Step-by-step explanation:

Figure 3 is a trapezoidal prism.

The total surface area of a trapezoidal prism is made up of 2 congruent trapezoid bases and 4 rectangular faces connecting the bases.

The formula for the area of a trapezoid is:

$\boxed{S.A.=(1)/(2)(a+b)h}$

where a and b are the bases, and h is the height.

From observation of the given diagram, the bases are 16 ft and 19 ft, and the height is 12 ft. Therefore, the area of each trapezoid base is:

$\begin{aligned}\textsf{Area of trapezoid base}&=(1)/(2)(16+19)\cdot 12\n\n&=(1)/(2)(35)\cdot 12\n\n&=17.5\cdot 12\n\n&=210\; \sf ft^2\end{aligned}$

To calculate the areas of all the rectangular faces, we first need to calculate the slant (s) of the trapezoid base by using the Pythagoras Theorem:

$\begin{aligned}s^2&=(19-16)^2+12^2\ns^2&=3^2+12^2\ns^2&=9+144\ns^2&=153\ns&=√(153)\end{aligned}$

The area of a rectangle is the product of its width and length.

Therefore, the sum of the areas of the rectangular faces is:

$\begin{aligned}\textsf{Area of rectangular faces}&=16\cdot13+12\cdot13+19\cdot13+√(153)\cdot13\n&=208+156+247+13√(153)\n&=771.801119...\n&=772\; \sf ft^2\;(nearest\;foot)\end{aligned}$

To find the total surface area of the given trapezoidal prism, sum the area of the two trapezoid bases and the area of the rectangular faces:

$\begin{aligned}\textsf{Total S.A.}&=2 \cdot 210+772\n&=420+772\n&=1192\; \sf ft^2\end{aligned}$

Therefore, the total surface area of the given trapezoidal prism is 1192 ft², rounded to the nearest foot.

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Plz help on question 15 through 17

It takes 12 hours to clean the windows of a certain office building. During the first day of cleaning, the workers were able to clean for 9 hours. If the variable t stands for the amount of time the workers have left to clean the windows, which of the following choices is the most reasonable value for t?A.
3 hours

B.
1 hour

C.
30 hours

D.
20 hours

Answers

the most reasonable value for t would be A. 3 hours.

Since it would take 12 hours to clean the place and the workers already cleaned for 9 hours, there is still 3 hours left to completely clean the office building. (12 - 9 = 3)

If you would like to know which of the following choices is the most reasonable value for t, you can calculate this using the following step:

t ... the amount of time the workers have left to clean the windows
t = 12 hours - 9 hours = 12 - 9 = 3 hours

The correct result would be A. 3 hours.

What is the distance between points (10, 7) and (2, 7) on a coordinate plane?

Answers

The distance between points (10, 7) and (2, 7) on a coordinate plane is 8 units.

The given coordinate points are (10, 7) and (2, 7).

What is distance formula?

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x1, y1) and (x2, y2) is Distance = √[(x2-x1)²+(y2-y1)²].

Substitute (x1, y1)=(10, 7) and (x2, y2)=(2, 7) in the distance formula, we get

Distance = √[(2-10)²+(7-7)²]

= √64

= 8 units

Therefore, the distance between points (10, 7) and (2, 7) on a coordinate plane is 8 units.

To learn more about the distance formula visit:

brainly.com/question/27262878.

#SPJ2

Hey there, you can solve this using the distance formula!

$Distance = \sqrt{(x_(2)- x_(1))^2+(y_(2)- y_(1))^2}$

Where $x_(1)$ = 10
$x_(2)$ = 2
$y_(1)$ = 7
$y_(2)$ = 7

So...
$Distance = √((2- 10)^2+(7- 7)^2)$
$Distance = √((-8)^2+(0))$
$Distance = √(64)$
Distance = 8 units

Find the exponential function that satisfies the given conditions: Initial value = 31, increasing at a rate of 10% per year f(t) = 10 ⋅ 1.1t
f(t) = 31 ⋅ 1.1t
f(t) = 31 ⋅ 0.1t
f(t) = 31 ⋅ 10t

Answers

Option 2: $f(t) = 31.(1.1)^t$ is the correct answer.

Step-by-step explanation:

Let t be the independent variable time and f(t) be the function that will be used to represent the exponential growth

The general form of an exponential function is given by:

$y = a(1+r)^t$

Here

a is the initial value of the function while r is the growth rate

and t is the number of years

Given

Initial value = 31

Growth rate = 10% per year

We have to convert the growth rate in decimal

So,

$r = (10)/(100) = 0.1$

Putting the values in the general form

$f(t) = 31 . (1+0.1)^t\nf(t) = 31 . (1.1)^t$

Hence,

Option 2: $f(t) = 31.(1.1)^t$ is the correct answer.

Keywords: Functions, exponential functions

Learn more about functions at:

#LearnwithBrainly

5 hundreds + 4 tens= ____ tens

Answers

Oh ok!

How many tens are in 100? =10

so, 10 * 5 = 50

Now, 50 + 4 = 54!

Hope so now i get it correct!

A function f is depicted in the graph. Find any input values that produce the indicated output. f(x) = -1

Answers

See that the point (-2,-1) belongs to graph, so (-2,-1) is one searched point

Y - 2 = 1/2 (x + 6) goes through which point?

Answers

According to the point slope formula:
y-y1=m(x-x1).
Here y1 = 2 according to the given equation.
and x1 = (-6).
Therefore,the line passes through the point P(x1,y1) or
P(-6,2).
Final Answer:P(-6,2).