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3 years ago

If w = 10 units, x= 5 units, and y= 6 units, what is the surface area of the figure?

Mathematics

1 answer:

qwelly [4]3 years ago

4 0

Answer:

456.2 units²

Step-by-step explanation:

The area of the square base is ...

base area = w² = (10 units)² = 100 units²

The lateral area is 4 times the area of one rectangular face:

lateral area = 4wx = 4(10 units)(5 units) = 200 units²

The area of one triangular face is half the product of its base length (w) and its slant height (h). The latter is found using the Pythagorean theorem:

h² = y² +(w/2)² = (6 units)² +((10 units)/2)² = 61 units²

h = √61 units

So, the area of 4 triangles is ...

area of triangular faces = 4(1/2)wh = 2(10 units)(√61 units) ≈ 156.2 units²

Now we have the areas of the parts, so we can add them together to get the total surface area:

surface area = base area + lateral area + area of triangular faces

= 100 units² + 200 units² + 156.2 units²

surface area = 456.2 units²

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What is the slope of the line on this graph

Free_Kalibri [48]

Answer:

m = 1/2

Step-by-step explanation:

Look at the points on the graph and determine what the slope would be using the slope formula. y2-y1 / x2-x1.

2 - 0 / 0 - (-4)

2/4

1/2

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2 years ago

Read 2 more answers

Jamal is helping pack prize bags for the school carnival. He has 73 pencils to put into 16 bags. He wants to put the same number

valentina_108 [34]

Answer:

Step-by-step explanation:

I73/16 = 4.52

If he wants to put the same number in each bag, he would put 4 in each bag because the pencils cannot be cut into 0.52

3 0

2 years ago

2x + 6 = 10 x= whats the answer?

vazorg [7]

Answer:

x is 2

Step-by-step explanation:

you need to do 10-6 is 4 then 2x? is 4

6 0

2 years ago

9. A ladder of length 23 feet leans against the side of a building. The angle of elevation of the ladder is 76. Find the distanc

irakobra [83]

<h3>Answer:</h3>

B) 22.32 feet

$\quad\rule{300pt}{1pt}$

<h3>Solution:</h3>

we are given that , a ladder is placed against a side of building , which forms a right angled triangle . We wre given one side of a right angled triangle ( hypotenuse ) as 23 feet and the angle of elevation as 76 ° . We can find the Perpendicular distance from the top of the ladder go to the ground by using the trigonometric identity:

$\qquad\quad\bull ~{\boxed{\bf{ Sin\theta =\dfrac{Perpendicular}{Hypotenuse}}} }~\bull$

Here,

hypotenuse = 23 feet
$\theta$ = 76°
Value of Sin $\theta$ = 0.97
Perpendicular = ?

$\quad\dashrightarrow\quad \sf { sin\theta =\dfrac{P}{H}}$

$\quad\dashrightarrow\quad \sf { sin76° =\dfrac{P}{23}}$

$\quad\dashrightarrow\quad \sf { 0.97=\dfrac{P}{23}}$

$\quad\dashrightarrow\quad \sf {P = 0.97 \times 23 }$

$\quad\dashrightarrow\quad \sf { P = 22.32}$

‎ㅤ‎ㅤ‎ㅤ~Hence, the distance from the top of the ladder to the ground is 22.32 feet !

$\rule{300pt}{2pt}$

4 0

2 years ago

Can anyone help? Thank you.

Tcecarenko [31]

Answer:

91.8 ft

Step-by-step explanation:

So we can talk about the diagram, let's name a couple of points. The base of the tree is point T, and the top of the tree is point H. We want to find the length of TH given the length AB and the angles HAT and ABT.

The tangent function is useful here. By its definition, we know that ...

TA/BA = tan(∠ABT)

and

TH/TA = tan(∠HAT)

Then we can solve for TH by substituting for TA. From the first equation, ...

TA = BA·tan(∠ABT)

From the second equation, ...

TH = TA·tan(∠HAT) = (BA·tan(∠ABT))·tan(∠HAT)

Filling in the values, we get ...

TH = (24.8 ft)tan(87.3°)tan(9.9°) ≈ 91.8 ft

The height h of the tree is about 91.8 ft.

6 0

3 years ago