An architect makes a scale drawing of a building. The scale used is 1 cm represents 20 m. Calculate the actual width of the building if the width on scale drawing is 24.5 cm

Given:

The height of the triangular prism is 15 cm.

The side lengths of the base are 3 cm, 4 cm and 5 cm.

To find:

The lateral surface area of the prism.

Solution:

The lateral surface area of the prism is:

[tex]LSA=Ph[/tex]

Where, P is the perimeter of base and h is the height of the prism.

We know that the perimeter of base is the sum of all sides of the base.

The perimeter of the prism is (3+4+5) cm and the height of the prism is 15 cm.

So, the lateral surface area of the prism is:

[tex]LSA=(3+4+5)\times 15[/tex]

[tex]LSA=(12)\times 15[/tex]

[tex]LSA=180[/tex]

Therefore, the lateral surface area of the prism is 180 square cm.

Answer:

D. Axis of symmetry: x = –0.5; Vertex: (–0.5, 0.75); f(x) = x2 + 2x + 1

Step-by-step explanation:

A. Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:  

( 1 /2 , 1 /4 )

Focus:  

( 1 /2 , 0 )

Axis of Symmetry:  

x

=

1

2

Directrix:  

y

=

1

2

x

y

− 2

− 6

− 1

− 2

1

2

1

4

1

0

2

− 2

B. Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

( − 1 /2 , 3 /4 )

Focus:  

( − 1 /2 , 1 )

Axis of Symmetry:  

x

=

−

1

2

Directrix:  

y

=

1

2

x

y

− 2

3

− 1

1

− 1

2

3

4

1

3

2

7

C. Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

( 1 /2 , 3 /4 )

Focus:  

( 1 /2 , 1 )

Axis of Symmetry:  

x

=

1

2

Directrix:  

y

=

1

2

x

y

− 2

7

− 1

3

1

2

3

4

1

1

2

3

D. Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:  

( − 1 , 0 )

Focus:  

( − 1 , 1 /4 )

Axis of Symmetry:  

x

=

− 1

Directrix:  

y

=

− 1

4

x

y

− 3

4

− 2

1

− 1

0

0

1

1

4

Answer:

x = 21

Step-by-step explanation:

For a pentagon, n = 5.

Each angle measures:

(n - 2)180/5 = (5 - 2)(180)/5 = 108

5x + 3 = 108

5x = 105

x = 21

Answer:

a

Step-by-step explanation:

calculator

Answer:

convert km into m

1 km=1000m

360 km=1000*360m

=360000m

again,convert 3 hours into seconds

3 hours=60*60*3

=10800 second

average spped=total distance /time taken

=360000/10800

=33.33 m/s

Step-by-step explanation:

Answer:

x=67

y=40

The angles equal 63 and 117

Step-by-step explanation:

88% sure

Answer:

x = 19°

Step-by-step explanation:

We know that ∠UTV and ∠RTS are vertical angles, therefore is the measure of ∠UTV = 85, then the measure of ∠RTS would also be 85, by the "Vertical angles are congruent theorem.

=> ∠UTV ≅ ∠RTS

=> ∠UTV = 85°

=> ∠RTS = 85°

Now that we know all three angles of within the triangle, we can say that the sum of all three angles within the triangle is 180, we can conclude;

∠R + ∠T + ∠S = 180°

(3x) + (85°) + (2x) = 180°

5x + 85° = 180°

5x = 180° - 85°

5x = 95

x = 95/5

x = 19°

Hence, there is you're answer! x = 19°

Hope this helps!

Answer:

The Richter scale and how it measures earthquake magnitude. The Richter scale calculates an earthquake's magnitude (size) from the amplitude of the earthquake's largest seismic wave recorded by a seismograph. ... (That is, an earthquake measuring 5.0 releases 31 times more energy than an earthquake measuring 4.0.)

Answer:

RS = 19

Step-by-step explanation:

Given a segment joining the midpoints of 2 sides of a triangle then it is half the length of the third side, that is

- 5x + 44 = [tex]\frac{1}{2}[/tex] (18 + 4x) ( multiply both sides by 2 to clear the fraction )

- 10x + 88 = 18 + 4x ( add 10x to both sides )

88 = 18 + 14x ( subtract 18 from both sides )

70 = 14x ( divide both sides by 14 )

5 = x

Then

RS = - 5x + 44 = - 5(5) + 44 = - 25 + 44 = 19

Answer:

47

Step-by-step explanation:

The missing angle is complementary to the angle shown and together they from 90.

Your missing angle is 90 - 43

Answer:

Find the are

Step-by-step explanation:

pi method

Answer:

$1182.65

Step-by-step explanation:

Given :

Fortnight gross pay = $1300

Given :

PAYE: $31.85 FNPF: 5% HEALTH INSURANCE: $20.50 calculate her fortnightly net pay

FNPF = 5% = 0.05 * $1300 = $65

PAYE = $31.85 ; HEALTH INSURANCE = $20.50

Total deduction = $(65 + 31.85 + 20.50) = $117.35

Net pay :

Gross pay - deduction

$1300 - $117.35 = $1182.65

Answer:

19.5 dollars

Step-by-step explanation:

9.75% of 200 is 19.5

Answer:

76 m²

Step-by-step explanation:

The figure has been decomposed into 3 rectangles as shown in the attachment. Therefore:

Area of the figure = area of rectangle 1 + area of rectangle 2 + area of rectangle 3

✔️Area of rectangle 1:

Area = L*W

L = 2 m

W = 4 m

Area = 2*4 = 8 m²

✔️Area of rectangle 2:

Area = L*W

L = 4 m

W = 6 - 4 = 2 m

Area = 4*2 = 8 m²

✔️Area of rectangle 3:

Area = L*W

L = 10 m

W = 6 m

Area = 10*6 = 60 m²

✅Area of the figure = 8 + 8 + 60

= 76 m²

Answer:

20.25

Step-by-step explanation:

21-3/4=20.25

Answer:

Step-by-step explanation:

a+b=21

a=21-b

b=3/4*a

b=3/4*(21-b)

b=3(21-b)/4

b=63-3b/4

4*b=63-3b

4b+3b=63

7b=63

b=63/7

b=9

Answer:

$318

Step-by-step explanation:

Calculation to determine the predicted end-of-year value of a portfolio

Given expression 1.08s + 1.02b

Now let determine the Predicted end-of-year value

Predicted end-of-year value=1.08(200) +1.02(100)

Predicted end-of-year value=216+102

Predicted end-of-year value=$318

Therefore the predicted end-of-year value of a portfolio will be $318

Step-by-step explanation:

I used Pythagoras Theorem to find the diagonal distance as placement of objects is right angles triangle.

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

a : Elm street

b : Birch street

c : Diagonal distance

c^2 = a^2 + b^2

c^2 = 15^2 + 8^2

c^2 = 225 + 64

c = √289

c = 17 blocks

I added the total distance of the original route Joline took

= 15 blocks + 8 blocks

= 23 blocks

How much less distance does she have to walk if she took the diagonal route

= Total distance of original route - distance of diagonal route

= 23 - 17

= 6 blocks

Joline have to walk less 6 blocks if she took the diagonal route compared to her original route

They have equal lengths is the correct answer

Answer:

62 degrees

Step-by-step explanation:

Every triangle needs to have 180 degrees. Simply you have to add 60+58 which is 118 degrees. Then you subtract 180-118 which equals to 62 degrees.

Answer:

1/4¹⁰

Step-by-step explanation:

this is the the simplified version for the question

Answer:

420

Step-by-step explanation:

just multiply all the numbers together

Answer: 420 cubic inches

Step-by-step explanation:

Use the formula V = lwh to solve.

V = L * W * H

V = 6 * 7 * 10

V = 420 cubic inches

Answer:

13

Step-by-step explanation:

3h - j

3(8) - 11

24 - 11

13

Answer:

It's

Step-by-step explanation:

4:45am. That's the correct answer

15 minutes before 5 in the morning is written as 4:45am

Answer:

x=2

Step-by-step explanation:

Hi there!

Whenever we're solving an algebraic equation, our goal is always to isolate the variable, which in this case is x. We would do this by performing inverse operations on both sides of the equal sign to cancel values out.

[tex]10-2x + 3 = 5x-9 + 4x[/tex]

Combine like terms on both sides of the equal sign

[tex]10+ 3-2x = 5x+ 4x-9 \\13-2x = 9x-9[/tex]

Add 2x to both sides to cancel out -2x (addition is the inverse of subtraction)

[tex]13-2x +2x = 9x-9 +2x\\13 = 11x-9[/tex]

Add 9 to both sides to cancel out -9 and isolate 11x (addition is the inverse of subtraction)

[tex]13+9 = 11x-9+9\\22=11x[/tex]

Divide both sides by 11 to isolate x (division is the inverse of multiplication)[tex]\frac{22}{11} =\frac{11x}{11} \\2=x[/tex]

Therefore, x=2.

I hope this helps!

Answer:

[tex]22[/tex]

Step-by-step explanation:

Similar shapes must have corresponding sides in a constant proportion. Therefore, we can set up the following equation and solve for [tex]?[/tex]:

[tex]\frac{28}{42}=\frac{?}{33}[/tex] (divide corresponding sides)

[tex]\frac{28}{42}=\frac{?}{33},\\\\?=\frac{28\cdot 33}{42}=\boxed{22}[/tex]

Answer:

I think the answer is 112.098 yards

Answer:

112 yards

It's 112.098, but the question says "about _____ yards", so I'd round it.

Step-by-step explanation:

Circumference is calculated by (2)(pi)(radius) or (pi)(diameter). We'll use the second one, since they gave you the diameter.

C = (pi)(diameter)

C = (3.14)(35.7)

C =112.098

Answer:

-50x+40

Step-by-step explanation:

Answer:

When you fold the number line ( vertically through the point zero on the number line ) you have successfully divided the number line into 2 equal halves.

Step-by-step explanation:

When you fold the number line ( vertically through the point zero on the number line ) you have successfully divided the number line into 2 equal halves. and this causes the points labelled on either side of the number line  to match up with with the points on the opposite side

Answer:

The volume of the hollow ball will be equal to the difference between the volume of a sphere with the outer radius and the volume of a sphere with the inner radius.

Remember that the volume of a sphere of radius R is given by:

V = (4/3)*pi*R^3

where pi = 3.14

Then if R is the outer radius, and r is the inner radius, the volume of the hollow ball is:

V = (4/3)*pi*( R^3 - r^3)

In this case, we have:

R = 200m

r = 100m

Then the volume of the hollow ball is:

V = (4/3)*3.14*( (200m)^3 - (100m)^3)

V = 29,306,666.67 m^3

Now, if this hollow ball is made of iron, we want to find the mass.

Remember the relation:

Mass = Density*Volume.

We know that the density of the iron is:

D = 7300 kg/m^3

Then the mass of this hollow ball is:

M = (7300 kg/m^3)*(29,306,666.67 m^3) = 213,938,666,666.6 kg