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3 years ago

27 is 12% of what number?

Mathematics

2 answers:

timofeeve [1]3 years ago

5 0

27 is 12% of 225

you can find this by dividing 27 by 0.12

umka21 [38]3 years ago

4 0

Let the value be x

putting it in eqn ;
12℅ of X = 27
so, x = 2700/12 = 225 !!

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Find the perimeter of Triangle ABC with the verticies A(-5,5) B(3,-5) and C(-5,1

finlep [7]

Hello!

Let's calculate a distance between two points using the Pythagorean theorem:

 $d ^ 2_ {AB} = (x_ {B} - x_ {A}) ^ 2 + (y_ {B} - y_ {A}) ^ 2$

Data:

$x_B = 3 

x_A = -5 

y_B = -5 

y_A = 5 

d_ {AB} =?$

Solving: distance from A to B

$d^ 2_ {AB} = (x_ {B} - x_ {A}) ^ 2 + (y_ {B} - y_ {A}) ^ 2 

d^ 2_ {AB} = (3 - (-5)) ^ 2 + (-5 - 5) ^ 2 

d^ 2_ {AB} = (8) ^ 2 + (-10) ^ 2 

d^ 2_ {AB} = 64 + 100 

d^ 2_ {AB} = 164 

d_{AB} = \sqrt {164} 

d_{AB} = \sqrt {2 ^ 2 * 41} 

\boxed {d_ {AB} = 2 \sqrt {41}}$

Solving:

distance from A to C

$d ^ 2_ {AC} = (x_ {C} - x_ {A}) ^ 2 + (y_ {C} - y_ {A}) ^ 2$

Data:

$x_C = -5
 
x_A = -5
 
y_C = 1 

y_A = 5 

d_ {AC} =?$

$d^ 2_ {AC} = (x_ {C} - x_ {A}) ^ 2 + (y_ {C} - y_ {A}) ^ 2 

d^ 2_ {AC} = (-5 - (-5)) ^ 2 + (1 - 5) ^ 2 

d^ 2_ {AC} = (0) ^ 2 + (-4) ^ 2 

d^ 2_ {AC} = 0 + 16 

d^ 2_ {AC} = 16 

d_ {AC} = \sqrt {16} 

\boxed {d_ {AC} = 4}
$

Solving:

distance from B to C

$d^ 2_ {BC} = (x_ {C} - x_ {B}) ^ 2 + (y_ {C} - y_ {B}) ^ 2$

Data:

$x_C = -5 

x_B = 3 

y_C = 1 

y_B = -5 

d_ {BC} =?$

$d^ 2_ {BC} = (x_ {C} - x_ {B}) ^ 2 + (y_ {C} - y_ {B}) ^ 2
 
d^ 2_ {BC} = (-5 - 3) ^ 2 + (1 - (-5)) ^ 2

d^ 2_ {BC} = (-8) ^ 2 + (6) ^ 2 

d^ 2_ {BC} = 64 + 36

d^ 2_ {BC} = 100 

d_ {BC} = \sqrt {100}

\boxed {d_ {BC} = 10}$

Now let's calculate the perimeter of the triangle ABC, knowing that the perimeter is the sum of the sides, then:

$p = d_ {AB} + d_ {AC} + d_ {BC} 

$

$p = 2\sqrt {41} + 4 + 10$

$
\boxed {\boxed {p = 14 + 2 \sqrt {41}}} \end {array}} \qquad \quad \checkmark$

8 0

3 years ago

Which property is displayed in the example below: 4(x + 3) = 4x + 12

Veseljchak [2.6K]

Answer:

This equation displays the distributive property which states that a(b + c) = a(b) + a(c).

3 0

3 years ago

Read 2 more answers

What is the volume of the prism?

Triss [41]

Answer:

volume of hexagonal prism = area of base * perpendicular height

Step-by-step explanation:

4 0

3 years ago

An airplane takes 4 hours to travel a distance of 2600 miles with the wind. The return trip takes 5 hours against the wind. Find

tankabanditka [31]

2,600/4 =650
650•5 =3,250

I found the unit rate of the 2,600 by dividing the per hour and then times it by the 5 hours

Hopefully that was what you were looking for

3 0

3 years ago

In a certain year, there were 92 female officials in Congress, which is comprised of the House of Representatives and the Senate

crimeas [40]

Answer:

There are 78 female members of the House of Representatives and 14 female members of the Senate.

Step-by-step explanation:

Let h equal the amount of female members of the House of Representatives and s equal the amount of female members in the Senate.

Since the amount of female officials in Congress is 92, and is made up of the House of Representatives and the Senate, we can represent this as the equation h+s=92

Since there are 64 more female members in the House of Representatives than female Senators, the senators would need 64 more female members to have the same amount as the House of Representatives. We can represent this as h=s+64.

Substituting, we get s+64+s=92, which simplifies to 2s+64=92. Subtracting 64 from both sides, we get 2s=28, which equals to s=14. There are 14 female senators. Substituting back into h+s=92, 14+s=92, and s=78. Therefore, there are 78 female members of the House of Representatives and 14 female members of the Senate.

8 0

2 years ago