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3 years ago

PLEASEEEE

Mathematics

1 answer:

belka [17]3 years ago

3 0

Answer:

The answer to your questions is: 25 new teachers

Step-by-step explanation:

Data

# of students = 2000

ratio = 3:80 teachers to students

New teachers = ?

Process

I suggest to use rule of three to solve this problem

3 teachers ---------------- 80 students

x ---------------- 2000 students

x = (2000 x 3) / 80 = 75 teachers

Number of initial teachers = 75

The ratio change to 1:20

1 teacher ------------------- 20 students

x ------------------- 2000 students

x = (2000 x 1) / 20

x = 100 teachers

Number of new teachers = 100 - 75 = 25

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In the circle below, suppose m VUX = 152° and mZUVW = 77º. Find the following.

bezimeni [28]

Given:

In the circle, $m(\overarc{VUX})=152^\circ$ and $m(\angle MUV)=77^\circ$ .

To find:

The following measures:

(a) $m\angle VUX$

(b) $m\angle UXW$

Solution:

According to the central angle theorem, the central angle is always twice of the subtended angle intercepted on the same same arc.

$m(VUX)=2\times m\angle VWX$

$152^\circ=2\times m\angle VWX$

$\dfrac{152^\circ}{2}=m\angle VWX$

$76^\circ=m\angle VWX$

In a cyclic quadrilateral, the opposite angles are supplementary angles.

UVWX is a cyclic quadrilateral. So,

$m\angle VUX+m\angle VWX=180^\circ$ [Opposite angles of a cyclic quadrilateral]

$m\angle VUX+76^\circ=180^\circ$

$m\angle VUX=180^\circ-76^\circ$

$m\angle VUX=104^\circ$

Now,

$m\angle UXW+m\angle UVW=180^\circ$ [Opposite angles of a cyclic quadrilateral]

$m\angle UXW+77^\circ =180^\circ$

$m\angle UXW=180^\circ-77^\circ$

$m\angle UXW=103^\circ$

Therefore, $m\angle VUX=104^\circ$ and $m\angle UXW=103^\circ$ .

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3 years ago

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2 years ago

Algebra There were 4 times the number of students in fourth grade at the basketball game.How many students attended the basketba

denis-greek [22]

Answer:

200 students attended the basketball game

Step-by-step explanation:

The complete question in the attached figure

Let

x ------> the number of students in fourth grade

s -----> the number of students at the basketball game

we know that

The number of students at the basketball game is four times the number of students in fourth grade

The linear expression is

$s=4x$ -----> equation A

$x=50\ students\ in\ fourth\ grade$ -----> equation B

substitute equation B in equation A and solve for y

$s=4(50)$

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therefore

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