For the polyhedron, use Euler's Formula to find the missing number.

7 + 2y = 8x 3x - 2y = 0 Solve the system of equations by substitution. (70/3, 140/9) (7/5, 21/10) no solution coincident

Wittaler [7]

So we have the system of equations:
$7+2y=8x$ equation (1)
$3x-2y=0$ equation (2)

To use substitution, we are going to solve for one variable in one of our equations, and then we are going to replace that value in the other equation:
Solving for $x$ in equation (2):
$3x-2y=0$
$3x=2y$
$x= \frac{2}{3}y$ equation (3)

Replacing equation (3) in equation (1):
$7+2y=8x$
$7+2y=8( \frac{2}{3} y)$
$7+2y= \frac{16}{3} y$
$7= \frac{10}{3} y$
$y= \frac{7}{ \frac{10}{3} }$
$y= \frac{21}{10}$ equation (4)

Replacing equation (4) in equation (3):
$x= \frac{2}{3}y$
$x=( \frac{2}{3} )( \frac{21}{10} )$
$x= \frac{7}{5}$

We can conclude that the solution of our system of equations is <span>(7/5, 21/10)</span>

5 0

3 years ago

Solve the system of equations by ELIMINATION.

Dafna1 [17]

Step-by-step explanation:

4x + 2y = 10 --------(1)

2x + 3y = 33 -----------(2)

Multiply 2 with eq. (1) and 4 with eq. (2)

8x + 4y = 20 ____________(3)

8x + 12y = 132 ______(4)

Subtracting (3) from (4),

8x + 4y = 20

- 8x -12y = -132

----------------------

0 -8y = -112

y = 112/8

y = 4 is the answer.

Putting the vakue of y in eq. (2),

2x + 12 = 33

2x = 33-12

2x = 21

x = 21/2 is the answer.

6 0

3 years ago

Area of a parallelogram if it was 2 cm and 6 cm

Contact [7]

You just multiply 2 times 6 which is 12

so 12 cm is your answer

7 0

3 years ago

Solve each triangle. Round your answers to the nearest tenth.<br>show work If possible

kvasek [131]

<h2>Answer:</h2>

∠ABC = 76°

BC = 20.1

CA = 28.0

<h2>Step-by-step explanation:</h2>

Solving the triangle means finding all unknown angles and sides of the triangle.

(i) Two of the angles (∠BCA = 60° and ∠CAB = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating <em>that the sum of angles of a triangle is equal to 180°.</em>

Therefore, the sum of angles of the triangle ABC is 180°. i.e

∠ABC + ∠BCA + ∠CAB = 180°

=> ∠ABC + 60° + 44° = 180°

=> ∠ABC + 104° = 180°

=> ∠ABC = 180° - 104°

=> ∠ABC = 76°

(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;

=> $\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}$

=> $\frac{sinBCA}{BA} = \frac{sinCAB}{BC} = \frac{sinABC}{CA}$

<em>Substitute the necessary values</em>

$\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}$ ---------------------(ii)

(a) To get side BC, use the first two terms of equation (ii)

$\frac{sin60}{25} = \frac{sin44}{BC}$

<em>Cross multiply</em>

BC x sin 60 = 25 x sin 44

BC x 0.8660 = 25 x 0.6947

0.8660 x BC = 17.3675

BC = $\frac{17.3675}{0.8660}$

BC = 20.05

=> BC = 20.1 to the nearest tenth

(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;

$\frac{sin60}{25} = \frac{sin76}{CA}$

<em>Cross multiply</em>

CA x sin 60 = 25 x sin 76

CA x 0.8660 = 25 x 0.9703

0.8660 x CA = 24.2575

CA = $\frac{24.2575}{0.8660}$

CA = 28.01

=> CA = 28.0 to the nearest tenth

5 0

3 years ago

Sambriddhi bent a rope to form a circle.If she got the circumference of the circle is 30cm more than its diameter. What was the

ivanzaharov [21]

easy peasy here we go..

so first circumference = 2π R

now it is given that circumference - 30 cm = Diameter;

Diameter = 2πR - 30 = 2 R { diameter = 2 times Radius}

now solving equations:

2πR -2R = 30

πR - R = 15

R ( π - 1 ) = 15

R ( 22/7 - 1) = 15

R ( 15/7 ) = 15

R = 15 x 7 / 15

R = 7 cm

Mark as brainliest

5 0

2 years ago

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