The length of a rectangle is 50m.this is 6m more than twice the width.find the width

Choose the correct option that explains what steps were followed to obtain the system of equations below

Dominik [7]

Answer:

option C is the correct answer

Step-by-step explanation:

System A: System B:

-x - 2y = 7 ........(1) -x - 2y = 7 .......(3)

5x - 6y = -3 ........(2) -16y= 32 ........(4)

Solution for system A: ( -3, -2)

For option A

Multiply the first equation by 3

3(- x - 2y) = 3(7) ⇒ - 3x - 6y = 21 ........... (5)

Add equation 2 and 5

5x - 6y = -3

- 3x - 6y = 21

2x -12y = 18 ⇒ 2( x - 6y ) = 2( 9 ) ⇒ x - 6y = 9

Option A is not equal to equation in system B so now we check option B.

For option B

Multiply the first equation by -5

-5(- x - 2y) = -5(7) ⇒ 5x + 10y = -35 ........... (6)

Add equation 2 and 6

5x - 6y = -3

5x + 10y = -35

10x + 4y = -38 ⇒ 2( 5x + 2y ) = 2(-19) ⇒ 5x + 2y = -19

Option B is not equal to equation in system B so now we check option C.

For option C

Multiply the first equation by 5

5(- x - 2y) = 5(7) ⇒ - 5x - 10y = 35 ........... (7)

Add equation 2 and 7

5x - 6y = -3

- 5x - 10y = 35

0 - 16y = 32 ⇒ -16y = 32

Option C is equal to equation in system b so now we check if the solution to system B is same as system A.

Solution to system B:

First, we find value of y from equation 4:

-16y = 32 ⇒ y = $\frac{32}{-16}$ ⇒ y = -2

Now, we put value of y in equation 3 to find value of x:

-x - 2y = 7 ⇒ -x - 2(-2) = 7 ⇒ -x + 4 = 7 ⇒ -x = 7 - 4 ⇒ -x = 3

multiply both sides by -1

-1 × (-x) = -1 × (3) ⇒ x = -3

Solution of system B = (-3, -2)

Solution of system B is the same as system A, so option C is correct.

6 0

3 years ago

Read 2 more answers

Please help me solve 5 and 6 for my homework

defon

Answer:

(5) The perpendicular height of the triangle is 8.48 mm.

(6) The 1184.86 cm far up the wall the ladder reach.

Step-by-step explanation:

Part (5):

When a perpendicular is drawn in an isosceles triangle then the perpendicular divided the base into 2 equal parts.

The figures is shown below.

In ΔABC,

CB = 6 mm

So,

CD = BD = 3 mm

Now calculating the perpendicular height of the triangle.

Using Pythagoras theorem in ΔADC:

$(AC)^2=(CD)^2+(AD)^2\\\\(9)^2=(3)^2+(AD)^2\\\\81=9+(AD)^2\\\\(AD)^2=81-9\\\\(AD)^2=72\\\\AD=8.48mm$

Thus, the perpendicular height of the triangle is 8.48 mm.

Part (6):

The figure is shown below.

Converting meter to centimeter:

1 m = 100 cm

So,

12 m = 1200 cm

Using Pythagoras theorem in ΔXYZ:

$(XZ)^2=(YZ)^2+(XY)^2\\\\(1200)^2=(190)^2+(XY)^2\\\\1440000=36100+(XY)^2\\\\(XY)^2=1440000-36100\\\\(XY)^2=1403900\\\\XY=1184.86cm$

Thus, 1184.86 cm far up the wall the ladder reach.

4 0

2 years ago

If you flip two coins 16 times, what is the best prediction possible for the number of times both coins will land on tails?

mr_godi [17]

Answer:

2×16

=32

Step-by-step explanation:

hope it helps..

8 0

3 years ago

2 At Bea's Pet Shop, the number of dogs, d, is initially five less than twice the number of cats, c. If she decides to add three

forsale [732]

Let D be dogs and C be cats

dogs, d, is initially five less than twice the number of cats, c

D + 5 = 2C

If she decides to add three more of each, the ratio of cats to dogs will be

D + 8 = 2C + 3

Could Bea's Pet Shop initially have 15 cats and 20 dogs?

Simply plug in the numbers

20 + 5 = 2(15)

This is clearly not true: 25 does not equal 30

7 0

3 years ago

The formula to find the spring constant, , for a spring with potential energy, , that has been stretched by length, , is shown b

aivan3 [116]

Answer:

the potential energy of the spring

5 0

3 years ago

Read 2 more answers