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3 years ago

Select all equations that have the solution x = 7.

Mathematics

2 answers:

shusha [124]3 years ago

3 0

Answer:

1st,2nd, and 4th

Step-by-step explanation:

2x + 14 = 28➡ x = 7

60 = 4x + 32 ➡ x = 7

2x - 6 -12 = -2x - 20 ➡ 4x = -2x = -1/2

3x - 15 = 1 + 5x - 30 ➡14 = 2x ➡ x = 7

Anestetic [448]3 years ago

3 0

Hey!

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Solve 2(x + 7) = 28 with x = 7.

2(7 + 7) = 28

2(14) = 28

28 = 28

TRUE

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

Solve 60 = 4(x + 8) with x = 7.

60 = 4(7 + 8)

60 = 4(15)

60 = 60

TRUE

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

Solve 6(2x - 1) - 12 = -2(x + 10) with x = 7.

6(2(7) - 1) - 12 = -2(7 + 10)

6(14 - 1) - 12 = -2(17)

6(13) - 12 = -2(17)

78 - 12 = -34

66 ≠ -34

FALSE

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

Solve 3(x - 5) = 1 + 5(x - 6) with x = 7.

3(7 - 5) = 1 + 5(7 - 6)

3(2) = 1 + 5(1)

6 = 1 + 5

6 = 6

TRUE

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

Hence, the correct answers are A, B, and D!

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

Hope This Helped! Good Luck!

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Answer:

a.(10,23)

b.(7,30)

e.(20,20)

Step-by-step explanation:

We are given that

x=Width of garden

y=Length of garden

According to question

$x\geq 5$

$y\geq 20$

Perimeter of rectangle= $2(x+y)$

Where x=Width of rectangle

y=Length of rectangle

Fencing used = $2(x+y)$

$2(x+y)\leq 80$

First we change inequality into equality

$x=5$ ...(1)

$y=20$ ...(2)

$2(x+y)=80$

$x+y=40$ ...(3)

Substitute x=0 in equation (3)

$y=40$

Substitute y=0 in equation (3)

$x=40$

Substitute x=0 and y=0 in equation (3)

$2(x+y)\leq 80$

$0\leq 80$

It is true. Therefore, the shaded region below the line.

$0\geq 5$

$0\geq 20$

These are false equation .Therefore, the shaded region above the line.

Substitute x=5 in equation (3)

$5+y=40$

$y=40-5=35$

Substitute y=20 in equation (3)

$x+20=40$

$x=40-20=20$

Intersection point of equation (1) and (3) is (5,35) and intersect point of equation (2) and (3) is (20,20).

Now,

a.(10,23)

Substitute in

$2(x+y)\leq 80$

$2(10+23)\leq 80$

$66\geq 80$

10>5 and 23>20

it satisfied all inequality.

Hence, it is a solution.

b.(7,30)

7>5

30>20

$2(7+30)=74$

it satisfied all inequality.

Hence, it is a solution.

c.(18,25)

18>5

25>20

$2(18+25)=86>80$

It does not satisfied third inequality

Hence, it is not a solution.

d.(8,35)

8>5

35>20

$2(8+35)=86>80$

It does not satisfied third inequality

Hence, it is not a solution.

e.(20,20)

$2(20+20)=80$

20>5

20=20

it satisfied all inequality.

Hence, it is a solution.

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