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nalin [4]
3 years ago
12

The graph of a system of equations shows the solution to be at (-6, 2). Which two of the following equations could

Mathematics
1 answer:
blondinia [14]3 years ago
4 0

Answer:

Step-by-step explanation:

The graph shows the solution (-6,2)

i.e at x= -6 y=2

Analysis of each of the answers, since we can't write the equation of a straight line with only that information i.e the single point

Then,

Option 1

1. 2x - 3y = -6

x= -6 y=2

Then let insert x=-6 and y =2

2(-6)-3(2)

-12-6

-18.

Since -18 ≠ -6, then this is not the equation of the line and doesn't make up the system

Option 2

2. 4x - y = 26

Inserting x=-6 and y=2

4(-6)-(2)

-24-2

-26

Since -26 ≠ 26, then this is not the equation of the line and doesn't make up the system

Option 3

3. 3x + 2y = -14

Inserting x=-6 and y=2

3(-6)+2(2)

-18+4

-14

Since -14 ≠ -14 then this is the equation of the line and it make up the system.

Option 4

x-y = -2

Inserting x=-6 and y=2

(-6)-(2)

-6-2

-8

Since -8≠ -2, then this is not the equation of the line and doesn't make up the system

Option 5

5. x+y=-4

Inserting x=-6 and y=2

(-6)+(2)

-6+2

-4

Since -4 ≠ -4, then this is the equation of the line and it makes up the system.

Then, there are two option that make up the system

3. 3x + 2y = -14

And

5. x+y=-4

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Sergeu [11.5K]

The lengths of HJ and JK are 50 and 72 respectively.

Given: J is between H and K. the length of HJ=2x+4, JK=3x+3, and HK=22.

The line HJ and JK are  collinear then the total length is given as: HJ+JK=HK

substitute values

⇒ (2x+4)+(3x+3)=22

⇒ 5x+7=22

⇒ 5x=22-7

⇒ 5x=15

⇒ x=3

Thus, the length of HJ is (2x+4)=(2*3+4)=10

And the length of JK is (3x+3)=(3*3+3)=12

Learn more about collinear lines here: brainly.com/question/27943430

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2 years ago
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What is the radius and center of the circle given by the equation (x-5)^{2}+(y+2)^{2} = 81/4
artcher [175]

Answer:

The center is (5, -2) and the radius is 9/2

Step-by-step explanation:

The equation of a circle can be written by

(x-h) ^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-5)^{2}+(y+2)^{2} = 81/4

( (x-5)^{2}+(y- -2)^{2} = (9/2)^2

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3 years ago
Please help me to solve this problem<br>​
faust18 [17]

Answer:

\sqrt{3} + \frac{5\sqrt{3} }{6}

Step-by-step explanation:

tan(30°) = \frac{\sqrt{3}}{3}

cot(30°) = \sqrt{3}

sin(60°) = \frac{\sqrt{3}}{2}

\frac{\sqrt{3} }{3} +\sqrt{3} +\frac{\sqrt{3}}{2}  = \sqrt{3} +\frac{5\sqrt{3} }{6}

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2 years ago
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What is an equation of the line that passes through the point (- 5, - 6) and is parallel to the line 4x - 5y = 35
Elena L [17]

Answer:

4x - 5y = 10

Step-by-step explanation:

Any line parallel to 4x - 5y = 35 will have the same equation EXCEPT that the constant will be different.

Starting with 4x - 5y = 35, replace x with the given x-coordinate -5 and the given y-coordinate -6, and finally the given 35 with the constant C:

4(-5) - 5(-6) = C, or

-20 + 30 = C.  Thus, C = 10, and the equation of the new line is

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7 0
3 years ago
Someone quickly hell
Elza [17]

Answer:

£3,780

Step-by-step explanation:

Total rows = 19 rows

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Cost of tickets per seats = £8.75

Total number of seats at the concert = Total rows × seats per row

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= 532 seats

The tickets for 100 seats have not been sold

Total number of tickets = sold tickets + unsold tickets

532 = sold tickets + 100

532 - 100 = sold tickets

432 = sold tickets

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