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AlekseyPX
3 years ago
6

Find the equation of the straight line which is parallel to 2x + 3y = 11 and such that the sum of the intercepts on axes is 15.

Mathematics
1 answer:
Burka [1]3 years ago
5 0

Answer: 2x+3y=18



Step-by-step explanation: Any line parallel to 2x+3y+11=0 is the form 2x+3y =k this can also be written as x/(k/2)+y/k/3 =1  this is the line whose sum of the intercepts is 15, then k/2 +k/3 = 15 after solving we get that indeedk= 18.

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The Johnsons want to cover their backyard with new grass. Their backyard is rectangular, with a length of 3x – 5 feet and a widt
kolezko [41]

Answer:

Step-by-step explanation:

The formula for determining the area of a rectangle is expressed as

Area = length × width

Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. This means that the area of the backyard is

(3x - 5)(4x - 10)

= 12x² - 30x - 20x + 15

= (12x² - 50x + 15) square feet

Their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. This means that the area occupied by the swimming pool and its surrounding patio is

(x + 8)(x - 2)

= x² - 2x + 8x - 16

= x² + 6x - 16

Assuming the swimming pool and its surrounding patio will not be covered with new grass, then the area of the region of the yard that they want to cover with new grass is

12x² - 50x + 15 - (x² + 6x - 16)

= 12x² - 50x + 15 - x² - 6x + 16

= 12x² - x² - 50x - 6x + 15 + 16

= 11x² - 56x + 31 square feet

3 0
3 years ago
a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to the curve at the given point.
xxMikexx [17]

Answer:

y = 13*( -x/9 + 1/5)

Step-by-step explanation:

Given:

- The curve has an equation as follows:

                               44 = 5x^2 + 3xy + 3y^2

Find:

a. Verify that the given point (2​,2​) lies on the curve.

b. Determine an equation of the line tangent to the curve at the given point.

Solution:

- To verify whether the point lies on the given curve we will substitute the coordinates of the point into the equation as follows:

                              44 = 5*(2)^2 + 3*(2)(2) + 3*(2)^2

                              44 = 20 + 12 + 12

                              44 = 44 ......Hence proven.

- The equation of the line tangent to the curve is expressed as a linear function as follows:

                              y = m*x + C

Where, m is the gradient of the line.

            C is the y-intercept.

                              m = Δy / Δx = dy/dx

- We will take the derivative of the given curve with respect to x as follows:

                             0 = 10x + 3*( y + xy' )  + 6y*y'\\\\-10x - 3y = y' ( 3x + 6y)\\\\ y' = - \frac{10x + 3y}{3x + 6y}

- Evaluate y' at the point (2,2) we get:

                            y' = - ( 10(2) + 3(2) ) / ( 3(2) + 6(2) )

                            y' = - ( 26 ) / (18)

                            y'= m = - 13/9

- To evaluate C, we will use the point (2,2) for linear expression above with m as follows:

                            y = -13*x/9 + C

                            2 =-13*(2)/9 + C

                            C = 13 / 5

- The equation of the tangent is as follows:

                            y = 13*( -x/9 + 1/5)  

8 0
3 years ago
Identify the determinants for the given linear system: 5x + 2y = 14 −3x − 5y = 3
sergeinik [125]

Answer:

Step-by-step explanation:

|A|= 5, 2, -3, -5

|Ax|= 14, 2, 3, -5,

|Ay|= 5, 14, -3, 3

8 0
3 years ago
WILL GIVE BRAINLIEST!!!
s2008m [1.1K]

1. Can you describe what needs to be done here?

2. 5a-2<18

5a<20

a<4

3. 2a+8≥ -4(a+1)

2a + 8 ≥ -4a - 4

6a ≥ -12

a ≥ -2

8 0
3 years ago
Determine whether the graph represents a proportional relationship.
olya-2409 [2.1K]

No, it is not a proportional relationship because the graph does not go through the origin. A proportional relationship is supposed to be a straight line, starting from the origin. It starts on the number 4.

8 0
3 years ago
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