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Ira Lisetskai [31]
3 years ago
10

Does anyone know how to do this ?

Mathematics
1 answer:
AysviL [449]3 years ago
8 0

9514 1404 393

Answer:

  y = 21

Step-by-step explanation:

In straightforward fashion, we can find the midpoints of the two segments, and set the distance between them equal to 10.

  M = midpoint of AB

  M = (A+B)/2 = ((-1, 0) +(-3, 6))/2 = (-4, 6)/2 = (-2, 3)

  N = midpoint of CD

  N = (C+D)/2 = ((3, 1) +(5, y))/2 = (8, 1+y)/2 = (4, (1+y)/2)

Then the distance MN is given by the distance formula.

  |N-M| = 10 = √((4 -(-2))² +((1+y)/2 -3)²) . . . . . distance formula*

  100 = 36 +((1+y)/2 -3)² . . . . . square both sides

  64 = ((1 +y)/2 -3)² . . . . . . . . . subtract 36

  8 = (1 +y)/2 -3 . . . . . . . . . . . . (positive) square root

  11 = 1+y/2 . . . . . . . . add 3

  22 = 1+y . . . . . . . . . multiply by 2

  21 = y . . . . . . . . . . . subtract 1

_____

* The distance formula is an application of the Pythagorean theorem. Basically, the differences of x- and y-coordinates are taken to be the legs of a right triangle. They length of the hypotenuse is the distance between the two points.

  d² = (x2 -x1)² +(y2 -y1)² . . . . . . . from the Pythagorean theorem

  d = √((x2 -x1)² +(y2 -y1)²) . . . . . the usual distance formula

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A right triangle has one vertex on the graph of y = 9 - x^2 , x > 0, at ( x , y ), another at the origin, and the third on th
jenyasd209 [6]

Answer:

  a.  A(x) = (1/2)x(9 -x^2)

  b.  x > 0 . . . or . . . 0 < x < 3 (see below)

  c.  A(2) = 5

  d.  x = √3; A(√3) = 3√3

Step-by-step explanation:

a. The area is computed in the usual way, as half the product of the base and height of the triangle. Here, the base is x, and the height is y, so the area is ...

  A(x) = (1/2)(x)(y)

  A(x) = (1/2)(x)(9-x^2)

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b. The problem statement defines two of the triangle vertices only for x > 0. However, we note that for x > 3, the y-coordinate of one of the vertices is negative. Straightforward application of the area formula in Part A will result in negative areas for x > 3, so a reasonable domain might be (0, 3).

On the other hand, the geometrical concept of a line segment and of a triangle does not admit negative line lengths. Hence the area for a triangle with its vertex below the x-axis (green in the figure) will also be considered to be positive. In that event, the domain of A(x) = (1/2)(x)|9 -x^2| will be (0, ∞).

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c. A(2) = (1/2)(2)(9 -2^2) = 5

The area is 5 when x=2.

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d. On the interval (0, 3), the value of x that maximizes area is x=√3. If we consider the domain to be all positive real numbers, then there is no maximum area (blue dashed curve on the graph).

5 0
3 years ago
Shreya and beth each improved their yards by planting rose bushes and ornamental grass. They brought their supplies from the sam
frutty [35]

Answer:

  • <u><em>The cost of one rose bush is $ 9 and the cost on one bunch pf ornamental grass is $ 8.</em></u>

Explanation:

Name the variables and build a system of two equations with two unknowns.

<u>1. Variable r</u>: cost of one rose bush

<u>2. Variable g</u>: cost of one bunch of ornamental grass.

<u>3. First equation</u>:

  • Shreya spent $68 on 4 rose bushes and 4 bunches of ornamental grass.

        4r + 4g = 68

<u>4. Second equation</u>:

  • Beth spent $115 on 11 rose bushes and 2 bunches of ornaments grass.

  • 11r + 2g = 115

<u>5. System of equations</u>:

  • 4r + 4 g = 68     equation 1
  • 11r + 2g = 115     equation 2

<u>6. Solve the system</u>

a) Divide the equation 1 by 2:

  • 2r + 2g  =  34     equation 1a
  • 11r + 2g = 115     equation 2

b) Subtract equation 1a from equation 2:

  • 11r - 2r = 115 - 34
  • 9r = 81
  • r = 81 / 9
  • r = 9

c) Substitute the value of r into the equation 1a:

  • 2(9) + 2g = 34
  • 9 + g = 17
  • g = 17 - 9
  • g = 8

<u>7. Conclusion</u>:

The cost of one rose bush is $ 9 and the cost on one bunch pf ornamental grass is $ 8.

7 0
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What is the value of (5ý + 3) + 5?​
strojnjashka [21]

Answer:

5y + 8

Step-by-step explanation:

5y + 3 + 5

5y + 8

<em><u>Hope this helped! Have a nice day! Plz mark as brainliest!!!</u></em>

<em><u>-XxDeathshotxX</u></em>

7 0
3 years ago
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mafiozo [28]

Answer: y = (1/7) x - 2

Step-by-step explanation:

The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.

The slope of an equation is the change in y over the change in x.

We can see from the image that every time the line increases by 1 in the rise (y), it increases by 7 in the run (x).

Therefore, the slope is 1/7.

The y-intercept of a line is the point at which it intercepts the y-axis.

From the image, we can see that it intersects at the point (0,-2)

Therefore, the slope-intercept form is y = (1/7) x - 2

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Answer:

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Step-by-step explanation:

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