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Mariulka [41]
2 years ago
13

Carlos is making a wood picture frame. the picture frame is 11 inches by 14 inches. after nailing the frame together, Carlos mea

sures the diagonal. if the diagonal is 19 inches long, does the frame have 90 degree corners? explain.
Mathematics
1 answer:
alexira [117]2 years ago
8 0
Answer:
Hope that helps! Have a good day :)

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X^2+4x+y^2-10y+20=30 find the center of the circle by completing the square
swat32

Answer:

a). Center of the circle = (-2, 5)

b). Equation of the line ⇒ y = -\frac{4}{5}x+\frac{58}{5}

Step-by-step explanation:

Equation of the circle is,

x² + 4x + y²- 10y + 20 = 30

a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30

   [x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30

   (x + 2)² + (y - 5)²- 29 + 20 = 30

   (x + 2)² + (y - 5)²- 9 = 30

   (x + 2)² + (y - 5)² = 39

By comparing this equation with the standard equation of a circle,

    Center of the circle is (-2, 5).

b). A point (2, 10) lies on this circle.

    Slope of the line joining this point to the center (-2, 5),

    m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

          = \frac{10-5}{2+2}

          = \frac{5}{4}

    Let the slope of the tangent which is perpendicular to this line is 'm_{2}'

    Then by the property of perpendicular lines,

          m_{1}\times m_{2}=-1

          \frac{5}{4}\times m_{2}=-1

                 m_{2}=-\frac{4}{5}

   Now the equation of the line passing though (2, 10) having slope m_{2}=-\frac{4}{5}

           y - y' = m_{2}(x-x')

           y - 10 = -\frac{4}{5}(x-2)

           y - 10 = -\frac{4}{5}x+\frac{8}{5}

                  y = -\frac{4}{5}x+\frac{8}{5}+10

                  y = -\frac{4}{5}x+\frac{58}{5}

Therefore, equation of the line will be, y = -\frac{4}{5}x+\frac{58}{5}

7 0
3 years ago
Find the difference: 101100012 - 11011012. Express your answer as a Base<br> 2 number.
Marizza181 [45]

Answer:

<h2>The answer is 1000100</h2>

Step-by-step explanation:

10110001 - 1101101 = 1000100

Hope this helps you

7 0
2 years ago
Which expression is equivalent to the given expression?
notka56 [123]
The answer is C.x(13-29)
6 0
3 years ago
I need help with Number 5
Nostrana [21]
You’re going it plug in the inputs for every input for the letter x. So the first one, fx= -4(-2)+1= 9. The second one fx= -4(0)+1=1. The third one fx= -4(5)+1=19.
4 0
2 years ago
Quadrilateral ABCD is similar to Quadrilateral EFGH. The scale factor is 3:2 if AB = 18, find EF
Marina86 [1]

Answer:

A... 12

Step-by-step explanation:

5 0
2 years ago
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