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ivolga24 [154]
3 years ago
10

What is the solution to 5x-8y=-45 9x-8y=49

Mathematics
1 answer:
Paladinen [302]3 years ago
6 0

Answer:

\large\boxed{x=\dfrac{47}{2},\ y=\dfrac{325}{16}\ or\ x=23.5,\ y=20.3125}

Step-by-step explanation:

\left\{\begin{array}{ccc}5x-8y=-45\\9x-8y=49&\text{change all signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}5x-8y=-45\\-9x+8y=-49\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-4x=-94\qquad\text{divide both sides by (-4)}\\\\.\qquad\dfrac{-4x}{-4}=\dfrac{-94}{-4}\\\\.\qquad \boxed{x=\dfrac{47}{2}=23.5}\\\\\text{Put the value of}\ x\ \text{to the first equation}\\\\5(23.5)-8y=-45\\\\117.5-8y=-45\qquad\text{subtract 117.5 from both sides}

-8y=-162.5\qquad\text{divide both sides by (-8)}\\\\\dfrac{-8y}{-8}=\dfrac{-162.5}{-8}\\\\y=\dfrac{1625}{80}\\\\\boxed{y=\dfrac{325}{16}=20.3125}

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d=12.0416

Step-by-step explanation:

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d=\sqrt{(2-(-6))^2+(7-(-2))^2}

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4 0
3 years ago
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3x - 12y = 24<br><br> Which of the following points represents the x and y intercepts?
umka21 [38]

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7 0
3 years ago
An arched drainage culvert can be modelled by the function:
Zanzabum

Substitute 136.5 for y.

136.5=\frac{x(191-x)}{60}

8190=x(191-x)

8190=191x-x^{2}

x^{2} -191x+8190=0

Compare this equation with ax^{2} +bx+c=0

a = 1, b = - 191, c = 8190

x=\frac{-b+\sqrt{b^{2}-4ac } }{2} or

x=\frac{-b-\sqrt{b^{2}-4ac } }{2}

x=\frac{191+\sqrt{191^{2}-4(1)(8190) } }{2} or

x=\frac{191-\sqrt{191^{2}-4(1)(8190) } }{2}

x=\frac{191+\sqrt{36481-32760 } }{2} or

x=\frac{191-\sqrt{36481-32760 } }{2}

x=\frac{191+\sqrt{3721 } }{2} or

x=\frac{191-\sqrt{3721 } }{2}

x=\frac{191+61}{2} or

x=\frac{191-61}{2}

x=\frac{252}{2} or

x=\frac{130}{2}

x = 126 or x = 65

Hence, the points on the curve are (65, 136.5) and (126, 136.5).

The width of the air space is the distance between these points.

Width = \sqrt{(x_{2}- x_{1})^{2} +( y_{2}- y_{1}) ^{2}

= \sqrt{(126- 65)^{2} +(136.5-136.5) ^{2}

= 126 - 65

= 61

Hence, width of the air space is 61m.



5 0
3 years ago
The number of student of schoolwas 450 last year and it is 396 this year.By how many percent did the number decrease
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