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MrMuchimi
1 year ago
13

ABCD is a rectangle in which AD = (2x + 1) cm and DC = (3x - 2) cm. PQRS is a trapezium in which PQ is parallel to SR, PQ = (x +

2) cm, SR = (5x − 8) cm and the shortest distance between PO and SR is (4x – 11) cm. The area of ABCD is twice the area of PQRS. Write down an equation in x to represent this information and show that it simplifies to 18x²89x + 68 = 0.​
Mathematics
2 answers:
In-s [12.5K]1 year ago
8 0
The answer would be
x=4
or
x=17/18
wlad13 [49]1 year ago
3 0
Hello hope this helps you! for this question, key concept is for you to know what’s the formula of a rectangle and a trapezium and from there you’ll be able to solve it! feel free to clarify if needed!

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Solve for x:a(a²+b²)x²+b²x-a​
m_a_m_a [10]

Answer:

x = a/(a² + b²) or x = -1/a  

Step-by-step explanation:

a(a²+ b²)x² + b²x - a =0

Use the quadratic equation formula:

x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} =\dfrac{-b\pm\sqrt{D}}{2a}

1. Evaluate the discriminant D

D = b² - 4ac = b⁴ - 4a(a² + b²)(-a) = b⁴ + 4a⁴ + 4a²b²  = (b² + 2a²)²

2. Solve for x

\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-b^{2}\pm\sqrt{(b^{2}+2a^{2})^{2}}}{2a(a^{2} + b^{2})}\\\\ & = & \dfrac{-b^{2}\pm(b^{2}+ 2a^{2})}{2a(a^{2} + b^{2})}\\\\x = \dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}\\\\x =\dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\\end{array}

\begin{array}{rcl}x = \large \boxed{\mathbf{\dfrac{a}{a^{2} + b^{2}}}}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2b^{2}- 2a^{2}}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2(a^{2}+ b^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\large \boxed{\mathbf{-\dfrac{1}{a}}}\\\\\end{array}

5 0
3 years ago
At 9 AM Monday morning Thomas feels a beaker with water and places it in the corner of the classroom. At 1 PM Tuesday Thomas exa
aev [14]

The level has dropped 11 mms in 22 hours

that is 0.5mm per hour

So the remaining 31 mm will be gone in 31 / 0.5 = 62 hours

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=  1 am Saturday.   answer

5 0
3 years ago
Read 2 more answers
Zachary and his children went into a grocery store and will buy bananas and peaches.
stealth61 [152]

Answer:

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Step-by-step explanation:

The inequality function is as follows:

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7 0
3 years ago
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Sophie [7]

Answer:

p = <u>T</u> - a - <u>b</u>

Step-by-step explanation:

Hope that helps, not sure if it is correct though.

7 0
3 years ago
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Ab and ba name the same ray.<br><br><br> always<br> sometimes<br> never
vekshin1

The <em><u>correct answer</u></em> is:

never

Explanation:

A ray is named using the endpoint first and then another point on the ray. This means that ray AB has endpoint A and point B on the ray; ray BA has endpoint B and point A on the ray. These are not the same ray, as they do not have the same endpoint.

7 0
3 years ago
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