Two times the quantity of eight times a number plus two is equal to three the quantity of two times the same number minus seven
1 answer:
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Answer:
A trapezoid ABCD is show below,
AB || CD
AC and BD are diagonals intersecting at P.
(a)
In Δ ABC and ABD,
Area of triangle ABC = Area of triangle ABD
Because,
Area of triangle ABC = 1/2 × Base × Height
Base = AB
Height = h, which is same for both the triangle that's why,
Area of triangle ABC = Area of triangle ABD
(b)
As we know that,
Area of triangle ABC = Area of triangle ABD
On subtracting the area of triangle ABP from both the triangles, we get
Area of triangle ABC - area of triangle ABP = Area of triangle ABD - area of triangle ABP
⇒ area of triangle BCP = area of triangle DAP
Hence, triangles BCP and DAP have the same area.
(c)
In triangle ABP and CDP,
∠ABP = ∠CDP (opposite interior angles are equal between two parallel lines)
∠APB = ∠CPD (opposite angles are equal)
∠BAP = ∠DCP (opposite interior angles are equal between two parallel lines)
Therefore,
By AAA similarity
Triangles ABP and CDP are similar.
(d)
In triangle BCP and DAP,
Only ∠BCP = ∠APD (opposite angles are equal).
Therefore,
Triangles BCP and DAP need not be similar.
Answer:
The product of two numbers changes by 2% when the first number increases by 70%, while the second number decreases by 40%.
Step-by-step explanation:
Let first number be x and second number be y .
Then product of x and y = xy ......(1)
Given the first number increases by 70%, while the second number decreases by 40% this means,
x is increased by 70% that is
increased value of x = x + 0.7(x) = 1.7 x
Similarly y is decreases by 40% that is
decreased value of y = y - 0.4(y) = 0.6y
New product will be = (increased value of x )( decreased value of y)
= (1.7x)(0.6y)
=1.02xy
Changed Percentage =
Substitute the values, we get,
Changed Percentage =
Changed Percentage =
Changed Percentage =
Changed Percentage =
Thus, the product of two numbers changes by 2% when the first number increases by 70%, while the second number decreases by 40%.