On the 10th birth day mother was of 30 year older (40-10 ) . Now - she is 60 years and my age is 30 years.
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Solution
Total 100 students
60 likes Maths means 40 dislikes maths
50 likes Science means 50 dislike Science.
10 dislikes both
That means 10 is part of 40 who dislike maths
Also 10 is part of 50 who dislike science.
Intersection is 10
Total students who dislike either maths or science. 100-(10+30+40) =20
Step-by-Step Solution
1. Use substitution:Let x = y + 25.This means:
• y + 20 = x - 5
• y + 30 = x + 5
2. Rewrite the equations with :The given equation becomes:
x^2 = 2023
The expression we need to find becomes: (x - 5)(x + 5)
3.Recall that (a - b)(a + b) = a^2 - b^2.Applying this to our expression: (x - 5)(x + 5) = x^2 - 5^2
(x - 5)(x + 5) = x^2 - 25
(x - 5)(x + 5) = 2023 - 25 (Since x^2 = 2023)
(y + 20) (y + 30) = 1998
4. Final Answer:The value is 1998.
Solution
Let the base = x
If x² + 4² = 8²
then x² = 8² - 4²
x² = 64 - 16
x² = 48
√x² = √48
x = 6.9 ft (base)
The boy sitting upright at 6 ft from the stem wouldn't be safe.
Solution
The Hour hand can move one resolution dot for every 12 min (60/5). So in the next 12 min it will align to hour position of 11:00 (upside down). Hence it is now 10:48
Solution
5/2(h)=20 cm2
h=8cm
Area of shaded=1/2(10)11-1/2(5)8
= 35cm2 ans
Solution:
If the ABCD trapezium area is 54cm*2, then
(AB+CD)×AD/2=54
at this condition AB=AD=(1/2)DC AB=X and we have
equality
(X+2X)×X/2=54
(3X*2/2)=54
X*2=54×2÷3=36
X=V36=6cm
So the trapezium sides length are AB=AD=6cm and CD=12cm
The circle radius is R=6÷2=3cm
Answer: the circle radius is 3cm
Solution
Area of big square+Area of small square
9^2+6^2=81+36=117cn^2
Area of big triangle =15×9/2=135/2=67.5cm^2
Area of two small triangles =1/2×6×6+1/2×3×9
18+13.5=31.5cm^2
Therefore,The Area of shaded region=117-(67.5+31.5)
117-99=18cm^2 Ans
Solution
2n + 2(n+3)= 26 , 4n = 20 , n = 5
But DC = n+3 = 5+3 = 8
Also DC = 2CE , 8 = 2CE , CE = 4
BC= AD = n = 5
Therefore Area of Triangle BCE
= 5×4/2 = 10 sq cm
Solution
c² = a² + b² for equal lines a=b
√32 = 2a²
2a² = 2√16
a²= √16
a =4
Therefore perimeter (P)
P = 4×4
= 16 units
Solution
Solution
In Left Triangle => 180-70-70=40
Exterior Angle of the same Triangle => 180-40=140
Remaining angle of Quadrilateral => 360-140-140=80
X => 180°-80°= 100° (ASP)
SOLUTION
1st square side=√144=12
2nd square side=6
3rd square side=3
Top square side=X
X²==9²+9²
X²=81+81
X²=162
Area=X²
Area=162 cm²
Answer:
Perimeter = (3*5)+(9*3)+6
= 15+27+6 = 48 cm.
Question
Question
Answer
Answer
𝒶 + 4𝒷 = 34
𝒶 + 𝒷 = 19
𝒶 + 4𝒷 - 𝒶 - 𝒷 = 34 - 19
= 3𝒷 = 15
𝒷 = ¹⁵∕₃ = 5
𝒶 + 𝒷 - 𝒷 = 19 - 5
= 𝒶 = 14
Angles in small isosceles triangle ACE are 20°, 80° and 80° ( Angle Sum Property)
Angle BEC= 100° (Linear Pair)
Angles in larger isosceles triangle EBC are 100°, 40 ° and 40°.( Angle Sum Property)
So x = 180° - 20° - 40° = 120°.
25(On the left half of the circle they all divide by 3 to give the answer opposite )
Buy 36 apples @ $2 =$72 + 12 apples free ( as per deal buy 3 get 1 free )
= 48 apples
Pay $ - 72
Answer is 1
Let, the weight of empty jar = x, and weight of liquid= y
Let, the weight of empty jar = x, and weight of liquid= y
For the first jar,
For the first jar,
weight of empty jar + weight of liquid, i.e.,
weight of empty jar + weight of liquid, i.e.,
x + y = 120 [Equation 1]\
x + y = 120 [Equation 1]\
And, for the second case,
And, for the second case,
weight of half filled second jar + empty second jar, i.e. {(x/2)+y} + y = 150
weight of half filled second jar + empty second jar, i.e. {(x/2)+y} + y = 150
or, (x/2) + 2y = 150,
or, (x/2) + 2y = 150,
or, x + 4y = 300. [Equation 2]
or, x + 4y = 300. [Equation 2]
\Now comparing Equation 1 with Equation 2, we can find,
\Now comparing Equation 1 with Equation 2, we can find,
3y = 180, or, y = 60
3y = 180, or, y = 60
Therefore, Weight of the empty jar is 60g.
Therefore, Weight of the empty jar is 60g.
Three friends are on a road trip, and they rent a triple room for a night. When they get to the hotel, they pay the fee of $30 and go up to their room. The porter brings up their bags and refunds them $5 because the hotel is running a weeknight special. The three friends each keep one of the dollars and give the porter a $2 tip. Later, they sit down to work out their expenses for the weekend and find they have a problem. They each paid $10 for the room and each got $1 back, making their contributions $9. Then they gave the porter a $2 tip. However, 9 times 3 is 27, plus 2 is $29. Where did the extra dollar go?
**Answer**: They didn’t spend $29, they spent $27: $25 on the room, and $2 for the porter’s tip. The three remaining dollars were returned to them!
**Answer**: They didn’t spend $29, they spent $27: $25 on the room, and $2 for the porter’s tip. The three remaining dollars were returned to them!
x^(64/x) = 4
x^(64/x) = 4
x^(1/x) = 4^(1/64)
x^(1/x) = 4^(4/256)
x^(1/x) = (4⁴)^(1/256)
x^(1/x) = 256^(1/256) [Note: 4⁴ =256]
Hence x = 256
Amazing Number Coincidence! Can you find another?
Amazing Number Coincidence! Can you find another?
Infinite a,b,c if bc-ab-ac=1 where a,b,c are integers > 0
Why 2WhyThe numbers 220 and 284 are called a pair of amicable numbers because each number is equal to the sum of the proper divisors of the other number.
Why 2WhyThe numbers 220 and 284 are called a pair of amicable numbers because each number is equal to the sum of the proper divisors of the other number.
A proper divisor is a positive factor of a number, excluding the number itself.
For 220, the proper divisors are: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110. If you add these up, the sum is 284.
For 284, the proper divisors are: 1, 2, 4, 71, and 142. If you add these up, the sum is 220.
So, each number is the sum of the proper divisors of the other number, which is the definition of amicable numbers. This concept has been known since ancient times and is a special case in number theory.
called pair of amicable numbers ?
called pair of amicable numbers ?
एक बैट और एक गेंद का मूल्य कुल मिलाकर 1.10 डॉलर है।
बैट का भाव गेंद से 1.00 डॉलर अधिक है।
गेंद का मूल्य क्या है?
एक बैट और एक गेंद का मूल्य कुल मिलाकर 1.10 डॉलर है।
बैट का भाव गेंद से 1.00 डॉलर अधिक है।
गेंद का मूल्य क्या है?
उत्तर है 5 सेंट।
As per L’Hopital’s rule it is in an indeterminate form meaning it has no value as is and is undefined.
0⁰ is one of the 7 indeterminate forms along with 0/0, ထ/ထ, ထ - ထ, ထx0, ထ^0, and 1^ထ
Which is not a leap year
Which is not a leap year
1900,1976,2000,2024
1900,1976,2000,2024
A year is 365.2422 days so adding a day every 4 years is almost sufficient, but then there should be exactly 365,25 days. Of that reason you have to “skip” some leap years. If it was exactly 364.24, you could just skip every 25th leap year, which is by every turn of century, but that is too much skipping, since it’s slightly longer with the added digits (365.2422 instead of 365.24). Therefore the rule is every year divisible by 4 is leap year, except years divisible by 100 i.e not those divisible by 400.
2000 is divisible by 100 but also 400, so it is actually a leap year.
1900 is divisible by 100 but not by 400, so NOT a leap year
1
Brainiac-The Brain ticklers
Brainiac-The Brain ticklers
The middle triangle is equilateral, so each angle is 60 degrees, the supplement of 180 -(60+56) = 64 . Likewise, the supplement of 180 - (60+36) = 84
angle a = 180 - (56 + 84) = 40
Since ab = ac, then < b = < c = (180 - 40)/2 = 70 degrees.
The red angle = 180 - (64 + 70) = 46 degrees
The plural words of Syllabus, locus, focus,index, formula and axis are Syllabi, loci, foci, indices, formulae, axes respectively.
Answer
Answer
Find Area of Shaded Region
Answer
Answer
You can use the angles to show all 3 triangles are similar . Thus all the angles are proportional. using the 2x2 square and its adjacent triangle, you can establish the ratio for all the triangles there to be 2:1. Now imagine an 5th larger triangle of height 6 and base 3 (as it would be also be similar to the others) with the hypotenuse as the side of the green square. You can then determine the side length of the square with the Pythagorean theorem - thus the side of the square is root 45. And area is then 45.
You can use the angles to show all 3 triangles are similar . Thus all the angles are proportional. using the 2x2 square and its adjacent triangle, you can establish the ratio for all the triangles there to be 2:1. Now imagine an 5th larger triangle of height 6 and base 3 (as it would be also be similar to the others) with the hypotenuse as the side of the green square. You can then determine the side length of the square with the Pythagorean theorem - thus the side of the square is root 45. And area is then 45.
<D=600 (Complete Angle)
& AD=DC (Given)
⇒ Angle A=Angle C=600
⇒Triangle ADC is equilateral
⇒AC=6 cm
⇒Area of Triangle ADC=15.57cm2 approx. (Heron’s Formula)
⇒Area of Triangle ABC=34.85cm2 approx. (Heron’s Formula)
⇒ Required Area= Area of Triangle ABC- Area of Triangle ADC
=34.85-15.57= 19.28 cm2
Three Red Balls =30 gm
One Red Balls =10 gm
One Red Ball+Two White Balls=30+30=60gm
10gm+Two White Balls=60gm
Two White Balls=50gm
One White Ball=25gm
25.
25.
(On the left half of the circle they all divide by 3 to give the answer opposite )
(On the left half of the circle they all divide by 3 to give the answer opposite )
Solution
The Hour hand can move one resolution dot for every 12 min (60/5). So in the next 12 min it will align to hour position of 11:00 (upside down). Hence it is now 10:48
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