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Time= distance/speed
= 2000/50
= 40 hours

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in my view the solution to your problem may be obtained by finding the average price of one widget so
average price = (22+15)/26
= 37/26
so price of 25 = 25 x 37/26
= 35.576

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let L,W,H be the dimensions of the box then volume= L x W x H=LWH now if we each of the dimension is quadruppled new dimension will be 4L,4W,4H so volume will be V=4L x 4W x 4H=64LWH so volume is increased by 64 times the original volume.
similarly surface area = 2(LW+LH+WH)
new surface area = 2(16LW+16LH+16HW)
=32(LW+LH+HW) surface area increased by 32 times

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consider x as an angle then its complement will be 90-x follow the condition
x=4(90-x)
x=360-4x
x+4x=360
5x=360
x=360/5
x=72 deg so angle is 72 deg.

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keyword in any word is the first letter in that word so keyword in lovely is L so L={l}

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if W is width then length will be W+3 now we know that perimeter is given by formula P=2L+2W
so P=2(W+3)+2W
78=2W+3+2W
78=4W+3 that is the equqtion of W

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8=2 x 2 x 2 =
=
= 2

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=8
=8 taking minus sign common
=-8 dividing by -1 both sides
=0
=0 breaking middle term
=0
x=4 or x=-2

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as both cars going in same direction so net velocity =(70-50)=20 mph
distance=60 miles use this fomula
Distance = velocity x time
60 = 20 x time
time = 60/20
time=3 hours
two cars will meet after 3 hours

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let x miles be the distance travelled by a car
rent by first company = (14+ 9x/100) in dollars
rent by second company = (19 + 6x/100) in dollars
follow the condition
14+9x/100=19+6x/100
9x/100-6x/100=19-14
(9x-6x)/100=5
3x=500
x=500/3
x=166.66 or x=167 miles approx.

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if height of the object is given as a function of time so its derivative gives velocity.as ball is thrown upward so its final velocity will be zero or dh/dt=0
differentiate h=64t-16t^2 w.r.t
dh/dt= 64-32t put dh/dt=0
64-32t=0
t=2 seconds.ball takes 2 seconds to attend maximum height and 2 seconds to return so total 4 seconds it remains in the air

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if we look at its general formula y=a(x-m)^2+k which gives vertex (m,k)comparing this with given curve y=8(x-3)^2+h we get m=3 and k=h since vertex is (3,-3) gives k=-3 so h=-3 as h=k

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a)f(x-3)
from given points we get f(-1)=3 , f(0)=4 and f(2)=7
take x-3=-1 then x=2 so point (-1,3) corresponds to (2,3)
similarly (0,4) gives (3,4) and (2,7) gives (5,7) in this way we got these three points lying on the graph
b)f(x)+3 now consider h(x) such that
h(x)=f(x)+3 if x=-1 then
h(-1)=f(-1)+3
h(-1)= 3+3 since f(-1)=3
h(-1)= 6 so point is (-1,6) other points can be obtained by same

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we define domain the set of all such values of x for which function has defined or finite value here f(x)= 10- we look for the values of function for which it has defined value we know that square root of positive number exists only so 3-x>=0 or 3>=x or x>=3 hence all values of x are permissible except x<3 domain = all R except x<3

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hyperbola always has two sheets if one sheet opens upward then other will open downward so there are almost two options either up and down or left or right

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find prime factors of 40 i-e 2,2,2,5 now form two factors whose difference is coefficient of middle term which is -3 this is called middle term breacking
x^2-8x+5x-40 -8+5=-3 and 8 x 5 = 40 so we r at right path
x(x-8)+5(x-8) taking pairwise common
(x-8)(x+5) required factors

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as the aeroplanes are coming towards each other so their speeds will sum up to get the total speed so (200+190)=390 mph since distance is 780 miles now use formula distance= speed x time
780 = 390 x time
time = 780/390
time = 2 hours

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let $x be invested at 5% then $(10000-x) be invested at 7%
now interest on $x at 5% will be =
and interest on $(10000-x) =
according to condition
5x/100+7(10000-x)/100=644
(5x+70000-7x)/100=644
-2x=100(644)-70000
-2x=64400-70000
-2x=-5600
2x=5600
x=5600/2
x=2800 hence 2800 is invested on 5% and 7200 on 7%

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80 people are there so first equation is
a+c=80....(1)
second equ formed by condition is
c=4a ....(2) subtacting both equations
a=80-4a
a+4a=80
5a=80
a=80/5
a=16 so c=4(16)=64 there were 64 children in the group

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we are given value of x in first equation we have to simplify it first then put this in second equ. to get value of y.try it otherwise write us back

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you have mistaken somewhere your answer is wrong.it should be -19/13.try it again yourself.if you feel any difficulty then free to write again to us .

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let x years be the age of petra and y be the age of her mother.according to conditions
x+y=45 .......(1)
y=2x+9........(2) from this equ: y=2x+9 putting in equ:(1)
x+2x+9=45
3x=45-9
3x=36
x=12 putting this in equ:2
y=2(12)+9
y=33
hence petra's age is 12 and her mother's age is 33

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I cant understand your question because it gives two meanings.if you mean to say then answer is and if you mean then we will get *

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first take these values equal =
Now by cross multiplication
4(p+2)=6(p-2)
4p+8=6p-12
6p-4p-12-8=0
2p-20=0
p-10=0 dividing by 2
this is an equation of a line .In order to draw a graph we must have two variables connected by either equality or inequality sign.but if we consider a variable like q and take its values on vertical line then graph of above equation will be a vertical line otherwise a horizontal line be formed.as first value is greater than second value so p-10>0.hence graph contains the set of all points on the left of this line.

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=
= CD=2BC and also AB=2BC
=
= after division

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cot90=0 it can directly be obtained from its trigonometric relation already proved which says that cotx=.so we can get the value of cot90 from this formula.Now
cot90=
cot90= because cos90=0 and sin90=1
hence we have shown that cot90=0

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it is simple problem just you need to apply the following formula
distance=speed x time
so time=distance/speed .

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we can get exactly three apples in ways but since we have to select four pieces so one orange can be selected in ways now by product rule
total ways to select four pieces = *
=*
= *
=12*3
=36

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*
*
*