48. A square's sides are equal, so we know that its area is a number multiplied by itself, or squared. To find the length of one side, you must take the square root of its area, 156.25, which is 12.5. To find the square's perimeter (how much fence we need to go around the garden) you must multiply that side by 4, to get 50. Antonine has 40 ft already, so he only needs 10 more ft, and each ft costs 4.97. Our final answer is 10*4.97, or $49.70.
49. The square root of 12 is about 3.46, plus 2 is our answer, about 5.46 cm.
Answer:-5
Step-by-step explanation:
2x+7-x+12=14
x+19=14
x=-5
Complete Question: A 25% vinegar solution is combined with triple the amount of a 45% vinegar solution and a 5% vinegar solution resulting in 20 milliliters of a 30% vinegar solution.
Write an equation that models this situation and explain what each part represents in the situation. Then solve the equation.
Step-by-step explanation:
let the volume of the 45% vinegar solution be x litres
,
the volume of the 25% vinegar solution be 3x
and the volume of the 5% vinegar solution be y
summation of all gives,
x+3x+y = 20
4x + y = 20
subtracting 4x from both sides to make y the subject of the equation, we have;
y = 20 - 4x
To the concentration:
substituting for the value of x and y into equation x + 3x + y = 20, we have,
.45x + .25(3x) + .05(20-4x) = .3(20)
multiplying through by 100 to make whole figures we have;
45x + 25(3x) + 5(20-4x) = 600
45x + 75x + 100 - 20x = 600
120x - 20x + 100 = 600
100x + 100 = 600
subtracting 100 from both sides, we have;
100x = 600 - 100
100x = 500
dividing both sides by 100,
x = 5.
Answer:
The surface area of right regular hexagonal pyramid = 82.222 cm³
Step-by-step explanation:
Given as , for regular hexagonal pyramid :
The of base side = 3 cm
The slant heights = 6 cm
Now ,
The surface area of right regular hexagonal pyramid = 
Where a is the base side
And h is the slant height
So, The surface area of right regular hexagonal pyramid = 
Or, The surface area of right regular hexagonal pyramid = 
Or, The surface area of right regular hexagonal pyramid = 23.38 + 9 × 
∴ The surface area of right regular hexagonal pyramid = 23.38 + 9 × 6.538
I.e The surface area of right regular hexagonal pyramid = 23.38 + 58.842
So, The surface area of right regular hexagonal pyramid = 82.222 cm³ Answer
First, you need to find the derivative of this function. This is done by multiplying the exponent of the variable by the coefficient, and then reducing the exponent by 1.
f'(x)=3x^2-3
Now, set this function equal to 0 to find x-values of the relative max and min.
0=3x^2-3
0=3(x^2-1)
0=3(x+1)(x-1)
x=-1, 1
To determine which is the max and which is the min, plug in values to f'(x) that are greater than and less than each. We will use -2, 0, 2.
f'(-2)=3(-2)^2-3=3(4)-3=12-3=9
f'(0)=3(0)^2-3=3(0)-3=0-3=-3
f'(2)=3(2)^2=3(4)-3=12-3=9
We examine the sign changes to determine whether it is a max or a min. If the sign goes from + to -, then it is a maximum. If it goes from - to +, it is a minimum. Therefore, x=-1 is a relative maximum and x=1 is a relative miminum.
To determine the values of the relative max and min, plug in the x-values to f(x).
f(-1)=(-1)^3-3(-1)+1=-1+3+1=3
f(1)=(1)^3-3(1)+1=1-3+1=-1
Hope this helps!!
