Answer:
see below
Step-by-step explanation:
g(x) = 3 − x^2
(a)g(30) = 3 - 30^2 = 3 - 900 = -897
(b)g(3)= 3- 3^2 = 3-9 = -6
(c)g(−1) = 3 - (-1)^2 = 3 - 1 = 2
(d)g(0.5) = 3 - (.5)^2 = 3 - .25 = 2.75
Because the balls or spheres are tightly packed in a cube, their radius is approximately equal to 2 ft. The volume of a sphere is calculated through the equation,
V = 4/3πr³
Substituting the known radius,
V = 4/3π(2 ft)³
V = 33.51 ft³
The 9 spheres will have a total volume of 301/59 ft³ which is also equal to 521152.52 in³.
Answer:
![area=\frac{85}{4}feet^{2}](https://tex.z-dn.net/?f=area%3D%5Cfrac%7B85%7D%7B4%7Dfeet%5E%7B2%7D)
Step-by-step explanation:
1. Approach
Since it is given that the garden box is a rectangle, then the opposite sides are congruent. One can use this to their advantage, by setting up an equation that enables them to solve for the width of the rectangle. After doing so, one will multiply the width by the given length and solve for the area.
2. Solve for the width
It is given that the garden box is a rectangle. As per its definition, opposite sides in a rectangle are congruent. The problem gives the length and the perimeter of the rectangle, therefore, one can set up an equation and solve for the width.
![perimeter=18\frac{1}{2}\\\\length=5](https://tex.z-dn.net/?f=perimeter%3D18%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5Clength%3D5)
![2(length+width)=perimeter](https://tex.z-dn.net/?f=2%28length%2Bwidth%29%3Dperimeter)
Substitute,
![2(5+width)=18\frac{1}{2}](https://tex.z-dn.net/?f=2%285%2Bwidth%29%3D18%5Cfrac%7B1%7D%7B2%7D)
Conver the mixed number to an improper fraction. This can be done by multiplying the "number" part of the mixed number by the denominator of the fraction. Then add the result to the numerator.
![2(5+width)=\frac{37}{2}](https://tex.z-dn.net/?f=2%285%2Bwidth%29%3D%5Cfrac%7B37%7D%7B2%7D)
Inverse operations,
![2(5+width)=\frac{37}{2}\\/2\\\\5+width=\frac{37}{4}\\-5\\\\width=\frac{17}{4}](https://tex.z-dn.net/?f=2%285%2Bwidth%29%3D%5Cfrac%7B37%7D%7B2%7D%5C%5C%2F2%5C%5C%5C%5C5%2Bwidth%3D%5Cfrac%7B37%7D%7B4%7D%5C%5C-5%5C%5C%5C%5Cwidth%3D%5Cfrac%7B17%7D%7B4%7D)
3. Solve for the area
Now that one has solved for the width of the box, one must solve for the area. This can be done by multiplying the length by the width. Since the width is a fraction, one must remember, that when multiplying an integer by a fraction, one will multiply the integer by the numerator (the top of the fraction), and then simplify by reducing the fraction, if possible. Reducing the fraction is when one divides both the numerator and the denominator by the GCF (Greatest Common Factor).
![length=5\\\\width = \frac{17}{4}](https://tex.z-dn.net/?f=length%3D5%5C%5C%5C%5Cwidth%20%3D%20%5Cfrac%7B17%7D%7B4%7D)
![length*width=area](https://tex.z-dn.net/?f=length%2Awidth%3Darea)
Substitute,
![5*\frac{17}{4}\\\\=\frac{85}{4}](https://tex.z-dn.net/?f=5%2A%5Cfrac%7B17%7D%7B4%7D%5C%5C%5C%5C%3D%5Cfrac%7B85%7D%7B4%7D)
![area=\frac{85}{4}feet^{2}](https://tex.z-dn.net/?f=area%3D%5Cfrac%7B85%7D%7B4%7Dfeet%5E%7B2%7D)
Answer:
e = 10
Step-by-step explanation:
9e+4=-5e+14+13e
Combine like terms
9e+4=14+8e
Subtract 8e from both sides
9e-8e+4=8e-8e +14
e +4 = 14
Subtract 4 from each side
e+4-4 = 14-4
e = 10
Answer:
Vertex: (-4, 1)
X intercepts: (-6, 0) and (-2, 0)
Y Intercepts: (0, -5)
Axis of Symmetry: X= -4
Step-by-step explanation:
Vertex of the parabola is the maximum or minimum point on the graph of the quadratic function
X intercepts are points of when a line or in this case a parabola intercepts the x axis, and where y = 0
Y intercepts are point of when a line or in this case a parabola intercepts the y axis, and where y = 0
Axis of symmetry is the point where if you divide the parabola in half, shows a symmetrical side