What I always do to solve this, is find a common factor for each number first.
Usually 4 or 5 works best. I'll use 4.
4 goes into 80 20 times, which means that 4 = 5% of 80.
If 4 = 5%, and 48 = 12 x 4, then 48 must equal 60% of 80.
(Another way to solve this problem is: simplify 48 / 80. This simplifies to 3/5.
3/5 = 60%)!
Answer:
Vertex form: f(x) = -10(x − 2)^2 + 3
Standard form: y = -10x^2 + 40x - 37
Step-by-step explanation:
h and k are the vertex coordinates
Substitute them in the vertex form equation:
f(x) = a(x − 2)^2 + 3
Calculate "a" by replacing "f(x)" with -7 and "x" with 1:
-7 = a(1 − 2)^2 + 3
Simplify:
-7 = a(1 − 2)^2 + 3
-7 = a(-1)^2 + 3
-7 = a + 3
-10 = a
Replace a to get the final vertex form equation:
f(x) = -10(x − 2)^2 + 3
Convert to standard form:
y = -10(x − 2)^2 + 3
Expand using binomial theorem:
y = -10(x^2 − 4x + 4) + 3
Simplify:
y = -10x^2 + 40x - 40 + 3
y = -10x^2 + 40x - 37
Answer:
g(1) = 0
Step-by-step explanation:
To evaluate g(1) , substitute x = 1 into g(x), that is
g(1) = 4 - 2(3 - 1)
= 4 - 2(2)
= 4 - 4
= 0
Answer:
<h2>
6 1/2 lbs</h2>
Step-by-step explanation:
Given the weight of granite to be 74 26/36 lbs,
Weight of quartz is 81 9/40 lbs.
To know how much more quartz weight than the granite, we will take the difference between the weight of quartz and granite as shown.
Weight of quartz - Weight of granite
= 81 9/40 - 74 26/36
= 3,249/40 - 2690/36
= (29, 241 - 26,900)/360
= 2,341/360
= 6 181/360
≈ 6 1/2 lbs
quartz weighs approximately 6 1/2 lbs much more than granite
Answer:
Ex = - 4 + 14xy
Ey = 7x² - 7z²
Ez = -14yz
Step-by-step explanation:
The relationship between Electric field Er(x, y, z) and Electric potential, V, is a differential relationship:
Er(x, y, z) = -dV/dr(x, y, z)
Where r(x, y, z) = distance in x, y and z components.
The x component of the electric field is:
Ex = -dV/dx
Given that:
V = 4x - 7x²y + 7yz²
Ex = -dV/dx
Ex = -(4 - 14xy)
Ex = -4 + 14xy
The y component of the electric field is:
Ey = -dV/dy
Ey = -(-7x² + 7yz²)
Ey = 7x² - 7z²
The z component of the electric field is:
Ez = -dV/dz
Ez = -(14yz)
Ez = -14yz
