Answer:
5 ≥ 9*.15 + x*.25
He can buy up to 14 candies
Step-by-step explanation:
Total money ≥number of peppermints * cost per peppermint + number of sour candies * cost per sour candy
We know he has 5 dollars. He bought 5 peppermints at $.15 cents each and x sour candies at $.25 each
Substituting in
5 ≥ 9*.15 + x*.25
5≥1.35 + .25x
Subtract 1.35 on each side
5-1.35 ≥ 1.35-1.35+.25x
3.65≥.25x
Divide by .25 on each side
3.65/.25 ≥ .25x/.25
14.6 ≥ x
He can buy up to 14 candies. You can't buy part of a candy
Answer:
Cavalier's principle can be used to find the volume of any solid.
Step-by-step explanation:
Cavalier's Principle:
- Cavalier introduced parallel planes and area to describe the relationship between solids.
- Cavalier stated if two solids have the same height and equal areas of the base everywhere along the height then the solids have the same volume.
- Suppose two regions are included between two parallel planes.
- If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
- The formula for the volume of a prism is the area of the base times the height.
The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].
<h3>What is an equation?</h3>
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given:
genera form of an exponential function is y=aeᵇˣ
Now, equation for f(x) is
f(x) = 
Similarly, graph for g(x) is
g(x) = 
Comparing the two function a relation can be establish
g(x) = -3[f(x)]
Learn more about Equation here:
brainly.com/question/2263981
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Answer:
a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Step-by-step explanation:
for the equation
(1 + x⁴) dy + x*(1 + 4y²) dx = 0
(1 + x⁴) dy = - x*(1 + 4y²) dx
[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx
∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx
now to solve each integral
I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁
I₂= ∫[-x/(1 + x⁴)] dx
for u= x² → du=x*dx
I₂= ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ = - tan⁻¹ (x²) +C₂
then
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C
for y(x=1) = 0
1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C
since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for π*N , we will choose for simplicity N=0 . hen an explicit solution would be
1/2 * 0 = - π/4 + C
C= π/4
therefore
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Answer:
6
Step-by-step explanation:
5% of 120 were late
= 
× 120
= 0.05 × 120
= 6
