Answer: x > 20
Step-by-step explanation:
x + 10 > 30
-10 -10
x > 20
The solutions of the quadratic equation x² - 5x - 36 = 0 are -4 and 9.
The graph is attached below.
- We are given a quadratic function.
- A polynomial equation of degree two in one variable is a quadratic equation.
- The function given to us is :
- y = x² - 5x - 36
- We need to find the solution of the quadratic function.
- To find the roots, let y = 0.
- x² - 5x - 36 = 0
- Use the quadratic formula.
- In elementary algebra, the quadratic formula is a formula that gives the solution(s) to a quadratic equation.
- x = [-b±√b²-4ac]/2a
- x = [-(-5) ± √25 - 4(1)(-36)]/2(1)
- x = (5 ± √25 + 144)/2
- x = (5 ± √169)/2
- x = (5 ± 13)/2
- x = 9 or x = -4
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Answer:
Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.
Step-by-step explanation:
Given : In the figure attached, Length of girl EC = 4 ft
Length of street light AB = 25 ft
Girl is moving away from the light with a speed = 6 ft per sec.
To Find : Rate () of the tip (D) of the girl's shadow (BD) moving away from th
light.
Solution : Let the distance of the girl from the street light is = x feet
Length of the shadow CD is = y feet
Therefore, feet per sec. [Given]
In the figure attached, ΔAFE and ΔADE are similar.
By the property of similar triangles,
25x = 21(x + y)
25x = 21x + 21y
25x - 21x = 21y
4x = 21y
y =
Now we take the derivative on both the sides,
=
=
≈ 1.14 ft per sec.
Since w = x + y
Therefore,
= 7.14 ft per sec.
Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.
A) y-axis
B) quad lll
C) x-axis
D) quad IV
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1.326 grams of NH3 are required to produce 4.65 g of HF.
Step-by-step explanation:
Balanced chemical reaction is written first to know the number of moles taking part in original reaction.
NH3 +3 F2 ⇒3 HF + NF3
Given:
mass of HF = 4.65
First the number of moles of HF in 4.65 grams is calculated by using the formula:
number of moles (n) =
atomic mass of HF = 20 grams/mole
putting the values in the above equation number of moles can be found.
n =
= 0.235 moles of HF are given.
From the equation it can be said that:
1 mole of NH3 reacts to form 3 moles of HF
so, x moles of NH3 would react to form 0.235 moles of HF
=
3x = 0.235
x =
x = 0.078 moles of NH3 is required.
The moles are converted to mass by applying the formula:
mass = atomic mass X number of moles (atomic mass of NH3 = 17 grams/mole)
putting the values in the formula
mass = 17 X 0.078
mass = 1.326 grams