The greatest possible value of x is the largest value that satisfies all of these inequalities. The largest value of x that satisfies all three inequalities is 6.4 .
In an obtuse triangle, the longest side is opposite the obtuse angle. To determine the greatest possible value of x, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the longest side measures 20 cm, and the two shorter sides are x cm and 3x cm. So, we have the following inequalities:
x + 3x > 20 (sum of the two shorter sides must be greater than the longest side)
20 + x > 3x (sum of the longest side and the shorter side must be greater than the other shorter side)
20 + 3x > x (sum of the longest side and the other shorter side must be greater than the remaining shorter side)
Let's solve these inequalities:
4x > 20
x > 5
20 + x > 3x
20 > 2x
10 > x
20 + 3x > x
20 > -2x
-10 < x
So, the greatest possible value of x is the largest value that satisfies all of these inequalities. The largest value of x that satisfies all three inequalities is 6.4 (rounded to the nearest tenth). Therefore, the greatest possible value of x is 6.4 cm.
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Answer:
7.1
Step-by-step explanation:
because pythagorean theorem
c² > a² + b²
20² > x² + 3x²
400 > 4x²
÷4 ÷4
100 > x²
10 > x 400 > 4(7.1)²
400 > 4(50.41)
400 > 201.64
Answer: The correct answer is D. 3,350
Step-by-step explanation:
To find the consumer surplus at equilibrium, we need to determine the equilibrium price and quantity first.
Equilibrium occurs when the quantity demanded equals the quantity supplied. In other words, when the demand function and supply function intersect.
Setting the demand and supply functions equal to each other, we get:
900 - Q^0.1 = 3Q^0.9
To solve this equation, we can use algebraic methods or graphing techniques.
Using algebra, we can simplify the equation to:
900 = 4Q^0.9
Dividing both sides by 4:
225 = Q^0.9
Taking both sides to the power of 1/0.9:
Q ≈ 52.38
Now that we have the equilibrium quantity, we can substitute it back into either the demand or supply function to find the equilibrium price.
Using the demand function:
P = 900 - Q^0.1
P = 900 - (52.38)^0.1
P ≈ 900 - 2.97
P ≈ 897.03
So, the equilibrium price is approximately 897.03.
To find the consumer surplus, we need to calculate the area between the demand curve and the equilibrium price line up to the equilibrium quantity.
The formula for consumer surplus is:
Consumer Surplus = 0.5 * (Q * P - ∫(0 to Q) D(x) dx)
Integrating the demand function from 0 to Q:
∫(0 to Q) D(x) dx = ∫(0 to 52.38) (900 - x^0.1) dx
By evaluating this integral, we find that the consumer surplus is approximately 3,350.
Therefore, the correct answer is D. 3,350.
I hope this helps :)
1. The sum of both numbers of a number is 14. On having exchanged the numbers of the tens with that of the units, the number increases in 18. It finds the original number.
2. The sum of two numbers is 21 and his difference is 5. ¿Which are the numbers?
Please I am grateful for them to him very much indeed ...:)
Answer:
19.2
Step-by-step explanation:
1st Case:
4 and 5 are legs of the right triangle.
Using the pythagorean therom: a^2+b^2=c^2
We can say that 4^2+5^2=x^2
16+25=x^2
41=x^2
x=√41
√41 is about 6.4
x=6.4
2nd Case
5 is the hypotenuse of the right triangle and 4 is the legs.
Using the pythagorean therom: a^2+b^2=c^2
We can say that 4^2+x^2=5^2
16+x^2=25
x^2=9
x=3
Final Step
We need to multiply the two possible lengths for x. So for case 1 the length of x was 6.4 and for case two the length was 3. 6.4*3=19.2
Anwser: 19.2
earns $8 each week mowing lawns and
spends $2 of it. Joe earns $10 each week
and spends $3 of it. Which expression can
be used to find out how many weeks it will
take for them to save for the video game?
52-[(8 + 2) - (10 + 3)]
b. 52 [(8-2) - (0 - 3)]
52 +[(8-2) + (10 - 3)]
d. 52 + [(8 + 2) + (10 + 3)1
a.
Answer:
52/[(8 - 2) + (10 - 3)]
Step-by-step explanation:
Jeff earns $8 and spends $2 each week.
Each week he keeps (8 - 2).
Joe earns $10 and spends $ each week.
Each week he keeps (10 - 3).
The total amount they keep each week is
(8 - 2) + (10 - 3).
If you divide the cost of the game by the amount they keep each week, you get the number of weeks.
Answer: 52/[(8 - 2) + (10 - 3)]