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3 years ago

Plz do this and show all the work. Use factoring

Mathematics

1 answer:

Anika [276]3 years ago

3 0

Answer:
x1=-1, x2=4/5

Step by step explanation:
5x^2 - 4 + x = 0
Use the commutative property to reorder the terms:
5x^2+x-4=0
Write x as a difference:
5x^2+5x-4x-4=0
Factor out 5x from the expression:
5xx(x-1)-4x - 4=0
Factor out -4 from the expression:
5xx(x+1) - 4 (x-1)=0
Factor out x+1 from the expression:
(x-1) x (5x-4) =0
When the product of factors equal 0 at least one factor is 0
X + 1 = 0
5x - 4 = 0
Solve the equation:
The equation has two solutions
X1=-1, x2 = 4/5

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A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet

abruzzese [7]

Answer:

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume is approximately 46.90 minutes

Step-by-step explanation:

The given parameters are;

The diameter of the balloon = 55 feet

The rate of increase of the radius of the balloon when inflated = 1.5 feet per minute

We have;

dr/dt = 1.5 feet per minute = 1.5 ft/min

V = 4/3·π·r³

The maximum volume of the balloon = 4/3 × 3.14 × 55³ = 696556.67 ft³

When the volume is two-thirds the maximum volume, we have;

2/3 × 696556.67 ft³ = 464371.11 ft³

The value of the radius, r₂ at that point is found as follows;

4/3·π·r₂³ = 464371.11 ft³

r₂³ = 464371.11 ft³ × 3/4 = 348278.33 ft³

348278.333333

r₂ = ∛(348278.33 ft³) ≈ 70.36 ft

The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)

The time for the radius to increase to the above length ≈ 70.369 ft/(1.5 ft/min) ≈ 46.90 minutes

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume ≈ 46.90 minutes.

4 0

3 years ago

One positive number is one-fifth of another number. The difference between the two numbers is 144, find the numbers.

liubo4ka [24]

Answer:

36, 180

Step-by-step explanation:

x = y/5, so y = 5x

y - x = 144

5x - x = 144

4x = 144

x = 144/4 = 36

y = 5x = 5*36 = 180

The two numbers are 36 and 180

7 0

2 years ago

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lutik1710 [3]

Answer:

Step-by-step explanation:

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3 years ago

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vladimir2022 [97]

Answer:

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4 years ago

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Veronica is choosing between two health clubs after how many months will the total cost for each health club be the same

Assoli18 [71]

Question:

Veronica is choosing between two health clubs. after how many months will the total cost for each health club be the same? yoga studio a: membership: $24.00 monthly fee: 21.50. yoga studio b: membership: $41.00 monthly fee: $17.25

Answer:

It takes 4 years for the total cost of each club to become equal

Step-by-step explanation:

Given:

For yoga studio A:

membership: $24.00

monthly fee: 21.50.

For yoga studio B:

membership: $41.00

monthly fee: $17.25

To Find:

Number of months after which the total cost for each health club be the same = ?

Solution:

Let x be the number of months of membership, and y be equal the total cost.

For Yoga club A

y = 21.50 x + 24

For Yoga club B

y = 17.25 x + 41.00

we know that the prices, y , would be equal, we can set the two equations equal to each other.

21.50 x + 24 =17.25 x+ 41.00

Grouping the like terms,

21.50x - 17.25 x= 41.00 - 24

4.25x=17

x= $\frac{17}{4.25}$

x = 4

6 0

3 years ago