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exis [7]
3 years ago
11

Lila covered 55 ft squared of her back yard with 3/4 of a load of sod. She has 3 loads of sod in all. If she wants to cover all

250 ft squared of her yard, does she have enough sod?
Mathematics
1 answer:
AnnyKZ [126]3 years ago
7 0

Answer:

More sod is needed

Step-by-step explanation:

Well we know that 3/4 of a bag of sod covers 55 ft^2  then  if we divide 55 by 3 we get 18.3333 we take that and multiply by 4 to get 73.333 or the amount one bag of sod can cover

73.333*3 cuz 3 bags of sod is 220 ft^2  

She needs more sod

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Which of the following reveals the minimum value for the equation 2x^2 − 4x − 2 = 0?
12345 [234]

Answer:

2(x-1)^{2}=4

Step-by-step explanation:

<u><em>The options of the question are</em></u>

2(x − 1)2 = 4

2(x − 1)2 = −4

2(x − 2)2 = 4

2(x − 2)2 = −4

we have

2x^{2} -4x-2=0

This is a vertical parabola open upward

The vertex represent the minimum value

The quadratic equation in vertex form is

y=a(x-h)^2+k

where

a is a coefficient

(h,k) is the vertex

so

Convert the quadratic equation in vertex form

Factor 2 leading coefficient

2(x^{2} -2x)-2=0

Complete the squares

2(x^{2} -2x+1)-2-2=0

2(x^{2} -2x+1)-4=0

Rewrite as perfect squares

2(x-1)^{2}-4=0

The vertex is the point (1,-4)

Move the constant to the right side

2(x-1)^{2}=4

3 0
3 years ago
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interv
sleet_krkn [62]

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

4 0
3 years ago
Select all the expressions that are equivalent to 4 - x.
Andre45 [30]
Im pretty sure it’s A,B,D
5 0
3 years ago
Please help meeeeeeeee
Dafna1 [17]

Answer:

Point D is at 3 this is the only correct point...

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Glenna says that the height of her house is 1 yard. is her claim reasonable?
qaws [65]
No! 1 yard is only 3 feet tall.
7 0
3 years ago
Read 2 more answers
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