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anyanavicka [17]
2 years ago
15

2. The Lamberti family is building a rectangular deck that measures 30 feet by 22 feet. They need to run an electric line across

the diagonal, underneath the deck. How long is the diagonal of the deck, to the nearest foot?
Mathematics
1 answer:
schepotkina [342]2 years ago
6 0

Answer:

37 ft

Step-by-step explanation:

The Pythagorean theorem tells you the length of the diagonal is the square root of the sum of the squares of the side lengths:

diagonal = √(30^2 +22^2) = √1384 ≈ 37 . . . . feet

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What is the common denominator as a fraction of 5/4 and 11/16
trasher [3.6K]
16 is the greatest common denominator
7 0
3 years ago
Read 2 more answers
The seventh term of an arithmetic progression is equal to twice the fifth term. The sum
mario62 [17]

Answer:

a₁ = - 24

Step-by-step explanation:

The n th term of an AP is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₇ = 2a₅ , then

a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )

- a₁ - 2d = 0 → (1)

The sum to n terms of an AP is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ]

Given S_{7} = 84 , then

\frac{7}{2} (2a₁ + 6d) = 84

3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )

2a₁ + 6d = 24 → (2)

Thus we have 2 equations

- a₁ - 2d = 0 → (1)

2a₁ + 6d = 24 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate d

- 3a₁ - 6d = 0 → (3)

Add (2) and (3) term by term to eliminate d

- a₁ = 24 ( multiply both sides by - 1 )

a₁ = - 24

6 0
3 years ago
A bakery bakes 26 batches of 69 cupcakes each week. How many individual cupcakes do they make each week
Vladimir79 [104]

Answer:

12558

Step-by-step explanation:

times all of them

4 0
3 years ago
I need help asap!!!!!!!!!!!!!!!!!!!!
kramer

Answer:

BC = 30

Step-by-step explanation:

3 0
3 years ago
Help me solve this please
damaskus [11]

1) A quadratic will have no real roots when its discriminant is negative


0 = ax^2 + bx + c = x^2 + 2k x + (4k-3)


d = b^2 - 4ac =  (2k)^2 - 4(1)(4k-3) = 4k^2 - 16k + 12 < 0


Dividing by 4,


k^2 - 4 k + 3 < 0 \quad\checkmark


We have a positive coefficient on k^2 so this parabola is a CUP (concave up positive) so has a minimum at the vertex. If the vertex y value is less than zero, the inequality will be true in the range between the zeros.


(k-3)(k-1)


That's true for


1 < k < 3


2) We look for the meet of the line and the parabola:


2x + k + 2 = 2x^2 + (k+2)x + 8


0 = 2x^2 + kx + (6-k)


For two intersections we need a positive discriminant:


k^2 - 4(6-k)(2) > 0


k^2 + 8k - 48 > 0


(k+12)(k-4) > 0


That's means two negative or two positive, so


k < 12 or k > 4


6 0
3 years ago
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