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Brums [2.3K]
3 years ago
9

a side of a square bulletin board measures 34 inches. Which of these is the closest length of a diagonal?

Mathematics
1 answer:
Delicious77 [7]3 years ago
6 0
If you diagonally slice the board, you get a right angle, which pyth thm can be used. side2 x side2 = diagonal2

34squared + 34squared = x (diagonal) squared
1156 + 1156 = x squared
2312 = x squared
x = 48.0832611207
so just correct it to the closest as 48 inches
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Answer: $189 000

brainliest or a thank you please :))

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6 0
3 years ago
Find the critical numbers of the function f(x) = x6(x − 1)5 what does the first derivative test tell you that the second derivat
patriot [66]
The given function is f(x) = x⁶(x-1)⁵

The first derivative is
f'(x) = 6x⁵(x-1)⁵ + 5x⁶(x-1)⁴
       = x⁵(x-1)⁴(6x - 6 + 5x)
       = x⁵(x-1)⁴(11x - 6)
The critical values are the zeros of f'(x). They are
x = 0, 6/11, and 1.
The critical values indicate that turning points exist for f(x) at the critical points. However, we do not know the nature of the turning points.

Write the first derivative in the form f'(x) = (x-1)⁴(11x⁶ - 6x⁵).
The second derivative is
f''(x) = 4(x-1)³(11x⁶ - 6x⁵) + (x-1)⁴(66x⁵ - 30x⁴)
        = (x-1)³(44x⁶ - 24x⁵ + 66x⁶ - 30x⁵ - 66x⁵ + 30x⁴)
        = (x-1)³(110x⁶ - 120x⁵ + 30x⁴)
        = 10x⁴(x-1)³(11x² - 12x + 3)
The sign of f''(x) at the critical values tell us the nature of the turning point.

f''(0) = 0, therefore a point of inflection exists at x = 0.
f''(6/11) > 0, therefore a local minumum exists at x = 6/11.
f''(1) = 0, therefore a point of inflection exists at x=1.

The graphs shown below confirm these results.

8 0
3 years ago
What is the solution to the system: 9x+3y=24 2y+4x=8
egoroff_w [7]

Answer:

x = 4, y = -4

Step-by-step explanation:

9x + 3y = 24

3x + y = 8                       divide both sides by 3

y = 8 - 3x                        subtract 3x from both sides

2y + 4x = 8

2(8 - 3x) + 4x = 8             replace y with 8 - 3x

16 - 6x + 4x = 8                distributive property

-6x + 4x = 8 - 16               subtract 16 from both sides

-2x = -8                            divide both sides by -2

x = 4

y = 8 - 3x

y = 8 - 3(4)                        replace x with 4

y = 8 - 12

y = -4

8 0
2 years ago
Read 2 more answers
Question: solve for x. ​<br><br>please someone help!
Dominik [7]

by angle sum property of triangle,

70+60+(x+60)=180

=> 190 +x = 180

=> x = 180-190

=> x = -10

5 0
3 years ago
– Jack can paint a room in 9 hours alone. If Sara helps, they can do the job in 5 hours. How long
Dafna11 [192]

Answer: 9

Step-by-step explanation:

If Jack can paint the room in 9 hours by his self she can only do the same

8 0
3 years ago
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