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butalik [34]
3 years ago
7

The function y= x2 - 10x+ 31 has a value of

Mathematics
1 answer:
Margarita [4]3 years ago
5 0

Answer:

  • y = 6 at x = 5

Step-by-step explanation:

It is assumed the question is about finding the minimum value as the given function has no maximum value, it is + ∞ as the coefficient of x² is positive

<u>The minimum/maximum value of a quadratic function is the vertex, which is at:</u>

  • x = -b/2a

<u>For the given function y = x² -10x + 31, the vertex is:</u>

  • x =  - (-10)/2*1 = 10/2 = 5

<u>The value of y at this point is:</u>

  • y = 5² - 10*5 + 31 = 25 - 50 + 31 = 6

<u>The point is </u>

  • (5, 6)

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The base of 40-foot ladder is 8 feet from the wall. How high is the ladder on the wall (round to the nearest foot)
Nina [5.8K]

Given:

The base of 40-foot ladder is 8 feet from the wall.

To find:

How high is the ladder on the wall (round to the nearest foot).

Solution:

Ladder makes a right angle triangle with wall and ground.

We have,

Length of ladder (hypotenuse)= 40 foot

Base = 8 foot

We need to find the perpendicular to get the height of the ladder on the wall.

Let h be the height of the ladder on the wall.

According to the Pythagoras theorem,

Hypotenuse^2=Base^2+Perpendicular^2

(40)^2=(8)^2+(h)^2

1600=64+h^2

1600-64=h^2

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Taking square root on both sides.

\pm \sqrt{1536}=h

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Height cannot be negative. Round to the nearest foot.

h\approx 39

Therefore, the height of the ladder on the wall is 39 foot.

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3 years ago
Write the sentence as an inequality. A number t multiplied by -4 is at least −2/5
OleMash [197]

Answer:

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Step-by-step explanation:

Given

A number t multiplied by -4 is at least −2/5

To determine

Write the sentence as an inequality.

For the inequalities, when we mention 'at least', we can term it as 'greater than or equal to' symbol such as '≥'.

It is stated that A number t multiplied by -4 is at least −2/5.

Let 't' be the number.

Multiplying t by -4 is: -4t

Thus,  A number t multiplied by -4 is at least −2/5 will be written as:

-4t ≥ -2/5

Therefore, we conclude that 'A number t multiplied by -4 is at least −2/5' can be algebraically written as inequality such as:

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3 years ago
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To find how many pounds you have of lime just subtract the amount of cherry.

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3 years ago
1/3y+1/4=5/12 i need 20 character
lys-0071 [83]
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