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vazorg [7]
3 years ago
12

Suppose the hypotenuse of a right triangle is 24 cm and one of the legs is 11 cm. Use the Pythagorean Theorem to find the measur

e of the triangle's other leg. Round the measure to the nearest tenth if needed. 1.None of these 2. 13 cm 3. 5.1 cm 4 21.3 cm 5. 26.4 cm

Mathematics
1 answer:
uysha [10]3 years ago
4 0

Answer:

The answer is number 4. 21.3 cm

Step-by-step explanation:

In the picture you can see the draw of the triangle and the formula of the Pythagorean Theorem.

We substitute the values in the Pythagorean Theorem

c² = a² + b²

We clear the equation for b

b² = c² - a²

b² = (24)² - (11)²

b² = 576 - 121

b² = 455

√b² = √455

b = 22.3 cm

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If a=(-1, -3) and b=(11, -8) what is the length of ab?
professor190 [17]

Answer: D.  The length is 13 units.

Step-by-step explanation:

(-1, -3 )    Find the difference between the x values and y values.

 (11, -8)  

-3-(-8) = 5

-1-11 =   -12    now find the  absolute values.

The absolute value of 5 is 5 .  The absolute value of  -12 is 12.

Now use the Pythagorean Theorem formula a^2 + b^2 =c^2  where c square is the length between AB.

5^2 + 13^2 = C^2

25 + 144 = c^2  

169=c^2

c= 13

8 0
3 years ago
House of Mohammed sells packaged lunches, where their finance department has established a
blagie [28]

The revenue function is a quadratic equation and the graph of the function

has the shape of a parabola that is concave downwards.

The correct responses are;

  • (a) <u>R = -x² + 82·x</u>
  • (b) <u>$1,645</u>
  • (c) The graph of <em>R</em> has a maximum because the <u>leading coefficient </u>of the quadratic function for <em>R</em> is negative.
  • (d)  <u>R = -1·(x - 41)² + 1,681</u>
  • (e) <u>41</u>
  • (f) <u>$1,681</u>

Reasons:

The given function that gives the weekly revenue is; R = x·(82 - x)

Where;

R = The revenue in dollars

x = The number of lunches

(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;

R = x·(82 - x) = 82·x - x²

Which gives;

  • <u>R = -x² + 82·x </u>

<em>Where, the constant term, c = 0</em>

(b) When 35 launches are sold, we have;

x = 35

Which by plugging in the value of x = 35, gives;

R = 35 × (82 - 35) = 1,645

  • The revenue when 35 lunches are sold, <em>R</em> = <u>$1,645</u>

(c) The given function for <em>R</em> is R = x·(82 - x) = -x² + 82·x

Given that the leading coefficient is negative, the shape of graph of the

function <em>R</em> is concave downward, and therefore, the graph has only a

maximum point.

(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;

(h, k) = The vertex of the equation

a = The leading coefficient

The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;

R = x·(82 - x) = -x² + 82·x

At the vertex, of the equation; f(x) = a·x² + b·x + c,  we have;

\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}

Therefore, for the revenue function, the x-value of the vertex, is; \displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}

The revenue at the vertex is; R_{max} = 41×(82 - 41) = 1,681

Which gives;

(h, k) = (41, 1,681)

a = -1 (The coefficient of x² in -x² + 82·x)

  • The revenue equation in the form, a·(x - h)² + k is; <u>R = -1·(x - 41)² + 1,681</u>

(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41

Therefore;

  • The number of lunches that must be sold for the maximum revenue to be achieved is<u> 41 lunches</u>

(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681

  • <u>The maximum revenue of the company is $1,681</u>

Learn more about the quadratic function here:

brainly.com/question/2814100

6 0
2 years ago
The graph showsf(x)and its transformationg(x).
svlad2 [7]

Answer:

hope this helps you out good luck

6 0
3 years ago
Shawn is conducting an experiment where he is flipping a fair coin (where the probability of the coin landing heads up is 50%).
Serhud [2]
I believe the answer is d
8 0
3 years ago
Are the ratios 7:9 and 3:6 equivalent?
Cloud [144]

Answer: No

Step-by-step explanation:

7 0
1 year ago
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