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4 years ago

In the diagram below, RSTU is a rectangle, and the two shaded regions are squares.

Mathematics

1 answer:

sdas [7]4 years ago

7 0

Answer:

length PQ = 8.9 m

Step-by-step explanation:

The picture below completes the question you asked. From the picture above RSTU is a rectangle . The two shaded square has a length of sides 8 m and 4 m respectively. The legs of the triangle is the sides of the 2 squares. Therefore, the triangle is a right angle triangle. The adjacent side is 4 m while the opposite side is 8 m.

Using Pythagoras theorem the hypotenuse of the triangle can be calculated below.

Pythagoras theorem

c² = a² + b² Therefore,

c² = 4² + 8²

c² = 16 + 64

c² = 80

square root both sides

c = √80

c = 8.94427191

c ≈ 8.9 m

length PQ = 8.9 m

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Answer:

y = $\frac{2}{5}$ x - 3

Step-by-step explanation:

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Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a

Alina [70]

Given:

30-hour review course average a score of 620 on that exam.

70-hour review course average a score of 749.

To find:

The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).

70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-620=\dfrac{749-620}{70-30}(x-30)$

$y-620=\dfrac{129}{40}(x-30)$

$y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)$

$y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}$

Adding 620 on both sides, we get

$y=\dfrac{129}{40}x-\dfrac{387}{4}+620$

$y=\dfrac{129}{40}x+\dfrac{2480-387}{4}$

$y=\dfrac{129}{40}x+\dfrac{2093}{4}$

We need to find the y-value for $x=57$ .

$y=\dfrac{129}{40}(57)+\dfrac{2093}{4}$

$y=183.825+523.25$

$y=707.075$

$y\approx 707.1$

Therefore, the required linear equation for the given situation is $y=\dfrac{129}{40}x+\dfrac{2093}{4}$ and the average score for persons taking a 57-hour review course is 707.1.

4 0

3 years ago

A production system has a total daily output of 400 units and a total labor of 350 hours, what kind of productivity measure can

fomenos

Answer:

1.14 products per hour of labor

Step-by-step explanation:

To calculate the daily productivity would be the amount of products per hour of labor.

That is: 400 products / 350 hours of labor, and that is approximately 1.14 products per hour of labor.

Which means that for every hour of labor, 1.14 products are produced in one day, which would be a factor of productivity.

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3 years ago

PLEASE PLEASE HELP WITH THIS

Phoenix [80]

Since triangles ABC and BCD are similar, we can establish a proportion between the lengths of corresponding sides:
$\frac{AC}{BC} = \frac{BC}{CD}$

We can infer from our picture that $BC=m$ . Also we can find the length of AC by adding AD and CD:
$AC=AD+CD$
$AC=11+7$
$AC=18$

Lets replace the values in our proportion:
$\frac{AC}{BC} = \frac{BC}{CD}$
$\frac{18}{m} = \frac{m}{7}$
Solving for $m$ :
$m^2=(18)(7)$
$m^2=126$
$m= \sqrt{126}$

We can conclude that the correct answer is: D $\sqrt{126}$

4 0

3 years ago