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Answer:
The percent increase is <u>18.75%</u>.
Step-by-step explanation:
Given:
Amber got a raise, and her hourly wage increased from $8 to $9.50.
Now, to find percent increase.
Previous wage = $8.
Wage raised = $9.50.
So, to get the increased wage we subtract the previous wage from the wage raised:
Now, to get the percent increase:
Therefore, the percent increase is 18.75%.
Answer:
The coordinates of the explosion is (3300, -2750)
Step-by-step explanation:
I have plot the points and attached to thus answer for easy understanding.
Now, from the question, since station A is the first to hear the explosion, we'll make it the foci of the parabola in the graph I attached and it will be horizontal since the distance between station C and A is much more than that between station B and A. Thus, the reason why station C will have to be the other foci with the hyperbola centred at the origin.
Now, sound travels at a speed of 1100 ft/s and station B is located 1100 ft from station A. Thus, the explosion would likely have occurred at a point on the line x = 3300ft . Since station A is 3300ft from centre C = 3300,hence C² = 3300² = 10,890,000. Since it takes 4 seconds longer for the sound to reach station C than A, the sound has traveled 4(1100)= 4400 ft.
Thus, 4400 = d1 = d2 = 2a
So,2a = 4400 and so, a =2200
a² = 2200² = 4,840,000 where d1 is the distance from station C to the explosion and d2 is the distance from station A to the explosion. To find b², let's use the equation ;
c² = a² + b² and so; b² = c² - a² = 10,890,000 - 4,840,000 = 6,050,000
Equation of hyperbola is given as;
(x²/a²) - (y²/b²) = 1
Plugging in the values of a² and b², we obtain ;
(x²/4,840,000) - (y²/6,050,000) = 1
Since we have deduced that the explosion must occur on the line x= 3300, we'll put in 3300 for x to obtain ;
(3300²/4,840,000) - (y²/6,050,000) = 1
2.25 - 1 = (y²/6,050,000)
y² = (1.25 x 6,050,000)
y² = 7562500
y = √7562500
y = ± 2750
Due to the fact that the explosion will occur at a point further from station B than from station A, the explosion will take place in quadrant 4. Thus, we will take the negative value of y which is - 2750.
So explosion will occur at the coordinate (3300, -2750)
The completed table for the Pythagorean triples are:
.
A trio of positive numbers known as a Pythagorean triple fits into the Pythagoras theorem's formula, which is written as a² + b² = c², where a, b, and c are all positive integers. Here, "a" and "b" make up the other two legs of the right-angled triangle, and "c" serves as the triangle's "hypotenuse," or longest side. In terms of the Pythagorean triples (a, b, c).
In the question, we are given that a triangle with side lengths x² - 1, 2x, x² + 1 is a right triangle, and are asked to fill in the missing table:
.
Taking x as 3, and putting in the sides, we get:
x² + 1 = 3² + 1 = 10.
2x = 2*3 = 6.
x² - 1 = 3² - 1 = 8.
Thus, the triplet is 6,8,10.
For the triplet 8,15,17, we get the x value as:
2x = 8,
or, x = 8/2 = 4.
Thus, the x-value for the triplet (8,15,17) is 4.
Taking x as 5, and putting in the sides, we get:
x² + 1 = 5² + 1 = 26.
2x = 2*5 = 10.
x² - 1 = 5² - 1 = 24.
Thus, the triplet is 10,24,26.
For the triplet 12,35,37, we get the x value as:
2x = 12,
or, x = 12/2 = 6.
Thus, the x-value for the triplet (12,35,37) is 6.
Thus, the completed table for the Pythagorean triples are:
.
Learn more about the Pythagorean triplets at
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The provided question is incomplete. The complete question is:
"We know that a triangle with side lengths x² - 1,2x and x² + 1 is a right triangle. Using those side lengths, find the missing triples and x-values.
Write the triples in parentheses, without spaces between the numbers, and with a comma between numbers. Write the triples in order from least to greatest.
Type the correct answer in each box.
.