Answer:
Answer: x= -6 and y= -7
Step-by-step explanation:
Substitute 2x+5 for y in y=3x+11:
y=3x+11
2x+5=3x+11
2x+5+−3x=3x+11+−3x(Add -3x to both sides)
−x+5=11
−x+5+−5=11+−5(Add -5 to both sides)
−x=6
−x−1=6−1(Divide both sides by -1)
x=−6
Step: Substitute −6 for x in y=2x+5:
y=2x+5
y=(2)(−6)+5
y=−7(Simplify both sides of the equation)
-Source: MathPapa
Step-by-step explanation:
7. 180 -92 -67 =21. 180-21 = 159
8.180-144 = 36 + 94 = 130 180-130 = 50
Answer:
16.38 meters represents the greatest amount of change in her depth over a single 5-minute period
Step-by-step explanation:
From time = 0 to time = 5 the amount of change in her depth was -12.45 - 0 = -12.45 meters
From time = 5 to time = 10 the amount of change in her depth was -9.7 - (-12.45) = -2.75 meters
From time = 10 to time = 15 the amount of change in her depth was -22.98 - (-9.7) = -13.28 meters
From time = 15 to time = 20 the amount of change in her depth was -6.6 - (-22.98) = 16.38 meters
Answer:

Step-by-step explanation:
<u>Given equation</u>:

This is an equation for a horizontal hyperbola.
<u>To complete the square for a hyperbola</u>
Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

Factor out the coefficient of the x² term and the y² term.

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:


Factor the two perfect trinomials on the left side:

Divide both sides by the number of the right side so the right side equals 1:

Simplify:

Therefore, this is the standard equation for a horizontal hyperbola with:
- center = (1, 2)
- vertices = (-2, 2) and (4, 2)
- co-vertices = (1, 0) and (1, 4)


Three consecutive integers that add up to 33 are 2 above and lower than a middle number. This means that the average of these 3 numbers will be the same. Therefore, 33/3=11 as the average. Therefore 11 is the middle number, 9 is 2 below (a consecutive odd integer) and 13 is 2 above (a third consecutive odd integer). Therefore the 3 numbers are 9, 11, and 13.