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scoray [572]
3 years ago
9

There are three consecutive even integers the sum of the second and third numbers decreased by the first is 72 what are the inte

gers
Mathematics
1 answer:
astraxan [27]3 years ago
3 0

Answer:

66, 68, 70

Step-by-step explanation:

68 + 70 = 138

138 - 66 = 72

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Write the phrase as an equation /
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4 = 20 + n, where n is the number

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Write the equation of a parabola with focus at (1,-4) and a directrix at X=2
konstantin123 [22]

Answer:

The equation of a parabola is

x =  \frac{1}{4(f - h)} (y - k) ^{2}  + h

Step-by-step explanation:

(h,k) is the vertex and (f,k) is the focus.

Thus, f = 1, k = −4.

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.

Solving the system, we get h = 3/2, k = -4, f = 1.

The standard form is:

x =  -  \frac{y ^{2} }{2}  - 4y -  \frac{13}{2}

The general form is:

2x +  {y}^{2}  + 8y + 13 = 0

The vertex form is:

x =  -  \frac{(y + 4) ^{2} }{2}  +  \frac{3}{2}

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.

The focal length is the distance between the focus and the vertex: 1/2.

The focal parameter is the distance between the focus and the directrix: 1.

The latus rectum is parallel to the directrix and passes through the focus: x = 1.

The length of the latus rectum is four times the distance between the vertex and the focus: 2.

The eccentricity of a parabola is always 1.

The x-intercepts can be found by setting y = 0 in the equation and solving for x.

x-intercept:

( -  \frac{13}{2}  \: ,0)

The y-intercepts can be found by setting x = 0 in the equation and solving for y.

y-intercepts:

(0, - 4 -  \sqrt{3)}

(0, - 4 +  \sqrt{3)}

3 0
3 years ago
You are given the system of equations to solve by the elimination method, which is an INCORRECT step that will NOT produce a sys
Dennis_Churaev [7]

Answer:

13x 5y

Step-by-step explanation:

3 0
3 years ago
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth.
Alex17521 [72]
-2x + 6y = -34
-x + 3y = -17
x = 3y +17

Sub this into 1st eqn
5(3y + 17) + 2y = 21
15y + 85 + 2y =21
17y = -64
y = -3.7647 (to 5 sig. fig.)
y = -3.8 (to nearest tenth)

Sub y = -3.7647 into 2nd eqn
x = 3(-3.7647) +17
x = 5.7 (to nearest tenth)
7 0
3 years ago
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