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Verdich [7]
3 years ago
12

Vertex form equation 4(x+2)^2-81 what is the solution?​

Mathematics
1 answer:
Andrei [34K]3 years ago
5 0

Answer:

<h3>            x₁ = 2.5 ,   x₂ = - 6.5               </h3>

Step-by-step explanation:

4(x+2)^2-81=0\\\\4(x+2)^2=81\\\\(x+2)^2=\frac{81}4\\\\x+2=\sqrt{\frac{81}4}\quad\vee\quad x+2=-\sqrt{\frac{81}4}\\\\x=\frac92-2\qquad\vee\quad\ x=-\frac92-2\\\\x=\frac52\qquad\vee\quad\ x=-\frac{13}2

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What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)?
GrogVix [38]
First find the slope of the given line like this:
5x + 2y = 12\\2y=-5x+12\\y=\frac{-5}{2}x+6
If two lines are parallel, then they have the same slope, so the equation we are looking for is in the form:
y=\frac{-5}{2}x+a and we have to find b using the given point like this:
Substitute x = -2 and y=4 in the above equation like this and solve for a:
4=\frac{-5}{2}(-2)+a 
4=5+a 
a=4-5=-1 
The equation of the line is then the following:
y=\frac{-5}{2}x-1.
3 0
4 years ago
Read 2 more answers
A ball is thrown upward with an initial velocity of 60 mph. it is thrown from a height of 5 feet. what is the maximum height it
natima [27]

Answer:

h = 61.25 m

Step-by-step explanation:

It is given that,

The initial velocity of the ball, v = 60 m/s

It is thrown from a height of 5 feet, h_o=5\ ft

We need to find the maximum height it reaches. The height reached by the projectile as a function of time t is given by :

h=-16t^2+vt+h_0

Putting all the values,

h=-16t^2+60t+5 .....(1)

For maximum height, put

\dfrac{dh}{dt}=0\\\\\dfrac{-16t^2+60t+5}{dt}=0\\\\-32t+60=0\\\\t=\dfrac{-60}{-32}\\\\t=1.875\ s

Put t = 1.875 in equation (1)

h=-16(1.875)^2+60(1.875)+5\\\\h=61.25\ m

So, the maximum height reached by the ball is 61.25 m.

8 0
3 years ago
Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept: (0,1)
Luda [366]

Answer:

y = (1/4)x² - (5/4)x + 1

Step-by-step explanation:

The x-intercepts of the quadratic equation are simply it's roots.

Thus, we have;

(x + 1) = 0 and (x - 4) = 0

Now, formula for quadratic equation is;

y = ax² + bx + c

Where c is the y intercept.

At y-intercept: (0,1), we have;

At (-1,0), thus;

0 = a(1²) + b(1) + 1

a + b = -1 - - - (1)

At (4,0), thus;

0 = a(4²) + b(4) + 1

16a + 4b = -1

Divide both sides by 4 to get;

4a + b = -1/4 - - - (2)

From eq 1, b = -1 - a

Thus;

4a + (-1 - a) = -1/4

4a - 1 - a = -1/4

3a - 1 = -1/4

3a = 1 - 1/4

3a = 3/4

a = 1/4

b = -1 - 1/4

b = -5/4

Thus;

y = (1/4)x² - (5/4)x + 1

6 0
3 years ago
Based on the diagram, what is the reduced area inside the blood vessel?
pychu [463]

Answer:

: Stroke Brain cells do not get the nutrients they need if blood flow to the brain …

Step-by-step explanation:

3 0
3 years ago
How do you find the area of a circle and what is the formula for it
mote1985 [20]

Answer:

Read Exp:

Step-by-step explanation:

Area = 3.14 x r^2

I've Included a picture to tell you how to get the diameter as well as the circumference.

3 0
3 years ago
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