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vagabundo [1.1K]
3 years ago
6

Solve y^2+7y+12=0 by completing the square.​

Mathematics
1 answer:
kkurt [141]3 years ago
8 0

Answer:

y = -3, -4

Step-by-step explanation:

Formula is (b/2)^2

So...

(y+7/2)^2 - 1/4 = 0

Add 1/4 to each side

(y+7/2)^2 = 1/4

Square root...

y+7/2 = +-1/2

Add

y = -3, -4

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Ann believes that y= 3x (x -7) is a quadratic function. Jordan says that she is wrong because the degree (highest exponent) is n
ad-work [718]

Answer:

Ann us correct. It's a quadratic function.

Step-by-step explanation:

Given equation is,

y = 3x(x - 7)

By converting this equation into the standard quadratic equation,

y = 3x² - 21x

Highest exponent of the polynomial equation is 2 (Exponent of highest degree variable x²). This decides that the given function is a quadratic function.

Therefore, Ann is correct. It's a quadratic function.

5 0
3 years ago
MATH HELP!
Irina18 [472]
You have the correct answer. Nice work. If you need to see the steps, then see below

-------------------------------------------------------------------------------

First we need to find the midpoint of H and I
The x coordinates of the two points are -4 and 2. They add to -4+2 = -2 and then cut that in half to get -1

Do the same for the y coordinates: 2+4 = 6 which cuts in half to get 3

So the midpoint of H and I is (-1,3). The perpendicular bisector will go through this midpoint

---------------------

Now we must find the slope of segment HI

H = (-4,2) = (x1,y1)
I = (2,4) = (x2,y2)
m = (y2 - y1)/(x2 - x1)
m = (4 - 2)/(2 - (-4))
m = (4 - 2)/(2 + 4)
m = 2/6
m = 1/3
Flip the fraction to get 1/3 ---> 3/1 = 3
Then flip the sign: +3 ----> -3

So the slope of the perpendicular bisector is -3

-----------------------

Use m = -3 which is the slope we found
and (x,y) = (-1,3), which is the midpoint found earlier
to get the following
y = mx+b
3 = -3*(-1)+b
3 = 3+b
3-3 = 3+b-3
0 = b
b = 0

So if m = -3 and b = 0, then y = mx+b turns into y = -3x+0 and it simplifies to y = -3x

So that confirms you have the right answer. I've also used GeoGebra to help confirm the answer (see attached)

7 0
3 years ago
If she is right, the object is worth $25, if she is wrong, the object is worth $4. How high does the probability of the object b
pickupchik [31]

Answer:

The expected value for an event with outcomes:

{x₁, x₂, ..., xₙ}

Each one with probability:

{p₁, p₂, ..., pₙ}

Is just:

Ev = x₁*p₁ + ... + xₙ*pₙ

here we have two outcomes:

x₁ = the object worths $25

x₂ = the object is worth $4.

Each one with probability p₁ and p₂ respectively, such that:

p₁ + p₂ = 1

Then the expected value is:

Ev = p₁*($25) + p₂*($4)

Now we want to know how should be the probabilities, such that buying the object for $16 is whort.

Well, the purchase will be whort if the expected value is larger than $16.

This is equivalent to:

p₁*($25) + p₂*($4) - $16 > $0

Knowing that:

p₁ + p₂ = 1

we can rewrite:

p₂ = 1 - p₁

replacing that in the above inequality we get:

p₁*($25) + ( 1 - p₁)*($4) - $16 > $0

Now we can solve this for p₁

p₁*($25 - $4) + $4 - $16 > $0

p₁*$21 - $12 > $0

p₁*$21 > $12

p₁ > $12/$21 = 0.571

The probability of the object being authentic should be larger than  0.571 to take the gamble.

5 0
3 years ago
The volume of a cylinder is 1029pi cmcubed. The radius of the base of the cylinder is 7 cm. What is the height of the​ cylinder?
DedPeter [7]

Answer:

Height is 21cm

Step-by-step explanation:

Volume of the cylinder = 1029pi

Base area = 7x7xpi = 49pi

Therefor the height = 1029pi/49pi=1029/49 = 21cm

4 0
3 years ago
Read 2 more answers
in a last minute deal a holiday is reduced from £540 to £459. Calculate the percentage reduction in the price
harkovskaia [24]

Answer:

15%

Step-by-step explanation:

A holiday is reduced from £540 to £459

Reduction = £540 - £459

= £81

Percentage reduction = reduction/initial amount x 100%

That’s £81/£540 x 100%

0.15 x 100%

15%

The percentage reduction in price is 15%

7 0
3 years ago
Read 2 more answers
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