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Veronika [31]
3 years ago
15

the standard form of the equation of a parabola is y=x^2 -8x + 29. what is the vertex form of the equation?

Mathematics
2 answers:
ankoles [38]3 years ago
5 0
Y - 29 = x² - 8x  ←I moved the constant to the other side
y - 29 + (-4)² = x² - 8x + (-4)² ← I just completed the square (b/2)² added to each side

y - 13 = (x - 4)² ← factored perfect square trinomial

y = (x - 4)² + 13 ← move constant back with binomial 
tatuchka [14]3 years ago
4 0
The vertex is (0,21)
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katovenus [111]

Answer:

Given: Two Isosceles triangle ABC and Δ PBC having same base BC. AD is the median of Δ ABC and PD is the median of Δ PBC.

To prove: Point A,D,P are collinear.

Proof:

→Case 1.  When vertices A and P are opposite side of Base BC.

In Δ ABD and Δ ACD

AB= AC   [Given]

AD is common.

BD=DC  [median of a triangle divides the side in two equal parts]

Δ ABD ≅Δ ACD [SSS]

∠1=∠2 [CPCT].........................(1)

Similarly, Δ PBD ≅ Δ PCD [By SSS]

∠ 3 = ∠4 [CPCT].................(2)

But,  ∠1+∠2+ ∠ 3 + ∠4 =360° [At a point angle formed is 360°]

2 ∠2 + 2∠ 4=360° [using (1) and (2)]

∠2 + ∠ 4=180°

But ,∠2 and ∠ 4 forms a linear pair i.e Point D is common point of intersection of median AD and PD of ΔABC and ΔPBC respectively.

So, point A, D, P lies on a line.

CASE 2.

When ΔABC and ΔPBC lie on same side of Base BC.

In ΔPBD and ΔPCD

PB=PC[given]

PD is common.

BD =DC [Median of a triangle divides the side in two equal parts]

ΔPBD ≅ ΔPCD  [SSS]

∠PDB=∠PDC [CPCT]

Similarly, By proving ΔADB≅ΔADC we will get,  ∠ADB=∠ADC[CPCT]

As PD and AD are medians to same base BC of ΔPBC and ΔABC.

∴ P,A,D lie on a line i.e they are collinear.

6 0
2 years ago
What function is graphed below?
tester [92]
The answer for the exercise shown above is the first option, which is:
<span> f(x)=log(x-3) 
 The explanation is shown below:
 If you substitute the x in the function for values, you will obtain the graph attached above. As you can see on the mentioned graph, when the variable x has the value 4, the value y is 0. Therefore, you have:
 </span> f(x)=log(x-3) 
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  f(x)=0<span>
 </span>
3 0
3 years ago
Read 2 more answers
there are 12 students who play the clarinet and 16 students who play the viola. what does the ratio 16:12 describe?​
Oksi-84 [34.3K]

Answer: The ratio 16:12 describes the ratio of the number of students who play the viola to the students who play the clarinet.

Step-by-step explanation:

Given : Number of students who play the clarinet= 12

Number of students who play the viola=16

We know that ratio of A to B is represented by A:B.

Since, the number '12' is representing " students who play the clarinet" and  number '16' is representing  " students who play the viola"

So , the ratio 16:12 describes the ratio of the number of students who play the viola to the students who play the clarinet.

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Answer:

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the recipe calls for one cup of water per two cups of dish soap, so if she uses two cups of dish soap she should use one cup of water and one tablespoon of corn syrup.

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