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Gnesinka [82]
3 years ago
13

If (a,b) is the vertex of the parabola whose equation is y= (x+3)^2 +3, what is the value of a+b?

Mathematics
1 answer:
Lerok [7]3 years ago
6 0
The vertex is (-3,3),so a =-3, b=3. a+b=0
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Identify the perimeter and area of a square with diagonal length 11in. Give your answer in simplest radical form. HELP PLEASE!!
Nataliya [291]

Answer:

  • Perimeter = 22*sqrt(2)
  • Area = 60.5 inches
  • D

Step-by-step explanation:

Remark

You need 2 facts.

  1. A square has 4 equal sides.
  2. It contains (by definition) 1 right angle but since we are not including and statement about parallel sides, it needs 4 right angles.

That means you can use the Pythagorean Theorem.

If one side of a square is a then the 1 after it is a as well.

Formula

  • a^2 + a^2 = c^2
  • 2a^2 = c^2

Givens

  • c = 11

Solution

  • 2a^2 = 11^2
  • 2a^2 = 121                    Divide by 2
  • a^2 = 121/2                  Take the square root of both sides
  • sqrt(a^2) = sqr(121/2)    
  • a = 11/sqrt(2)                Rationalize the denominator
  • a = 11 * sqrt(2)/[sqrt(2) * sqrt(2)]
  • a = 11 * sqrt(2) / 2

<em><u>Perimeter</u></em>

P = 4s

  • P = 4*11*sqrt(2)/2
  • P = 44*sqrt(2)/2
  • P = 22*sqrt(2)

You don't need the area. The answer is D

<em><u>Area</u></em>

  • Area = s^2
  • Area = (11*sqrt(2)/2 ) ^2
  • Area = 121 * 2 / 4
  • Area = 60.5


8 0
3 years ago
Which of the following is true?
gtnhenbr [62]

Answer:

C..... I think it is a answer

6 0
3 years ago
emilys meal costs 32.75 and darren's meal costs 39.88. emily treats darren by paying for both meals, and leaves a 14 percent tip
tamaranim1 [39]
The total cost would be $82.80.
5 0
3 years ago
Read 2 more answers
In a photograph, a house is 4 inches wide and 6 inches tall. The photograph is enlarged while keeping proportional dimensions, a
AlekseyPX

Since you keep proportional dimensions, the proportion between the old and new dimensions must be the same. So, if we call the new height h, the preservation of the width/height ratio is written as


4 \div 6 = 9 \div h


Solving the proportion for h yields


h = \frac{6\cdot 9}{4} =\frac{3\cdot 9}{2} = \frac{27}{2} = 13.5

6 0
3 years ago
Read 2 more answers
Find m∠DEC (the picture is not drawn to scale).
pochemuha

Answer:

M∠DEC equals 123º.

Step-by-step explanation:

The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.

180 - {(x - 45)+(x - 12)} = m∠DEC

m∠DEC + x = 180

<u>(x - 45) + (x - 12) = x</u>

Solving for x:

(x - 45) + (x - 12) = x

x - 45 + x - 12 = x                             Remove parenthesis

2x - 57 = x                                       Combine like terms

2x = x + 57                                      Add 57 to both sides

<u>x = 57</u><u>                                             Subtract x from both sides</u>

Finding m∠D:

x - 45 = ?

<u>57 - 45 = </u><u>12º                                          </u>

Finding m∠C:

x - 12 = ?

<u>57 - 12 = </u><u>45º                                           </u>

<em>** </em><em>(Checking x: 12 + 45 = 57) </em><em>**</em>

<em>Finding </em>m∠DEC:

AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:

180 - 57 = 123º

Hope this helps,

❤<em>A.W.E.</em><u><em>S.W.A.N.</em></u>❤

8 0
3 years ago
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