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icang [17]
3 years ago
10

A^2+14a-51=0 solve the quadratic by completing the square.

Mathematics
2 answers:
Stells [14]3 years ago
8 0
A^2+14a-51=0
Add 51 to both sides
a^2+14a-51+51=0+51
a^2+14a=51
add (14/2)^2
a^2+14a+(14/2)^2=100
Solve a+7=+sqrt 100: a=3
Solve a-7 = -sqrt 100: a=-17
a=3 a=-17




ehidna [41]3 years ago
7 0
Steps if you have ax^2+bx+c=0
1. put vairable on other side (-c from both sides)
2. make sure that leading term is 1 (ax^2+bx+c=0 where a=1)
3. take half of  b and square it

so
a^2+14a-51=0
move c to other side
add 51 to both sides
a^2+14a=51
leading term is 1
take 1/2 of b and square
14/2=7, 7^2=49
add that to both sides
a^2+14a+49=51+49
factor perfect square
(a+7)^2=100
square root both sides
a+7=+/-10

a+7=10
a+7=-10


a+7=10
minus 7
a=3

a+7=-10
subtract 7
a=-17


a=3 or -17
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Answer:

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Step-by-step explanation:

Given f(x)=\sqrt{x+3}

Let y=\sqrt{x+3}

Interchange x and y

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Solve for y, by first squaring both sides

x^2=y+3

x^2-3=y

Hence

f^{-1}(x)=x^2-3

The last choice is correct

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Suppose that an experiment consists of flipping a coin 3 times and observing the resulting sequence of heads and tails. Find the
ki77a [65]

Using the binomial distribution, it is found that there is a 0.125 = 12.5% probability of observing exactly 3 tails.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

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In this problem, considering 3 tosses of a fair coin, the parameters are n = 3 and p = 0.5.

The probability of 3 tails is P(X = 3), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125

0.125 = 12.5% probability of observing exactly 3 tails.

More can be learned about the binomial distribution at brainly.com/question/24863377

3 0
2 years ago
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erastovalidia [21]

Answer: 10 and 11, also -11 and -10

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Sqrt 121 is 11

Step-by-step explanation:

Positive Sqrt is monotone increasing

So Sqrt 105 is between sqrt 100 and sqrt 121


Second answer

Sqrt 100 is less well known to also be -10

Negative sqrt is monotone decreasing

Sqrt 121 is also -11

Sqrt 105 is also between -121 and -100

4 0
3 years ago
A Ladder that is 32 ft long leans against a building. The angle of elevation of the ladder is 70 degrees. To the nearest tenth o
kolezko [41]
See the picture attached to better understand the problem

we know that
in the right triangle ABC
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in this problem
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sin 70°=AB/32------> AB=32*sin 70°-----> AB=30.07 ----> AB=30.1 ft


4 0
3 years ago
Read 2 more answers
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