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Fed [463]
1 year ago
10

Find the term that must be added to the equation x2 4x=1 to make it into a perfect square.

Mathematics
1 answer:
AVprozaik [17]1 year ago
8 0

The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.

<h3>What is Quadratic equation?</h3>

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.

<h3>Why is it called a quadratic equation?</h3>

This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.

<h3>According to the given information:</h3>

x²+4x=1

as, the x has coefficient 4.

so,

half the coefficient of x and add and subtract the square of the remaining.

x²+4x + 2 ² - 2² =1

Now,

make the whole square term

x²+4x + 2 ² - 4 - 1=0

( x + 2)² -5= 0

To know  more about quadratic equation visit:

brainly.com/question/17177510

#SPJ4

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The sum of two integers is 81.if the product is 1088.what are the integers
arlik [135]

Answer:

(a;b)={(17; 64); (64; 17)}

Step-by-step explanation:

a+b=81 => b=81-a

a*b=1088

a*(81-a)=1088

-a²+81a=1088

a²-81a+1088=0

a²-64a-17a+1088=0

a(a-64)-17(a-64)=0

(a-17)(a-64)=0

=> a=17 and a=64

for a=17 => b=81-17=64

for a=64 => b=81-64=17

(a;b)={(17; 64); (64; 17)}

3 0
3 years ago
What is the answer of this on (if 3 pieces of candy cost $2.10 how much would four pieces cost)
ale4655 [162]

Answer:

70 hope it helps

Step-by-step explanation:

210/3=70

5 0
2 years ago
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains
AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

f(x) = (1-p)^{x}p

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

\mu = \frac{1-p}{p}

The standard deviation of the geometric distribution is given by the following formula:

\sigma = \sqrt{\frac{1-p}{p^{2}}

In this problem, we have that:

p = 0.383

So

\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61

\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05

(a) What is the probability that a drought lasts exactly 3 intervals?

This is f(3)

f(x) = (1-p)^{x}p

f(3) = (1-0.383)^{3}*(0.383)

f(3) = 0.09

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is P = f(0) + f(1) + f(2) + f(3)

f(x) = (1-p)^{x}p

f(0) = (1-0.383)^{0}*(0.383) = 0.383

f(1) = (1-0.383)^{1}*(0.383) = 0.236

f(2) = (1-0.383)^{2}*(0.383) = 0.146

Previously in this exercise, we found that f(3) = 0.09

So

P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4).

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

P(X \leq 3) + P(X \geq 4) = 1

0.855 + P(X \geq 4) = 1

P(X \geq 4) = 0.145

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

8 0
3 years ago
A fruit bowl contains 2 bananas, 5 oranges, and 4 apples in the simplest form, what is the ratio of apples to bananas in the fru
prisoha [69]

Answer:

Ratio of apple to banana is 2:1

Step-by-step explanation:

To find ratio of x type of one thing and y type of other thing we divide

x by y and ratio is written as

ratio = x:y

_________________________________

Number  of banana = 2

Number  of apples = 4

Ratio of apple to banana = Number  of apples :Number  of banana

Ratio of apple to banana = 4:2

since 4 is divisible by 2 , to get the ratio in simplest form

we divide both numerator and denominator by 2

Ratio of apple to banana = 4/2:2 /2 = 2:1

Thus,

Ratio of apple to banana is 2:1

3 0
3 years ago
The table shows the number of students in a class who play on a school team and/or are members of a school club:
eimsori [14]
This one is very simple.

create a simple equation to find out

15 = 12 + x

subtract 12 from each side

x= 3

the missing number is 3

or, to be even simpler, take the total, subtract the total from the number you know and the difference is the missing number.

hope I helped



ALSO, we can check going down vertically. 3 + 10 =13. this is the total listed at the bottom.
3 0
2 years ago
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