All categories

1 year ago

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

You might be interested in

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:

$p = 0.383$

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

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

(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 $f(3) = 0.09$

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

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