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3 years ago

A quadratic equation is shown below:

1 answer:

4 0

Part A)

The given equation is:

$25 x^{2} +10x+1=0$

The radicand or discriminant(d) of the equation will be:

$d=(10)^{2}-4(25)(1) \\ \\ 
d=100-100 \\ \\ 
d=0$

Since the discriminant is equal to 0, the given quadratic equation has only 1 root. In other words we can say the the given equation is a perfect square.

Part B)

The given equation is:

$4 x^{2} -4x+1=0$

We can solve this expression by factorization. Factors of middle term are to be made in such a way that their product equals the product of first and third term and sum is equal to the middle term i.e. product should be 4x² and sum should be -4x.
So the two such terms are -2x and -2x. Using the factors and simplifying the equation by taking common we get:

$4 x^{2} -2x-2x+1=0 \\ \\ 
2x(2x-1)-1(2x-1)=0 \\ \\ 
(2x-1)(2x-1)=0 \\ \\ 
(2x-1) ^{2}=0 \\ \\ 
2x-1=0 \\ \\ 
x= \frac{1}{2}$

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A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of

professor190 [17]

The fuel consumption of each of the cars during the week are as follows;

The first car consumes 20 gallons of fuel.

The second car consumes 30 gallons of fuel.

Reasons:

Fuel efficiency of the first car = 15 miles per gallon

Fuel efficiency of the second car = 35 miles per gallon

Combined distance traveled by the two cars in a week = 1,350 miles

The total gas consumption during the week = 50 gallons

Let x represent the number of gallons consumed by the first car, and let y

represent the number of gallons consumed by the second car, we get the

following system of simultaneous equations;

15·x + 35·y = 1,350...(1)

x + y = 50...(2)

Therefore;

y = 50 - x

Which gives;

15·x + 35 × (50 - x) = 1,350

15·x + 1,750 - 35·x = 1,350

1,750 - 1,350 = 35·x - 15·x = 20·x

400 = 20·x

x = 400 ÷ 20 = 20

The number of gallons consumed by the first car, x = 20 gallons

From equation (2), we have;

x + y = 50

y = 50 - x

Therefore;

y = 50 - 20 = 30

The number of gallons consumed by the second car, y = 30 gallons

Learn more about word problems that lead to simultaneous equations here:

brainly.com/question/1717365

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2 years ago

Maggie is practicing her penalty kicks for her upcoming soccer game. During the practice, she attempts 10 penalty kicks. If each

arlik [135]

Answer:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)$

And we can find the individual probabilities like this:

$P(X=8)=(10C8)(0.65)^0 (1-0.65)^{10-8}=0.176$

$P(X=9)=(10C9)(0.65)^1 (1-0.65)^{10-9}=0.072$

$P(X=10)=(10C10)(0.65)^2 (1-0.65)^{10-10}=0.013$

And adding we got:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)= 0.176+0.072+0.013=0.262$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.65)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

For this case we want to find this probability:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)$

And we can find the individual probabilities like this:

$P(X=8)=(10C8)(0.65)^0 (1-0.65)^{10-8}=0.176$

$P(X=9)=(10C9)(0.65)^1 (1-0.65)^{10-9}=0.072$

$P(X=10)=(10C10)(0.65)^2 (1-0.65)^{10-10}=0.013$

And adding we got:

$P(X \geq 8)= P(X=8) +P(X=9) +P(X=10)= 0.176+0.072+0.013=0.262$

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3 years ago

Newberg has a population of 31,000 people. The town has been seeing its population decline by 10% every year. If this trend cont

valentina_108 [34]

Answer:

13,000

Step-by-step explanation: 10% of 31,000= 3,100 x 6= 18,600

31,000-18,600=13,000

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3 years ago

Find the geometric sum: 40 + 20 + 10 + … + 0.078125

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This algebra lesson explains geometric series. ... To find the sum of the first n terms of a geometric sequence: Sn = the summation of ... 5 , -10 , 20 , -40 , 80 , .

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3 years ago

Which expression is equivalent to (2x + 1)?

Akimi4 [234]

Answer:

Step-by-step explanation:

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3 years ago

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