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3 years ago

Using the quadratic equation formula to solve 7x^2-x=7, what are the values of x

Mathematics

1 answer:

Gennadij [26K]3 years ago

8 0

quadratic formula:

x = -b ± √(b² - 4ac)

7x² - x = 7

subtract 7 from both sides:

7x² - x - 7 = 0

plug values into the quadratic formula:

x = -(-1) ± √((-1)²- 4(7)(-7))

2(7)

simplify:

x = 1 ± √(197)

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Find the area between the graph of the function and the x-axis over the given interval, if possible.

vodomira [7]

Answer:

$A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5$

So then the integral converges and the area below the curve and the x axis would be 5.

Step-by-step explanation:

In order to calculate the area between the function and the x axis we need to solve the following integral:

$A = \int_{-\infty}^1 \frac{5}{(x-2)^2}$

For this case we can use the following substitution $u = x-2$ and we have $dx = du$

$A = \int_{a}^b \frac{5}{u^2} du = 5\int_{a}^b u^{-2}du$

And if we solve the integral we got:

$A= -\frac{5}{u} \Big|_a^b$

And we can rewrite the expression again in terms of x and we got:

$A = -\frac{5}{x-2} \Big|_{-\infty}^1$

And we can solve this using the fundamental theorem of calculus like this:

$A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5$

So then the integral converges and the area below the curve and the x axis would be 5.

7 0

2 years ago

The radius of the sun is approximately 700,000 kilometers. What is the volume of the sun?

Anit [1.1K]

The radius of the sun is approximately 700,000 kilometers. What is the volume of the sun? V = F | m. 4)(700000km)? V = 1.436 X 1018 km3. The volume of the sun is approximately 1.436 X 1018 km². 6. An ice cream cone has a diameter of 3 inches.

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3 years ago

50 points! help me! Real answers PLEASE!

Alika [10]

Step-by-step explanation:

Your previous questions answer is

v=23

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if you satisfied in my answers please please mark as brainleiest and follow me

4 0

2 years ago

Read 2 more answers

What is the other solution??

Vladimir79 [104]

Answer:

The other solution is 12.

Step-by-step explanation:

Break the solution into groups: (x^2+2x)+(-12x-24)

Factor out the x^2 from the first group to get x(x+2)

Factor out the -12 out of the second group to get -12(x-12)

Here we get (x-12)(x+2)

You can see solutions are -2 and 12.

4 0

2 years ago

Read 2 more answers

. At a clothing store, 12 people purchased blue sweaters, 8 purchased green sweaters, 4 purchased gray sweaters, and 7 purchased

DedPeter [7]

Answer:

The probability that they purchased a green or a gray sweater is $\frac{12}{31}$

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{number of possible cases}$

The addition rule is used when you want to know the probability that 2 or more events will occur. The addition rule or addition rule states that if we have an event A and an event B, the probability of event A or event B occurring is calculated as follows:

P(A∪B)= P(A) + P(B) - P(A∩B)

Where:

P (A): probability of event A occurring.

P (B): probability that event B occurs.

P (A⋃B): probability that event A or event B occurs.

P (A⋂B): probability of event A and event B occurring at the same time.

Mutually exclusive events are things that cannot happen at the same time. Then P (A⋂B) = 0. So, P(A∪B)= P(A) + P(B)

In this case, being:

P(A)= the probability that they purchased a green sweater
P(B)= the probability that they purchased a gray sweater
Mutually exclusive events

You know:

8 purchased green sweaters
4 purchased gray sweaters
number of possible cases= 12 + 8 + 4+ 7= 21

So:

$P(A)=\frac{8}{31}$

$P(B)=\frac{4}{31}$

P(A⋂B) = 0

Then:

P(A∪B)= P(A) + P(B)

P(A∪B)= $\frac{8}{31}+ \frac{4}{31}$

P(A∪B)= $\frac{12}{31}$

The probability that they purchased a green or a gray sweater is $\frac{12}{31}$

5 0

2 years ago