All categories

3 years ago

How many solutions are there to this equation 3x(x-4)+5-x=2x-7

Mathematics

1 answer:

stich3 [128]3 years ago

4 0

Answer:

2 solutions

Step-by-step explanation:

I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...

x = 1
x = 4

To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:

3x(x -4) +5 -x -(2x -7) = 0

3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses

3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms

3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor

The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.

<em>Alternate method</em>

Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...

d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c

d = (-15)^2 -4(3)(12) = 225 -144 = 81

This positive value means the equation has 2 real solutions.

You might be interested in

What is the difference of two positive rational number always positive?

Alexeev081 [22]

No, while the difference represents the absolute magnitude of two numbers . . . for example . . .

The difference between 5 and 2 is . . . 3
The difference between 6.4 and 9.5 is . . . 3.1

. . . there is still the chance that the difference may be zero . . . in which case the difference is neither positive nor negative

. . . so in short . . . the answer is . . . <span>NO</span>

6 0

3 years ago

Find the value of x. Then find the measure of each labeled angle.

Nat2105 [25]

Answer:

x = 70; the labeled angles are 110º and 70º.

Step-by-step explanation:

The full degrees will add up to 180º. There are 2x and +40.

Equation: $2x+40=180$

Solve: $2x+40=180\\\\180-40=140\\\\2x=140\\\\x=70$

Since x=70, 70+40 will equal to 110.

Therefore, "x = 70; the labeled angles are 110º and 70º." is correct.

7 0

3 years ago

Read 2 more answers

Following a group of truck drivers and noting the number of miles traveled for one year refers to which type of statistical stud

maria [59]

Considering that the data is only noted and not changed, this is an example of an observational study.

<h3>What are observational and experimental studies?</h3>

Experimental study: In an experimental study, there is an intervention in a sample, and it's effect is studied.

Observational study: In an observational study, the sample is just analyzed, without any intervention.

In this problem, the data, which is the number of miles traveled, is only analyzed, no interventions are made, hence this is an example of an observational study.

More can be learned about observational studies at brainly.com/question/24321224

#SPJ1

6 0

2 years ago

If two sides of a triangle are 10 units and 13 units,a possible third side for the could be?

IrinaK [193]

Pythagorean theorem:

a^2+b^2=c^2

substitute:

10^2+13^2=c^2

simplify:

100+169=c^2

simplify:

269=c^2

take the square root:

c=16.4

The answer is 16.4

5 0

3 years ago

A store is having a Back To School Sale.The total for a skirt,a pair of shoes,and a pair of socks is $34.95 before tax.The pair

Veronika [31]

Answer:

15.60

Step-by-step explanation:

The sub total before tax is 34.95. You know the socks cost 3.75 and the skirt and shoes are the same or equal price. This means after subtracting the cost of the socks, you spent 34.95 - 3.75 = 31.20. Since the skirt and shoes cost the same, divide 31.20 by 2. This is $15.60.

4 0

3 years ago