All categories

3 years ago

Solve for x.

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

8 0

Answer:

$\boxed{x=5},x=-9$

Step-by-step explanation:

To rid the denominators, multiply both sides by $(x-3)(x+1)$ .

We get:

$6(x+1)-12(x-3)=(x-3)(x+1)$

Simplifying, we have:

$6x+6-12x+36=x^2-3x+x-3,\\-6x+42=x^2-2x-3,\\x^2+4x-45=0$

Solving, we get:

$x^2+4x-45=0,\\(x-5)(x+9)=0,\\x=5,x=-9$

Therefore, the solution with the greatest value is $x=\boxed{5}$

You might be interested in

5(x+2)=6x+3x-14 please solve

zavuch27 [327]

Answer:

5(x+2)=6x+3x−14

Step 1: Simplify both sides of the equation.

5(x+2)=6x+3x−14

(5)(x)+(5)(2)=6x+3x+−14(Distribute)

5x+10=6x+3x+−14

5x+10=(6x+3x)+(−14)(Combine Like Terms)

5x+10=9x+−14

5x+10=9x−14

Step 2: Subtract 9x from both sides.

5x+10−9x=9x−14−9x

−4x+10=−14

Step 3: Subtract 10 from both sides.

−4x+10−10=−14−10

−4x=−24

Step 4: Divide both sides by -4.

−4x

−4

−24

−4

x=6

Answer:

x=6

7 0

3 years ago

MAVERICK [17]

Answer:

$15\ units$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and the corresponding angles are congruent

In this problem Triangles PQT and RQS are similar by AA Similarity Theorem (The three angles are congruent)

therefore

$\frac{12}{16}=\frac{x}{20}\\ \\x=12*20/16\\ \\x=15\ units$

6 0

4 years ago

There are 16 kids on a soccer team. The players are either boys or girls, and they either prefer playing offense or defense. The

Mariana [72]

Answer:

$P(B|A)=\frac{2}{7}$

Step-by-step explanation:

The probability of $P(B|A)$ can be read as the probability of event B occurring given event A. In this question, event A occurs when the chosen player is a girl. There are 7 girls on the soccer team. Event B occurs when the chose player plays defense. Since $P(B|A)$ stipulates that event A already occurred, we want the probability of choosing a player who prefers defense from the 7 girls. There are 2 girls who prefer defense, hence $P(B|A)=\boxed{\frac{2}{7}}$ .

<u>Alternative:</u>

For dependent events $A$ and $B$ , the conditional probability of event B occurring given A is given by:

$P(B|A)=P(B\cap A)\div P(A)$

$P(B\cap A)$ indicates the intersection of $P(B)$ and $P(A)$ . In this case, it is the probability that both events occur. Since there are 16 kids on the soccer team and only 2 are girls and prefer defense, $P(B\cap A)=\frac{2}{16}=\frac{1}{8}$ . The probability of event A occurring (chosen player is a girl) is equal to the number of girls (7) divided by the number of kids on the team (16), hence $P(A)=\frac{7}{16}$ .