Help i dont get it. pleas

Rainbow [258]

The last one: -4(3n+5)

4 0

2 years ago

Divide the rational expressions and express in simplest form. When typing your answer for the numerator and denominator be sure

Veseljchak [2.6K]

Dividing by a fraction is equivalent to multiply by its reciprocal, then:

$\begin{gathered} \frac{3y^2-7y-6}{2y^2-3y-9}\div\frac{y^2+y-2}{2y^2+y-3^{}}= \\ =\frac{3y^2-7y-6}{2y^2-3y-9}\cdot\frac{2y^2+y-3}{y^2+y-2}= \\ =\frac{(3y^2-7y-6)(2y^2+y-3)}{(2y^2-3y-9)(y^2+y-2)} \end{gathered}$

Now, we need to express the quadratic polynomials using their roots, as follows:

$ay^2+by+c=a(y-y_1)(y-y_2)$

where y1 and y2 are the roots.

Applying the quadratic formula to the first polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{7\pm\sqrt[]{(-7)^2-4\cdot3\cdot(-6)}}{2\cdot3} \\ y_{1,2}=\frac{7\pm\sqrt[]{121}}{6} \\ y_1=\frac{7+11}{6}=3 \\ y_2=\frac{7-11}{6}=-\frac{2}{3} \end{gathered}$

Applying the quadratic formula to the second polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot2\cdot(-3)}}{2\cdot2} \\ y_{1,2}=\frac{-1\pm\sqrt[]{25}}{4} \\ y_1=\frac{-1+5}{4}=1 \\ y_2=\frac{-1-5}{4}=-\frac{3}{2} \end{gathered}$

Applying the quadratic formula to the third polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{3\pm\sqrt[]{(-3)^2-4\cdot2\cdot(-9)}}{2\cdot2} \\ y_{1,2}=\frac{3\pm\sqrt[]{81}}{4} \\ y_1=\frac{3+9}{4}=3 \\ y_2=\frac{3-9}{4}=-\frac{3}{2} \end{gathered}$

Applying the quadratic formula to the fourth polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot1\cdot(-2)}}{2\cdot1} \\ y_{1,2}=\frac{-1\pm\sqrt[]{9}}{2} \\ y_1=\frac{-1+3}{2}=1 \\ y_2=\frac{-1-3}{2}=-2 \end{gathered}$

Substituting into the rational expression and simplifying:

$\begin{gathered} \frac{3(y-3)(y+\frac{2}{3})2(y-1)(y+\frac{3}{2})}{2(y-3)(y+\frac{3}{2})(y-1)(y+2)}= \\ =\frac{3(y+\frac{2}{3})}{2(y+2)}= \\ =\frac{3y+2}{2y+4} \end{gathered}$

8 0

8 months ago

Skylar is filling a barrel with water. The graph shows the relationship between time in minutes and the gallons of water in the

lisov135 [29]

Answer:

$t>15$ will be inequality which shows the times there will be more than 10 gallons in the barrel.

Step-by-step explanation:

To determine:

Write an inequality showing the times there will be more than 10 gallons in the barrel.

Information Fetching and Solution Steps:

Skylar is filling a barrel with water.

The graph shows the relationship between time in minutes and the gallons of water in the barrel.

As the questions asks to determine the inequality showing the times there will be more than 10 gallons in the barrel.

For inequalities with 'more than', we use the 'greater than' symbol.

The graph shows that at time 15 minutes, the number of gallons of water is being shown as 10. As we have to determine the inequality for the time there will be more than 10 gallons in the barrel. So, time must be greater than 15 when there will be more than 10 gallons in the barrel.

If time is represented by 't', then the inequality showing the times there will be more than 10 gallons in the barrel will be:

$t>15$

Therefore, $t>15$ will be inequality which shows the times there will be more than 10 gallons in the barrel.

4 0

3 years ago

Find the value of x. Show all of your work!

Georgia [21]

Answer:

145⁰

Step-by-step explanation:

180 minus 73⁰ plus 62⁰

which is 180 minus 135

145⁰

7 0

3 years ago

Solve for the given variable.<br> a. 4y + 3 = 19<br><br> b. 1<br> 2n - 3 = 5

kotegsom [21]

Answer:

y=4

Step-by-step explanation:

4y+3=19

=4y=19-3

=y=16/4=4

4 0

2 years ago

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