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3 years ago

(a + 3)(a - 2) I need help answering this but don't know the answer. Can someone please help?

Mathematics

1 answer:

SVETLANKA909090 [29]3 years ago

3 0

(a+3)(a-2)

(a² -2a +3a - 6) =0

(a² + a - 6 ) = 0

Use splitting the middle term

a² + 3a - 2a - 6 = 0

a(a+3) - 2(a+3) = 0

(a-2)(a+3) = 0

Values of a are

a - 2 = 0

a = 2 .....(i)

a+3 = 0

a = -3 .....(ii)

You might be interested in

The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the stan

torisob [31]

The point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $\fbox{\begin\\\ \math 2x+5y=-15\\\end{minispace}}$ i.e., $\fbox{\begin\\\ \bf option C\\\end{minispace}}$ .

Further explanation:

It is given that line passes through the points $(-5,-1)$ and $(10,-7)$ .

The objective is to determine the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ .

The options given are as follows:

Option A: 2x-5y=-15

Option B: 2x-5y=-17

Option C: 2x+5y=-15

Option D: 2x+5y=-17

Consider the point $(-5,-1)$ as $(x_{1},y_{1})$ and $(10,-7)$ as $(x_{2},y_{2})$ .

Slope of a curve is defined as the change in the value of $y$ with respect to change in value of $x$ .

The slope of the line is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

To obtain the value of slope substitute the value of $x_{1},y_{1},x_{2},y_{2}$ in the above equation.

$\begin{aligned}m&=\dfrac{-7-(-1)}{10-(-5)}\\&=\dfrac{-6}{15}\\&=\dfrac{-2}{5}\end{aligned}$

Therefore, the slope of the line is $\fbox{\begin\\\ \math m=\dfrac{-2}{5}\\\end{minispace}}$

The general way to express the equation of a line in its point slope form is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}$

To obtain the point slope form of the equation of the line substitute the value of $m$ , $x_{1}$ and $y_{1}$ in the above equation.

$\begin{aligned}(y-(-1))&=\dfrac{-2}{5}(x-(-5))\\(y+1)&=\dfrac{-2}{5}(x+5)\\5y+5&=-2x-10\\5y+2x&=-15\end{aligned}$

From the above calculation it is concluded that the point slope form the equation of a line is $\fbox{\begin\\\ \math 5y+2x=-15\\\end{minispace}}$

Figure 1 (attached in the end) represents the graph of the function $5y+2x=-15$ .

This implies that the correct option for the point slope form of the line is option C.

Therefore, the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $2x+5y=-15$ i.e., option C.

Learn more:

1. A problem to complete the square of quadratic function brainly.com/question/12992613

2. A problem to determine the slope intercept form of a line brainly.com/question/1473992

3. Inverse function brainly.com/question/1632445.

Answer details

Grade: High school

Subject: Mathematics

Chapter: Linear equation

Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.

6 0

3 years ago

Read 2 more answers

Two planes start flying towards each other simultaneously from two different cities. The distance between the cities is 960 mile

ANTONII [103]

Answer:

257.5 mph

332.5 mph

Step-by-step explanation:

The initial distance between the two planes is 960 miles, while the final distance (after t=1.5 h) is 75 miles, so the total distance covered by the two planes in 1.5h is

$d=960-75=885$ miles

Calling v1 and v2 the velocities of the two planes, we have the following equations:

(1) $v_1 = v_2 + 75$ --> velocity of plane 1 exceeds velocity of plane 2 by 75 mph

(2) $v_1 t+ v_2 t=885$ --> the total distance covered by the two planes is 885 miles (t=1.5 h is the time, and the products v1 t and v2 t represent the distance covered by each plane)

Substituting t=1.5 h, the second equation becomes:

$1.5 v_1+1.5 v_2=885\\v_1 + v_2 = 590$

By substituting (1) into this last equation, we find:

$(v_2+75)+v_2 = 590\\2v_2 + 75 = 590\\2v_2 = 515\\v_2=257.5$

And substituting this back into eq.(1), we find

$v_1 = 257.5 + 75=332.5$

So, the speeds of the two planes are

257.5 mph

332.5 mph

3 0

3 years ago

MARKING AS BRAINLIEST!!

devlian [24]

Answer: They are inverses of each other

============================================================

Explanation:

We need to check two things:

f(g(x)) = x
g(f(x)) = x

If both of those equations are true, then f and g are inverses of each other.

----------------

Part 1

$f(x) = -3x-12\\\\f(g(x)) = -3( g(x) )-12\\\\f(g(x)) = -3\left( \frac{-12-x}{3} \right)-12\\\\f(g(x)) = 12+x-12\\\\f(g(x)) = x\\\\$

So far, so good. Now we need to check the other equation mentioned.

------------------

Part 2

$g(x) = \frac{-12-x}{3}\\\\g(f(x)) = \frac{-12-( f(x) )}{3}\\\\g(f(x)) = \frac{-12-( -3x-12 )}{3}\\\\g(f(x)) = \frac{-12+3x+12}{3}\\\\g(f(x)) = \frac{3x}{3}\\\\g(f(x)) = x\\\\$