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3 years ago

Match the items to the correct match

1 answer:

5 0

<span>The pairs correspond to the roots of the equations.

I factored all the equations and placed the roots next to each one. Here you have the equations matched with their corresponding roots.

x^2 - 5x - 6 = 0 = (x-6)(x+1) => roots x=6, x=-1

x^2 - 5x + 6 = 0 = (x-3)(x-2) => roots x =2, x=3

3x^2 - 2x - 8 = 0 = (x-2)(3x+4) => roots x = 2, x = -4/3

2x^2 + 9x + 10 = 0 = (x+2)(2x+5) => roots x = -2, x = -5/2

4x^2 + 12x - 7 = 0 = (2x-1)(2x+7) => roots x = 1/2, x = -7/2)

6x^2 - x - 2 = 0 = (2x+1)(3x-2) => roots x =-1/2, x = 2/3

12x^2 - 7x + 1 = 0 </span>=(3x-1)(4x-1) => roots x = 1/3, x = 1/4

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What’s the correct answer for this question?

sesenic [268]

Answer:

Step-by-step explanation:

All of the above transformations can be done

1) a translation placing point O onto point O1

2) a rotation about M

3) a reflection across line t

6 0

3 years ago

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

Woman salary is $2,800 in 1988 and was 15% more in 1989. If she paid a tax of 12.5% of her salary, how much tax did she pay in 1

iris [78.8K]

So first step is to find out how much the woman's salary is in 1989. We can do this by multiplying 0.15 (15% in decimal form) and $2,800 together, then adding that product by $2,800.

$2800*0.15= \$ 420\\ 2800+420= \$ 3220$