Find two consecutive even integers

Mathematics

1 answer:

Fantom [35]3 years ago

8 0

You can set up a system of equations with x being the smaller number and y being the larger number. So the first equation would be 2y=5x-14 and the second equation would be x=y-2. You can solve by substitution and substitute y-2 into the x in the first equation to get 2y=5(y-2)-14. You can solve this out and it ends up simplifying to y=8. So you know the larger number is 8. So since the larger number is 8 and they are consecutive even integers, the smaller number must be 6. So the two numbers would be 6 and 8.

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Write the equation of a line that passes through the points (−3, 7) and (3, 3)

Dennis_Churaev [7]

Step-by-step explanation:

You can write an equation of a line conveniently by point-slope form. It's in the form of $y -a = m(x -b)$ where $(b,a)$ is the coordinates of a point that's on the line and $m$ is the slope of the line.

Now choose a point (It doesn't really matter which one) and plug that in the equation. I'll choose $(-3,7)$ where $a = 7$ and $b = -3$

$y -a = m(x -b) \\ y -7 = m(x -(-3)) \\ y -7 = m(x +3)$

The next thing we have to do now is finding the slope, $m$ , where it's equal to $\frac{y_{2} -y_{1}}{x_{2} -x_{1}}\\$ . I'll make $(-3,7)$ point 1 and $(3,3)$ point 2.

$m = \frac{3 - 7}{3 -(-3)} \\ m = \frac{3 - 7}{3 +3} \\ m = \frac{-4}{6} \\ m = -\frac{2}{3}$

Now let's plug that to our equation.

$y -7 = m(x +3) \\ y -7 = -\frac{2}{3}(x +3)$

Now we have the equation but out of all the choices it seemed that all of them are in slope-intercept form all you have to do now is make our equation rewrite it in slope-intercept form.

$y -7 = -\frac{2}{3}(x +3)\\ y -7 = -\frac{2}{3}x -\frac{2}{3}(3) \\ y - 7 = -\frac{2}{3}x -2\\ y = -\frac{2}{3}x +5$

<h3>Answer:</h3>

$y = -\frac{2}{3}x +5\\$ is your equation.

3 0

2 years ago

Help plss i need help

andrew11 [14]

It’s b. you divide by 5 on both sides and at the end you’ll get x= 6

3 0

2 years ago

Let x = a bi and y = c di and z = f gi which statements are true? check all of the boxes that apply. x y = y x (x × y) × z = x ×

Alex73 [517]

A complex number is a part of a number system that includes a real unit and an imaginary unit. All the statements are true except C and E.

<h3>What is a Complex Number?</h3>

A complex number is a part of a number system that includes the real numbers as well as a particular element labelled i, sometimes known as the imaginary unit, and which obeys the equation i² = 1.

As it is given that x=(a+bi), y=(c+di), and z=(f+gi), therefore, we need to plug in the values to check which all are true.

A.) x+y=y+x

$x+y=y+x\\a+bi+c+di=c+di+a+bi$

As the two sides of the equation are equal, the equation is true.

B.) (x × y) × z = x × (y × z)

$(x \times y) \times z = x \times (y \times z)\\\\\ [ (a+bi) \times (c+di) ]\times (f+gi) = (a+bi) \times [(c+di) \times (f+gi)]\\\\(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)$