Help me answer this question

saveliy_v [14]

So for this equation we're going to complete the square.

Firstly, what two terms have a product of 120x^2 and a sum of 29x? 24x and 5x. Replace 29x with 24x + 5x: $4x^2+24x+5x+30=0$

Next, factor 4x^2 + 24x and 5x + 30 separately. Make sure that they have the same quantity inside the parentheses: $4x(x+6)+5(x+6)=0$

Now you can rewrite the equation as: $(4x+5)(x+6)=0$

Now using zero product property, solve for x:

$4x+5=0\\ 4x=-5\\ x=-1.25\\ \\ x+6=0\\ x=-6$

In short, x = -1.25 and -6

8 0

4 years ago

Team Green and Team Blue play in a competition. Team Green has twelve more points than Team Blue.

valentinak56 [21]

Answer:

Team blue points = 4 points

Team green points = 16 points

Step-by-step explanation:

Let

Team blue points = x

Team green points = (x + 12) points (1)

Team green points = 4x (2)

Equate equation (1) and (2)

x + 12 = 4x

12 = 4x - x

12 = 3x

x = 12/3

x = 4 points

Team blue points = x

= 4 points

Team green points = (x + 12)

= 4 + 12

= 16 points

Team green points = 4x

= 4(4)

= 16 points

4 0

3 years ago

How can you find the equation of a line that is parallel/perpendicular to a given line

alexdok [17]

In the Slope-Intercept Form, m is the slope and b is the y-intercept.

<u>Finding The Equation of a Line Parallel to the Given Line:</u> Let the given line be line a and the parallel line be line b.

1) Find the slope of line a.

Example: Line a --> $y = 5x + 2$ . The slope is 5.

2) Find the y-intercept of line b.

To do this, you need to be given the coordinates of a point located on line b.

Example: The slope is 5 and the point is (2, 3), use the Slope-Intercept Formula, $y=mx+b$ ---> $3 = 5(2) + b$ . Then you solve for b.

$3 = 5(2) + b$

$3 = 10 + b$

$3 - 10 = 10 - 10 + b$

$-7 = b$ $b=-7$

The y-intercept of line b is -7

3) Finally, plugin the slope and the y-intercept into the Slope-Intercept Form.

Example: The slope of line b is 5 and the y-intercept is -7. The equation of line b is $y = 5x - 7$ .

<u>Finding The Equation of a Line Perpendicular to The Given Line:</u> Let the given line be line a and the perpendicular line be line b.

1) Find the opposite reciprocal of the slope of line a.

Example: Line a --> $y=5x+2$ . The slope is 5, to find the opposite reciprocal of the slope you use n --> $-\frac{1}{n}$ . In this case, it would be $-\frac{1}{5}$ . The opposite reciprocal of the slope of line a is $-\frac{1}{5}$ , which would be the slope of line b.

2) Find the y-intercept of line b.

To do this, you need to be given the coordinates of the point where line a and line b both intersect.

Example: The slope of line b is $-\frac{1}{5}$ and the point is (1, 7), use the Slope-Intercept Formula, $y=mx+b$ ---> $7=-\frac{1}{5}(1) + b$ . Then you solve for b.

$7=-\frac{1}{5}(1) + b$

$7=-\frac{1}{5} + b$

$7+\frac{1}{5}=-\frac{1}{5} + \frac{1}{5} + b$

$7\frac{1}{5} =b$ $b=7\frac{1}{5}$

The y-intercept of line b is $7\frac{1}{5}$ .

3) Finally, plugin the slope and the y-intercept into the Slope-Intercept Form.

Example: The slope of line b is $-\frac{1}{5}$ and the y-intercept is $7\frac{1}{5}$ . The equation of line b is $y=-\frac{1}{5}x+7\frac{1}{5}$ .

4 0

3 years ago

Someone please explain the differentiation product rule. It'd be great if you can use the example question given below.

Vikentia [17]

Answer:

The product rule is if the two "parts" of the function are being multiplied together, and the chain rule is if they are being composed. For instance, to find the derivative of f(x) = x² sin(x), you use the product rule, and to find the derivative of g(x) = sin(x²) you use the chain rule.

(sorry i didn't use the example but i hope this sort of helps!)

3 0

3 years ago

Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax u

galina1969 [7]

A had it before tee her

8 0

3 years ago