Solve the following system by graphing and identify the point of intersection 5x+3y=-15 , 2x-y=-6

Which is the correct label of the parallel lines? (4 points) Parallel lines a and b are shown. Points A and B lie on line a whil

ddd [48]

The same way you number

5 0

2 years ago

P (6,6) y=2/3x

matrenka [14]

Answer:

$y = -\frac{3}{2}x+15$

Step-by-step explanation:

Given:

Given point P(6, 6)

The equation of the line.

$y = \frac{2}{3}x$

We need to find the equation of the line perpendicular to the given line that contains P

Solution:

The equation of the line.

$y = \frac{2}{3}x$

Now, we compare the given equation by standard form $y = mx +c$

So, slope of the line $m_{1} = \frac{2}{3}$ , and

y-intercept $c=0$

We know that the slope of the perpendicular line $m_{1}\times m_{2} = -1$

$m_{2}=-\frac{1}{m_{1}}$

$m_{2}=-\frac{1}{\frac{2}{3} }$

$m_{2}=-\frac{3}{2}$

So, the slope of the perpendicular line $m_{2}=-\frac{3}{2}$

From the above statement, line passes through the point P(6, 6).

Using slope intercept formula to know y-intercept.

$y=mx+c$

Substitute point $P(x_{1}, y_{1})=P(6, 6)$ and $m = m_{2}=-\frac{3}{2}$

$6=-\frac{3}{2}\times 6 +c$

$6=-3\times 3 +c$

$c=6+9$

$c=15$

So, the y-intercept of the perpendicular line $c=15$

Using point slope formula.

$y=mx+c$

Substitute $m = m_{2}=-\frac{3}{2}$ and $c=15$ in above equation.

$y = -\frac{3}{2}x+15$

Therefore: the equation of the perpendicular line $y = -\frac{3}{2}x+15$

8 0

3 years ago

Jenny thinks that the expression below is equal to x²-4. If you agree, show that she is correct. If you disagree, show that she

sergiy2304 [10]

Answer:

Jenny is wrong the correct answer is x²+ 4 - 4 x.

Step-by-step explanation:

Given that

(x-2)³∕x-2

(x-2)³∕(x-2) =(x-2) (x-2)²∕(x-2)

(x-2)³∕(x-2) = (x-2)²

As we know that

(a-b)² = a²+b² - 2 ab

So

(x-2)² = x²+ 2² - 2 ˣ 2 ˣ x = x²+ 4 - 4 x

(x-2)² = x²+ 4 - 4 x

It means that

(x-2)³∕(x-2) = (x-2)² = x²+ 4 - 4 x

So Jenny is wrong the correct answer is x²+ 4 - 4 x.

8 0

2 years ago

If theta is an acute angle and sin=1/2 , then cos theta =

lilavasa [31]

$\pi /6$ is the only acute angle whose sin = 1/2. Therefore, cos ( $\pi /6$ ) = $\sqrt{3} /2$

7 0

3 years ago

Which of the following comparisons is FALSE?

dybincka [34]

Answer:

A

Step-by-step explanation:

Let's check each one-by-one.

a.

we know 3.79 liters is 1 gallon, so 4 liters IS NOT LESS THAN 1 gallon

THis is false.

b.

We know 1 feet is 0.30 meters, so definitely 1 foot is less than 1 meter.

This is true.

c.

we know around 28.35 grams is 1 ounce, so definitely 25 grams is less than 1 ounce.

THis is true.

d.

We know 1 km is approximately 0.62 miles so 10 km would be around 0.62*10 = 6.2 miles

So definitely 9 miles IS GREATER than 10 km.

THis is true.

So answer choice A is false, only.

4 0

3 years ago