All categories

3 years ago

Solve by substitution

1 answer:

3 0

4x - 2y = 14
y = 1/2x - 1

4x - 2(1/2x - 1) = 14
4x - x +2 = 14
3x + 2 - 2 = 14 - 2
3x = 12
3x / 3 = 12/3
x = 4

2x = y -10
2x + 7 = 2y

y - 10 + 7 = 2y
y -y -10 + 7 = 2y - y
-3 = y

8x - 1/3 y = 0
12x + 3 = y

8x - 1/3y = 0
8x -1/3( 12x + 3) = 0
8x - 4x - 3 = 0
4x -3 + 3 = 0 + 3
4x / 4 = 3/4
x = 3/4

You might be interested in

Y=-1/3x^2-4x-5 in vertex form

grigory [225]

Answer:

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

Step-by-step explanation:

Given function:

$Y=-\frac{1}{3}x^2-4x-5$

We need to find the vertex form which is.,

$y=a(x-h)^2+k$

where $(h,k)$ represents the co-ordinates of vertex.

We apply completing square method to do so.

We have

$Y=-\frac{1}{3}x^2-4x-5$

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

$-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5$

$-3Y=x^2+12x+15$

Isolating $x^2$ and $x$ terms on one side.

Subtracting both sides by 15.

$-3Y-15=x^2+12x-15-15$

$-3Y-15=x^2+12x$

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of $x$ term, square it and add it both sides side.

square of half of the co-efficient of $x$ term = $(\frac{1}{2}\times 12)^2=(6)^2=36$

Adding 36 to both sides.

$-3Y-15+36=x^2+12x+36$

$-3Y+21=x^2+12x+36$

Since $x^2+12x+36$ is a perfect square of $(x+6)$ , so, we can write as:

$-3Y+21=(x+6)^2$

Subtracting 21 to both sides:

$-3Y+21-21=(x+6)^2-21$

$-3Y=(x+6)^2-21$

Dividing both sides by -3.

$\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}$

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

8 0

3 years ago

How do you do this question?

mihalych1998 [28]

Answer:

C) π/6

Step-by-step explanation:

The area under the curve from x=-π/2 to x=k is 3 times the area under the curve from x=k to x=π/2.

$\int\limits^k_{-\frac{\pi }{2}} {cos\ x} \, dx = 3\int\limits^{\frac{\pi }{2}}_k {cos\ x} \, dx\\sin\ x\ |^{k}_{-\frac{\pi }{2}} = 3\ sin\ x\ |^{\frac{\pi }{2}}_k\\(sin\ k - (-1)) = 3\ (1 - sin\ k)\\sin\ k + 1 = 3 - 3\ sin\ k\\4\ sin\ k = 2\\sin\ k = \frac{1}{2}\\k = \frac{\pi}{6}$

Graph: desmos.com/calculator/mezlen9hb4

3 0

3 years ago

One sprinter has a stride of 120cm, another 75cm. How many steps do they each take if they run a 100m race?

Olenka [21]

Answer:

1m = 100 cm

First sprinter stride is 120 cm. Steps he will take

= 100/1.2 = 83 1/3 steps

Second sprinter takes a stride of 75 cm

= 100/0.75 = 133 1/3 steps

3 0

3 years ago

Which type of structure means the sales people are only paid when they make sales?

Illusion [34]

Answer:

Step-by-step explanation:

commission is what you get when you make sales

4 0

3 years ago

Read 2 more answers

???????????????????????????

love history [14]

Answer:

11/9

Step-by-step explanation:

Additive inverse is just another overly-complicated word for opposite. The answer is 11/9.

7 0

3 years ago