All categories

1 year ago

How many solutions does the system of equations have? y=-2x+3 y = x² - 6x +3

Mathematics

1 answer:

Mashutka [201]1 year ago

6 0

Answer:

2 solutions

Step-by-step explanation:

y = - 2x + 3 → (1)

y = x² - 6x + 3 → (2)

substitute y = x² - 6x + 3 into (1)

x² - 6x + 3 = - 2x + 3 ( subtract - 2x + 3 from both sides )

x² - 4x = 0 ← factor out x from each term on the left side

x(x - 4) = 0

equate each factor to zero and solve for x

x = 0

x - 4 = 0 ⇒ x = 4

substitute these values into (1)

x = 0 : y = - 2(0) + 3 = 0 + 3 = 3 ⇒ (0, 3 )

x = 4 : y = - 2(4) + 3 = - 8 + 3 = - 5 ⇒ (4, - 5 )

the 2 solutions are (0, 3 ) and (4, - 5 )

You might be interested in

What is (x − 3)(x − 5) = 35

JulijaS [17]

Answer:

x=10 x=-2

Step-by-step explanation:

(x − 3)(x − 5) = 35

FOIL

x^2 -5x-3x+15 = 35

Combine like terms

x^2 -8x+15 = 35

Subtract 35 from each side

x^2 -8x+15-35 = 35-35

x^2 -8x-20 =0

Factor

What 2 numbers multiply to -20 and add to -8

-10*2 = -20

-10 +2 = -8

(x-10)(x+2) =0

Using the zero product property

x-10 =0 x+2 = 0

x=10 x=-2

6 0

3 years ago

Raffia had a board that that was 15 1/2 feet long he put three pieces off the board that are each 3 7/8 feet long how much of th

Sonbull [250]

11 5/8 of the board is left.

4 0

2 years ago

Someone please help me I’ll give out brainliest please dont answer if you don’t know

sveta [45]

Answer:

it's 1130.97

Step-by-step explanation:

V = A h.

Since the area of a circle = π r 2 , then the formula for the volume of a cylinder is:

V = π r 2 h.

7 0

3 years ago

Read 2 more answers

For f(x)= x+5 and g(x)=4x+2 <br> find (fog)(x) And (gof)(x)

Svetllana [295]

Composing functions means that the input of the outer functions is the output of the inner function.

In fact, you can rewrite the circle notation as

$(f\circ g)(x)=f(g(x)),\quad (g\circ f)(x)=g(f(x))$

So, we can substitute g(x) with its expression:

$(f\circ g)(x)=f(g(x))=f(4x+2)$

And since f(x)=x+5, we simply have to add 5 to its input:

$f(4x+2)=(4x+2)+5=4x+7$

Similarly, we have, substituting f with its expression,

$(g\circ f)(x)=g(f(x))=g(x+5)$

And since g(x)=4x+2, we have to multiply the input by 4 and add 2:

$g(x+5)=4(x+5)+2=4x+20+2=4x+22$

7 0

3 years ago

Jerry planted a pine tree that was 5 feet tall and a maple tree that was 10 feet tall. The pine tree grew 3 feet taller per year

stich3 [128]

The initial length of the pine tree=5 feet.

Groth rate of pine tree =3 feet/year.

The initial length of the pine tree =10 feet.

Groth rate of the maple tree =2 feet/year.

After x years, the height of the pine tree= 5+3x feet and

after x years, the height of the maple tree= 10+2x feet.

The inequality for which, after x year, the pine tree is taller than the maple tree is

$5+3x>10+2x$

$\Rightarrow x>5$ .

The inequality for which, the pine tree is at least as tall as the maple tree is $5+3x\geq10+2x$ .

$\Rightarrow x\geq 5$ .

Again, after 3x years, the height of the pine tree= 5+3(3x)=5+9x feet and

after 2x years, the height of the maple tree= 10+2(2x)=10+4x feet.

The inequality for which, after 3x years, the pine tree is taller than the maple tree was after 2x years is

$5+9x>10+4x$

$\Rightarrow 5x>5$

$\Rightarrow x>1.$

The inequality for which, the pine tree is at least as tall as the maple tree is $5+9x\geq10+4x$ .

$\Rightarrow 5x\geq5$

$\Rightarrow x\geq 1.$

5 0

3 years ago