All categories

3 years ago

How many solutions does the following system of equations have? 2y= 5x + 4 1 = 3x + 2

1 answer:

4 0

Looks like a pretty regular system, no parallel lines. In fact the second equation is a vertical line as written; not sure if that's a typo. Either way,

Answer: EXACTLY ONE SOLUTION

You might be interested in

`find the equatifindon of tangent and normal of parabola y²=16ax at point whose coordinate is -5a.

marusya05 [52]

Answer:

$\rm \displaystyle y _{ \rm tangent} = - \frac{8}{5} x - \frac{5}{2} a$

$\rm \displaystyle y _{ \rm normal} = \frac{5}{8} x - \frac{765}{128} a$

Step-by-step explanation:

we are given a equation of parabola and we want to find the equation of tangent and normal lines of the Parabola

finding the tangent line

equation of a line given by:

$\displaystyle y = mx + b$

where:

m is the slope
b is the y-intercept

to find m take derivative In both sides of the equation of parabola

$\displaystyle \frac{d}{dx} {y}^{2} = \frac{d}{dx} 16ax$

$\displaystyle 2y\frac{dy}{dx}= 16a$

divide both sides by 2y:

$\displaystyle \frac{dy}{dx}= \frac{16a}{2y}$

substitute the given value of y:

$\displaystyle \frac{dy}{dx}= \frac{16a}{2( - 5a)}$

simplify:

$\displaystyle \frac{dy}{dx}= - \frac{8}{5}$

therefore

$\displaystyle m_{ \rm tangent} = - \frac{8}{5}$

now we need to figure out the x coordinate to do so we can use the Parabola equation

$\displaystyle ( - 5a {)}^{2} = 16ax$

simplify:

$\displaystyle x = \frac{25}{16} a$

we'll use point-slope form of linear equation to get the equation and to get so substitute what we got

$\rm \displaystyle y - ( - 5a)= - \frac{8}{5} (x - \frac{25}{16} a)$

simplify which yields:

$\rm \displaystyle y = - \frac{8}{5} x - \frac{5}{2} a$

finding the equation of the normal line

normal line has negative reciprocal slope of tangent line therefore

$\displaystyle m_{ \rm normal} = \frac{5}{8}$

once again we'll use point-slope form of linear equation to get the equation and to get so substitute what we got

$\rm \displaystyle y - ( - 5a)= \frac{5}{8} (x - \frac{25}{16} a)$

simplify which yields:

$\rm \displaystyle y = \frac{5}{8} x - \frac{765}{128} a$

and we're done!

( please note that "a" can't be specified and for any value of "a" the equations fulfill the conditions)

8 0

3 years ago

Read 2 more answers

Solve 5x^2-4x-2=0 by completing the square

konstantin123 [22]

Answer:

Hello

Here's the answer:

2x^2 + 5x + 2 = 0\\
2x^2+4x+x+2=0\\
2x(x+2)+1(x+2)=0\\
(2x+1)(x+2)=0\\
x=-\frac{1}{2} \vee x=-2

x^2-4x+1=0\\
x^2-4x+4-3=0\\
(x-2)^2=3\\
x-2 =\sqrt3 \vee x-2=-\sqrt3\\
x=2+\sqrt3 \vee x=2-\sqrt3

Step-by-step explanation:

5 0

2 years ago

London has a collection of 260 coins. How many coins represent 25% of her collection?

Sergeu [11.5K]

Answer:

65 coins

Step-by-step explanation:

Set this problem up with a porportion.

$\frac{?}{260} \frac{25}{100}$

After that, cross multiple and divide.

25 times 260. Then divide by 100. That is then your answer.

8 0

2 years ago

If the length of FH is 18 units, what is the value of x?

valentinak56 [21]

Well if FG is 4x and GH is 2x the you add them to get 6x for FH. Solve for x so 6x=18 which means x=3. Hope this helps

5 0

3 years ago

Read 2 more answers

Need help urgently extra points and mark brainlist sorry this is not math it’s reading and is very easy

erma4kov [3.2K]

Answer:

people who live in a place

Step-by-step explanation:

duh

3 0

2 years ago