All categories

3 years ago

Y-x-4 equals 0. What is the equation written in function notation?

Mathematics

1 answer:

dimaraw [331]3 years ago

5 0

$y - x - 4 = 0$

$y = x + 4$

$f(x) = x + 4$

You might be interested in

Solve 5x^2 − 3x + 17 = 9.

Vedmedyk [2.9K]

Answer:

The roots of the equation are x = $\frac{3+\sqrt{151}i}{10}$ and x = $\frac{3-\sqrt{151}i}{10}$

and there are no real roots of the equation given above

Step-by-step explanation:

To solve:

5x² − 3x + 17 = 9

⇒ 5x² − 3x + 17 - 9 = 0

⇒ 5x² − 3x + 8 = 0

Now,

the roots of the equation in the form ax² + bx + c = 0 is given as:

x = $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

in the above given equation

a = 5

b = -3

c = 8

therefore,

x = $\frac{-(-3)\pm\sqrt{(-3)^2-4\times5\times8}}{2\times5}$

x = $\frac{3\pm\sqrt{9-160}}{10}$

x = $\frac{3+\sqrt{-151}}{10}$ and x = $\frac{3-\sqrt{-151}}{10}$

x = $\frac{3+\sqrt{151}i}{10}$ and x = $\frac{3-\sqrt{151}i}{10}$

here i = √(-1)

Hence,

The roots of the equation are x = $\frac{3+\sqrt{151}i}{10}$ and x = $\frac{3-\sqrt{151}i}{10}$

and there are no real roots of the equation given above

7 0

2 years ago

The fair spinner shown in the diagram above is spun.

Katena32 [7]

Unable to provide a definitive answer due to lack of diagram.

Answer: 1/4

Step-by-step explanation:

Multiples of 6:

Multiples of 6 are numbers obtained when 6 is multiplied by an integer. Such as

(6*1) = 6, (6*2)=12, (6*3) = 18..... and so on.

Probability is calculated by finding the ratio of the required outcome and total possible outcomes.

Probability = required outcome / Total possible outcomes

P(multiple of 6) = number of multiples of 6 / total number of possible outcomes

If number of 6 multiples = 5 and

Total number of faces in the spinner = 20

Then :

P(multiple of 6) = 5/20 = 1/4

5 0

3 years ago

How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

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

3 0

8 months ago

At Dave's diner, 2 sandwiches and 2 drinks cost $12. You can buy 5 drinks for the cost of one sandwich.

hram777 [196]

If you’re asking for the cost of the drink, the drink would be $1. This is because 2 sandwiches would cost $10 and that means 1 sandwich would make it $5. If 2 sandwiches cost $10, the remaining $2 in the $12 dollars would be the drinks. 2 drinks for $2 would make 1 drink for $1. So the cost of 5 drinks is $5 or $1 per drink.

If confused, don’t be shy to ask :)

8 0

2 years ago

Plz help will mark brainliest

Kryger [21]

∆ABC=∆DEF

AB=DE –>String

BC=EF–> Rib

m<C=m<F=90° –>List

AC=DF

So m<A=m<D=35 (It is not clear whether the number is 35 or 36, but the same number)

8 0

2 years ago