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Naddik [55]
2 years ago
10

Is the following relation linear, quadratic, or cubic? If it is linear, find the equation. Explain your reasoning and include al

l of your work in your final answer. R = {(x, y) : (2,3), (4,4), (6,5), (8,6), ...}
Mathematics
1 answer:
Sergio [31]2 years ago
8 0

The given relation is linear. Equation of the linear function; (Y-y1)/(x-x1)= m Or Y= 1/2x +2.

<h3>What is a linear equation?</h3>

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

Where m is the slope and c is the y intercept.

WE have given R = {(x, y) : (2,3), (4,4), (6,5), (8,6), ...}

Let's use these two points to determine both the slope and the equation;

(2, 3), (4,4)

Slope= (y2-y1)/(x2-x1)

Slope= (4-3)/(4-2)

Slope= 1/2

Then Equation of the linear function;

(Y-y1)/(x-x1)= m

(Y-3)/(x-2)= 1/2

2(y-3) = x-2

2y -6 = x-2

2y= x-2+6

2y= x+4

Y= 1/2x +2

Hence, the given relation is linear. Equation of the linear function; (Y-y1)/(x-x1)= m Or Y= 1/2x +2.

Learn more about linear equations;

brainly.com/question/10413253

#SPJ1

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If log x+y/5 = 1/2(log x + log y) the find the value of x/y + y/x ?​
V125BC [204]

Given that

log (x+y)/5 =( 1/2) {log x+logy}

We know that

log a+ log b = log ab

⇛log (x+y)/5 =( 1/2) log(xy)

We know that log a^m = m log a

⇛log (x+y)/5 = log (xy)^1/2

⇛log (x+y)/5 = log√(xy)

⇛(x+y)/5 = √(xy)

On squaring both sides then

⇛{ (x+y)/5}^2 = {√(xy)}^2

⇛(x+y)^2/5^2 = xy

⇛(x^2+y^2+2xy)/25 = xy

⇛x^2+y^2+2xy = 25xy

⇛x^2+y^2 = 25xy-2xy

⇛x^2+y^2 = 23xy

⇛( x^2+y^2)/xy = 23

⇛(x^2/xy) +(y^2/xy) = 23

⇛{(x×x)/xy} +{(y×y)/xy} = 23

⇛(x/y)+(y/x) = 23

Therefore, (x/y)+(y/x) = 23

Hence, the value of (x/y)+(y/x) is 23.

4 0
3 years ago
Match each pair of points to the equation of the line that is parallel to the line passing through the points.
Luba_88 [7]

Answer:

B(5,2) \:\: C(7,-5) \:\: \rightarrow y=-3.5x-15

D(11,6)\:\: E(5,9)\:\: \rightarrow y=-0.5x-3

H(4,4)\:\: I(8,9) \:\: \rightarrow y=1.25x+4

L(5,-7)\:\: M(4,-12)\:\: \rightarrow y=5x+9

Step-by-step explanation:

We need to match the slope of the function with the slope of the lines connecting the two points given. The slope of the lines are as follows:

B(5,2) \:\: C(7,-5)=\frac{2--5}{5-7} =-3.5

D(11,6)\:\: E(5,9)=\frac{6-9}{11-5} =-0.5

H(4,4)\:\: I(8,9)=\frac{4-9}{4-8} =1.25

L(5,-7)\:\: M(4,-12)=\frac{-7--12}{5-4} =5

F(-7,12)\:\: G(3,-8)=\frac{12--8}{-7-3}=-2

J(7,2)\:\:K(-9,8) =\frac{2-8}{7--9} =-0.375

Now,

the slope of the line BC matches with the slope of  y=-3.5x-15.

the slope of the line DE matches with the slope of y=-0.5x-3.

the slope of the line HI matches with the slope of y=1.25x+4.

the slope of the line LM matches with the slope of  y=5x+9.

and the slopes of the lines FG and JK do not match with any of the functions given.

Thus,

B(5,2) \:\: C(7,-5) \:\: \rightarrow y=-3.5x-15

D(11,6)\:\: E(5,9)\:\: \rightarrow y=-0.5x-3

H(4,4)\:\: I(8,9) \:\: \rightarrow y=1.25x+4

L(5,-7)\:\: M(4,-12)\:\: \rightarrow y=5x+9

4 0
3 years ago
Read 2 more answers
P(x) = -2x – 2; Find p(-3)
irinina [24]
P(-3)= -2(-3) -2
p(-3)= 6-2
p(-3)= 4
5 0
2 years ago
Read 2 more answers
A wire is (7x – 3) meters long. A length of (3x – 4) meters is cut for use(a) How much wire is left?
ipn [44]

Answer:

The amount of wire left is 4x + 1

Step-by-step explanation:

Initially, the wire is (7x - 3) meters long.

A length of (3x - 4) meters is cut.

How much wire is left?

Initial amount subtracted by the amount that is cut. So

(7x - 3) - (3x - 4) = 7x - 3 - 3x + 4

We combine the like terms

7x - 3x - 3 + 4 = 4x + 1

The amount of wire left is 4x + 1

6 0
3 years ago
58 = 7/4x well, basically I am really bad with fractions, and I'm supposed to do this on a computer, I don't have a calculator I
KiRa [710]
58=7/4x
Multiply both sides by 4 so the fraction cancels out:
232=7x
Divide both sides by 7:
x=33.14 (rounded)

Hope this helps :)
4 0
3 years ago
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