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Tasya [4]
3 years ago
15

How can you determine whether a relationship is linear from a graph, a table, or an equation

Mathematics
1 answer:
natulia [17]3 years ago
7 0
If the graph is a straight line, then it is linear. And If the y values is the same. The power of each, x and y in the equation is one.
You might be interested in
La suma dels quadrats de tres nombres naturals consecutius i múltiples de 3 és igual a 450. Planteja una equació de segon grau i
Firlakuza [10]

Answer:

The 3 numbers are 9, 12, and 15.

Step-by-step explanation:

I will answer in English, below the answer you can see a translation in Catalan.

This can be translated to:

The sum of the squares of three consecutive and multiple natural numbers of 3 is equal to 450. Pose a quadratic equation and calculate the three numbers.

First, a multiple of 3 can be written as:

3*n

The consecutive multiple of 3 is:

3*n + 3

The consecutive multiple of 3 is:

3*n + 3 + 3

Then the sum of their squares is:

(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2

And we know that this is equal to 450, then we need to solve the equation:

(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2 = 450

let's solve this:

9*n^2 + (9*n^2 + 2*(3*n)*3 + 9) + (9*n^2 + 2*(3*n)*6 + 36) = 450

27*n^2 + 54*n + 45 = 450

we can write this as:

27*n^2 + 54*n + 45 - 450 = 0

27*n^2 + 54*n - 405 = 0

The solutions of this equation are given by the Bhaskara's formula, and the solutions are:

n = \frac{-54 \pm \sqrt{54^2 -4*27*(-415)}  }{2*27} = \frac{-54 \pm 216 }{54}

we know that our numbers are naturals, then the numbers are positives, which means that we only care for the positive solution of n, which is:

n = (-54 + 216)/54 = 3

Then the 3 numbers are:

3*n = 3*3 = 9

(3*n + 3) = (3*3 + 3) = 12

(3*n + 6) = (3*3 + 6) = 15

In Catalan:

En primer lloc, es pot escriure un múltiple de 3 com:

3 * n

El múltiple consecutiu de 3 és:

3 * n + 3

El múltiple consecutiu de 3 és:

3 * n + 3 + 3

Llavors, la suma dels seus quadrats és:

(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2

I sabem que això és igual a 450, llavors hem de resoldre l’equació:

(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2 = 450

resolem això:

9 * n ^ 2 + (9 * n ^ 2 + 2 * (3 * n) * 3 + 9) + (9 * n ^ 2 + 2 * (3 * n) * 6 + 36) = 450

27 * n ^ 2 + 54 * n + 45 = 450

podem escriure això com:

27 * n ^ 2 + 54 * n + 45 - 450 = 0

27 * n ^ 2 + 54 * n - 405 = 0

Les solucions d’aquesta equació vénen donades per la fórmula de Bhaskara, i les solucions són:

n = \frac{-54 \pm \sqrt{54^2 -4*27*(-415)}  }{2*27} = \frac{-54 \pm 216 }{54}

sabem que els nostres nombres són naturals, aleshores els nombres són positius, cosa que significa que només ens importa la solució positiva de n, que és:

n = (-54 + 216) / 54 = 3

Llavors els 3 nombres són:

3 * n = 3 * 3 = 9

(3 * n + 3) = (3 * 3 + 3) = 12

(3 * n + 6) = (3 * 3 + 6) = 15

7 0
3 years ago
Consider the quadratic function LaTeX: f\left(x\right)=8x^2-7x+6f ( x ) = 8 x 2 − 7 x + 6. What is the constant of the function?
jekas [21]

Answer:

6

Step-by-step explanation:

Suppose we have a quadratic function f(x) in the following format:

f(x) = ax^{2} + bx + c, a \neq 0

The constant is the value of c.

Also, another way to find the constant is calculating f(0).

In this problem, we have that:

f(x) = 8x^{2} - 7x + 6

So

a = 8, b = -7, c = 6

The constant is c = 6.

Also

f(0) = 8*(0)^{2} - 7*(0) + 6 = 6

So the correct answer is:

6

4 0
3 years ago
Read 2 more answers
The plan of a terrace is shown at right. The scale is 2 inches : 6 feet. What are the length and width of the terrace? Find the
galina1969 [7]

Answer:

Part 1) The length of the terrace is 15 feet

Part 2) The width of the terrace is 6 feet

Part 3) The area of the terrace is 90 square feet

Step-by-step explanation:

<u><em>The picture of the question in the attached figure </em></u>

we know that

The scale of the plan is \frac{2}{6} \frac{in}{ft}

step 1

Find the length of the terrace

we know that

The length of a terrace in the plan is equal to 5 inches

so

by proportion

Find the length of the terrace in the actual

\frac{2}{6} \frac{in}{ft}=\frac{5}{x} \frac{in}{ft}\\ \\x=6*5/2\\ \\x=15\ ft

step 2

Find the width of the terrace

we know that

The width of a terrace in the plan is equal to

so

by proportion

Find the width of the terrace in the actual

\frac{2}{6} \frac{in}{ft}=\frac{2}{x} \frac{in}{ft}\\ \\x=6*2/2\\ \\x=6\ ft

step 3

Find the area of a terrace

we know that

The area of a terrace is equal to

A=LW

we have

L=15\ ft\\W=6\ ft

substitute

A=15*6=90\ ft^{2}

7 0
3 years ago
Hellllllllppppppppppppp
Tju [1.3M]

Answer:

maybe 42

Step-by-step explanation:

by the way am bad in maths but still

4 0
3 years ago
Determine whether the given value is a solution of the equation x over nine=4; x=36
Citrus2011 [14]
Yes ; "x = 36" , is, in fact, a solution.
________________________________________________________
Given the equation:  "x / 9 = 4" ; 
________________________________________________________
"x = 36" is a solution ;  since "36 ÷ 9 = 4" ;  and since x = (4)*(9) = 36.
_________________________________________________________
8 0
3 years ago
Read 2 more answers
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