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damaskus [11]
2 years ago
10

Are the equation linear or nonlinear?​

Mathematics
1 answer:
I am Lyosha [343]2 years ago
8 0

Answer:

<em>Results below</em>

Step-by-step explanation:

<u>Equation of the line</u>

A straight line can be written in the form:

y = ax + b

Where a and b are constants and x is the independent variable.

The essential condition for an equation to be linear is that the x must be powered to the exponent 1, which is usually not written.

From the equations presented in the table:

y = x^1+2 is linear because the exponent of the x is 1

y = 5(x+2) = 5x + 10 is linear with a=5 and b=10.

y = x is linear with a=1 and b=0

y = x^2+1 is not linear because the exponent of x is 2

y = x(x) = x^2 is not linear because the exponent of x is 2

The table below summarizes the results

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The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than
svlad2 [7]

The shop sold 36 sundaes and 28 banana spilts

<em><u>Solution:</u></em>

Let "a" be the number of sundaes sold

Let "b" be the number of banana spilts sold

Cost of 1 sundaes = $ 2

Cost of 1 banana spilt = $ 3

<em><u>On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156</u></em>

Therefore,

Number of sundaes sold = 8 + number of banana spilts sold

a = 8 + b ------- eqn 1

<em><u>Also, given that they made $ 156</u></em>

<em><u>Therefore, we frame a equation as</u></em>:

Number of sundaes sold x Cost of 1 sundaes + number of banana spilts sold x Cost of 1 banana spilt = 156

a \times 2+b \times 3 = 156

2a + 3b = 156 ---------- eqn 2

<em><u>Substitute eqn 1 into eqn 2</u></em>

2(8 + b) + 3b = 156

16 + 2b + 3b = 156

16 + 5b = 156

5b = 156 - 16

5b = 140

<h3>b = 28</h3>

<em><u>Substitute b = 28 in eqn 1</u></em>

a = 8 + 28

<h3>a = 36</h3>

Thus the shop sold 36 sundaes and 28 banana spilts

4 0
3 years ago
A line with a slope of 2 passes through the points (0,4) and (-6,v). What is the value of v?
krok68 [10]

To solve this problem, we should create an equation using the given information.  To do this, we should calculate the slope between the two points as if they were regular points, giving us:

change in y/change in x = (v-4)/(-6-0) = (v-4)/(-6)

Since we know that the slope is 2, we can set our calculated value for the slope of the line for the equation (v-4)/(-6) equal to 2, as shown below:

(v-4)/(-6) = 2

To solve this equation, we should multiply both sides of the equation by -6 to get rid of the denominator on the left side of the equation.

v-4 = -12

Next, we should add 4 to both sides of the equation to get the variable v alone on the left side of the equation, as shown below:

v = -8

Therefore, v =-8 is your answer.

Hope this helps!

4 0
3 years ago
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