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chubhunter [2.5K]
3 years ago
10

1.) Is (0, 3) a solution to the equation y= x+3

Mathematics
2 answers:
Delvig [45]3 years ago
8 0
1. yes
2. no
3. (4,0) and (3,-1)
4. 8 crackers in 1 serving....so in 12 servings, there is (12 * 8) = 96 crackers
5. x + 5 = 10 (open equation)
6. ?
7. y = 1.5x....y being the cost of the pizza and x being the number of slices
abruzzese [7]3 years ago
6 0

1. The answer is Yes


The equation:

y=x+3

represents a <em>straight line </em>with slope m=1 and y-intercept b=3. To know if the point (0,3) is a solution to the equation, let's substitute the x and y coordinates into the equation, therefore:

(3)=(0)+3 \\ \\ \therefore 3=3 \ True!


Since our result is true, this point is a solution to the equation.


2. The answer is No


The equation:

y=-2x

represents a <em>straight line </em>with slope m=-2 and no y-intercept, that is, it passes through the origin. By substituting this point into the equation:

(-4)=-2(1) \\ \\ \therefore -4=-2 \ False!


Since our result is false, this point is not a solution to the equation.


3. In this problem, we have four points, so let's solve it step by step. Our equation is:

y=x-4

and represents a <em>straight line </em>with slope m=1 and y-intercept b=-4


3.1 <u>For the point</u> (4, 0)

<em>This point is a solution to the equation y = x - 4</em>


By substituting this point into the equation, we have:

y=x-4 \\ \\ \therefore (0)=(4)-4 \\ \\ \therefore 0=0 \ True!


Since our result is true, this point is a solution to the equation.


3.2 <u>For the point</u> (3, -1)

<em>This point is a solution to the equation y = x - 4</em>


By substituting this point into the equation, we have:

y=x-4 \\ \\ \therefore (-1)=(3)-4 \\ \\ \therefore -1=-1 \ True!


Since our result is true, this point is a solution to the equation.


3.3 <u>For the point</u> (6, 3)

<em>This point is not a solution to the equation y = x - 4</em>


By substituting this point into the equation, we have:

y=x-4 \\ \\ \therefore (3)=(6)-4 \\ \\ \therefore 3=2 \ False!


Since our result is false, this point is not a solution to the equation.


3.4 <u>For the point</u> (2, -4)

<em>This point is not a solution to the equation y = x - 4</em>


By substituting this point into the equation, we have:

y=x-4 \\ \\ \therefore (-4)=(2)-4 \\ \\ \therefore -4=-2 \ False!


Since our result is false, this point is not a solution to the equation.


4. In this problem we have:

  • There are 8 crackers in 1 serving.
  • There are 16 crackers in 2 servings.
  • There are 24 crackers in 3 servings, and so on.

So, there is a <em>linear relationship</em> between crackers and servings. Thus, it is easy to write a linear equation like this:

y=8x \\ \\ \\ where: \\ \\ y:Represents \ crackers \\ \\ x:Represents \ servings


Therefore, for x = 12 servings, we have:

y=8(12)=96


Finally:

<em>There are 96 crackers in 12 servings</em>


5. An open equation is an equation containing one or more <em>variables </em>such that the <em>truth or falsehood </em>of the equation depends on the values of the variables assumed in a specific instance. An example of an open equation is:

2x-16=-2


  • If x = 7

2(7)-16=-2 \\ \\ \therefore -2=-2 \ True!


For this particular x-value, the equation is true.


  • If x = 3

2(3)-16=-2 \\ \\ \therefore -10=-2 \ False!

For this particular x-value, the equation is false.


So, we can conclude that this equation is  only  true  when  x = 7


6. Equations can be used to model and solve  real-life problems. In this way, we can make predictions from an equation that models a real-life situation. For instance, a kitchen an <em>appliance manufacturing company </em>can determine the total cost in  dollars of producing units of a blender by using the equation:


C=20x+2500


Thus, the cost of producing zero units is $2500, found by the y-intercept, that is the fixed cost of production. It includes costs that must be paid regardless  of the number of units produced. The slope m=20 means that the cost of  producing each unit is $20, called by the Economists <em>the marginal cost </em>(cost per unit).


7. In this exercise, pizza costs $1.50 per slice. This can be modeled by the following equation:


C=1.50s \\ \\ \\ where: \\ \\ s:Represents \ the \ number \ of \ slices \\ \\ C:Represents \ the \ total \ cost


This can be represented by the following Table as well:

\begin{array}{cc}&#10;s(slices) & C(\$)\\&#10;1 & 1.50\\&#10;2 & 3.00\\&#10;3 & 4.50\\&#10;4 & 6.00\\&#10;5 & 7.50&#10;\end{array}


So, in this Table we have indicated the total cost up to 5 slices of pizza.

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Two regular pentagons have areas of 20 mm² and x² - x mm². What values of x make the pentagons congruent?
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<u>Answer</u>

5 and -4


<u>Explanation</u>

If the two triangle are congruent then they have the same area.

20 = x² - x

x² - x - 20 = 0

x² - x + (1/2)² = 20 + (1/2)²

(x - 1/2)² = 20.25

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x - 1/2 = 4.5                             or    x - 1/2 = - 4.5

x = 4 1/2 + 1/2                                      x = -4 1/2 + 1/2

   = 5                                                      = -4

The values of x are 5 and -4.



8 0
3 years ago
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