1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Write the equation of the line that passes through the points (1, -7) and (-6, -9).
jek_recluse [69]

Answer:

y = 2/7 x - 51/7

Step-by-step explanation:

Equation of the line

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

(y-(-7)/(-9-(-7) = (x-1)/(-6-1)

(y+7)/-2 = (x-1)/-7

(-y-7)/2 = (-x+1)/7

-y-7 = -2/7 x + 2/7

-y = -2/7x +2/7 + 7

y = 2/7 x - 2/7 - 7

y = 2/7 x + (-2-49)/7

y = 2/7 x - 51/7

3 0
3 years ago
Find the measure of angle b 59=b​
IRISSAK [1]

Answer:

A.

Step-by-step explanation:

5 0
2 years ago
Interior angle of a regular hexagon
zmey [24]

Answer:

120 degrees the sum of all angle is 720 degrees In the above

8 0
3 years ago
Read 2 more answers
Please help.. thank you for your assistance :)
ludmilkaskok [199]

Answer:

the slope is 1 so D

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Which equation in point slope form is shown in the graph below
oee [108]

Answer:

D

Step-by-step explanation:

I know that its correct because I got it correct

it should equal to y=-2/7x+13/7

3 0
3 years ago
Other questions:
  • Simplify (4x1/8w)-3/5x
    5·1 answer
  • How to factor polynomials
    13·1 answer
  • Ebuka's monthly rent is
    7·2 answers
  • Please help the following questions
    8·1 answer
  • Radian question. Answer asap please!!!
    10·1 answer
  • Solve for -2x + 3 &lt; 5.
    13·2 answers
  • What is 7x+5y=-7 and 9x-2y=-9
    7·2 answers
  • What is the range of the function y= e^4x
    12·1 answer
  • What is the slope of the line shown below?
    12·1 answer
  • The table shows how many books the students in Bergdalsskolan list during the summer. There were 48 students who list 4 books. a
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!