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Galina-37 [17]
3 years ago
12

The relation between the cost of a certain gem and its weight is linear. In looking at two gems, we find that one of the gems we

ighs 0.3 carat and costs $3,457, while the other gem weighs 0.5 carat and costs $4,373. Find a linear function that relates the price of a gem, C(x), to its weight, x, treating weight as the independent variable.
I appreciate anyone who can help me. I will be reporting any foolish answers.
Mathematics
1 answer:
Ivahew [28]3 years ago
4 0
Treat each of the rings as a point on a graph the point being (carat, Cost ring)
Knowing this we have 2 points which we need to form a line. 
(0.3, 3457); (0.5, 4373)  From this we can for a slope and then an equation.
slope =
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Solve for x<br> x + y = 1<br> x + 7y = -4<br> 2x - 6y = 4<br> 5x + 15y = -10<br> 2x + 6y = 10
Arada [10]
X + y = 1
add - y both sides
x + y +  - y = 1 +  - y
x =  - y + 1
Answer: x =  - y + 1
Graph: y =  - x + 1


x + 7y =  - 4
add - 7 both sides
x + 7y +   - 7y = - 4 +  -7y
x =  - 7y  - 4
Answer: x = - 7y   - 4
Graph: y = 0.142857x  -  0.571429


2x  - 6y = 4
add 6y to both sides
2x  - 6y + 6y = 4 + 6y
2x = 6y + 4
divide both sides by 2
2x/2 = 6y + 4/2
x = 3y + 2
Answer: x = 3y + 2
Graph: y = 0.333333x  -  0.666667



5x + 15y = - 10
add - 15 to both sides
5x + 15y +   - 15y = - 10 +  - 15y
5x = - 15y  - 10
divide both sides by 5
5x/5 =  - 15y - 10/5
x = - 3y  - 2
Answer: x = - 3y - 2
Graph: y =  - 0.333333x  -  0.666667



2x + 6y = 10
add - 6y to both sides
2x + 6y +  - 6y = 10 +  - 6y
2x =  - 6y + 10
divide both sides by 2
2x/2 = - 6y + 10/2
x =  - 3y + 5
Answer: x =  -3y + 5
Graph: y =  - 0.333333x  +  1.666667





Hope that helps!!!
8 0
3 years ago
Point Q'Q ′ Q, prime is the image of Q(0,6)Q(0,6)Q, left parenthesis, 0, comma, 6, right parenthesis under the translation (x,y)
Marina86 [1]

Q is located at (0,6)

The translation rule is (x,y) \to (x+7,y-5) which says to add 7 to the x coordinate and subtract 5 from the y coordinate. Doing that to (0,6) moves it to (7,1) which is where point Q' is located.

In other words, if you shift point Q(0,6) seven units to the right and five units down, then it arrives at Q ' (7,1)

<h3>Answer: (7, 1)</h3>

8 0
3 years ago
Find the volume, in cubic centimeters, of the rectangular prism pictured below.
never [62]

Answer:

V= 18.75 cm^3

Step-by-step explanation:

  • The formula for finding the volume for <em>any</em> given shape is V = L x W x H.
  • So, multiply 2 1/2 cm x 2 1/2 cm x 3 cm.
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3 years ago
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.
trasher [3.6K]

Answer:

\frac{xe^{7x}}{7} + \frac{e^{7x}}{49}

Step-by-step explanation:

Given the integral equation

\int\limits{xe^{7x}} \, dx \\

According to integration by part;

\int\limits {u} \, dv = uv +  \int\limits {v} \, du

u = x, dv = e^7x

du/dx = 1

du = dx

v = \int\limits {e^{7x}} \, dx \\v = e^7x/7

Substitute the given values into the formula;

\int\limits {xe^{7x}} \, dx = x(e^{7x}/7) + \int\limits ({e^{7x}/7}) \, dx\\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{7*7} \\\int\limits {xe^{7x}} \, dx = \frac{xe^{7x}}{7} + \frac{e^{7x}}{49}

3 0
3 years ago
Given the function g(x)=√x+4, which of the following values cannot be the domain of g?
Gennadij [26K]

Answer:

  D.  x = -5

Step-by-step explanation:

The square root function is only defined for non-negative arguments. For the function ...

  g(x)=\sqrt{x+4}

this means we must have ...

  x +4 ≥ 0

  x ≥ -4 . . . . . . subtract 4 from both sides

All of the numbers on your answer choice list are more than -4 except -5.

  x = -5 is not in the domain of g(x)

6 0
2 years ago
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