The answer you are looking for is C
The graph of the function -3x+5y=-15 is a linear function we can draw it by finding the values of y for every value of x.
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
-3x + 5y = -15
The above function shows a linear function we can write it as:
5y = 3x - 15
y = (3x - 15)/5
If x = 0, y = -3
x = 1, y = -2.4
x = 2, y = -1.8
x = -1, y = -3.6
x = -2, y = -4.2
Thus, the graph of the function -3x+5y=-15 is a linear function we can draw it by finding the values of y for every value of x.
Learn more about the function here:
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Answer:
<span>=3<span>√6</span>−3<span>√5</span></span>
Explanation:
<span>3<span><span>√5</span>+<span>√6</span></span></span>
We rationalise the denominator by multiplying the expression by the conjugate of the denominator. <span><span>√5</span>−<span>√6</span></span>
<span><span>3⋅<span>(<span>√5</span>−<span>√6</span>)</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span>
<span>=<span><span>3⋅<span>(<span>√5</span>)</span>+3⋅<span>(−<span>√6</span>)</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span></span>
<span>Applying identity
<span><span>(a+b)</span><span>(a−b)</span>=<span>a2</span>−<span>b2</span></span> to the denominator.</span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span><span><span>(<span>√5</span>)</span>2</span>−<span><span>(<span>√6</span>)</span>2</span></span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span>5−6</span></span></span>
<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span>−1</span></span></span>
<span>=−3<span>√5</span>+3<span>√6</span></span>
<span>=3<span>√6</span>−3<span>√<span>5
</span></span></span>
Answer:
The dimension of the cardboard is 34 cm by 34 cm by 17 cm.
Step-by-step explanation:
Let the dimension of the cardboard box be x cm by y cm by z cm.
The surface area of the cardboard box without lid is
f(x,y,z)= xy+2xz+2yz.....(1)
Given that the volume of the cardboard is 19,652 cm³.
Therefore xyz =19,652
......(2)
putting the value of z in the equation (1)
The partial derivatives are
To find the dimension of the box set the partial derivatives 
and 
.Therefore 
.......(3)
and 
.......(4)
Now putting the x in equation (3)
⇒y=34 cm
Then 
=34 cm.
Putting the value of x and y in the equation (2)
=17 cm.
The dimension of the cardboard is 34 cm by 34 cm by 17 cm.
A. -2x + 3y = -15
-2x + 2x + 3y = 2x - 15
3y = 2x - 15
3 3
y = ²/₃ - 5
A is correct.
B. y = ²/₃ - 5
B is also correct.
C. 6y = 4x - 30
6 6
y = ²/₃x - 5
C is also correct.
D. y + 3 = ²/₃(x - 3)
y + 3 = ²/₃(x) - ²/₃(3)
y + 3 = ²/₃x - 2
- 3 - 3
y = ²/₃x - 5
D is also correct.
The answer to the problem is A, B, C, and D.
