Answer:
49/8 is the value of k
Step-by-step explanation:
We have the system
x = -2y^2 - 3y + 5
x=k
We want to find k such that the system intersects once.
If we substitute the second into the first giving us k=-2y^2-3y+5 we should see we have a quadratic equation in terms of variable y.
This equation has one solution when it's discriminant is 0.
Let's first rewrite the equation in standard form.
Subtracting k on both sides gives
0=-2y^2-3y+5-k
The discriminant can be found by evaluating
b^2-4ac.
Upon comparing 0=-2y^2-3y+5-k to 0=ax^2+bx+c, we see that
a=-2, b=-3, and c=5-k.
So we want to solve the following equation for k:
(-3)^2-4(-2)(5-k)=0
9+8(5-k)=0
Distribute:
9+40-8k=0
49-8k=0
Add 8k on both sides:
49=8k
Divide both sides by 8"
49/8=k
Answer:
Apprentice = $800
Journeyman = $1600
carpenter = $4000
Step-by-step explanation:
Let the apprentice earns X dollars.
Then ,
Journeyman will make 200% of apprentice's earning which is 2X.
Also,
Carpenter makes 250% of the earning that journeyman makes.
Which is 2.5(2X) = 5X
Their total earning should come to $6400.
Thus,
X + 2X + 5X = 6400
8X = 6400.
X = $800
So,
Earning of apprentice = X = $800
Earning of Journeyman = 2X = $1600
Earning of carpenter = 5X = $4000
Answer:
* Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.
* Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I.
Step-by-step explanation:
Equation I: 4x − 5y = 4
Equation II: 2x + 3y = 2
These equation can only be solved by Elimination method
Where to Eliminate x :
We Multiply Equation I by a coefficient of x in Equation II and Equation II by the coefficient of x in Equation I
Hence:
Equation I: 4x − 5y = 4 × 2
Equation II: 2x + 3y = 2 × 4
8x - 10y = 20
8x +12y = 6
Therefore, the valid reason using the given solution method to solve the system of equations shown is:
* Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.
* Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I.
Answer:
500 boxes
Step-by-step explanation:
<em>hey there,</em>
<em />
< Since "p" stands for profits, change "p" to 0 (since the question says 0 profits).
Here is how your equation would look like:
Pretend like "n" is "x" since that is the variable we are trying to find here.
Solve for "n". Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
"n" actually ends up equaling 500, -200.
Obviously, negative can't be the answer because you can't have a negative amount of boxes. So 500 boxes would be your answer. 200 CAN'T be your answer <em>either </em>because it is a negative!! >
<u>Hope this helped! Feel free to ask anything else.</u>
Your answer is angle JCL.
Angle JCL+Angle LCT = 90°
