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:
<h2>416m^2</h2>
Step-by-step explanation:
<h3>Area = Length * Width</h3><h3>Volume = Length * Width * Height</h3>
<h3>As we all can see,from the question we were given the parameters for calculating volume instead of the ones for calculating "area"</h3>
<h3>But from the the parameters, we can calculate for the total surface area</h3>
<h3>Floor = 12m ×10m = 120m^2</h3>
<h3>Roof = 12m × 10m = 120m^2</h3>
<h3>Front and back walls (x2) = 10m × 4m ×2 = 80m^2</h3>
<h3>Side walls (x2) = 12m × 4m × 2 = 96m^2</h3><h3>Total surface area</h3>
<h3>= 120m^2 + 120m^2 + 80m^2 + 96m^2</h3>
<h3>= 416 m^2</h3>
Answer:
3 1/4 + 2 1/3 = 67 / 12 = 57 1/2
Step-by-step explanation:
Conversion a mixed number to a improper fraction: 3 1/4 = 3 · 4 + 1
4
= 13
4
Conversion a mixed number to a improper fraction: 2 1/3 = 2 · 3 + 1
3
= 7
3
Add: 13
4
+ 7
3
= 13 · 3
4 · 3
+ 7 · 4
3 · 4
= 39
12
+ 28
12
= 39 + 28
12
= 67
12
