Answer:
Vanilla = 10 sundaes
Step-by-step explanation:
Total sundaes = 25
1/5 of the sundaes are mint ice cream
Mint ice cream = 1/5 of 25
= 1/5 * 25
= 25/5
= 5
Sundaes remaining = total sundaes - sundaes for mint ice cream
= 25 - 5
= 20 sundaes
Sundaes remaining = 20 sundaes
1/2 of the remaining sundaes are chocolate
= 1/2 of 20
= 1/2 * 20
= 20/2
= 10
Chocolate ice cream = 10
The rest will be vanilla
Sundaes remaining = 20 - 10
= 10 sundaes
Vanilla = 10 sundaes
Answer:
You have to put this in a bar model yourself so convert it later
She bought 10 apples
Step-by-step explanation:
3x + 2 = 14
why i did this
because she bought 2 times the amount of bananas, it should be x + 2x = 3x
then i added two because she bought two extra apples
so 3x+2 = 14
subtract 2
3x = 12
x = 4
So now we substitute x in apples
2x +2 = # of apples
8 +2 = 10
check
10 - 2 = 8
8/2 = 4
4 = # of bananas
Answer:
B(1.25,5)
Step-by-step explanation:
y... -5, 0, 5
x... -0.5, 1.25, 3
Answer:
Step-by-step explanation:
Given the matrix
[5 3]
[-4 4]
The characteristic polynomial is expressed as |A - λI| = 0 where λ are the eigen values and I is am identity matrix A 2*2 identity matrix is expressed as;
[1 0]
[0 1]
Substitute into expression will give;
![= \left[\begin{array}{cc}5&3\\-4&4\\\end{array}\right] - \lambda \left[\begin{array}{cc}1&0\\0&1\\\end{array}\right] = 0\\= \left[\begin{array}{cc}5&3\\-4&4\\\end{array}\right] - \left[\begin{array}{cc}\lambda &0\\0&\lambda \\\end{array}\right] = 0\\= \left[\begin{array}{cc}5-\lambda&3\\-4&4-\lambda\\\end{array}\right] = 0](https://tex.z-dn.net/?f=%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%263%5C%5C-4%264%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%20-%20%5Clambda%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%200%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%263%5C%5C-4%264%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%20-%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%20%260%5C%5C0%26%5Clambda%20%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%200%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5-%5Clambda%263%5C%5C-4%264-%5Clambda%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%20%3D%200)
Find the determinant of the resulting matrix;
|A - λI| = (5- λ)(4- λ)- 3(-4) = 0
|A - λI| = 20-5 λ-4 λ+ λ²+12 = 0
|A - λI| = 20-9λ+λ²+12 = 0
-9λ+λ²+32 = 0
Rearrange;
λ²-9λ+32 = 0
Hence the characteristic polynomial is expressed as λ²-9λ+32 = 0
Get the eigen values by finding the roots of the equation;
λ = 9±√9²-4(1)(32)/2
λ = 9±√81-(128)/2
λ = 9±√-47/2
λ = 9±√-47/2
λ₁ = 9-√47 i/2 and λ₂ = 9+√47 i/2
