In Amy's garden the ratio of herbs to plants is 5:2. If there are 40 herb plants, how many vegetable plants are in her garden?

A plane flew 2,190 kilometers from Chicago to Flagstaff. Another plane flew 2,910 kilometers from Chicago to Oakland. How much f

DiKsa [7]

The answer is 720.hope it helps.

3 0

3 years ago

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Help please!!!!!!!!!

In-s [12.5K]

ANSWER

24

EXPLANATION

For a matrix A of order n×n, the cofactor $C_{ij}$ of element $a_{ij}$ is defined to be

$C_{ij} = (-1)^{i+j} M_{ij}$

$M_{ij}$ is the minor of element $a_{ij}$ equal to the determinant of the matrix we get by taking matrix A and deleting row i and column j.

Here, we have

$C_{11} = (-1)^{1+1} M_{11} = M_{11}$

M₁₁ is the determinant of the matrix that is matrix A with row 1 and column 1 removed. The bold entries are the row and the column we delete.

$\begin{aligned} A=\begin{bmatrix} \bf 1 & \bf -6 & \bf -4\\ \bf 7 & 0 & -3 \\ \bf -9 & 8 & -8 \end{bmatrix} \implies M_{11} &= \text{det}\left(\begin{bmatrix} 0&-3 \\ 8&-8 \end{bmatrix} \right) \end{aligned}$

Since the determinant of a 2×2 matrix is

$\det\left( \begin{bmatrix} a & b \\ c& d \end{bmatrix} \right) = ad-bc$

it follows that

$\begin{aligned} A=\begin{bmatrix} \bf 1 & \bf -6 & \bf -4\\ \bf 7 & 0 & -3 \\ \bf -9 & 8 & -8 \end{bmatrix} \implies M_{11} &= \text{det}\left(\begin{bmatrix} 0&-3 \\ 8&-8 \end{bmatrix} \right) \\ &= (0)(-8) - (-3)(8) \\ &= -(-24) \\ &= 24 \end{aligned}$

so $C_{11} = M_{11} = 24$

4 0

3 years ago

adult tickets at a football game cost $6 and student tickets cost $2. A total of $1776 was collected on 372 tickets. How many ad

postnew [5]

Answer:

258

Step-by-step explanation:

Set up the two equations needed (x is the adult tickets and y is the student tickets)

x+y=372

6x+2y=1776

Solve by elimination

-2(x+y=372)

=-2x-2y=-744

Cancel like figures:

-2x-2y=-744

6x+2y=1776

= 4x=1032

x=258

6 0

2 years ago

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Solve for b <br>r=x (a+b)

Delvig [45]

R=xa+xb, r-xa=xb, b=r-xa/x

5 0

3 years ago

The perimeter of a triangle is not greater than 12 and the lengths of sides are natural numbers.

weqwewe [10]

Answer:

3 triangles

Step-by-step explanation:

Perimeter of triangle = a + b + c

Given that :

P = 12

and a, b, c are natural numbers

Let :

Side A = a

Side B = b

Side C = 12 - (a + b)

Side A + side B > side C - - - (condition 1)

a + b > 12 - (a + b)

a + b > 12 - a - b

a + a + b + b > 12

2a + 2b > 12

2(a + b) > 12

a + b > 6

Side A - side B < side C

a - b < 12 - (a + b)

a - b + a + b < 12

2a < 12

a < 6

b < 6 (arbitrary point)

Going by the Constraint above :

The only three possibilities are :

(2, 5, 5)

(3, 4, 5)

(4, 4, 4)

Total number of triangle = 3

Equilateral triangle (all 3 sides equal) = (4, 4, 4) = 1

Isosceles triangle (only 2 sides equal) = (2, 5, 5) = 1

3 0

2 years ago