Answer:
y = 5
Step-by-step explanation:
The triangles will be congruent when corresponding sides are congruent. __
We already have ...
KL ≅ NP . . . = 15 mm
JL ≅ MP . . . = 22 mm
So, we need ...
JK ≅ MN
4y +12 = 32 . . . . substitute given values
This will be the case when ...
4y = 20 . . . . . subtract 12
y = 5 . . . . . . . divide by 4
The value of y that makes the triangles congruent is 5.
Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
<h3>
What is a matrix?</h3>
- A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.
- For instance, consider a matrix with two rows and three columns.
To find the order of matrix:
- We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.
- Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.
- Dimension is assigned to the provided matrix: 6 × 5
- This means the given matrix contains six rows and five columns.
- As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.
- The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.
To prove:
- In other words, the inner products of the dimensions should be equal.
- That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.
- The dimensions of the matrix are given by, row × column.
Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
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Answer:
- The system has infinitely many solutions when a = 3/4 and b = 1/2
<h3>Given </h3>
System of linear equations
<h3>To find </h3>
- Values of a and b that leads to infinitely many solutions
<h3>Solution</h3>
The linear system of equations has infinitely many solutions when lines overlap, so both have same slope and y-intercept.
We can solve it in two different ways
1. Note that when the first equation is multiplied by 4, it has same value of constant as the second equation, which is 64.
- 4ax + 4by = 64
- 3x + 2y = 64
When compared it gives us:
- 4a = 3 ⇒ a = 3/4
- 4b = 2 ⇒ b = 2/4 = 1/2
2. Convert both equations from standard to slope-intercept form and compare:
- ax + by = 16
- by = -ax + 16
- y = - (a/b)x + 16/b
- 3x + 2y = 64
- 2y = - 3x + 64
- y = - (3/2)x + 32
Work out values of a and b:
- 16/b = 32 ⇒ b = 16/32 ⇒ b = 1/2
- - (a/b) = - 3/2 ⇒ a/b = 3/2 ⇒ a = 3b/2 ⇒ a = 3(1/2)/2 ⇒ a = 3/4