Answer:
3. Option D
5. Option B
13. Option D
17. Option B
Step-by-step explanation:
<u>Question 3</u>
4C means that, multiply 4 with all the terms in the matrix A . We get option D.
<u>Question 5</u>
Matrix A + matrix B means that add corresponding terms of each matrix.
We get option B.
<u>Question 13</u>
Here we have to find a₁,₂ (the term in which first row second column)
a₁,₂ = 2
We get option D.
<u>Question 17</u>
B - CF - First multiply matrix C with matrix F and subtract it from Matrix B.
We get option B
Answer:14.8
Step-by-step:
Use the equation a^2+b^2=c^2
Plug in 13 for a and 7 for b
13^2+7^2=c^2
Multiply the number by themselves
13•13+7•7=c^2
169+49=c^2
218=c^2
Square root both side
14.76=c
Round the nearest tenth
14.8
Answer:
The number of Pencils purchased and the cost of pencils represents a proportional relationship.
Step-by-step explanation:
As we know that proportional relationships between two variables have equivalent ratios.
For example,
3/12 = 9/36 is a TRUE proportions because both fractions reduces to 1/4, and because 12 × 9 = 3 × 36.
As our problem suggests whether the number of Pencils purchased and the cost of pencils represent a proportional relationship?
Given
It means ach pencil costs $0.25.
So
- If Sarah buys 1 pencil it would cost = $0.25
- If Sarah buys 2 pencils it would cost = $0.5
- If Sarah buys 3 pencils it would cost = $0.75
- If Sarah buys 4 pencils it would cost = $1
Lets make a table:
No of Pencils Purchased Cost
1 $0.25
2 $0.5
3 $0.75
4 $1
so
Cost/No of Pencils Purchased = 0.25/1 = 0.5/2 = 0.75/3 = 1/4
So cost per pencil = 0.25 : 1
Since all of the ratios are equivalent, this table is a proportional relationship.
Therefore, the number of Pencils purchased and the cost of pencils represents a proportional relationship.
3⁻¹ is <u>greater than </u>1/4
<u>Step-by-step explanation:</u>
3⁻¹ is nothing but the inverse of 3 .
So it can be written as 1/3.
Value of 1/3 can be found by dividing 1 by 3 to be 0.333...
Value of 1/4 can be found by dividing 1 by 4 to be 0.25
So 0.333 > 0.25
1/3 > 1/4
∴ 3⁻¹ > 1/4
a. The expression y=5x represent the number of small marbles she has.
b. The expression z=3x+2 represents the number of large marbles she has.
c. Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Medium marbles = x
Let,
Small marbles = y
According to given statement;
She has five times as many small marbles as medium marbles.
y = 5x Eqn 1
The expression y=5x represent the number of small marbles she has.
b. Write an algebraic expression to represent the number of large marbles she has.
Let,
Large marbles = z
The number of large marbles is two more than three times the number of medium marbles.
z = 3x+2 Eqn 2
The expression z=3x+2 represents the number of large marbles she has.
c. If Amy has a total of 560 marbles, how many of each size does she have?
x+y+z= 560 Eqn 3
Putting value of y and z from Eqn 1 and 2 in Eqn 3
Dividing both sides by 9
Putting x=62 in Eqn 1
Putting x=62 in Eqn 2
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Keywords: linear equation, substitution method
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