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Solve exercise 57 page 49 Math 7 Textbook Volume 2
Exercise:
Write an algebraic expression of two variables x, y satisfying each of the following conditions:
a) The expression is a monomial.
b) The expression is a polynomial but not a monomial.
Answer:
Solving exercise 58 page 49 Math 7 Textbook Volume 2
Exercise:
Calculate the value of each expression at x = 1; y = -1 and z = -2:
Answer:
Solving exercise 59 page 49 Math 7 Textbook Volume 2
Exercise:
Fill in the appropriate monomial in each blank below:
Solving exercise 60 page 49 Math 7 Textbook Volume 2
Exercise:
There are two water faucets, the first one flows into tank A, the second one flows into tank B. Tank A already contains 100 liters of water, Tank B is empty. Each minute, the first faucet can flow 30 liters, and the second faucet can flow 40 liters.
a) Calculate the amount of water in each tank after 1, 2, 3, 4, 10 minutes and fill in the table below (assuming the tanks are large enough to hold the water).
b) Write an algebraic expression representing the amount of water in each tank after x minutes.
Answer:
a) Fill in the results
Explanation:
After 1 minute, tank A has 100 + 30 = 130 (liters), tank B has 40 (liters)
=> Both tanks have 170 liters
After 2 minutes, tank A has 100 + 2.30 = 160 (liters), tank B has 40.2 = 80 (liters)
=> Both tanks have 240 liters
After 3 minutes, tank A has 100 + 3.30 = 190 (liters), tank B has 40.3 = 120 (liters)
=> Both tanks contain 310 liters
After 4 minutes, tank A has 100 + 4.30 = 220 (liters), tank B has 40.4 = 160 (liters)
=> Both tanks contain 380 liters
After 10 minutes, tank A has 100 + 10.30 = 400 (liters), tank B has 40.10 = 400 (liters)
=> Both tanks contain 800 liters
b) (From the explanation above, we can easily derive the following two algebraic expressions:)
- The number of liters of water in tank A after x minutes:
100 + 30x
- The number of liters of water in tank B after x minutes:
40x
Solving exercise 61 page 50 SGK Toán 7 Tập 2
Exercise:
Calculate the product of the following monomials and then find the coefficient and degree of the resulting product.
Answer:
Solving exercise 62 page 50 SGK Toán 7 Tập 2
Exercise:
Given two polynomials:
a) Arrange the terms of each polynomial based on the decreasing exponent of the variable.
b) Calculate P(x) + Q(x) and P(x) - Q(x).
c) Demonstrate that x = 0 is a root of polynomial P(x) but not a root of polynomial Q(x).
Answer:
Solving exercise 63 page 50 Math 7 Textbook Volume 2
Exercise:
Answer:
Solving exercise 64 page 50 Math 7 Textbook Volume 2
Exercise:
Answer:
Solving exercise 65 page 51 Math 7 Textbook Volume 2
Exercise:
Among the numbers on the right side of the following polynomials, which one is a root of the polynomial on its left?
Answer:
We try each value into the polynomial on the left, the value that makes the polynomial equal to 0 is a root of the polynomial.
The solutions are:
a) 3
b) -1/6
c) 1; 2
d) -6; 1
e) -1; 0
