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3 years ago

4m-2+3m+5 terms, like terms, coefficient, and constant

Mathematics

1 answer:

san4es73 [151]3 years ago

3 0

Answer:

As the expression $4m-2+3m+5$ has terms 4m, -2, 3m and 4. So, there are total four terms.

The constants in the expression $4m-2+3m+5$ are -2 and 5.

There are two sets of like terms in the expression $4m-2+3m+5$ . 4m and 3m are like terms. Also the constants -2, and 5 are like terms. Like terms can be combined.
The coefficients in the expression $4m-2+3m+5$ are 4 and 3.

Step-by-step explanation:

As the given algebraic expression is

$4m-2+3m+5$

We have to determine

total number of terms
like terms
coefficient
constant

The coefficients are the numbers that multiply the variables or letters. For example the term 3m has the coefficient 3 which multiplies the variable 3.
Like terms are considered the terms which contain the same variable raised to the same power. For example, 2x + 4x has the like terms 2x and 4x.
Constants are said to be the terms without variables. For example, the algebraic expression 2x + 4x + 6 has a constant which is 6.

Let's check the expression $4m-2+3m+5$ now.

According to discussion we have,

$4m-2+3m+5$

As the expression $4m-2+3m+5$ has terms 4m, -2, 3m and 4. So, there are total four terms.

The constants in the expression $4m-2+3m+5$ are -2 and 5.

There are two sets of like terms in the expression $4m-2+3m+5$ . 4m and 3m are like terms. Also the constants -2, and 5 are like terms. Like terms can be combined.
The coefficients in the expression $4m-2+3m+5$ are 4 and 3.

Keywords: like terms, coefficients, constants

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Answer:

Length of rectangle is 31 yards and Width is 24 yards.

Given:

The length of a rectangle is 7 more than the width.
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Solution:

Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.

Using formula

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On Substituting the required values, we get;

$\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x = 24 \: or \: - 31 \\ \\$

As we know that width of the rectangle can't be negative. So x = 24

Hence,

Width of rectangle = x = 24 yards
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$\therefore$ Length of rectangle is 31 yards and Width is 24 yards.

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