Explanation

A function f: A → B is into if it doesn't cover the entire codomain B, meaning there are elements in B that aren't mapped to by any element in A. 

This happens when the range of f (the set of elements in B that are actually mapped to) is a proper subset of B.

Therefore, f is into if Range f ≠ B.

Explanation

To solve the equation:

5 - 4x = 7

Step 1: Subtract 5 from both sides  

5 - 4x - 5 = 7 - 5  

-4x = 2

Step 2: Divide both sides by -4  

x = 2 / -4  

x = -0.5

Final Answer:  

x = -0.5

Explanation

Given function: f(x) = x^3 + 4x + 12

Given x = -1:

f(-1) = (-1)^3 + 4(-1) + 12

f(-1) = -1 - 4 + 12

f(-1) = 7

Explanation

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Checking the options

1. 2m, 3m, 4m:

2 + 3 > 4 (True)

3 + 4 > 2 (True)

2 + 4 > 3 (True)

2. 3m, 4m, 8m:

3 + 4 > 8 (False)

3. 4m, 6m, 9m:

4 + 6 > 9 (True)

6 + 9 > 4 (True)

4 + 9 > 6 (True)

4. 5m, 7m, 10m:

5 + 7 > 10 (True)

7 + 10 > 5 (True)

5 + 10 > 7 (True)

The answer is 3m, 4m, 8m.

Explanation

If a/2+4 = 7/2, the a =?

A/ 2+4 = 7/2

a/ 4 = 7

4 - 7 =  a

-3 =  a

 -3/ 3 = a

-1 = a

Explanation

Total points scored = 210

Total questions = 110

Points for each correct answer = 3

Points for each wrong answer = 1

Let's say the number of correct answers is x.

Then, the number of wrong answers is (110 - x).

The total points scored can be represented as: 3x + (110 - x) = 210

Simplify the equation: 3x + 110 - x = 210

Combine like terms: 2x + 110 = 210

Subtract 110 from both sides: 2x = 100

Divide both sides by 2: x = 50

So, the number of correct answers is 50.

Now, let's find the number of wrong answers:

Number of wrong answers = Total questions - Number of correct answers

= 110 - 50

= 60

Explanation

Explanation

X + 7 = 77

Subtract 7 from both sides:

X = 77 - 7

X = 70

Now that we know X, we can find the product of 7 and X:

7 × X = 7 × 70

= 490

Explanation

8^𝑎 = 16^𝑏

We can rewrite 16 as 2^4, so:

(2^3)^𝑎 = (2^4)^𝑏

Using the power rule (a^m)^n = a^(mn), we get:

2^(3𝑎) = 2^(4𝑏)

Since the bases are equal (both are 2), we can equate the exponents:

3𝑎 = 4𝑏

Now, divide both sides by 3𝑏:

𝑎/𝑏 = 4/3

So, the ratio of 𝑎 to 𝑏 is 4:3 or 4/3.

Explanation

An expression consisting of two terms is called a binomial.

A binomial is a polynomial with two terms, such as: 2x + 3

Monomial: An expression with only one term, such as 2x or 3.

Trinomial: An expression with three terms, such as 2x + 3y - 4.

Additional points:

• Polynomial: An expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
• Multinomial: An expression with more than two terms.
• Uninomial: An expression with only one term (synonym for monomial).