What value is equivalent to 5 − 4(1 + 23
)?
Responses
A -103-103
B -31-31
C 6464
D 99
E -511
5 − 4(1 + 23) is -91. Therefore, the answer is A) -103.
Which expression is equivalent to 5(x + 7)?
Responses
A 5x + 125x + 12
B 5x + 75x + 7
C 40x40x
D 5x + 35
Using distributive property, 5(x + 7) can be expanded to 5x + 35. Therefore, the answer is D) 5x + 35.
Divide: 78
÷ 38
Responses
A 37
3 7
B 2164
21 64
C 73
7 3
D 6421
Using long division, we get:
```
2 R 2
--------
38 | 78
76
--
2
```
Therefore, 78 ÷ 38 is equal to 2 with a remainder of 2, which can be expressed as a mixed number 2 2/38 or simplified to 2 1/19. The answer closest to this is A) 37. (Note: option B is incorrect as it is a mixed number and not a single digit.)
The area of a triangle is 15 square inches. The triangle's height is 5 inches. What is the length of the base?
Responses
A 6 inches6 inches
B 10 inches10 inches
C 4 inches4 inches
D 8 inches8 inches
E 12 inches
The area of a triangle is given by the formula A = (1/2)bh, where A is the area, b is the length of the base, and h is the height. Plugging in the given values, we have:
15 = (1/2)(b)(5)
Multiplying both sides by 2/5, we get:
6 = b
Therefore, the length of the base is 6 inches. The answer is A) 6 inches.
The product of two numbers is 48, and one of the numbers is 12. Find the other number.
Which equation can be used to solve this problem?
Responses
A 48x = 1248x = 12
B x48
= 12x 48 = 12
C x12
= 48x 12 = 48
D 12x = 48
The problem states that the product of two numbers is 48, and one of the numbers is 12. Let the other number be x. Then we have:
12x = 48
Dividing both sides by 12, we get:
x = 4
Therefore, the other number is 4. The answer is not in the options, but the equation used to solve it is D) 12x = 48.
To find the value that is equivalent to the expression 5 - 4(1 + 23), we need to follow the order of operations, also known as PEMDAS: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
Let's break down the expression step by step:
1. Start with the inner parentheses: (1 + 23). Add 1 and 23 to get 24.
2. Replace the expression with the simplified result: 5 - 4(24).
3. Apply the multiplication: 4 multiplied by 24 equals 96.
4. Replace the expression with the simplified result: 5 - 96.
5. Apply the subtraction: 5 minus 96 equals -91.
Therefore, the value that is equivalent to 5 - 4(1 + 23) is -91.
Out of the given options, none of them matches the result of -91.