Could someone please check my math questions? your help would be greatly appreciated!!
Simplify #1 through 3.
1. 20/2 – 32 – (-2)2
a. -3
b. 5
c. 16
d. 24
2. 3(x – 5) – (x + 2)
a. 2x – 13
b. 3x – 13
c. 2x – 3
d. 2x – 17
3. (¾) / (2/5)
a. 3/10
b. 8/15
c. 1 7/8
d. 3 1/3
For #4 and #5 choose the property that is best illustrated in the statement.
4. x - (3a + 2) = x - 3a - 2
a. Associative Property
b. Commutative Property
c. Distributive Property
d. Substitution
5. x – 3a + 3a + 6 = x + 6
a. Additive Inverses Property
b. Additive Identity Property
c. Distributive Property
d. Substitution
6. Find the simplest algebraic expression for the following situation.
Susie, Sarah, and Tamera are planning to knit sweaters for their family. The sweaters will be made with yellow and blue yarn.
Susie needs to order 5 skeins of yellow yarn and 3 skeins of blue yarn.
Sarah needs to order 12 skeins of yellow yarn and 4 skeins of blue yarn.
Tamera needs to order 8 skeins of yellow yarn and 10 skeins of blue yarn.
How much total yarn should be ordered?
a. 25y + 17b
b. 20y + 22b
c. 42by
d. none of these
7. Simplify the algebraic expression by combining like terms:
2a – (a – 3b) – 5b
a. a – 8b
b. 3a – 8b
c. 3a – 2b
d. a – 2b
8. -14.2 belongs to which set of numbers?
a. {integers}
b. {whole numbers}
c. {rational numbers}
d. all of the sets listed above
9. Which number is the multiplicative inverse of -42?
a. –42
b. –1/42
c. 1/42
d. 42
10. You are buying 4 new pairs of slacks. All of the slacks are on sale for 24.97. What expression would you use to mentally find the total cost of the slacks?
a. 4(25) + 0.03
b. 4(25 + 0.03)
c. 4(25) – 0.03
d. 4(25 – 0.03)
11. Which variable expression is a translation of “5 times the difference of 8 and a number x”?
a. 5(8 – x)
b. x – 5(8)
c. 5(8) – x
d. 5 – 8x
12. The number of students on the football team is 2 more than 3 times the number of students on the basketball team. If the basketball team has y students, write a variable expression for the number of students on the football team.
a. 3y
b. 3y - 2
c. 2 + 3y
d. 2y + 3
14. Between what two integers is √39 ?
a. 3 and 4
b. 4 and 5
c. 5 and 6
d. 6 and 7
15. If the US Senate, with 140 members, contains 20 more Democrats than Republicans, how many Republicans does it contain?
a. 20
b. 40
c. 60
d. 80
My answers~
1.a
2.d
3.a
4.c
5.a
6.a
7.d
8.d
9.b
10.a
11.a
12.c
14.d
15.c
It's a little easier to check if you mark your answers with the questions. Saves a lot of scrolling back and forth. However, the wily teacher opens a 2nd window to avoid that, too!
#1:
20/2 – 32 – (-2)2
= 10 - 32 - (-4)
= 10 - 32 + 4
= -22+4
= -18
Since that's not one of the choices, I suspect a typo in your presentation.
#3: (3/4)/(2/5) = (3/4)(5/2) = 15/8, so C
#8: C 14.2 is certainly not an integer!
#10: 24.97 = (25-0.03)
That's the cost of one pair. You want 4 pairs, so D
The rest look good.
Okay, thank you, soo much for your help!! and Yes sir/ma'am there was a typo! I really apologize! the question was supposed to be 20/2 – 3^2 – (-2)^2
Sure! Let's go through each question and check your answers.
Question 1:
To simplify the expression, we'll work step by step:
20/2 – 32 – (-2)2
= 10 - 32 - (-4)
= 10 - 32 + 4
= -18 + 4
= -14
So the correct answer is actually none of those options. It should be -14.
Question 2:
Simplifying the expression:
3(x – 5) – (x + 2)
= 3x - 15 - x - 2
= 2x - 17
So the correct answer is option d) 2x - 17.
Question 3:
Simplifying the expression:
(3/4) / (2/5)
= (3/4) * (5/2)
= 15/8
So the correct answer is option b) 8/15.
Question 4:
This question asks you to choose the property that is best illustrated in the statement:
x - (3a + 2) = x - 3a - 2
The property illustrated in this statement is the Distributive Property, because the parentheses are being removed by distributing the negative sign to both terms inside the parentheses.
So the correct answer is option c) Distributive Property.
Question 5:
This question also asks you about a property illustrated in the given statement:
x – 3a + 3a + 6 = x + 6
The property illustrated in this statement is the Additive Identity Property, because the term "3a" cancels out with its additive inverse "-3a", leaving just "x + 6".
So the correct answer is option b) Additive Identity Property.
Question 6:
To find the total yarn that should be ordered, we need to add up the quantities of yellow and blue yarn needed by each person:
5 skeins of yellow yarn + 12 skeins of yellow yarn + 8 skeins of yellow yarn = 25 skeins of yellow yarn
3 skeins of blue yarn + 4 skeins of blue yarn + 10 skeins of blue yarn = 17 skeins of blue yarn
So the simplest algebraic expression for the total yarn needed is 25y + 17b.
So the correct answer is option a) 25y + 17b.
Question 7:
Simplifying the expression:
2a – (a – 3b) – 5b
2a - a + 3b - 5b
a - 2b
So the correct answer is option d) a - 2b.
Question 8:
The number -14.2 belongs to the set of rational numbers because it can be expressed as a fraction, -14.2 = -142/10.
So the correct answer is option c) {rational numbers}.
Question 9:
The multiplicative inverse of a number is the reciprocal of that number. The reciprocal of -42 is -1/42.
So the correct answer is option b) -1/42.
Question 10:
To find the total cost of the 4 new pairs of slacks on sale for $24.97 each, we multiply the cost per pair by the number of pairs:
4(24.97)
So the correct answer is option b) 4(25 + 0.03).
Question 11:
"5 times the difference of 8 and a number x" can be expressed as 5(8 - x).
So the correct answer is option a) 5(8 - x).
Question 12:
If the basketball team has y students, then the number of students on the football team is 2 more than 3 times y, which can be expressed as 3y + 2.
So the correct answer is option d) 2y + 3.
Question 14:
To find the two integers between which √39 lies, we can calculate the square roots of integers near 39:
√39 ≈ 6.24
So the two integers are 6 and 7.
So the correct answer is option d) 6 and 7.
Question 15:
We are given that the US Senate contains 140 members, and there are 20 more Democrats than Republicans. Let's assume the number of Republicans is x. So the number of Democrats is x + 20.
According to the information given, the total number of members can be expressed as: x + (x + 20) = 140.
Combining like terms, we have: 2x + 20 = 140.
Solving for x, we subtract 20 from both sides: 2x = 120, and x = 60.
Therefore, the correct answer is option c) 60.
Overall, your answers were mostly correct. Great job!