1.
Illustrate commutative property of addition using the expression (3 + x) + y
Explanation
Review
Two basic properties of addition:
Commutative property â€“ terms may be switched but it wonâ€™t affect its value.
Illustration:
apple + banana = banana + apple
A + B = B + A
Associative property â€“ Changing terms in a grouping is a change in association.
Illustration:
(Lyca + John) + Trish = (Lyca + Trish) + John
(L + J) + T = (L + T) + J
2.
On a scale was an apple. Two apples were added per hour. As a result, The weight increased.
What model of addition is being illustrated above?
Correct Answer
D. Putting together model
Explanation
*Models of addition
Two models
Putting-together model â€“ putting two or more things together is the same as adding.
Put 2 apples and 3 apples in one.
2 Apples + 3 Apples = 5 Apples
Slide-model- increase in distance or scale on a plane is also addition
My body temperature rose 4 degrees up.
Body temp + 4 degrees
3.
Below is the solution for solving X + 2 = - ( - 3) and its corresponding property.
X + 2 = - ( - 3) Property applied
X + 2 = 3 Opposites of opposites property -(- a) = +a
X + 2 + ? = 3 + ? Property of Opposites
X + 0 = 1 ?
X = 1
What's missing above?
Correct Answer
C. -2 and Identity property of Addition
Explanation
Please see explanation in the book... lesson 3-2
4.
The vertices of a triangle are A(1, 1), B(2, -1), and C(-1, 0). Moving all the points 3 units to the left and 1 units up. Locate the image of point B.
Correct Answer
D. X-axis
Explanation
Moving all the points 3 units to the left and 1 unit up would result in the new coordinates for point B being (-1, 0). This means that the image of point B would be located on the X-axis.
5.
Simplify the following expression.
3(x + 2) – 2(x - 3)
Correct Answer
B. X +12
Explanation
Steps:
Step 1: distribute to remove parenthesis
Step 2: switch all similar terms right next to each other.
Step 3: add similar terms.
Note: we canâ€™t add 3x and 4. 3x has a variable while does not.
Tracing Misconception!
if you answered A:
you need to distribute 3 and -2 to all its corresponding terms inside each pair of parentheses "()"
if you answered c:
you probably forgot to include the sign of 2 in distributing.
if you answered d:
you probably added x + 12. Remember that they are dissimilar terms.
for more info: check video on 3 - 9
6.
Given the figure above. Solve for x, if the to total area is 50 ft^{2}.
Correct Answer
B. 8 ft
Explanation
Use the formula: Area = Length x Width
Given:
Area = 50
Length = 5
Width = X + 2
injecting all values into the formula...
A = L * W
50 = 5 (X + 2)
then solve...
50 = 5x + 10
50 - 10 = 5x + 10 - 10
40 = 5x
40/5 = 5x/5
8 = x
or
x = 8
7.
Simplify!
Correct Answer
B. 2x
Explanation
This is an example of addition of similar algebraic fractions. To add this type fractions, simply copy the denominator and add the numerators. See examples from the book and video.
8.
Describe the pattern using an expression.
Correct Answer
B. 4x+1
Explanation
remember
ax + b ....expression
y = ax + b ... equation
a is the increase of the number of circles... and b is the constant circle or the first instance minus the 'a'.
9.
Correct Answer
D. 17
10.
Solve!
2x = 3
x = ?
Correct Answer
1.5
3/2
one and a half
3 over 2
Explanation
The equation 2x = 3 can be solved by dividing both sides of the equation by 2. This gives us x = 3/2, which is equivalent to 1.5. Therefore, the answer is 1.5.
11.
Solve!
x - 1 = 3
x = ?
Correct Answer
4
Explanation
To solve the equation x - 1 = 3, we need to isolate the variable x. To do this, we can add 1 to both sides of the equation. This will cancel out the -1 on the left side, leaving us with x = 4. Therefore, the value of x is 4.
12.
In the inequality
2x - 1 > 7,
x can never be equal to 2!
Correct Answer
A. True
Explanation
In the given inequality 2x - 1 > 7, the goal is to solve for x. To isolate x, we first add 1 to both sides of the inequality, which gives 2x > 8. Then, we divide both sides by 2 to get x > 4. This means that x can take any value greater than 4. Since x cannot be equal to 2, the statement "x can never be equal to 2" is true.
13.
Problem Solving
The sum of a number and 7 is 33. What is the number?
Correct Answer
B. 26
Explanation
To find the number, we can set up an equation based on the information given. Let's call the number "x". The sum of the number and 7 is equal to 33, so we can write the equation as x + 7 = 33. To solve for x, we can subtract 7 from both sides of the equation. This gives us x = 33 - 7, which simplifies to x = 26. Therefore, the number is 26.
14.
Problem solving
Jane paid P pesos, per day, for the replacement of the tiles in her bathroom. If labor cost was 250 pesos a day and each tile costs 15 pesos, how much will it cost her in a day T tiles are used?
Correct Answer
A. P = 15T + 250
Explanation
Pattern
Y = ax + b
b = labor cost which is constant per day
a = number of tile which may change depending on how many are used...
Y is the P or the total cost per day..cause it depends on the number of tiles used in a day.
X is the T which independent variable...
15.
Jolibee is X years old now... . How old will he bee two years from now?
Correct Answer
C. X + 2
Explanation
Jolibee is currently X years old. Two years from now, he will be X + 2 years old.