Can you check the folowing problems.
1. 8(10) + 8(4) = 8(14) is an example of which property?
A. Distributive property
B. Associative property
C. Identiy property
D. Commutative property
Ans:A
2. By Saturday night, 3 inches of rain had fallen in Happy Valley. The weekend
forecast predicted at least 8 inches of rain. How much more rain must fall on Sunday for this forecast to be correct?
A. at most 5 in.
B. at least 5 in.
C. at most 11 in.
D. at least 11 in.
Ans: B. at least 5 in.
3. Solve 5 - (x/9) <= 17
A. x >= 108
B. x >= -108
C. x <= 108
D. x <= -108
Ans: B. x >= -108
4. In a photograph, the height of table is 3.8cm. If the scale factor is 1/25, what is the actual height of the table?
Ans: 3.8(25) = 95cm
But not sure how to prove to use 25 or represent it. I know that it should be the whole since 1/25 is the reduced scale. Can you explain?
5. Solve (2/9)x + 2 = 1/18
(2/9)x = 1/18 - 2
(2/9)x = 1/18 - 1 18/18
(2/9)x = -1 17/18
(2/9)x = -35/18
(9/2)(2/9)x = -35/18(9/2)
x = -35/4
Ans x = -8 3/4
all correct
4.
ratio of model to full scale is 1/25
1/25 = 3.8/h
h = 25 * 3.8 = 95 yes
THank you.
Sure! Let's go through each problem step by step:
1. The problem states 8(10) + 8(4) = 8(14), and asks which property is being used. To figure this out, we need to simplify both sides of the equation.
On the left side, we perform the multiplication within the parentheses: 8(10) = 80 and 8(4) = 32.
Now, our equation becomes 80 + 32 = 8(14).
We simplify further by adding 80 and 32, which gives us 112. So our equation now reads 112 = 8(14).
To determine which property is being used, let's examine the right side of the equation. The expression 8(14) means multiplying 8 by 14, which yields 112.
Since both sides of the equation are equal, we can conclude that the Distributive Property is being used.
Therefore, the answer is A. Distributive property.
2. The problem gives us information about the amount of rain that has fallen in Happy Valley and the forecasted amount for the weekend. We need to determine how much more rain must fall on Sunday for the forecast to be correct.
According to the information provided, 3 inches of rain had fallen by Saturday night, and the forecast predicts at least 8 inches of rain in total.
To find out how much more rain must fall on Sunday, we subtract the amount that has already fallen from the forecasted total.
8 inches (forecasted total) - 3 inches (rain fallen by Saturday night) = 5 inches.
This calculation tells us that at least 5 more inches of rain must fall on Sunday for the forecast to be correct.
Therefore, the answer is B. at least 5 in.
3. The problem gives us an inequality to solve: 5 - (x/9) <= 17.
To solve this inequality, we need to isolate the variable x.
First, we subtract 5 from both sides of the inequality: 5 - 5 - (x/9) <= 17 - 5.
Simplifying this gives us: -x/9 <= 12.
Next, we multiply both sides of the inequality by -9 to get rid of the fraction and keep the inequality direction the same.
Remember, multiplying or dividing by a negative number flips the inequality sign: (-9)(-x/9) >= 12(-9).
Simplifying this leads to: x >= -108.
Therefore, the answer is B. x >= -108.
4. In this problem, we are given the height of a table in a photograph (3.8 cm) and the scale factor (1/25). We need to find the actual height of the table.
To do this, we multiply the height in the photograph (3.8) by the scale factor (1/25): 3.8 * (1/25).
Multiplying these two fractions gives us: 3.8/25.
To get the decimal equivalent, we divide 3.8 by 25, which equals 0.152.
So the actual height of the table is 0.152 cm.
If you need the answer in centimeters, you can multiply 0.152 by 100 to convert it to centimeters: 0.152 * 100 = 15.2 cm.
Therefore, the actual height of the table is 15.2 cm.
5. In this problem, we need to solve the equation (2/9)x + 2 = 1/18 for x.
First, let's eliminate the fraction on the left side by multiplying both sides of the equation by the least common denominator, which is 18 in this case.
By multiplying (2/9)x by 18, we get (18/9)x = 2x. The equation now becomes: 2x + 2 = 1/18 * 18, which simplifies to 2x + 2 = 1.
Next, we subtract 2 from both sides of the equation: 2x + 2 - 2 = 1 - 2.
This gives us 2x = -1.
To solve for x, we divide both sides of the equation by 2: (2x)/2 = -1/2.
Simplifying further, we have x = -1/2.
However, it seems there was a mistake made during the calculation. Let's correct it.
To find x, we divide both sides of the equation by 9/2 and simplify: (9/2)(2/9)x = -35/18 / 9/2.
This gives us x = -35/4, which can be written as x = -8 3/4.
Therefore, the correct answer is x = -8 3/4.
I hope this explanation helps! Let me know if you have any further questions.