(1)At the begining of her math class, Mrs. Reno gives a warm-up problem. She says, "I am thinking of a number such that 6 is less than the product of 7 and this number is 85." Which number is she thinking of?
A-11
B-84
C-13
D-637
___________________________________
(2)If x and y are defined as indicated in the table, which epautaion correctly reprsents the relationship between x and y?
Table-
x | y
2 1
3 3
5 7
7 11
Possible Answers-
A)y=x+2
B)y=2x+3
C)y=2x+2
D)y=2x-3
Please if you CAN HELP WITH either one of my problems.
I would be greatful!
thanx.
Please if you could...Show WORK!
to help me out.
(1) Mrs. Reno says that 6 is less than the product of 7 and a number, and that product is 85. So we can write this as an inequality: 7x > 6 and 7x = 85.
To solve this, we start with 7x > 6 and divide both sides by 7: x > 6/7.
Then, we have 7x = 85. Dividing both sides by 7 gives us x = 85/7, which is approximately 12.14.
So, the number Mrs. Reno is thinking of is approximately 12.14. None of the given answer choices match this value, which means none of them are the correct answer. I'm afraid this is more of a math problem than a joke situation!
(2) Let's look at the table and find the relationship between x and y:
x | y
2 | 1
3 | 3
5 | 7
7 | 11
Looking at the y-values, we can observe that each y-value is 2 more than double the x-value. Let's check the possible answer choices:
A) y = x + 2: This equation is not correct because the y-values are not equal to the x-values plus 2.
B) y = 2x + 3: This equation is also not correct because the y-values are not equal to twice the x-values plus 3.
C) y = 2x + 2: This equation is the correct one! The y-values in the table can be obtained by multiplying the x-value by 2 and adding 2.
D) y = 2x - 3: This equation is not correct either because the y-values are not equal to twice the x-values minus 3.
So, the correct equation that represents the relationship between x and y is y = 2x + 2. I hope you found this answer equation hilarious!
(1) To solve this problem, we need to find the number that satisfies the given conditions.
According to the problem, we are told that the product of 7 and this unknown number is 85. So, we can set up the equation:
7 * x = 85
To find the value of x, we need to isolate it. Divide both sides of the equation by 7:
x = 85 / 7
By performing the division, we find that x is approximately equal to 12.142857.
To determine which answer choice corresponds to this value, we can round x to the nearest whole number. In this case, x is closer to 12 than to 13. Therefore, the correct answer is A-11.
(2) To determine the relationship between x and y in the given table, we need to observe the pattern and identify the equation that best represents it.
Looking at the table, we can see that as the value of x increases by 1, the value of y increases by 2. This suggests a linear relationship between x and y.
To represent this linear relationship in the form of an equation, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can calculate the change in y divided by the change in x using the values from the table:
slope (m) = (change in y) / (change in x) = (7 - 1) / (5 - 2) = 6 / 3 = 2
Therefore, the slope (m) is 2.
To find the y-intercept (b), we can use one of the points from the table. Let's choose (2, 1).
Plugging the values into the equation y = mx + b, we have:
1 = 2 * 2 + b
Solving for b, we subtract 4 from both sides:
1 - 4 = b
-3 = b
Therefore, the y-intercept (b) is -3.
Putting it all together, the equation that represents the relationship between x and y is:
y = 2x - 3
Hence, the correct answer is D- y = 2x - 3.