Find two consecutive positive integers such that the square of the first decreased by 67 is equal to three times the second
Answers
Answer:
The numbers are 10 and 11.
Step-by-step explanation:
Let and
be consecutive positive integers.
When the problem says that the square of the first decreased by 67 this means and this is equal to three times the second
.
So will be our equation.
Next, we solve the equation:
Solve by factoring
Using the Zero Factor Principle: If ab = 0, then either a = 0 or b = 0, or both a and b are 0.
And
Because the numbers need to be positive integers, we only take x = 10 as a valid solution.
The numbers are 10 and 11.
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Answers
Answer:
R = {(10,2), (10,4), (10,6), (10,8), (2,10), (2,2), (2,4), (2,6), (2,4), (4,10), (4,2), (4,6), (6,10), (6,2), (6,4), (6,8)}
Step-by-step explanation:
A = (10, 1, 2, 3, 4, 5, 6)
B = (10, 1, 2, 3, 4, 5, 6, 7, 8)
R is a relation and defined as
R: A→B
R: The greatest common divisor of a and b is 2
To find the elements of R we need to find pair from A and B respectively.
R = {(10,2), (10,4), (10,6), (10,8), (2,10), (2,2), (2,4), (2,6), (2,4), (4,10), (4,2), (4,6), (6,10), (6,2), (6,4), (6,8)}
Now, these pairs were found by picking one element from A and checking with elements of B if they have a gcd of 2. If yes, they fall under the defined relation.
Answers
Use order of operations, or PEMDAS which stands for Parenthesis, Exponent, Division, Addition, and Subtraction.
Do those operations in that order. Can you try?
What will be the first thing you do here, according to PEMDAS?
Answers
Answer
4. E
use PEMDAS
5. 36+18=54 so C
plug in x
6. 15=5x
x=3 so C
11. B
break the absolute value into pos and neg components
12.D
is not equal to so open circle
2x=14
2x=8
so 4 and 7 with open circles
Step-by-step explanation:
On a coordinate plane, a function is shown. It approaches the x-axis in quadrant 2 and then increases into quadrant 1. It goes through (0, 1) and (1, 2).
On a coordinate plane, a function is shown. It approaches the y-axis in quadrant 4 and approaches y = 2 in quadrant 1. It goes through (1, 0) and (3, 1).
On a coordinate plane, a hyperbola is shown.
Answers
Answer:
the third one
Step-by-step explanation:
you can cross out parabola and hyperbola. the second graph is an exponential function because exponential functions go through (0,1), While logarithmic functions go through (1,0).
Answer:
Option 3
Step-by-step explanation:
Edge 2021
Answers
Final answer:
The number 68,979 is divisible by 3 but not by 5, 6, or 11.
Explanation:
To test a number for divisibility by 3, we sum up its individual digits. If the sum is divisible by 3, then the number itself is divisible by 3. For the number 68,979, the sum of its digits is 6 + 8 + 9 + 7 + 9 = 39. Since 39 is divisible by 3, 68,979 is also divisible by 3.
To test a number for divisibility by 5, we simply check if the last digit is either 0 or 5. In the number 68,979, the last digit is 9, which is neither 0 nor 5. Therefore, 68,979 is not divisible by 5.
To test a number for divisibility by 6, we need to check if it is divisible by both 2 and 3. From the previous tests, we already know that 68,979 is divisible by 3, so we now need to check if it is divisible by 2. Since the last digit is 9, which is an odd number, 68,979 is not divisible by 2, and therefore not divisible by 6.
To test a number for divisibility by 11, we take the alternating sum of its digits. In this case, we have 6 - 8 + 9 - 7 + 9 = 9. Since 9 is not divisible by 11, 68,979 is not divisible by 11.
Learn more about divisibility here:
A. 4.1 ≤ h ≥ 4.3, alkaline
B. 4.1 < h < 4.3, alkaline
C. 4.1 ≤ h ≤ 4.3, acidic
D. 4.1 ≤ h < 4.3, acidic
Answers
If we are to write the pH range for the Jerry's Fizzy Cola as an inequality and label the substance as acidic or alkaline, given the data 4.1 through 4.3 (inclusive), this would be the result:
C. 4.1 ≤ h ≤ 4.3, acidic