5. Sarahi found the distance between two points on a coordinate plane to be √74. Can this answer be simplified? Explain.
1 answer:
Answer:
The answer can't be simplified.
Step-by-step explanation:
In order to answer the question, you have to calculate the prime factors of 74 to see if the expression can be simplified.
If at least one of the prime factors has an exponent bigger or equal than 2 (because the expression has a squareroot), then the expression can be simplified using the properties of exponential numbers and irrational numbers to extract the factor or the factors from the squareroot.
(For example the property )
Calculating the prime factors:
74/2 = 37 but 37 is a prime number so:
37/37 =1
74 = 2 x 37
Therefore, can't be expressed as a simplier number.
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Answer:
Range is {y | y ≥ –11}
Step-by-step explanation:
This is quadratic equation.
<em>A quadratic equation's range can be found if we find the vertex.</em>
For quadratic equations that have a positive number in front of , it is upward opening and thus <u>all the numbers greater than or equal to the minimum value of vertex is the range.</u>
The formula for vertex of a parabola is:
Vertex =
Where,
is the coefficient of
is the coefficient of
From our equation given, and
Now, coordinate of vertex is
coordinate of the vertex IS THE MINIMUM VALUE that we want. We get this by plugging in the
value [
] into the equation. So we have:
Hence, the range would be all numbers greater than or equal to
Third answer choice is the right one.
Answer:
Step-by-step explanation:
So we have the expression:
Recall the order of operations or PEMDAS:
P: Operations within parentheses must be done first. On a side note, do parentheses before brackets.
E: Within the parentheses, if exponents are present, do them before all other operations.
M/D: Multiplication and division next, whichever comes first.
A/S: Addition and subtraction next, whichever comes first.
(Note: This is how the order of operations is traditionally taught and how it was to me. If this is different for you, I do apologize. However, the answer should be the same.)
Thus, we should do the operations inside the parentheses first. Therefore:
The parentheses is:
Square the 6 and the 4:
Do the operations from left to right. 36 divided by 3 is 12. 12 times 4 is 48:
Therefore, the original equation is now:
Multiply with the brackets:
Subtract with the brackets:
Two negatives make a positive. Add:
Therefore: