∆ABC and ∆FDE are congruent by the criterion. (Use the three-letter abbreviation without spaces.)
2 answers:
Response:
x equals 11 and y equals 8.
Detailed explanation:
It is stated that ΔABC and ΔFDE are congruent.
The corresponding segments of congruent triangles are also congruent.
(CPCTC)
.... (1)
(CPCTC)
Subtracting 3 from both sides yields the following results.
So, x is found to be 11.
Inserting x=11 into equation (1).
Adding y to both sides leads to the following procedure.
Removing 3 from both sides produces the final result.
And we find y to be 8.
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Answer:
The recorded temperature is -0.675ºC.
Detailed explanation:
To tackle problems involving normally distributed samples, the z-score formula can be utilized.
In a distribution with mean and standard deviation
, the z-score for a specific measure X is calculated as follows:
The Z-score indicates how many standard deviations a given measure deviates from the mean. Once the Z-score is determined, we refer to the z-score table to obtain the corresponding p-value. This p-value represents the likelihood that the measure's value is less than X, thereby indicating the percentile of X. By taking 1 minus the p-value, we find the probability that the measure's value exceeds X.
For this scenario, we know that:
Assuming the thermometer readings follow a normal distribution with a mean of 0◦ and a standard deviation of 1.00◦C, this leads us to
We need to determine P25, which is the 25th percentile.
This represents the value of X corresponding to Z with a p-value of 0.25, thus we utilize , applicable between
and
.
The recorded temperature is -0.675ºC.
Answer:
Detailed solution:
Given:
The problem to solve is:
Convert the equation into the standard quadratic form , where
represent constants.
So, by adding to both sides, we get:
Note that .
The roots of this quadratic are found by applying the quadratic formula given as:
Substitute into the formula and calculate for
.
Hence, the roots are:
