How do I factorize a quadratic expression ?
1 answer:
Answer:
Please check below the step-by-step explanation.
Step-by-step explanation:
Considering the quadratic expression
" "
For example, multiplying and
together will bring
i.e.
Therefore, and
are factors of
Keywords: factorize, quadratic expression
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A right triangle will be formed with 2.2 km as the hypotenuse, 0.5 degrees as the angle, and an unknown height (see attachment).
Recall the trigonmetric ratios sine, cosine, and tangent that can be used for right triangles.
Sin<span>θ = opposite side/hypotenuse
</span>Cos<span>θ = adjacent side/hypotenuse
</span>tan<span>θ = opposite side / adjacent side
</span>θ (theta) refers to the angle (not the right angle). In this case, θ is the given angle of 0.5°.
In this problem, you will use sine because there is a side opposite to the angle (the unknown side h) and the hypotenuse, and sine relates those two sides.
Let the variable h represent the unknown opposite side, the height.
sin(0.5°) = h / (2.2km)
h = (2.2km)sin(0.5<span>°)
h = 0.019 km
Hope I helped! If you have questions on any of the steps, please comment below.</span>
Recall the trigonmetric ratios sine, cosine, and tangent that can be used for right triangles.
Sin<span>θ = opposite side/hypotenuse
</span>Cos<span>θ = adjacent side/hypotenuse
</span>tan<span>θ = opposite side / adjacent side
</span>θ (theta) refers to the angle (not the right angle). In this case, θ is the given angle of 0.5°.
In this problem, you will use sine because there is a side opposite to the angle (the unknown side h) and the hypotenuse, and sine relates those two sides.
Let the variable h represent the unknown opposite side, the height.
sin(0.5°) = h / (2.2km)
h = (2.2km)sin(0.5<span>°)
h = 0.019 km
Hope I helped! If you have questions on any of the steps, please comment below.</span>
Answer:
1st, 4th and 6th statements are true.
Step-by-step explanation:
We have been given two dot-plots and we are asked to select all the true statements about given dot plots.
Let us write all the data points of both dot plots.
Data set 1:
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 7.
Data set 2:
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4.
1. The mean of data set 1 is greater than the mean of data set 2.
Let us find mean of both data sets.
We can see that mean of data set 1 is greater than mean of data set 2, therefore, 1st statement is true.
2. The mean of data set 1 is equal to the mean of data set 2.
Since mean of data set 1 is greater than mean of data set 2, therefore, 2nd statement is false.
3. The median of data set 1 is greater than the median of data set 2.
Since data set 1 has 19 data points, so median of data set 1 will be value of 10th data set, that is 2.
Our data set 2 has 18 data points, so median of data set 2 will be the average of 9th and 10th data points.
Since median of data set 2 is also 2, therefore, 3rd statement is not true.
4. The median of data set 1 is equal to the median of data set 2.
Since both data set's median is 2, therefore, 4th statement is true.
5. The standard deviation of data set 1 is smaller than the standard deviation of data set 2.
Using online SD calculator we get SD of data set 1 is 1.422 and SD of data set 2 is 0.936. Since 1.422 is greater than 0.936, therefore, 5th statement is false.
6. The data sets have the same interquartile range.
Since both data set's IQR is 2, therefore, 6th statement is true.