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3 years ago

Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?

Mathematics

2 answers:

snow_lady [41]3 years ago

3 0

The converse alternate exterior angles theorem justifies why lines j and k must be parallel.

The converse alternate exterior angles theorem states that if two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

prisoha [69]3 years ago

3 0

Answer:

Step-by-step explanation:

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What two mixed numbers between 3 and 4 have a product of 9 and 12

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It's a trick question. There are an infinite number of mixed numbers between 3 and 4 that can multiply to equal 12 (for example, 3 and 3/7 times 3 and 1/2), but there are no mixed numbers between 3 and 4 that can multiply to equal 9. 3 times 3 is not between them but is 3, but that quantity is excluded because 3<x<4. Anything even a small bit above the number 3 would have to be multiplied by 2 and some fraction, which would not be between 3 and 4.

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3 years ago

Rewrite the perimeter formula, P = 2/ + 2w, to solve for the length, I, and then

Vinvika [58]

P = 2l + 2w

Subtract both sides by 2w

P - 2w = 2l

Divide both sides by 2

(P - 2w) / 2 = l

In our problem,

w = 7 in

P = 42 in

Let's plug our values into the formula above.

(42 in - 2(7 in) / 2 = l

(42 in - 14 in) / 2 = l

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3 years ago

Find the values of the measures shown when each value in the data set increases by 25. Mean: 109 Median: 104 Mode: 96 Range: 45

Vikki [24]

Answer:

The new values are as follows:

Mean: 134

Median: 129

Mode: 121

Range=45

Standard Deviation=3.6

Step-by-step explanation:

When a k real number is added to all the elements of the dataset, the new measures of center (mean, median, and mode) are simply found by adding the value k to the previous values. Thus

$Mean_{new}=Mean_{old}+k$

Here $Mean_{old}$ is 109 and k is 25 thus

$Mean_{new}=Mean_{old}+k\\Mean_{new}=109+25\\Mean_{new}=134$

Similarly

$Median_{new}=Median_{old}+k$

Here $Median_{old}$ is 104 and k is 25 thus

$Median_{new}=Median_{old}+k\\Median_{new}=104+25\\Median_{new}=129$

Also

$Mode_{new}=Mode_{old}+k$

Here $Mode_{old}$ is 96 and k is 25 thus

$Mode_{new}=Mode_{old}+k\\Mode_{new}=96+25\\Mode_{new}=121$

When a k real number is added to all the elements of the dataset, the new measures of variation (range and standard deviation) remain the same thus.

$Range_{new}=Range_{old}\\Range_{new}=45$

Similarly

$Standard\ Deviation_{new}=Standard\ Deviation_{old}\\Standard\ Deviation_{new}=3.6$

So the new values of mean, median, mode, range, and standard deviation are 134, 129, 121, 45, and 3.6 respectively.

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3 years ago