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3 years ago

Line segment TU has endpoints (-7,10) and (-6,-5). What is the length of TU to the NEAREST TENTH?

Mathematics

1 answer:

Sindrei [870]3 years ago

7 0

Answer: 15 units

Step-by-step explanation:

Given

The endpoints of the line segment are $(-7,10)\ \text{and}\ (-6,-5)$

The length of the line segment is given by the distance formula i.e.

$d=\sqrt{\left( x_2-x_1\right)^2+\left( y_2-y_1\right)^2}$

Insert the values,

$\Rightarrow d=\sqrt{\left( -6+7\right)^2+\left( -5-10\right)^2}\\\Rightarrow d=\sqrt{1^2+\left( -15\right)^2}\\\Rightarrow d=\sqrt{1+225}\\\Rightarrow d=15.0\ \text{units}$

Therefore, the length of line segment TU is 15 units

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3 years ago

For a certain candy, 20% of the pieces are yellow, 15% are red, 20% are blue, 20% are green, and the rest are brown. a

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Answer:

Step-by-step explanation:

Based on the question we are given the percentages of each of the types of candies in the bag except for brown. Since the sum of all the percentages equals 75% and brown is the remaining percent then we can calculate that brown is (100-75 = 25%) 25% of the bag. Now we can show the probabilities of getting a certain type of candy by placing the percentages over the total percentage (100%).

Brown: $\frac{25}{100}$
Yellow or Blue: $\frac{20}{100} +\frac{20}{100} = \frac{40}{100}$ ....add the numerators

Not Green: $\frac{80}{100}$ .... since the sum of all the rest is 80%

Stiped: $\frac{25}{100}$ .... there are 0 striped candies.

Assuming the <u><em>ratios/percentages</em></u> of the candies stay the same having an infinite amount of candy will not affect the probabilities. That being said in order to calculate consecutive probability of getting 3 of a certain type in a row we have to multiply the probabilities together. This is calculated by multiplying the numerators with numerators and denominators with denominators.

3 Browns: $\frac{25*25*25}{100*100*100} = \frac{15,625}{1,000,000} = \frac{1.5625}{100}$

the 1st and 3rd are red while the middle is any. We multiply 15% * (total of all minus red which is 85%) * 15% like so.

$\frac{15*85*15}{100*100*100} = \frac{19,125}{1,000,000} = \frac{1.9125}{100}$

None are Yellow: multiply the percent of all minus yellow three times.

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3 years ago

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Step-by-step explanation:

l x 3 = c

k + 5 = l

(c + l + k) x 2 = 25

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l = 11

k = 6

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4 years ago

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3 years ago

What is the average rate of change of the line whose equation is:

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Answer:

Rate of change = -12

Step-by-step explanation:

y − 3 = −12(x + 4)

Expanding, we have;

y - 3 = -12x - 48

y = -12x - 48 + 3

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Now, formula for rate of change is;

Rate of change = (y(x + h) - y)/h

y(x + h) is; y = -12(x + h) - 45

This gives;

Rate of change = (-12(x + h) - 45 + 12x + 45)/h

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