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sleet_krkn [62]
3 years ago
13

Write these two statements as a biconditional: If a triangle is equilateral then it is equangular and if a triangle is equiangul

ar then it is equilateral.
Mathematics
1 answer:
dexar [7]3 years ago
8 0

Answer:

If a triangle is equilateral, then it must also be equiangular and vice versa.

Step-by-step explanation:

A biconditional statement denotes that both a statement AND its reciprocal statement must be true.

Given the two statements:

If a triangle is equilateral, then it must also be equiangular

and

If a triangle is equiangular, then it must also be equilateral.

As both of these statements are always true, we can combine them into one biconditional statement (meaning two conditions are met)

If a triangle is equilateral, then it must also be equiangular and vice versa.  

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In a fruit cocktail, for every 30 ml of orange juice you need 20 ml of apple juice and 50 ml of coconut milk. What proportion of
KengaRu [80]

Answer:

first things first, you need to find out how much juice you have: 30 + 20 + 50 = 100, so 100 ml of juice. all together, the juice is 100%, or 1. separated, the amounts are 30%, 20%, and 50%, therefore the amount of coconut milk in the cocktail you have is 50%, or 1/2.

3 0
3 years ago
The given line segment has a midpoint at (3, 1).
Katena32 [7]

Answer:

y=\frac{1}{3}x

Step-by-step explanation:

The given line segment has a midpoint at (3, 1) and goes through (2, 4), (3, 1), and (4, -2). We can use any two of the three points to calculate the equation of the line. Let us use the points (2, 4) and (4, -2)

Therefore the line goes through (2, 4) and (4, -2). The equation of a line passing through (x_1,y_1)\ and\ (x_2,y_2) is:

\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}.

Therefore the line passing through (2, 4) and (4, -2) has an equation:

\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\\\frac{y-4}{x-2}=\frac{-2-4}{4-2}\\\frac{y-4}{x-2}=\frac{-6}{2}\\y-4=x-2(-3)\\y-4=-3x+6\\y=-3x+10

Comparing with the general equation of line: y = mx + c, the slope (m) = -3 and the intercept on the y axis (c) = 10

Two lines are said to be perpendicular if the product of their slope is -1. If the slope of line one is m1 and the slope of line 2 = m2, then the two lines are perpendicular if:

m_1m_2=-1.

Therefore The slope (m2) of the perpendicular bisector of y = -3x + 10 is:

m_1m_2=-1\\-3m_2=-1\\m_2=\frac{1}{3}

Since it is the  perpendicular bisector of the given line segment, it passes through the midpoint (3, 1). The equation of the perpendicular bisector is:

\frac{y-y_1}{x-x_1}=m\\\frac{y-1}{x-3}=\frac{1}{3}\\ y-1= \frac{1}{3}(x-3)\\ y-1=\frac{1}{3}x-1\\y=\frac{1}{3}x

the equation, in slope-intercept form, of the perpendicular bisector of the given line segment is y=\frac{1}{3}x

7 0
3 years ago
Read 2 more answers
Use a related equation that has the variable on one side. Then simplify the other side. T/3 = 15. (A t = 15 ÷ 3; t = 5.)
gregori [183]
It’s D bc Dt= 15x3 and it’s not that hard to solve
6 0
3 years ago
Mr. Wilson is giving his students a vocabulary test tomorrow over all the terms they have learned from this semester. Today, he
Y_Kistochka [10]
The population in the above situation is the total number of students under Mr. Wilson.

A sample is a part of the population that may best represent the population. There is no sample  in the above situation because Mr. Wilson made all students pick 5 note cards. He will be able to determine the performance of each student based on their performance in picking 5 note cards and defining the terms in each card.




5 0
3 years ago
A manufacturer of new light bulbs claims the average lifetime of its long-life bulb is more than 4000 hours. To test this claim,
natka813 [3]

Answer: C. 12.5

Step-by-step explanation:

Given : A manufacturer of new light bulbs claims the average lifetime of its long-life bulb is more than 4000 hours.

Population mean :  \mu=4000

Sample size : n= 100

Sample mean : \overline[x}=4500

Standard deviation: s=400

The value of test-statistic is given by :-

z=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}\\\\\Rightarrow\ z=\dfrac{4500-4000}{\dfrac{400}{\sqrt{100}}}\\\\\Rightarrow\ z= 12.5

Hence, the value of the test statistic for this problem is 12.5.

5 0
3 years ago
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