Answer: m∡7 = 57° .
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Explanation:
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m∡7 = m∡1 ; SInce these angles are vertical; and vertical angles are congruent.
m∡1 + m∡2 = 180 ; since these angles are supplementary; and by definition; supplementary angles "add up" to 180.
Given: m∡2 = 123 ;
m∡1 + 123 = 180 ;
Since m∡1 = m∡7 ; and we wish to find: "m∡7" ; we can rewrite as:
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m∡7 + 123 = 180 ; solve for "m∡7" ;
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Subtract "123" from EACH SIDE of the equation:
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m∡7 + 123 - 123 = 180 - 123 ;
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m∡7 = 57° .
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Answer:
8.5
Step-by-step explanation:
10x+2=9x(3)
10x+2=27x
2=17x
x=8.5
Answer: P(22 ≤ x ≤ 29) = 0.703
Step-by-step explanation:
Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = output of the machine in ounces per cup.
µ = mean output
σ = standard deviation
From the information given,
µ = 27
σ = 3
The probability of filling a cup between 22 and 29 ounces is expressed as
P(22 ≤ x ≤ 29)
For x = 22,
z = (22 - 27)/3 = - 1.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.047
For x = 29,
z = (29 - 27)/3 = 0.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.75
Therefore,
P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703
our X is 30 because 3x = 90 and if we divide that by 3 then we are left with 30, I knew it was equal to 90 degrees because of the little red box that symbolizes a 90 degree angle.
So now that we know X = 30 we can plug it in for (2x + 3y)
2(30) + 3y is equal to (60 + 3y) and if we equal that to the other side 3x and plug in for x on that side, we have a new equation of 90 = 60 + 3y so then from here we subtract 60 from both sides and are left with 30 = 3y and finally we divide 3
and our final answer is Y = 10 (((((((((((((((((((((((((((((:
