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3 years ago

Determine whether each number is rational or irrational

Mathematics

1 answer:

Ratling [72]3 years ago

8 0

A is rational

B is irrational

Product of a and b is irrational.

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The quotient of 5n^2(m^2+2m-3)/10n(m^2-3m+2) divided by n^2(m^2-3m-18)/4n^2(m^2-8m+12)

slavikrds [6]

$\dfrac{ 5n^2(m^2+2m-3)}{10n(m^2-3m+2)} \div \dfrac{n^2(m^2-3m-18)}{4n^2(m^2-8m+12)}$

$\dfrac{ 5n^2 (m + 3)(m - 1)}{10n( (m - 1)(m - 2)} \div \dfrac{n^2(m + 3)(m - 6)}{4n^2(m - 2)(m - 6)}$

$\dfrac{ 5n^2 (m + 3)(m - 1)}{10n( (m - 1)(m - 2)} \times \dfrac{4n^2(m - 2)(m - 6)}{n^2(m + 3)(m - 6)}$

$= 2n$

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3 years ago

A recently negotiated union contract allows workers in a shipping department 24 minutes for rest, 10 minutes for personal time,

Alik [6]

Answer:7.125 min

Step-by-step explanation:

Given

Resting time =24 min

Personal time=10 min

Delay=14 min

Observed Time=6min/cycle

Performance Rating=95%

Allowance Time=Rest time+Personal time+delay

Allowance time=24+10+14=48 min

$Allowance %=\frac{Allowance Time}{Total Time}=\frac{48}{4\times 60}=20 \%$

Allowance Factor= $\frac{1}{1-0.20}=\frac{5}{4}$

Calculate the Normal Time

Normal time=Observed time $\times$ personal Time=6\times 0.95=5.7 min

Standard time=Normal time $\times$ Allowance Factor

Standard time = $NT\times Allowance factor=5.7\times 1.25$ =7.125 min

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3 years ago

Leona has a large bag of apples. There are 180 apples in the bag. She uses 14of the apples to make some juice. She uses 20% of t

andreev551 [17]

Answer:

132.8 are left enjoy

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2 years ago

At a school event there were 96 girls .the ratio of number of girls to the number of boys was 4:5

valina [46]

144, 4:6 simplifies to 2:3, if you divide 96 by 2 you get 48, and 48 x 3 = 144

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3 years ago

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ______ units. The poi

nalin [4]

Circle formula
(x-h)^2+(y-k)^2=r^2 where (h,k) is the center
and r=radius

to find the radius
we are given one of the points and the center
distnace from them is the radius
distance formula
D= $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$
points (-3,2) and (1,5)
D= $\sqrt{(1-(-3))^{2}+(5-2)^{2}}$
D= $\sqrt{(4)^{2}+(3)^{2}}$
D= $\sqrt{16+9}$
D= $\sqrt{25}$
D=5

center is -3,2
r=5
input
(x-(-3))^2+(y-2)^2=5^2
(x+3)^2+(y-2)^2=25 is equation
radius =5
input -7 for x and solve for y
(-7+3)^2+(y-2)^2=25
(-4)^2+(y-2)^2=25
16+(y-2)^2=25
minus 16
(y-2)^2=9
sqqrt
y-2=+/-3
add 2
y=2+/-3
y=5 or -1

the point (-7,5) and (7,-1) lie on this circle

radius=5 units
the points (-7,5) and (-7,1) lie on this circle

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3 years ago