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NeX [460]
3 years ago
7

PQR is congruent to JKL. Which sequence of transformations maps PQR onto JKL?

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
7 0
Reflection over the y axis and a translation 2 units down.
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Ms. Liebowitz has a choice of driving or flying from Morgantown, West Virginia to Washington, D.C. for a one-day business trip.
den301095 [7]

Answer:

Step-by-step explanation:

If she travels by air, she will be able to work seven hours in D.C. work four hours once there. Her expected income from each hour of work in D.C. is $40. This means that the total amount that she earns in 7 hours would be

40 × 7 = $280

if she drives, she will only have time to work four hours once there. This means that the total amount that she earns in 4 hours would be

40 × 4 = $160

The difference in both amounts would be

280 - 160 = $120

she will chose to fly if and only if the price differential (air cost minus driving cost) is less than $120

7 0
3 years ago
Determine the astm grain size number if 33 grains per square inch are measured at a magnification of 270×
strojnjashka [21]
8.9

The equation for the grain size is expressed as the equality:
Nm(M/100)^2 = 2^(n-1)
where
Nm = number of grains per square inch at magnification M.
M = Magnification
n = ASTM grain size number

Let's solve for n, then substitute the known values and calculate.
Nm(M/100)^2 = 2^(n-1)

log(Nm(M/100)^2) = log(2^(n-1))
log(Nm) + 2*log(M/100) = (n-1) * log(2)
(log(Nm) + 2*log(M/100))/log(2) = n-1
(log(Nm) + 2*log(M/100))/log(2) + 1 = n

(log(33) + 2*log(270/100))/log(2) + 1 = n
(1.51851394 + 2*0.431363764)/0.301029996 + 1 = n
(1.51851394 + 0.862727528)/0.301029996 + 1 = n
2.381241468/0.301029996 + 1 = n
7.910312934 + 1 = n
8.910312934 = n

So the ASTM grain size number is 8.9

If you want to calculate the number of grains per square inch, you'd use the
same formula with M equal to 1. So:
Nm(M/100)^2 = 2^(n-1)
Nm(1/100)^2 = 2^(8.9-1)
Nm(1/10000) = 2^7.9
Nm(1/10000) = 238.8564458
Nm = 2388564.458

Or about 2,400,000 grains per square inch.
7 0
3 years ago
What is the value of 5^3i^9?
Yakvenalex [24]

Answer:

\displaystyle 125^i

Step-by-step explanation:

<u>Extended Information </u><u>on</u><u> </u><u>the</u><u> Complex Number System</u>

\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\:[all\:multiples\:of\:four]

I am joyous to assist you at any time.

All work is shown above. ↑

4 0
3 years ago
Plz help I don’t understand how to find x?
Oliga [24]

Answer:

x = -4

Step-by-step explanation:

First lets add 82 + 55 which equals 137, then 137 +47 which equals 184

Now we know that a triangle equals 180 degrees (cannot go over 180), so this tells us x is a negitive number.

-x + 184 = 180

-x = -4

Another way to look at it is; 184 minus what equals 180? 4 does, so it translates into -4.

4 0
3 years ago
Read 2 more answers
You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. Wha
aleksandr82 [10.1K]

Answer:

The approximate height of the paint can is 8.2 in

Step-by-step explanation:

we know that

The volume of the cylinder ( can of paint) is equal to

V=\pi r^{2} h

we have

V=231\ in^{3}

r=3\ in

\pi=3.14

Substitute the values and solve for h

231=(3.14)(3)^{2} h

h=231/(3.14*9)=8.2 in

3 0
2 years ago
Read 2 more answers
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