Find the LCM of 6 and 14.

Given: circle k(O), m LM = 164° m WK = 68°, m∠MLK = 65° Find: m∠LMW

Semenov [28]

Let P be a point outside the circle such that triangle LMP has legs coincident with chords MW and LK (i.e. M, W, and P are colinear, and L, K, and P are colinear). By the intersecting secants theorem,

$m\angle LPM=\dfrac{m\widehat{LM}-m\widehat{WK}}2\impliesm\angle LPM=48^\circ$

The angles in any triangle add to 180 degrees in measure, and $\angle MLK\congruent\angle MLP$ and $m\angle LMW=m\angle LMP$ , so that

$m\angle MLK+m\angle LPM+m\angle LMP=180^\circ$

$\implies\boxed{m\angle LMW=67^\circ}$

6 0

3 years ago

The rate of U.S. per capita sales of bottled water for the period 2007–2014 could be approximated by s(t) = 0.25t2 ? t + 29 gall

julsineya [31]

Answer:

117 gallons

Step-by-step explanation:

The expression that describes the rate of U.S. per capita sales of bottled water for the period 2007–2014 is:

$s(t) = 0.25t^2-t+29$

Since t=0 at 2007. At 2009 and 2013, t is:

$t_1=2009-2007 = 2\\t_2=2013-2007 = 6$

The definite integral of the expression from t=2 to t=6 is:

$s(t) = 0.25t^2-t+29\\\int\limits^6_2 {s(t)} \, dt= \int\limits^6_2 {(0.25t^2-t+29)} \, dt\\\int\limits^6_2 {s(t)} \,dt= (\frac{t^3}{12} -\frac{t^2}{2}+29t +c)|^6_2 \\S(6) -S(2) = (\frac{6^3}{12} -\frac{6^2}{2}+29*6 +c) - (\frac{2^3}{12} -\frac{2^2}{2}+29*2 +c)\\S(6) -S(2) = 117.333\ gallons$

Rounded to the nearest gallon, the estimated total U.S. per capita sales of bottled water from the start of 2009 to the start of 2013 is 117 gallons.

6 0

3 years ago

Triangle ABC is a right triangle.

Nastasia [14]

Answer:

mZA=50

mZB=28

mZC=90

value of x is 28 how i got it was 32-4.

5 0

2 years ago

Find x, y, and z x = 39 x = 29 y = 61 y = 29 z = 61 z = 29

nikdorinn [45]

answer:

x = 29

y = 29

z = 61

step-by-step explanation:

all angles in a triangle must equal 180 degrees.

we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.

the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.

so to figure out y,

we must add 61+90 and then subtract the sum of that from 180.

so, 61+90 = 150 and 180-151 = 29

therefore,

we can conclude that y = 29

now, to determine the degrees of x and z we do the same thing.

we already know one angle equals 90 degrees.

180-90 = 90

that concludes that x and z must have a sum of 90.

if we use our choices,

39+61 = 100 (no)

39+29 = 68 (no)

29+61 = 90 (CORRECT)

29+29 = 28 (no)

therefore, x = 29 and z = 61

so, in total :

x = 29

y = 29

z = 61

hope this helps :)

-audrey <3

5 0

3 years ago

(a) Work out 8 × 1/1/1 x 3 Give your answer as a mixed numbers

Mama L [17]

Answer:

well.. 1/1/1 would be 1.

8 x 3 = 24

24x 1 = 24

sooo the answer would be 24...

Step-by-step explanation:

3 0

1 year ago

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