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motikmotik
3 years ago
7

Bob, Celia, Sam and Daniel gave money to buy their boss a retirement gift. Sam and Daniel each gave the same amount of money. Ce

lia gave $12 more than Daniel. Bob gave half as much as Celia gave. If the four workers contributed a total of $81, how much did Celia give?
Mathematics
1 answer:
cricket20 [7]3 years ago
8 0

here's the equation: x+x+(x+12)+ 1/2(x+12) =81

combine like terms

(x+x+x+1/2x) + (12+6) = 81

simplify

7/2x +18=

subtract 18 from both sides.

7/2x=63

multiply by reciprocal (aka 2/7)

x=18

18+12=30 so celia gave 30.

Hope this helps!

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Answer:

h = 36.9 cm

Step-by-step explanation:

The function given to us is:

h(t) = 51 + 20 sin(225t)

Where h(t) is the function of the height in centimeters while t represents the time in seconds.

We have to find the height h(t) when the time is equal to 19 seconds.

Substitute t=19 into the given function

h(19) = 51 + 20 sin(225(19))

h(19) = 51 + 20 sin(4275)

h(19) = 51 + 20 (-0.7071)

h(19) = 51 + (-14,1421)

h(19) = 36.8579 cm

Rounding off to nearest 10th

h = 36.9 cm

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3 years ago
1) ACT Prep: Linear Pair angles have measures (6x -9)°and (9x-6)° 1.
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The measure of angles are 69 degree and 111 degree

<em><u>Solution:</u></em>

Given is linear pair angles

The measure of angles are: (6x - 9) degrees and (9x - 6) degrees

A linear pair of angles is formed when two lines intersect.

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Therefore,

(6x - 9) + (9x - 6) = 180\\\\\text{Remove the parenthesis and solve}\\\\6x - 9 + 9x - 6 = 180\\\\\text{Combine the like terms}\\\\6x + 9x - 15 = 180\\\\15x - 15 = 180\\\\\text{Move the constants to right side}\\\\15x = 180 + 15\\\\15x = 195\\\\x = 13

<em><u>Thus the measure of angles are:</u></em>

(6x - 9) \text{ degrees } = 6(13) - 9 = 78-9 = 69 \text{ degrees }\\\\(9x - 6) \text{ degrees } = 9(13) - 6 = 117 - 6 = 111 \text{ degrees }

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