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Dahasolnce [82]
1 year ago
15

Patrick can paint a house by himself in t+4 hours. Karen can paint the same house by herself in t+9 hours. If they work together

, they can paint the house in t hours. How much time will it take for Patrick to paint the house by himself?
Mathematics
1 answer:
vladimir2022 [97]1 year ago
7 0

Patrick will be able to paint the home on his own after a ten-hour effort.

This is further explained below.

<h3>How much time will it take for Patrick to paint the house by himself?</h3>

Generally, the equation for time is  mathematically given as

1/(t+4)  +  1/(t+9)  = 1/t

Therefore

[1/(t+4)] (t+4)(t+9)(t) +  [1/(t+9)](t+4)(t+9)(t) =  (1/t)(t+4)(t+9)(t)  

(t² + 9t)  + (t² + 4t) = t² + 13t + 36

Place the equation on the left side of the page and make it equal to 0. Use the additive inverse property as follows:

t² + t² - t² + 9t + 4t - 13t - 36 = 0

2t² - t² + 13t - 13t - 36 = 0

t² - 36 = 0

Calculate the product of the difference of two squares using the formula t2 - 36 = 0.

Both the total and the difference between the two terms constitute the factors.

(t + 6) (t - 6) = 0

t + 6 = 0

t = -6

t - 6 = 0

t = 6

Choose the positive value for time, t = 6 hours.

It will take 10 hours for Patrick to paint the house alone.

Patrick will be able to paint the home on his own after a ten-hour effort.

Read more about time

brainly.com/question/28050940

#SPJ1

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Novay_Z [31]

Answer:

X =  1

Step-by-step explanation:

Just distribute properly, and distribute the fraction multiplying the numerator by 4 and 2

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Given the slopes of three lines, m1 = 2, m2 = 5. m3 = -4, which line would you say is
bagirrra123 [75]

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4 0
2 years ago
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The expression 120-15x represents how many invitations Luanne has to address after x days. The expression 120 + 15(7-x) represen
Aloiza [94]

Answer:

not possible.

Step-by-step explanation:

number of invitations luanne  has to address after x days = 120-15x

number of invitations  Darius has to address after x days =  120 + 15(7-x)

so, if the number of invitations should be the same for both of them,

we have to equate their number of invitations

120-15x =  120 + 15(7-x)

subtracting 120 from both the sides,

-15x = 15(7-x) = 105 -15x

adding we 15x on both sides, we wont find any solution for x.

so, this isnt possible or the question must be wrong.

8 0
3 years ago
I need help.Thanks!​
IgorLugansk [536]

Answer:

35×14-16

Step-by-step explanation:

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3 0
3 years ago
A tennis ball is 2 inch in diameter. How many tennis ball will fill a room of 20ft by 16ft by 18ft if no space wasted?
krek1111 [17]

The number of tennis ball that will fill the room is <u>1,371 tennis balls.</u>

<em><u>Given</u></em>:

Diameter of ball (d) : 2 inch

Radius (r) = half of diameter = 1 inch

Dimension of room = 20ft by 16ft by 18ft

Number of balls that will fill the room = Volume of each ball/volume of the room

Volume of the ball = volume of a sphere = \frac{4}{3} \pi r^{3}

Where,

r = 1

let \pi = 3.14

<em>Substitute</em>:

Volume = \frac{4}{3} \times 3.14 \times 1^{3} \\Volume = 4.2in^{3}

Volume of the room = 20 \times 16 \times 18 \\

= 5,760

Therefore:

number of tennis balls that will fill the room = \frac{5,760}{4.2} = 1,371.4

Therefore, the number of tennis ball that will fil the room will be <u>approximately 1,371.</u>

Learn more about volume here:

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7 0
2 years ago
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