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3 years ago

9

Elaine is 8 years younger than her brother Tyler. The sum of their age is 34. Define a variable and them write and solve an equa

tion to find Elaine's and Tyler's ages.

1 answer:

andreev551 [17]3 years ago

6 0

34÷T-8= a is the variable

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Two vertical poles of length 10 and 12 feet, respectively, stand 17 feet apart. A cable reaches from the top of one pole to the

Marat540 [252]

Answer:

$L=\sqrt{x^{2}+100}+\sqrt{x^{2}-34x+433} ft$

Step-by-step explanation:

let length of calble = L

distance from 10-foot pole = x ft

Moving from the top of the 10-foot pole to point x, we have

From the diagram that

$x^{2} +10^{2}=L_{1} ^{2} \\x^{2} + 100 = L_{1} ^{2}$

Take the square root of both sides

$\sqrt{x^{2}+100}=\sqrt{L_{1} ^{2}}\\ \sqrt{x^{2}+100}= L_{1}$

Moving from point x to the top of the 12-foot pole, we have

From the diagram that

$(17-x)^{2}+12^{2}=L_{2} ^{2} \\289-34x+x^{2} +144=L_{2} ^{2}\\x^{2} -34x+433=L_{2} ^{2}$

Take the square root of both sides

$\sqrt{x^{2}-34x+433}=\sqrt{L_{2} ^{2}} \\\sqrt{x^{2}-34x+433}=L_{2}$

Amount of cable used, L = L1 + L2

$L=\sqrt{x^{2}+100}+\sqrt{x^{2}-34x+433}$

3 0

3 years ago

Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 cm longer than twice the length of

g100num [7]

STEP 1:
convert meters to centimeters
100 cm= 1 meter

= 100 cm/m * 2.5 m
= 250 cm

STEP 2:
x= length of first shelf
2x+18= length of second shelf
x-12= length of third shelf
x+4= length of fourth shelf

since the whole board has to be used, add lengths of all shelves and set it equal to the whole length of the board (250 cm).

x + (2x+18) + (x-12) + (x+4)= 250 cm
combine like terms
5x + 10= 250
subtract both sides by 10
5x= 240
divide both sides by 5
x= 48

STEP 3:
find length of second shelf
= 2x + 18
= 2(48) + 18
= 114 cm

CHECK:
x + (2x+18) + (x-12) + (x+4)= 250
48 + (2(48)+18) + (48-12) + (48+4)= 250
48 + (96+18) + 36 + 52= 250
48 + 114 + 36 + 52= 250
250= 250

ANSWER: Shelf two is 114 cm.

Hope this helps! :)

8 0

3 years ago

I need to know the equation?

liberstina [14]

$55.00+$8.50=x x=$123

6 0

3 years ago

Read 2 more answers

Samantha is deciding between two different movie streaming sites to subscribe to. Plan A costs $18 per month plus $1 per movie w

WARRIOR [948]

Answer:

Samantha would have to watch 4 Movies so x=4

Step-by-step explanation:

6 0

3 years ago

Anya’s team won 4 games out of every 9 games this season. If the team played 45 games, how many games did they win?

tiny-mole [99]

Answer:20

Step-by-step explanation:4:9

9x5=45

4x5=20

20:45

8 0

3 years ago