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3 years ago

The length of a rectangle is 15ft greater than the width. The area is 100 square ft. Find the length and the Width.

Mathematics

2 answers:

gogolik [260]3 years ago

7 0

Step-by-step explanation:

so let's say that the width is x then the length is x+15

and the area of a square is length times width

x(x+15)=100

x^2+15x-100=0

(x+20)(x-5)=0

x=5 or x=-20 but a side length can't be negative so x would equal 5

Length=x+15 with 5 as x

Length=20

Width=5

Hope that helps :)

cluponka [151]3 years ago

5 0

Answer:

Let the Width be x then ATQ ,length would be x+15

Area of a Rectangle

$length \times width$

Step-by-step explanation:

$(x + 15) \times x = 100 \\ x {}^{2} + 15x = 100 \\ x {}^{2} + 15x - 100 = 0 \\ x {}^{2} + 20x - 5x - 100 = 0 \\ x(x + 20) - 5x(x + 20) \\ (x - 5)(x + 20) \\ so...... \\ x = 5 \:$

<h2>x = 5=> Width</h2><h2>x +15 = 20=> Length </h2>

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Butoxors [25]

a function that model the number of people that receives email in week t is $P(t)=37(4)^{\frac{t}{9.1}}$ .

<u>Step-by-step explanation:</u>

Here we have , Tobias sent a chain letter to his friends . The number of people who receives the email increases by a factor of 4 in every 9.1 weeks , and can be modeled by a function P, which depends on the amount of time t weeks . Tobias initially sent letter to 37 friends . We need to write a function that model the number of people that receives email in week t . Let's find out:

Basically it's an exponential function as

$f(x) = e^{ax}$ , In question initial value is 37 & and for every 9.1 weeks there is increase in people by a factor of 4 i.e.

⇒ $P(t)=37(4)^t$

But , wait ! People increase in every 9.1 weeks not every week so modified equation will be :

⇒ $P(t)=37(4)^{\frac{t}{9.1}}$

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3 years ago

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Airida [17]

Answer:

The answer to the first question is B.) The student should have subtracted the 4 first, instead of adding, because it is positive originally. And the answer to the second one is D.) Distribute the -2.

Step-by-step explanation:

Hope this helps! :)

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3 years ago

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ch4aika [34]

horizontal shift: 3 units to the left
vertical shift: 4 units down

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3 years ago

Read 2 more answers

Use the intersect method to solve the equation. 14x^3-53x^2+41x-4=-4x^3-x^2+1x+4

UNO [17]

Answer:

x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

Step-by-step explanation:

Solve for x over the real numbers:

14 x^3 - 53 x^2 + 41 x - 4 = -4 x^3 - x^2 + x + 4

Subtract -4 x^3 - x^2 + x + 4 from both sides:

18 x^3 - 52 x^2 + 40 x - 8 = 0

Factor constant terms from the left hand side:

2 (9 x^3 - 26 x^2 + 20 x - 4) = 0

Divide both sides by 2:

9 x^3 - 26 x^2 + 20 x - 4 = 0

Eliminate the quadratic term by substituting y = x - 26/27:

-4 + 20 (y + 26/27) - 26 (y + 26/27)^2 + 9 (y + 26/27)^3 = 0

Expand out terms of the left hand side:

9 y^3 - (136 y)/27 - 1780/2187 = 0

Divide both sides by 9:

y^3 - (136 y)/243 - 1780/19683 = 0

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

-1780/19683 - 136/243 (z + λ/z) + (z + λ/z)^3 = 0

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 136/243) - (1780 z^3)/19683 + z^2 (3 λ^2 - (136 λ)/243) + λ^3 = 0

Substitute λ = 136/729 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 - (1780 u)/19683 + 2515456/387420489 = 0

Find the positive solution to the quadratic equation:

u = (2 (445 + 27 i sqrt(591)))/19683

Substitute back for u = z^3:

z^3 = (2 (445 + 27 i sqrt(591)))/19683

Taking cube roots gives 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) times the third roots of unity:

z = 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = -1/27 (-2)^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = 1/27 (-1)^(2/3) 2^(1/3) (445 + 27 i sqrt(591))^(1/3)

Substitute each value of z into y = z + 136/(729 z):

y = (68 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 1/27 (2 (27 i sqrt(591) + 445))^(1/3) or y = (68 (-2)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) - 1/27 (-2)^(1/3) (27 i sqrt(591) + 445)^(1/3) or y = 1/27 (-1)^(2/3) (2 (27 i sqrt(591) + 445))^(1/3) - (68 (-1)^(1/3) 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3))

Bring each solution to a common denominator and simplify:

y = (2^(1/3) ((27 i sqrt(591) + 445)^(2/3) + 68 2^(1/3)))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = 1/27 2^(1/3) (-1/(445 + 27 i sqrt(591)))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3))

Substitute back for x = y + 26/27:

Answer: x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

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The length of a rectangle is 15ft greater than the width. The area is 100 square ft. Find the length and the Width.​

The length of a rectangle is 15ft greater than the width. The area is 100 square ft. Find the length and the Width.