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3 years ago

Given (x – 7)2 = 36, select the values of x.

Mathematics

1 answer:

Gre4nikov [31]3 years ago

8 0

Answer:

x = 13 and x = 1

Step-by-step explanation:

(x-7)² = 36

simplify left side of equation

x² - 14x + 49 = 36

Our object now is to get every thing on the left side of the equal sign so we can factor. To do this, we subtract 36 from both sides

x² - 14x + 13 = 0

we then factor the left side of the equation

( x - 1 ) ( x - 13 ) = 0

we then set factors equal to 0 and solve both factors for x

x - 1 = 0

add 1 to both sides

x = 1

x - 13 = 0

add 13 to both sides

x = 13

The values of x are x = 13 and x = 1

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3 years ago

What is the value of x? 0.6x − 3.2=0.4 − 0.3x

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Answer:

x=4

step by step:

0.6x-3.2=0.4-0.3x

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Ethan has $150. He wants to buy 4 identical bouquets of flowers but he needs to have at least $20 left after buying the flowers.

pochemuha

150-4x>=20
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3 years ago

Cynthia besch wants to buy a rug for a room that is 23ft wide and 26ft long. She wants t ok leave a uniform strip of floor aroun

Lostsunrise [7]

Answer:

Dimension of rug is $(15\times 18)\ ft$

Step-by-step explanation:

Given: Area of rug= 270 ft²

Cynthia besch wants to buy a rug for a room that is 23ft wide and 26ft long.

Let´s assume the uniform strip size of floor around rug be "x".

As given, Cynthia wants to leave a uniform strip of floor around the rug.

∴ Rug dimension will be $(23-2x)\times (26-2x)$

We know, area of rectangle= $width\times length$

Forming an equation for area of rug.

⇒ $270= (23-2x)\times (26-2x)$

Now solving the equation to find the dimension of rug.

$270= (23-2x)\times (26-2x)$

Using distributive property of multiplication.

⇒ $270= 598-46x-52x+4x^{2}$

⇒ $598-98x+4x^{2}= 270$

Subtracting both side by 270

⇒ $4x^{2}-98x+328= 0$

using quadratic formula to solve the equation.

⇒ Formula: $\frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}$

∴ In the expression , we have a= 4, b= -98 and c= 328.

Now, subtituting the value in the formula.

= $\frac{-(-98)\pm \sqrt{-98^{2}-4(4\times 328) } }{2\times 4}$

= $\frac{98\pm \sqrt{9604-4(1312) } }{8}$

Opening parenthesis.

= $\frac{98\pm \sqrt{9604-5248 } }{8}$

= \frac{98\pm \sqrt{4356}}{8}

We know 66²=4356 and √a²=a or -a

= $\frac{98\pm 66}{8}$

= $\frac{98+66}{8}\ or \ \frac{98-66}{8}$

= $20.5 \ or\ 4$

∴ Value of x will be either 20.5 ft or 4 ft

Ignoring decimal value, therefore taking value of x is 4 ft

Subtituting the value of x to find the dimension of rug.

Width of rug= $(23-2x)$

⇒ Width of rug= $23- 2\times 4$

⇒ Width of rug= $23-8= 15\ ft$

Next, Length of rug= $(26-2x)$

⇒ Length of rug= $(26-2\times 4)$

⇒ Length of rug= $26-8= 18\ ft$

Hence, dimension of rug is $(15\times 18)\ ft$

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3 years ago

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$( \frac{3}{2} \: ,\frac{9}{2} )$

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