What 826,497 in standard form answer

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 $(15\times 18)\ ft$

6 0

3 years ago

Out of numbers: 5, 7, 21, 25, 28, 35, 42, 56, 75, and 80, choose those which are not factors of 42

Blizzard [7]

Answer:

5, 25, 28, 35, 56, 75 80 are not the factors of 42

6 0

3 years ago

Read 2 more answers

The formula for the area A of a trapezoid is A=1/2(b1+b2)h, where b1 and b2 represents the lengths of the bases and h represents

Vsevolod [243]

The answer: [B]: h = 2A / (b1 + b2) .
__________________________________________________________
Explanation:

Given: A = (½) * (b1 + b2) * h ;
________________________________
→Multiply EACH side of the equation by "2", to get rid of the fraction, "<span>½";
</span>____________________________________________________________
→ 2*A = 2 * (½) * (b1 + b2) * h ;

→ 2* A = 1 * (b1 + b2) * h ;

→ 2A = (b1 + b2) * h ;
____________________________
→ Now, divide EACH side of the equation by: "(b1 + b2)" ; to isolate "h" on one side of the equation;
__________________________________________________________
→ 2A / (b1 + b2) = [(b1 + b2) * h] / (b1 + b2) ;

→ 2A / (b1 + b2) = h ; ↔ h = 2A / (b1 + b2) ; which corresponds to:
"Answer choice: [B]" .
_____________________________________________________________

8 0

4 years ago

100 POINTS - FIRST TO ANSWER CORRECTLY GETS BRAINLIEST

Rudik [331]

Answer:

30 easy

Step-by-step explanation:

8 0

3 years ago

To join a local square dancing group Jane has to pay $100 sign up fee plus $25 per month write an equation for the cost (y) base

ollegr [7]

The equation is 100 + 25x = y. Do you want the answer too?

6 0

4 years ago