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Mekhanik [1.2K]
3 years ago
13

Solve the problem by entering and solving an equation.

Mathematics
1 answer:
geniusboy [140]3 years ago
5 0

Given : A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 12 inches.

To Find : The width of the frame .

Solution : Let us take the width of the frame be x . So , we know the formula to find the perimeter of rectangle as ;

\boxed{\red{\bf Perimeter_{rectangle}=2(l+b)}}

Where , l is the length of the rectangle and b is the breadth of the rectangle .

⇒ Perimeter = 2 ( l + b ) .

⇒ 52 in. = 2 ( 12 + x ) in.

⇒ 52 in.= 24in. + 2x .

⇒ 2x =( 52 - 24 ) in

⇒ 2x = 28 in.

⇒ x = 28/2 in.

⇒ x = 14 in.

<u>Henc</u><u>e</u><u> the</u><u> </u><u>width</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>recta</u><u>ngle</u><u> </u><u>is</u><u> </u><u>1</u><u>4</u><u> </u><u>inches</u><u>.</u>

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Now we need to split the b term into two pieces that multiply to -60 and add to 4.

-6 and 10 will work.

Now group one part of b with the 15x^2 and the other part with -4.

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Now factor both terms.

5x(3x+2) - 2(3x+2)

3x+2 is one of our factors and 5x-2 is the other.

(3x+2)(5x-2)=0

Now just find the zeros.

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And

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So the answer is x = -2/3 and x = 2/5






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3 years ago
The water level of a river is 170 feet. The river recedes 4 feet each year. Ingrid claims that the equation that represents this
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Sample Answer: No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.


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9514 1404 393

Answer:

  (c) 14.5 cm

Step-by-step explanation:

The relevant trig relation is ...

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<em>Additional comment</em>

As is often the case, a simple estimate is all that is needed to identify the correct answer choice.

You only need to know how the long side of a right triangle compares to the others. In an isosceles right triangle, both legs are √2/2 ≈ 0.71 times the hypotenuse. The long side of a right triangle will never be shorter than that. This means the long side must be greater than about 11.2, and cannot be greater than 16. There is only one answer choice in that range.

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