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3 years ago

7

Mario is constructing a frame for 10 in. by 8 in. photo. He wants the frame to be the same with all the way around in the same a

rea of the frame and photo to be 120 square inches
What is the dimension of the frame?

1 answer:

Yuri [45]3 years ago

5 0

Answer: 12 in. by 10 in.

Step-by-step explanation:

Given: The dimensions of photo is 10 in. by 8 in.

Therefore, Area of photo= $10\times8=80\ in.^2$

Area of frame with photo=120 square inches

Let x be the width of the frame, then we have

Length of frame with photo= 10+2x inches

Width of frame with photo =8+2x inches

Now, $(10+2x)(8+2x)=120$

$80+16x+20x+4x^2=120\\\Rightarrow\ 4x^2+36x-40=0\\\Rightarrowx^2+9x-10=0\\\(x-1)(x+10)=0\\\Rightarrow\ x=1,...........[text{Since length can not be negative so it cannot be -10}]$

Thus, dimension of frame = $(10+2(1))(8+2(1))=12\ in.\ by\ 10\ in.$

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Answer:

The solutions to the system of the equations by the elimination method will be:

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Step-by-step explanation:

Given the system of the equations

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solving the system of the equations by the elimination method

$\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}$

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$\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}$

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$\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}$

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$4y-9\left(-1\right)=17$

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2 years ago

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Cancelling out $a.b^x$ we get:

$\frac{f(x + 1)}{f(x)} = b$

This shows that the ratio is always a constant and that constant is equal to b.

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