3 years ago

Evaluate the expression 2^3[1/4+4(36÷12)]

Mathematics

1 answer:

jeka57 [31]3 years ago

4 0

Answer:

Step-by-step explanation:

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A rectangle has a perimeter of 14 inches. A similar rectangle has a perimeter of 10 inches. If the length of the larger rectangl

Jet001 [13]

Answer:

2.9 in.

Step-by-step explanation:

Let x in be the width of the larger rectangle. If the length of the larger rectangle is 4 inches and the perimeter of the larger rectangle is 14 in, then

$x+4+x+4=14,\\ \\2x=14-8,\\ \\2x=6,\\ \\x=3\ in.$

If two rectangles are similar, then their lengths and widths are proportional with the scale factor k. Thus, the length of the smaller rectangle is $4k$ in and the width of the smaller rectangle is $3k$ in. If the perimeter of the smaller rectangle is 10 in, then

$4k+3k+4k+3k=10,\\ \\14k=10,\\ \\k=\dfrac{10}{14}=\dfrac{5}{7},\\ \\4k=\dfrac{20}{7}\approx 2.9\ in,\\ \\3k=\dfrac{15}{7}\approx 2.1\ in.$

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3 years ago

Find all values of k so that the trinomial x^2 + kx - 35 can be factored using integers

Korvikt [17]

$(x-r_1)(x-r_2)=x^2-(r_1+r_2)x+r_1r_2$

So the trinomial $x^2+kx-35$ can be factored as long as

$\begin{cases}r_1+r_2=-k\\r_1r_2=-35\end{cases}$

has integer solutions for $r_1,r_2$ . Clearly, both have to be factors of -35, which leaves only a handful of cases:

$(r_1,r_2)=(1,-35)\implies r_1+r_2=-34$
$(r_1,r_2)=(-1,35)\implies r_1+r_2=34$
$(r_1,r_2)=(5,-7)\implies r_1+r_2=-2$
$(r_1,r_2)=(-5,7)\implies r_1+r_2=2$

So the possible values of $k$ are $\pm34$ and $\pm2$ .

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3 years ago