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2 years ago

3. How many solutions does the equation have?

Mathematics

1 answer:

Pepsi [2]2 years ago

3 0

An infinite number of solutions since the right side is equal the left side for every value of x.

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Vince has a rectangular rug in his room with an area of 10 ft the length of the rug is 18 inches longer than the width what coul

aev [14]

The length of the rug is 4 ft.

The width of the rug is 2.5 ft.

Explanation:

The area of the rug is 10 ft.

The length of the rug be l.

Let us convert the inches to feet.

Thus, $18 inches = 1.5 ft$

Thus, the length of the rug is $l=1.5+w$

Let the width of the rug be w.

Substituting these values in the formula of area of the rectangle, we get,

$A=length\times width$

$10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0$

Solving the expression using the quadratic formula,

$w=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Substituting the values, we have,

$$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\$

$w=\frac{-15 \pm \sqrt{4225}}{20}$

$w=\frac{-15 \pm 65}{2 0}$

Thus,

$w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5$ and $w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4$

Since, the value of w cannot be negative, the value of w is 2.5ft

Thus, the width of the rug is 2.5ft

Substituting $w=2.5$ in $l=1.5+w$ , we get,

$l=1.5+2.5\\l=4$

Thus, the length of the rug is 4 ft.

4 0

3 years ago

8/1 ÷ 1/4 what's the result?

jonny [76]

The correct answer is 32

3 0

3 years ago

Read 2 more answers

There is a photo attached<br><br>tan 270 is incorrect!

wlad13 [49]

$\dfrac{1-\cos135^\circ}{\sin135^\circ}=\dfrac{1-\left(\cos^2 67.5^\circ-\sin^2 67.5^\circ\right)}{2\sin67.5^\circ\cos67.5^\circ}=\dfrac{1-\left(1-\sin^2 67.5^\circ-\sin^2 67.5^\circ\right)}{2\sin67.5^\circ\cos67.5^\circ}=\medskip\\=\dfrac{2\sin^2 67.5^\circ}{2\sin67.5^\circ\cos67.5^\circ}=\dfrac{\sin 67.5^\circ}{\cos 67.5^\circ}=\tan 67.5^\circ$