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3 years ago

Find the polynomial for the area.Ax+8yThe area is

Mathematics

1 answer:

lara31 [8.8K]3 years ago

7 0

Answer:

1/2(x² + 7xy - 8y²) or 1/2x² + 7/2xy - 4y²

Step-by-step explanation:

1/2(x+8y)(x-y)

1/2(x² - xy + 8xy - 8y²)

1/2(x² + 7xy - 8y²)

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Solve the equation 2 sec² x = 3 - tan x for the domain 0° ≤ x ≤ 360°

vodka [1.7K]

$2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\$

$\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\$

$x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\$

$\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]$

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2 years ago

What is the Area of a triangle with the height of 0.7 cm and a base of 6cm

Mashcka [7]

Answer: Area = 2.1 $cm^{2}$

Step-by-step explanation:

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2 years ago

Walt and Hank collect quarters from different states. Walt collected q quarters. Hank collected four fewer quarters than Walt. T

SpyIntel [72]

Answer:

Walt has 37 quarters. Hank has 33.

Step-by-step explanation:

Solve the given equation for q:

0.25q + 0.25q - 1.00 = 17.50

Simplify this, obtaining:

0.50q = 18.50

Simplifying this by multiplying both terms of this result by 100:

50 q = 1850

Thus, q = 1850/50 = 37

Walt has 37 quarters. Hank has 33.

Note that 37 + 33 = 70, and that 70($0.25) = $17.50. So our results are correct.

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3 years ago

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Answer:

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Step-by-step explanation:

I think... I haven't done this sort of question in a while

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2 years ago

Write a system of linear equations for the graph below.

Vanyuwa [196]

Answer:

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Step-by-step explanation:

because (x,y) the x coordinate is -3 and the y coordinate is -2

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2 years ago

Find the polynomial for the area.Ax+8yThe area is​

Find the polynomial for the area.Ax+8yThe area is