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3 years ago

Solve the quadratic equation by square roots: 1. 4x²= 81 2. (4x-3)²+7=39

Mathematics

1 answer:

Nataly [62]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

(1)

given

4x² = 81 ( divide both sides by 4 )

x² = $\frac{81}{4}$ ( take the square root of both sides )

x = ± $\sqrt{\frac{81}{4} }$ = ± $\frac{9}{2}$

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(2)

subtract 7 from both sides

(4x - 3)² = 32 ( take the square root of both sides )

4x - 3 = ± $\sqrt{32}$ = ± 4 $\sqrt{2}$

Add 3 to both sides

4x = 3 ± 4 $\sqrt{2}$ ( divide both sides by 4 )

x = $\frac{3}{4}$ ± $\sqrt{2}$

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Jada purchases movie tickets online. She buys 2 tickets for adults and 4 tickets for children. The cost of a ticket for a child

grandymaker [24]

Answer:

Step-by-step explanation:

58 is the answer without tax

so the cost of an adult ticket is 13 dollars

and the kids ticket is 8 dollars

use system of equations to solve this.

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8 0

3 years ago

Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar

Brrunno [24]

The distance between the two points is $d=8.6m$

The polar coordinate of A is $\left(4.47,296.57\right)$

The polar coordinate of B is $\left(4.24,135\right)$

Explanation:

The two points are $A(2,-4)$ and $B(-3,3)$

The distance between two points is given by,

$d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6$

Thus, the distance between the two points is $d=8.6m$

The polar coordinates of A can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $A(2,-4)$ , we get,

Distance = $\sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{-4}{2}=-63.43$

To make the angle positive, let us add 360,

$\theta=360-63.43=296.57$

The polar coordinate of A is $\left(4.47,296.57\right)$

Similarly, The polar coordinate of B can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $B(-3,3)$ , we get,

Distance = $\sqrt{(3)^{2}+(3)^{2}}=4.24$

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To make the angle positive, let us add 360,

$\theta=180-45=135^{\circ}$

The polar coordinate of B is $\left(4.24,135\right)$

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3 years ago

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lbvjy [14]

Answer:

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Step-by-step explanation:

y=-4+9y

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8y=4

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Answer/Step-by-step explanation:

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