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2 years ago

Please answer this question

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

8 0

The area of the base (six triangles with a base 15m and a height 7.5√3m):

$A_B=6\cdot\dfrac{1}{2}\cdot15\cdot7.5\sqrt3\approx585\ m^2$

The area of side walls (six triangles with a base 15m and a height 12m)

$A_W=6\cdot\dfrac{1}{2}\cdot15\cdot12=540\ m^2$

The surface area:

$A_B+A_W=585+540=1,125\ m^2$

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The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.

andrezito [222]

Answer:

Given the equation: $3x^2+10x+c =0$

A quadratic equation is in the form: $ax^2+bx+c = 0$ where a, b ,c are the coefficient and a≠0 then the solution is given by :

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

Simplify:

$x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}$

Also, it is given that the difference of two roots of the given equation is $4\frac{2}{3} = \frac{14}{3}$

i.e,

$x_1 -x_2 = \frac{14}{3}$

Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

then;

$\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}$

simplify:

$\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}$

$\sqrt{100- 12c} = 14$

Squaring both sides we get;

$100-12c = 196$

Subtract 100 from both sides, we get

$100-12c -100= 196-100$

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve $x_1 , x_2$

$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

$x_1 = \frac{-10 + \sqrt{100- 96}}{6}$ or

$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

Now, to solve for $x_2$ ;

$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

Simplify:

$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

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2 years ago

A shirt originally cost $42.39, but it is an sale for $38.15. What is the percentage decrease of the price of the shirt? If nece

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C. 42.39 times 0.1 is 4.239. 42.39-4.239= 38.151 which rounds to 38.15

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2 years ago

A drawing of a man is 3 inches high. The actual man is 75

oksano4ka [1.4K]

Answer:

1 to 25

Step-by-step explanation:

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2 years ago

Olivia and Camille went clothes shopping. Camille spent $19.40 less than twice what Olivia spent. In total, they spent $272.35.

nydimaria [60]

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Camille spent: 175.10 and

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2 years ago

Which ordered pair is not a solution of y = 2x + 1?

Dmitrij [34]

Answer:

(-1,1)

Step-by-step explanation:

All you have to do is plug it in the equation:

(x,y)

For (-1,1)

1=2(-1)+1

Simplify:

1=-1 but you know that 1≠-1 so (-1,1) is not it

For (3,7)

7=2(3)+1

Simplify:

7=7

For (-3,-5)

-5=2(-3)+1

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Simplify:

For (0,1)

1=2(0)+1

1=1

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2 years ago

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