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3 years ago

Please please help me out..........

Mathematics

1 answer:

Tema [17]3 years ago

7 0

Answer:

For the parallelogram to be a rectangle, at least one angle must be a right angle or a 90° angle, we know that:

13x + 34° + 10x + 10° = 90°

=> 13x + 10x = 90° - 34° - 10°

=> 23x = 46°

=> x = 46°/23 = 2°

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Alfonso is trying to move a new sofa into his apartment. Unfortunately, he forgot to measure the size of his doors and it turns

lara [203]

Answer:

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Step-by-step explanation:

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3 years ago

A bag contains 31 checkers—13 red and 18 black. Determine whether the events "a red checker is selected, not replaced and then a

Ipatiy [6.2K]

Answer:

dependent, 39/155

Step-by-step explanation:

Since the checkers are not replaced, the events are dependent since the number of checkers in the bag when you pick the second time depends on the first pick.

31 checkers—13 red and 18 black.

P(red) = red/ total

= 13/31

Keep the checker

Then 30 checkers—12 red and 18 black.

P(black) = black/ total

= 18/30 = 3/5

P ( red, keep,black) = 13/31 *3/5

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3 years ago

Y = -4x + 6<br> y = -2x - 2<br><br> Solve for x and y

Oduvanchick [21]

Answer:

(4,-10)

Step-by-step explanation:

You set them equal to each other.

You get x=4

Sub in 4 for one of the equations

y=-10

7 0

3 years ago

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A rectangular swimming pool is bordered by a concrete patio. the width of the patio is the same on every side. the area of the s

andre [41]

Answer:

$x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)$

where

l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Explanation:

Let

x = width of the patio
l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Since the pool is bordered by a complete patio,

Length of the pool (with the patio)
= (length of the pool (w/o the patio)) + 2*(width of the patio)
Length of the pool (with the patio) = l + 2x

Width of the pool (with the patio)
= (width of the pool (w/o the patio)) + 2*(width of the patio)
Width of the pool (with the patio) = w + 2x

Note that

Area of the pool (w/o the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
Area of the pool (w/o the patio) = lw

Area of the pool (with the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
= (l + 2x)(w + 2x)
= w(l + 2x) + 2x(l + 2x)
= lw + 2xw + 2xl + 4x²
Area of the pool (with the patio) = 4x² + 2x(l + w) + lw

Area of the patio
= (Area of the pool (with the patio)) - (Area of the pool (w/o the patio))
= (4x² + 2x(l + w) + lw) - lw
Area of the patio = 4x² + 2x(l + w)

Since the area of the patio is equal to the area of the surface of the pool, the area of the patio is equal to the area of the pool without the patio. In terms of the equation,

Area of the patio = Area of the pool (w/o the patio)
4x² + 2x(l + w) = lw
4x² + 2x(l + w) - lw = 0 (1)

Let

a = numerical coefficient of x² = 4
b = numerical coefficient of x = 2(l + w)
c = constant term = -lw

Then using quadratic formula, the roots of the equation 4x² + 2x(l + w) - lw = 0 is given by

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\\ = \frac{-2(l + w) \pm \sqrt{(2(l + w))^2 - 4(4)(-lw)}}{2(4)} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l + w)^2) + 16lw}}{8} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2) + 4(4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2 + 4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 6lw + w^2)}}{8}$
$= \frac{-2(l + w) \pm 2\sqrt{l^2 + 6lw + w^2}}{8} \\= \frac{2}{8}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\x = \frac{1}{4}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right) \text{ or }}
\\\boxed{x = -\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

Since $(l + w) + \sqrt{l^2 + 6lw + w^2} \ \textgreater \ 0$ , $-\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2}\right)$ is negative. Since x represents the patio width, x cannot be negative. Hence, the patio width is given by

$\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

7 0

3 years ago

Please solve this question.

Fantom [35]

Answer:

2 by 2

Step-by-step explanation:

$A = \begin{pmatrix} 1 & 2\\3 & 4\end{pmatrix}$

Since, given matrix has 2 rows and 2 columns.

So, Its a 2 by 2 order matrix.

6 0

3 years ago

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