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2 years ago

Select the true statement about triangle ABC.

Mathematics

1 answer:

zmey [24]2 years ago

3 0

Answer:

Step-by-step explanation:

sin C=12/13

cos A=12/13

so sin C=cos A

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5/8 of the staff are male. 5/12 of the staff works part time at the aquarium. What is the fraction of the staff being a female?

mestny [16]

Answer:3/8

Step-by-step explanation:

5/8 of the staff are male. The entire staff is represented by the fraction 8/8. Taking 5/8 from this, what we have left is

8/8-5/8 = 3/8 of the staff are female.

5 0

3 years ago

A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a di

zhannawk [14.2K]

To solve this problem, we simply use the equation of volume for hollow cylinders:

V = π h (R^2 – r^2)

where V is volume, h is height = 10, R is outer radius = 8.4/2 = 4.2, r is inner radius = 6/2 = 3

V = π (10) (4.2^2 – 3^2)

3 0

3 years ago

Read 2 more answers

Write the follow ratio is lowest terms, 49:21

Alik [6]

Looking at 49 and 21, you immediately know that 7 can be divided out of both.

49:21
=49/7:21/7
=7:3

7:3 is the answer.

Hope this helps!

5 0

3 years ago

Read 2 more answers

Solve. Good luck! Please do not try to google this.

Elena L [17]

$\frac{x^{2} + x - 2}{6x^{2} - 3x} = \sqrt{2x} + \frac{3x^{2}}{2}$
$\frac{x^{2} + 2x - x - 2}{3x(x) - 3x(1)} = \frac{2\sqrt{2x}}{2} + \frac{3x^{2}}{2}$
$\frac{x(x) + x(2) - 1(x) - 1(2)}{3x(x - 1)} = \frac{2\sqrt{2x} + 3x^{2}}{2}$
$\frac{x(x + 2) - 1(x + 2)}{3x(2x - 1)} = \frac{2\sqrt{2x} + 3x^{2}}{2}$
$\frac{(x - 1)(x + 2)}{3x(2x - 1)} = \frac{2\sqrt{2x} + 3x^{2}}{2}$
$\frac{(x - 1)(x + 2)}{3x(2x - 1)} = \frac{2\sqrt{2x} + 3x^{2}}{2}$
$3x(2x - 1)(2\sqrt{2x} + 3x^{2}) = 2(x + 2)(x - 1)$
$3x(2x(2\sqrt{2x} + 3x^{2}) - 1(2\sqrt{2x} + 3x^{2}) = 2(x(x - 1) + 2(x - 1))$
$3x(2x(2\sqrt{2x}) + 2x(3x^{2}) - 1(2\sqrt{2x}) - 1(3x^{2})) = 2(x(x) - x(1) + 2(x) - 2(1)$
$3x(4x\sqrt{2x} + 6x^{3} - 2\sqrt{2x} - 3x^{2}) = 2(x^{2} - x + 2x - 2)$
$3x(4x\sqrt{2x} - 2\sqrt{2x} + 6x^{3} - 3x^{2}) = 2(x^{2} + x - 2)$
$3x(4x\sqrt{2x}) - 3x(2\sqrt{2x}) + 3x(6x^{3}) - 3x(3x^{2}) = 2(x^{2}) + 2(x) - 2(2)$
$12x^{2}\sqrt{2x} - 6x\sqrt{2x} + 18x^{4} - 9x^{3} = 2x^{2} + 2x - 4$
$12x^{2}\sqrt{2x} - 6x\sqrt{2x} = -18x^{4} + 9x^{3} + 2x^{2} + 2x - 4$
$6x\sqrt{2x}(2x) - 6x\sqrt{2x}(1) = -9x^{3}(2x) - 9x^{3}(-1) + 2(x^{2}) + 2(x) - 2(2)$
$6x\sqrt{2x}(2x - 1) = -9x^{3}(2x - 1) + 2(x^{2} + x - 2)$

5 0

3 years ago

Mark the statement either true (in all cases) or false (for at least one example). If false, construct a specific example to sho

LUCKY_DIMON [66]

Answer with Step-by-step explanation:

We are given that $v_1,v_2,..,v_4$ are in $R^4$ and $v_1,v_2,v_3$ is linearly dependent then {v_1,v_2,v_3,v_4}[/tex] is also linearly dependent.

We have to find that given statement is true or false.

Dependent vectors:Dependent vectors are those vectors in which atleast one vector is a linear combination of other given vectors.

Or If we have vectors $x_1,x_2,....x_n$

Then their linear combination

$a_1x_1+a_2x_2+.....+a_nx_n=0$

There exist at least one scalar which is not zero.

If $v_1,v_2,v_3$ are dependent vectors then

$a_1v_1+a_2v_2+a_3v_3=0$ for scalars $a_1,a_2,a_3$

Then , by definition of dependent vectors

There exist a vector which is not equal to zero

If vector $v_3$ is a linear combination of $v_1\;and \;v_2$ , So at least one of vectors in the set is a linear combination of others and the set is linearly dependent.

Hence, by definition of dependent vectors

{ $v_1,v_2,v_3,v_4$ } is linearly dependent.

Option B is true.

8 0

3 years ago