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Montano1993 [528]
3 years ago
10

What are two partial products you would add to find 21 x 509?​

Mathematics
1 answer:
Mama L [17]3 years ago
3 0
45 and 63.9 I believe
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7.Find the lengths of the missing sides in the triangle. If your answer is not an integer, leave it in simplest radical form. Th
Fed [463]

Here a right angled triangle given. one angle with measure 45^o given. The three sides of the triangle given 4, x, y.

We have to find, the sides which is opposite, adjacent and hypotenuse here.

We know that the side opposite to right angle is always hypotenuse. So, hypotenuyse = y.

The side adjacent to the given angle 45^o is x. So, here adjacent = x.

The opposite side is opposite to the given angle. So, opposite = 4.

Now we will use SOHCAHTOA that is sin(x) =\frac{Opposite}{Hypotenuse} , cos(x) =\frac{Adjacent}{Hypotenuse} , tan(x) =\frac{Opposite}{Adjacent}, where x is the angle given.

To get x, we will use tan. So we will get,

tan(45^o) = \frac{4}{x}

We know the value of tan(45^o) = 1. By substituting the value we will get,

1 =\frac{4}{x}

To find x, we have to move x here to the left side by multiplying it to both sides. We will get,

(1)(x) = (\frac{4}{x}) (x)

x = 4

So we have got the value of x here.

Now to find y, we will use the trigonometric function sine.

sin(45^o) =\frac{4}{y}

we know the value of sin(45^o) =\frac{\sqrt{2}}{2}

By substituting the value we will get,

\frac{\sqrt{2}}{2}  = \frac{4}{y}

By cross multiplying we will get,

(\sqrt{2}) (y) = (4)(2)

\sqrt{2}y = 8

We will get y by dividing both sides by \sqrt{2}, we will get,

\frac{\sqrt{2}y}{\sqrt{2}}   =\frac{8}{\sqrt{2} }

y =\frac{8}{\sqrt{2}  }

Now we will rationalize the denominator by multiplying \sqrt{2} to the top and bottom.

y =\frac{8\sqrt{2}}{(\sqrt{2})(\sqrt{2})}

y =\frac{8\sqrt{2}}{2}

y = 4\sqrt{2}

So we have got the required values of x and y.

8 0
3 years ago
Read 2 more answers
Which expression is equivalent to -4(2x+3)-(3x+5)
vfiekz [6]

Answer:

5x-7

Step-by-step explanation:

= -8x - 12 - 3x + 5

= -8x - 3x - 12 + 5

= 5x-7

5 0
2 years ago
Read 2 more answers
PLEASE Answer! I'll Give Brainliest And A Thanks For A GOOD Answer.
melisa1 [442]

Answer: Your welcome the answer is in the attached Image.

Step-by-step explanation: mark me brainliest.

5 0
2 years ago
Which is the completely factored form of 4x2 28x 49? (x 7)(4x 7) 4(x 7)(x 7) (2x 7)(2x 7) 2(x 7)(x 7)
natima [27]

The completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

<h3>How to find the factors of a quadratic expression?</h3>

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

b = \alpha + \beta \\ ac =\alpha \times \beta

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

For this case, the given quadratic expression is:

4x^2 + 28x + 49

So we've to find two numbers such that:

Their sum = b =  28

Their product = ac = 4\times 49 = 196

We can see that 196 is square of 14, and that 14 added twice forms 28, thus:

14 + 14 = 28

14×14 = 196

Writing b = 28 as sum of 14 twice, we get:

4x^2 + 28x + 49 = 4x^2 + 14x + 14x +49 \\4x^2 + 28x + 49 =  2x(2x+7) + 7(2x + 7)\\4x^2 + 28x + 49  = (2x+7)(2x+7)

Thus, the completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

Learn more about factorization of quadratic expression here:

brainly.com/question/26675692

8 0
2 years ago
A given line has the equation 2x + 12y = −1. What is the equation, in slope-intercept form, of the line that is perpendicular to
VikaD [51]

Answer:

y = 6x + 9

Step-by-step explanation:

The equation of a line in slope- interceot form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 12y = - 1 into this form

Subtract 2x from both sides

12y = - 2x - 1 ( divide all terms by 12 )

y = - \frac{1}{6} x - \frac{1}{12} ← in slope- intercept form

with slope m = - \frac{1}{6}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{-\frac{1}{6} } = 6

Note the line passes through (0, 9) on the y- axis ⇒ c = 9

y = 6x + 9 ← equation of perpendicular line

3 0
2 years ago
Read 2 more answers
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