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3 years ago

11

Im stuck on this one

1 answer:

nika2105 [10]3 years ago

5 0

ABC is a right triangle, so by Pythagoras' theorem,

$AB^2+AC^2=BC^2\implies BC=\sqrt{4^2+9^2}=\sqrt{97}$

Then by the law of sines,

$\dfrac{\sin A}{BC}=\dfrac{\sin C}{AB}\iff\dfrac1{\sqrt{97}}=\dfrac{\sin C}4\implies\sin C=\dfrac4{\sqrt{97}}$

$\implies C=\sin^{-1}\dfrac4{\sqrt{97}}\approx24^\circ$

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A recipe for fruit punch calls for 3 cups of sugar and 8 cups of water. How much sugar is used per cup of water?

Vera_Pavlovna [14]

Answer:

Im not exactly sure but i think it's 1/4 or 1/5.

Step-by-step explanation:

This was based on my work I did.

5 0

3 years ago

Read 2 more answers

85 points, Brainliest, ill report random answers>ban

Leya [2.2K]

all the coordinates of the original triangle have been multiplied by 1/2

A (-4,-6) x 1/2 = -2,-3

B (-8,2) * 1/2 = -4,1

C (-2,4) *1/2 = -1,2

so the scale factor is 1/2

Answer is B

8 0

3 years ago

Read 2 more answers

The partial fraction decomposition of 9 x 11 6 x 2 23 x 21 can be written in the form of f ( x ) 2 x 3 g ( x ) 3 x 7 , where

svlad2 [7]

Answer:

$f(x) = -1$

$g(x) =6$

$\frac{-1}{2x + 3} + \frac{6}{3x + 7}$

Step-by-step explanation:

The question is unreadable, however the real polynomial is:

The polynomial fraction is:

$P = \frac{9x + 11}{6x^2 + 23x + 21}$

And the decomposition is:

$\frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}$

The solution is as follows:

$P = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}$

Substitute the expression for P

$\frac{9x + 11}{6x^2 + 23x + 21} = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}$

Expand the numerator of the polynomial

$\frac{9x + 11}{(2x + 3)(3x + 7)} = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}$

Take LCM

$\frac{9x + 11}{(2x + 3)(3x + 7)} = \frac{f(x)*(3x + 7) + g(x)*(2x + 3)}{(2x + 3)(x + 7)}$

Cancel out both denominators

$9x + 11} = f(x)*(3x + 7) + g(x)*(2x + 3)$

Represent f(x) as A and g(x) as B

$9x + 11} = A*(3x + 7) + B*(2x + 3)$

Open bracket

$9x + 11} = 3Ax + 7A + 2Bx + 3B$

$9x + 11} = 3Ax + 2Bx+ 7A + 3B$

$9x + 11} = (3A + 2B)x+ 7A + 3B$

By comparison:

$3A + 2B = 9$ ---- (1)

$7A + 3B =11$ ---- (2)

Make B the subject in (1)

$B = \frac{9 - 3A}{2}$

Substitute $B = \frac{9 - 3A}{2}$ in (2)

$7A + 3(\frac{9 - 3A}{2}) = 11$

Multiply through by 2

$2*7A +2* 3(\frac{9 - 3A}{2}) = 11*2$

$14A + 3(9 - 3A) = 22$

$14A + 27 - 9A = 22$

Collect Like Terms

$14A - 9A = 22-27$

$5A = -5$

$A = \frac{-5}{5}$

$A = -1$

Recall that:

$B = \frac{9 - 3A}{2}$

$B = \frac{9 - 3 * -1}{2}$

$B = \frac{9 + 3}{2}$

$B = \frac{12}{2}$

$B = 6$

A = -1 and B = 6

$3A + 2B = 9$ ---- (1)

$7A + 3B =11$ ---- (2)

So:

$f(x) = A$

$f(x) = -1$

$g(x) =B$

$g(x) =6$

And the decomposition is:

$\frac{-1}{2x + 3} + \frac{6}{3x + 7}$

6 0

3 years ago

Solve:<br><br> 7 = x + 12<br> A) -19 <br> B) -5 <br> C) 4 <br> D) 5

DaniilM [7]

<em><u>Hello, there! :)</u></em>

<u><em>Answer:</em></u>

<u><em>x=-5 </em></u>

<u><em>B. -5</em></u>

<u><em>*The answer must have a negative sign.*</em></u>

Step-by-step explanation:

Definition of subtraction property of equality.

Subtraction property of equality is subtracting the same number from both sides of an equation does not change the equation.

$a-c=b-c$

First, you had to switch sides.

$x+12=7$

Then, you subtract by 12 from both sides of an equation.

$x+12-12=7-12$

And finally, simplify or solve.

$7-12=-5$

$x=-5$

Hope this helps!

Thanks!

-Charlie

:)

8 0

3 years ago

How do you write 400,000+30,000+800+20+5 in standard form

____ [38]

400,000 + 30,000 + 800 + 20 + 5 written in standard form is

430,825

As you can see, each digit in 430,825 is equal to 430,825 written in expanded from

Hope this helps

-AaronWiseIsBae

6 0

3 years ago

Read 2 more answers