Determine whether the equation has one solution, no solution, or infinite solutions.
Explain your reasoning.
9x + 2 = -4(x + 6)

Given:

In triangle ABC, AB=8.2 cm, C=13.5 cm and angle A= 81 degrees.

To find:

The length of AC.

Solution:

According to the Law of Sines:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

Using Law of Sines, we get

[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c}[/tex]

[tex]\dfrac{\sin (81^\circ)}{13.50}=\dfrac{\sin C}{8.2}[/tex]

[tex]\dfrac{\sin (81^\circ)\times 8.2}{13.50}=\sin C[/tex]

[tex]\sin^{-1}\dfrac{\sin (81^\circ)\times 8.2}{13.50}= C[/tex]

[tex]C\approx 36.86^\circ[/tex]

Using angle sum property, we get

[tex]\angle A+\angle B+\angle C=180^\circ[/tex]

[tex]81^\circ+\angle B+36.86^\circ=180^\circ[/tex]

[tex] \angle B =180^\circ-81^\circ-36.86^\circ [/tex]

[tex] \angle B =62.14^\circ [/tex]

Now,

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]

[tex]\dfrac{\sin (81^\circ)}{13.50}=\dfrac{\sin (62.14^\circ)}{b}[/tex]

[tex]b=\dfrac{13.50\times \sin (62.14^\circ)}{\sin (81^\circ)}[/tex]

[tex]b\approx 12.08[/tex]

Therefore, the length of AC is 12.08 cm.

Answer:

1-8/27

Step-by-step explanation:

[tex](\frac{2}{3})^3=\frac{8}{27}[/tex]

[tex](\frac{3}{4})^0=1[/tex] (anything to the zeroth power is 1)

[tex]1+\frac{8}{27}=1\frac{8}{27}[/tex]

We cannot simplify, so 1-8/27 is our answer.

Hope this helps. Have a nice day.

Answer:  y = 0.0005x+1

This is the same as saying y = (1/2000)x + 1

===============================================================

Explanation:

The blue line goes through (0,1) and (2000,2)

The slope is

m = (y2-y1)/(x2-x1)

m = (2-1)/(2000-0)

m = 1/2000

This says that each time we move up 1, we move to the right 2000 units.

Think of it as slope = rise/run = 1/2000

The slope 1/2000 means that each time you make 2000 soccer balls, it will cost you $1000. Keep in mind that y is in thousands (eg: y = 1 means 1000). This further implies that the marginal cost is ($1000)/2000 = $0.50 = 50 cents. The marginal cost is the cost to make one extra unit.

The fraction 1/2000 converts to the decimal form 0.0005 after using a calculator. So m = 0.0005 is the decimal form of the slope.

The y intercept of the blue line is b = 1 as this is the location where the blue line crosses the vertical y axis. The y intercept represents the fixed costs needed to set up production, for example: buying the machinery needed is a fixed cost.

-------------------

Since m = 0.0005 and b = 1, we go from y = mx+b to y = 0.0005x+1

We could say y = (1/2000)x + 1, though I think it's probably easier to use a decimal in this case.

Answer:

B :  y axis is parallel

     x axis is perpendicular

  4:     (4,8) (4,10)

5: (4,25)

Step-by-step explanation:

Hope this helps, and if you can please mark me Brainiest.

Answer:

y = - 5/2

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

2(x - 5) = 2(x - 3)

2x -10 = 2x -6  When we subtract 2x from both sides we are left with a false statement.

-10 [tex]\neq[/tex] -6

Thus, no solution.

Answer:

2 t-shirts, 3 cd's, 5 books.

Step-by-step explanation: Johnson wants to spend $105 in total, get 10 items total, and get at least 1 t-shirt, 1 cd, and 1 book. If he did not want to buy 10 items then he could buy 21 books, 10 cd's and 1 book, or 4 t-shirts and 1 book. But because of all the conditions Johnson should buy 2 t-shirts ($50), 3 cd's ($30), and 5 books ($25). $105 total, and as much of each item as possible.

Answer:

Where is the homework?

Step-by-step explanation:

Answer:

9x = x + 56

Step-by-step explanation:

Answer:

I believe the correct answer would either be B or D.

Step-by-step explanation:

I'm not 100% certain but I have doe similar questions so I'm quite sure.

Answer:

x = 9

Step-by-step explanation:

x−(3)(3=x+−9 )

Answer:

Not any whole numbers!

Step-by-step explanation:

Answer:

choice 4) sq rt 69 ft

Step-by-step explanation:

13^2 - 10^2

169-100 = 69

sq rt 69

Answer:

c wich is sevenths

Step-by-step explanation:

The probability the teacher that chooses a girl to write the date on the board is :

C) 3 sevenths.

Given:

Boys =12

Girls =9

Total number of students = 12 + 9 = 25.

So the probability of choosing a girl is = n(girl) / n(all students) = [tex]\frac{9}{25}[/tex]

This is close to 3 sevenths.

Learn more about probability:

https://brainly.com/question/25870256

Answer:

376-182=194

so 194 us the 1st

182 is the 2nd

Answer:

45/49

Step-by-step explanation:

Answer:

second option

Step-by-step explanation:

mark me brainliest pls

Step-by-step explanation:

a + 9 = 6

p + 20 = -30

Answer:

When you multiply a whole number by a square root, you just put the two together, with the whole number in front of the square root. For example, 2 * (square root of 3) = 2(square root of 3). If the square root has a whole number in front of it, multiply the whole numbers together.

Step-by-step explanation:

its there

Answer:

See below.

Step-by-step explanation:

[tex] y_2 = 4x^2 [/tex]

[tex] x = 1 [/tex]

[tex] y_2 = 4(1)^2 = 4 = a [/tex]

a = 4

[tex] y_3 = 4^x [/tex]

[tex] x = 1 [/tex]

[tex] y_3 = 4^1 = 4 = b [/tex]

b = 4

[tex] y_1 = 4x [/tex]

[tex] x = 2 [/tex]

[tex] y_1 = 4(2) = 8 = c [/tex]

c = 8

[tex] y_3 = 4^x [/tex]

[tex] x = 2 [/tex]

[tex] y_3 = 4^2 = 16 = d [/tex]

d = 16

[tex] y_1 = 4x [/tex]

[tex] x = 3 [/tex]

[tex] y_1 = 4(3) = 12 = e [/tex]

e = 12

[tex] y_2 = 4x^2 [/tex]

[tex] x = 3 [/tex]

[tex] y_2 = 4(3)^2 = 36 = f [/tex]

f = 36

[tex] y_3 = 4^x [/tex]

[tex] x = 3 [/tex]

[tex] y_3 = 4^3 = 64 = g [/tex]

g = 64

Answer:

The arrow hits the ground after 2.25 seconds

the height the arrow is shot from is (0,18) or 18 units up

Step-by-step explanation:

Answer:

PR = 6.93 units

PQ = 13.86 units

Step-by-step explanation:

From ΔPQR,

m∠Q = 30°

QR = 12

By applying tangent rule for the given angle in the triangle,

tan(30°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

tan(30°) = [tex]\frac{PR}{QR}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{PR}{12}[/tex]

PR = [tex]\frac{12}{\sqrt{3} }[/tex]

PR = 4√3 ≈ 6.93

Now we apply cosine rule,

cos(30°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{\sqrt{3} }{2}=\frac{QR}{PQ}[/tex]

[tex]\frac{\sqrt{3} }{2}=\frac{12}{PQ}[/tex]

PQ = [tex]\frac{24}{\sqrt{3} }[/tex]

PQ = 8√3 ≈ 13.86

Answer:

Multiply it by 4 and divide it by 100.  It should be1,100. Now multiply it by12. it should be 13200 . Now subtract that to the original price.  14300

Step-by-step explanation:

PLEASE rate follow and thank

Answer: 6281

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

:)

Answer:

1/8 in decimal form is 0.125

Answer:

40 seconds

Step-by-step explanation:

8         20

16        40

32

40

40 seconds

It will take 40seconds to both the lights to flash at the same time again.

" Least common multiple is defined as the smallest common multiple of the given set of numbers."

According to the question,

Given ,

Time to flash Light A is  every 8 seconds.

Time to flash Light B is every 20 seconds.

Condition given

Both the lights flash at the same time

Least common multiple (8, 20) = 40seconds

Light A flashes in

8seconds , 16seconds , 24seconds , 32seconds, 40seconds

Light B flashes in

20seconds , 40seconds

Hence, both the light flashes at the same time again is at 40seconds.

Learn more about least common multiple here

https://brainly.com/question/11533141

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