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butalik [34]
3 years ago
9

Which expression is equivalent to 27 ?

Mathematics
1 answer:
vfiekz [6]3 years ago
8 0

Answer:

Last one

Step-by-step explanation:

3^4*3^-7

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Complete the table using the equation y = 9x + 8.
Volgvan

Answer:

Y  =  (  -1) | 8 | 17 | 26 | 35|

Step-by-step explanation:

y = 9x + 8  \\ \\  \\ x = ( - 1) \\ y = 9( - 1) + 8 \\ y =  - 9 + 8 =  - 1 \\  \\ x = 0 \\ y = 9(0) + 8 \\ y = 0 + 8 = 8 \\  \\ x = 1 \\ y = 9(1) + 8 \\ y = 9 + 8 = 17 \\  \\ x = 2 \\ y = 9(2) + 8 \\ y = 18 + 8 = 26 \\  \\ x = 3 \\ y = 9(3) + 8 \\ y = 27 + 8 = 35 \\  \\  \\  Y  =  (  - 1) | 8 | 17 | 26 | 35|

7 0
3 years ago
Solving a trigonometric equation involving an angle multiplied by a constant
PIT_PIT [208]

In these questions, we need to follow the steps:

1 - solve for the trigonometric function

2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.

3 - Complete these angles with the complete round repetition, by adding

2k\pi,k\in\Z

4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.

1 - To solve, we just use algebraic operations:

\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}

2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:

The value for the angle that give positive

+\frac{\sqrt[]{3}}{3}

is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of

-\frac{\sqrt[]{3}}{3}

Are:

\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}

3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:

\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}

Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:

\theta=\frac{5\pi}{6}+k\pi,k\in\Z

4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:

\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}

So, the solutions are:

x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z

4 0
1 year ago
Factorise fully<br> -X – 10<br><br> Pls help
Nataly_w [17]

Answer:

-X – 10=-1(x+10) is your answer

3 0
2 years ago
11x+4y=-46<br> 7x-4y=10 <br> Find x and y
UNO [17]

Answer:x=-2 y=-6

Step-by-step explanation:

11x+4y=-46..........(1)

7x-4y=10..............(11)

Add (1) and (11)

11x+7x+4y-4y=-46+10

18x=-36

Divide both sides by 18

18x/18=-36/18

x=-2

substitute x=-2 in (11)

7x-4y=10

7(-2)-4y=10

-14-4y=10

Collect like terms

4y=-14-10

4y=-24

Divide both sides by 4

4y/4=-24/4

y=-6

3 0
3 years ago
Jon ran around a track that was 1/8 of a mile long,he ran around the track 24 times,how many miles did Jon run
Sonbull [250]
Hi there 

So, if the track is 1/8 of a mile, let's call every lap a "one-eighth mile" run. We know John ran 24 laps, or that he ran 24 "one-eighth miles," just consecutive, one right after another. Let's stop worrying about rates or tricks or math for a second, and just ask: how many real miles is 24 "one-eighth" miles? We know it's less than 24---a lot less, since you have to go around 8 times just to get to 1 mile. Well wait, if we go around 8 times, we get 1 mile. That means if we go around 28, or 16 times, we get 2 miles; And let's just think to the next full mile---if we go 38, or 24 times, we get 3 miles. He did go around 24 times, so he must have run 3 miles on a 1/8 track.

Division and multiplication are inverses of each other. So we solved this by looking for an intuition for how many full miles corresponded to how many laps, with a bunch of steps of multiplication. But you can cut right to the chase and solve it faster with division---24 laps * 1 mile per 8 laps, means:

total distance = 24 Lap (1 mi / 8 Lap) total distance = 24/8 total distance = 3

6 0
3 years ago
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