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Katarina [22]
3 years ago
6

PWEEZ HELPPPPPPPPPPPPPP

Mathematics
1 answer:
garik1379 [7]3 years ago
5 0

1. m∠1 + m∠2 = 180°

2. Definition of bisector

3. m∠1 + m∠3 = 180°

4. Substitution Property of Equality

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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.
Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have S_1=3\times2^{1-1}+2(-1)^1=3-2=1, which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}

and

S_k=3\times2^{k-1}+2(-1)^k

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}

From the given recurrence, we know

S_{k+1}=S_k+2S_{k-1}

so that

S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)

S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}

S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)

S_{k+1}=3\times2^k-2(-1)^k

S_{k+1}=3\times2^k+2(-1)(-1)^k

\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}

which is what we needed. QED

6 0
3 years ago
Write an equation parallel to the given line through the given line through the given point.
Law Incorporation [45]
The format of a line equation is y = mx + b
When two lines are parallel, their 'm' variables are equal.
Knowing this, the unknown line equation, so far, would look like this:
y = 9x + b
Since we know that the line equation goes through the point (2, 7)
7 = 18 + b
b = -11
y = 9x - 11
6 0
3 years ago
(x – 2) / 4 – (3x + 5) / 7 = – 3, x = ?<br><br> WILL GIVE BRAINLIEST
balu736 [363]

Answer:

under

Step-by-step explanation:

change the underminator, we have

7×(x-2)-4×(3x+5)=-3×7×4

7x-14-12x-20=-84

-5x=-50

x=10

6 0
3 years ago
Anna, Beth and Colleen are softball players. This season, Anne had 65 base hits in 160 at-bats. Beth batting average was 0.399,
zheka24 [161]

Answer:

Anne is the best hitter as she has the best hitting average of 0.406

Step-by-step explanation:

Anne hits 65 bases out of 160 at - bats.

Beth's betting average = 0.399

Collin's hit = 40%

Now, we need to convert all the three hitting rates into same parameters to compare them with each other.

Average hit rate of Anne = \frac{\textrm{Total numberof base}}{\textrm{Total number of  at - bats}}

= \frac{65}{160}  = 0.406

⇒The betting average of Anne = 0.406

Now, The hit - rate of Collin = 40%

Converting the percentage rate into decimal, we get the hit rate of Collin

= \frac{40}{100}  = 0.40

Hence, we get that Hitting Average of :

<u>Anne = 0.406</u>,  Beth = 0.3999 and Collin = 0.400

Hence, from the above data Anne is the best hitter as she has the best hitting average of 0.406.

6 0
3 years ago
Read 2 more answers
3. (05.06 MC)
AveGali [126]

Answer:

Step-by-step explanation:

y > 3x + 10

y < -3x - 1

<h3> Part A:</h3>

You'd graph the given systems of linear inequalities the same way as you graph the linear equations.  

To graph y > 3x + 10, plot the y-intercept, (0, 10), then use the slope, m = 3 (rise 3, run 1), to plot other points on the graph.  Use a dashed line (because of the ">" symbol).  

Follow the same steps for the other linear inequality. Plot the y-intercept, (0, -1), then use the slope, m = -3 (down 3, run 1) to plot other points. Use a dashed line (because of the "<" symbol).  

Pick a test point on either side of the boundary line and plug it into the original problem.  This will help determine which side of the boundary line is the solution.  Plug in a test point that is not on the boundary line.

Use the point of origin, (0, 0) as the test point. Plug in these values into the given systems of linear inequalities to see whether it will provide a true statement.  

y > 3x + 10

0 > 3(0) + 10

0 > 0 + 10

0 > 10 (False statement).  

y < -3x - 1

0 < -3(0) - 1

0 < 0 - 1

0 < -1 (false statement).  

Since the point of origin provided a false statement to the given systems of linear inequalities, you must shade the half-plane region where it doesn't contain the test point.  

<h3>Part B: </h3>

You'll do the same process as what I've done for the test point. Plug in the values of (8, 10) into the given systems of linear inequalities. If it provides a false statement, then it means that it is not a solution to the system.  

y > 3x + 10

10 > 3(8) + 10

10 > 24 + 10

10 > 34 (False statement).  

y < -3x - 1  

10 < -3(8) - 1

10 < -24 - 1

10 < -25 (false statement).  

Therefore, (8, 10) is not a solution to the system.    

8 0
3 years ago
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