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3 years ago

Are opposite angles of two intersecting lines congruent?

Mathematics

1 answer:

Mamont248 [21]3 years ago

3 0

Answer:

They are Equal

Step-by-step explanation:

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A 208-yard-long road is divided into 16 parts of equal length. Mr. Ward paints a 4-yard-long strip in each part. How long is the

laila [671]

We have been given that a 208-yard-long road is divided into 16 parts of equal length.

Let us find length of each part.

$\text{Length of each part}=\frac{208}{16}$

$\text{Length of each part}=13$

Length of each part will be 13 yards.

We are told that Mr. Ward paints a 4-yard-long strip in each part.

Now we will subtract length of painted strip from length of each equal part to find length of unpainted strip of each part of the road.

$\text{Length of unpainted strip}=13-4$

$\text{Length of unpainted strip}=9$

Therefore, length of each unpainted strip will be 9 yards.

5 0

3 years ago

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 S₁ = 1.

• Assume the closed form is correct for all n up to n = k. 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 n = k + 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

The daytime temperature in Apple Valley is falling by 2.5 degrees each day. What will the net change in the daily temperature be

nexus9112 [7]

Answer:

Option D -17.5 degrees is correct answer

Step-by-step explanation:

Since a calendar week has 7 days. and temperature is falling by -2.5 daily.

So, On Day 1 Temperature is -2.5 degrees

On Day 2 Temperature is -2.5 + -2.5 = -5 degrees

On Day 3 Temperature is = -5 + -2.5 = -7.5 degrees

On Day 4 Temperature is = -7.5 + -2.5 = -10 degrees

On Day 5 Temperature is = -10 + -2.5 = -12.5 degrees

On Day 6 Temperature is = -12.5 + -2.5 = -15 degrees

On Day 7 Temperature is = -15 + -2.5 = -17.5 degrees

So, Option D -17.5 degrees is correct answer.

3 0

3 years ago

Read 2 more answers

Algebra 1

mojhsa [17]

Answer:

None

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is the theoretical probability of picking a diamond, not replacing it, and then picking another diamond? Write your answer

BARSIC [14]

You start with a 1/4 chance of picking a diamond.
you remove it from the deck you now have a 12/51 chance of picking a diamond
1/17 is your answer!

Like my answer? Make it a Brainliest! Thanks!

3 0

3 years ago