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Anton [14]
2 years ago
7

The lucas sequence is the sequence 1, 3, 4, 7, 11, $\ldots$ where the first term is 1, the second term is 3 and each term after

that is the sum of the previous two terms. what is the remainder when the $100^{\mathrm{th}}$ term of the sequence is divided by 8?
Mathematics
1 answer:
nexus9112 [7]2 years ago
7 0
Mod 8, the sequence repeats after 12 terms:
  1 3 4 7   3 2 5 7   4 3 7 2

Thus the 100th term, mod 8, will be the 4th term of this sequence: 7
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Triangle NLM is reflected over the line segment as shown, forming triangle ABC. Which congruency statement is correct? ΔNLM ≅ ΔC
algol13
<span>Given that triangle NLM is reflected over the line segment as shown, forming triangle ABC.

When a point is refrected across a line, the relative distance form the point to the line of refrection is preserved. That is the distance from the point to the line of refrection is equal to the distance of the image to the line of refrection.

Thus, from the figure, it can be seen the point B is of the same distance to the line of refrection as point M, so is point A to point L and point C to point N.

Thus, </span><span>ΔNLM is similar to </span><span><span>ΔCAB

Therefore, the</span> congruency statement that is correct is ΔNLM ≅ ΔCAB</span>
9 0
2 years ago
Read 2 more answers
Alayna parks her car in a lot that charges by the quarter hour. The table shows the parking fee, in dollars, with respect to the
riadik2000 [5.3K]

Answer:

time should be placed on the independent/y-axis

parking fee should be placed on the dependent/x-axis

Step-by-step explanation:

good luck.

give me brainliest please:)

7 0
2 years ago
What is the true solution to the equation below?
jarptica [38.1K]

Answer:

Step-by-step explanation:

some rules of logarithmic function

ln(a) - ln(b)=ln(\frac{a}{b})

e^{ln(a)}=a

ln(a)^{n}=nln(a) vice-versa nln(a)=ln(a)^{n}

If ㏑(a) = ㏑(b), then a = b

∴ 2ln(e^{ln(2x)})-ln(e^{ln(10x)})=ln(30)

Use the 2nd rule to simplify it

e^{ln(2x)}=2x\\e^{ln(10x)}=10x\\

2㏑(2x) - ㏑(10x) = ㏑(30)

Use the 3rd rule in the 1st term

∵ 2㏑(2x) = ㏑(2x)² = ㏑(4x²)

∴ ㏑(4x²) - ㏑(10x) = ㏑(30)

- Use the 1st rule with the left hand side

ln(4x^{2})-ln(10x)=ln(\frac{4x^{2}}{10x})\\\\ln(\frac{4x^{2}}{10x})=ln(30)\\\\ \frac{4x^{2}}{10x}=\frac{2x}{5}=\frac{2}{5}x\\\\ ln(\frac{2}{5}x)=ln(30)

Use the 4th rule

\frac{2}{5} x = 30

Multiply both sides by 5

∴ 2 x = 150

- Divide both sides by 2

∴ x = 75

The value of x = 75

3 0
2 years ago
Consider the following formula used to estimate height, h, of a seedling after w weeks since planting:
svp [43]

Answer:

Option B. w=5h-8

Step-by-step explanation:

we have

h=(\frac{1}{5})w+(\frac{8}{5})

Solve for w

That means ----> isolate the variable w

Multiply by 5 both sides to remove the fraction

5h=w+8

subtract 8 both sides

5h-8=w+8-8

5h-8=w

Rewrite

w=5h-8

4 0
2 years ago
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents th
Novay_Z [31]

Answer:

Step-by-step explanation:

I use  84+ CE

stat edit, then fill in the #s

then

vars 5

then

2'nd stat plot, on

then, click stat

Click arrow 1 time to the left to get to Calc

then click (4)(LinReg(ax+b))

then click enter 5 times

(y=-25.31428571x+1000.285714

y=-25.3x+1000.3

now, lets use computer:

y=-25.31(543)+1000.3

y=-12743.03

round to the biggest whole number )

this doesn't really work, so I will put 1999, 2000, 2001, 2002, 2003, 2004 instead of 0, 1, 2, 3, 4, 5 and do the same thing

now I get

y=-25.31428571x+51603.54286

y=-25.3x+51603.5

now, lets use computer:

y=-25.3(543)+51603.5

y=37865.6

round to the biggest whole number:

y=37866

so, year 37866

7 0
2 years ago
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