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iren [92.7K]
3 years ago
5

You roll a number cube 20 times. The number 4 is ro

Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
5 0
It would be 40 answer A
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In an arithmetic sequence, t4 + t5 + t6 = 300, and t15 +t16+ t17 = 201. Find t18.
stiks02 [169]
In an arithmetic sequence:
Tn=t₁+(n-1)d

t₄=t₁+(4-1)d=t₁+3d
t₅=t₁+(5-1)d=t₁+4d
t₆=t₁+(6-1)d=t₁+5d

t₄+t₅+t₆=(t₁+3d) +(t₁+4d)+(t₁+5d)=3t₁+12d

Therefore:
3t₁+12d=300    (1)


t₁₅=t₁+(15-1)d=t₁+14d
t₁₆=t₁+(16-1)d=t₁+15d
t₁₇=t₁+(17-1)d=t₁+16d

t₁₅+t₁₆+t₁₇=(t₁+14d)+(t₁+15d)+(t₁+16d)=3t₁+45d

Therefore:
3t₁+45d=201    (2)

With the equations (1) and (2) we make an system of equations:

3t₁+12d=300
3t₁+45d=201

we can solve this system of equations by reduction method.

  3t₁+12d=300
-(3t₁+45d=201)
-----------------------------
       -33d=99      ⇒d=99/-33=-3

3t₁+12d=300
3t₁+12(-3)=300
3t₁-36=300
3t₁=300+36
3t₁=336
t₁=336/3
t₁=112

Threfore:

Tn=112+(n-1)(-3)
Tn=112-3n+3
Tn=115-3n

Now, we calculate T₁₈:

T₁₈=115-3(18)=115-54=61

Answer: T₁₈=61




5 0
3 years ago
7: In the rhombus, m∠1=10x, m∠2=x + y, and m∠3= 5z. Find the values of x, y, and z.
malfutka [58]
Angles 1, 2, and 3 are all 90°.

10x = 90
.. x = 9

x +y = 90
.. y = 81

5z = 90
.. z = 18

The values of (x, y, z) are (9, 81, 18).

7 0
3 years ago
Please help me with this math problem. Only type answer please dont upload files
posledela
3) 3(8b + 3)
4) 57

I’m pretty sure that this is the answer
8 0
2 years ago
Kenzie finds purple, blue, and silver space rocks while exploring, 2/3 of the rocks are purple and 3/4 of the remainder are blue
Nadya [2.5K]

Answer:

There were 36 space rocks in total.

Step-by-step explanation:

First, you need to find what fraction of the original rocks are silver.

If 2/3 are purple, then 1/3 of them are not.

If 3/4 of the remaining 1/3 are blue, then 3/4 x 1/3 = 3/12 rocks are blue.

2/3 of the rock are purple, 3/12 of them are blue, and the remaining is silver.

So, you need to do 2/3 - 3/12, then find common denominators so, 8/12 - 3/12 which = 1/12.

This means 1/12 of the rocks are silver. If there are silver rocks, you need to find a suitable equation that needs to be solved.

So:

1/12r = 3

r = 36 silver rocks

There were 36 space rocks in total.

hope this helps :)

3 0
3 years ago
Read 2 more answers
R is (-8,2) and RS is (-1,5) what are the coordinates of S?
Alexxx [7]

Answer:

detailed

Step-by-step explanation:

answer

7 0
3 years ago
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