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yawa3891 [41]
3 years ago
8

For Problem 10, simplify the expressions using properties of operations. 10. (t - 1) – (-7t+2)​

Mathematics
1 answer:
zvonat [6]3 years ago
4 0

Answer:

8t-3

Step-by-step explanation:

(t-1)-(-7t+2)

t-1+7t-2

t+7t-1-2

8t-1-2

8t-3

You might be interested in
1 point
galina1969 [7]

Answer:

(B) 20

Step-by-step explanation:

Let small puppet be represented by-----------------s

Let large puppet be represented by-----------------l

Total number of puppets expression will be: s+l =25---------a

The expression for total costs will be : 1$ s + $2l=$30-------b

Equation a can be written as; s= 25-l ------------c

Use equation c in equation b as

$1( 25-l )+$ 2l = $30

25-l + 2l = 30

25+l =30

l= 30-25 =5

l, large puppets = 5

s, small puppets = 25-5 = 20

Answer choice A is incorrect because 25 is the total number of all puppets

Answer choice C and D are incorrect because the numbers are less that that of small puppets.

3 0
3 years ago
five consecutive terms of an arithmetic sequence have a sum of 40. The product of the middle and the two end terms is 224. Find
ratelena [41]
Let the five terms be: a, a + d, a + 2d, a + 3d, a + 4d, then
a + a + d + a + 2d + a + 3d + a + 4d = 5a + 15d = 40
i.e. a + 3d = 8
Also, (a + 2d)(a + 3d)(a + 4d) = 224
(a + 3d - d)(a + 3d)(a + 3d + d) = 224
(8 - d)(8)(8 + d) = 224
(8 - d)(8 + d) = 224/8 = 28
64 - d^2 = 28
d^2 = 64 - 28 = 36
d = sqrt(36) = 6
But a + 3d = 8
a + 3(6) = 8
a = 8 - 18 = -10

Therefore, the term of the sequence is: -10, -10 + 6, -10 + 2(6), -10 + 3(6), -10 + 4(6)
= -10, -4, -10 + 12, -10 + 18, -10 + 24
= -10, -4, 2, 8, 14

4 0
3 years ago
Two angles of a triangle have a sum of 110. the sum of all three angles is 180 .what is the measure of the third angle
defon
Well by the looks of it The missing angle is 70 degrees. I say this because 110 + 70 = 180. If you were asking what were the two angles just divide.
6 0
3 years ago
Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5
zaharov [31]

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}} or \displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}

Therefore, the solution is 31.

__________________________________________________________

Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as \displaystyle \large{a_{n-1} \cdot r = a_n} meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

\displaystyle \large{r=\frac{a_{n+1}}{a_n}}

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}

Above should be applied for series that have common ratio not equal to 1.

\displaystyle \large{S_n=a_1 \cdot n}

Above should be applied for series that have common ratio exactly equal to 1.

__________________________________________________________

Topics

Sequence & Series — Geometric Series

__________________________________________________________

Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

__________________________________________________________

7 0
2 years ago
The area of the rectangle below is __sq. units.<br> 5<br> 16
SIZIF [17.4K]

Answer:

C.

Step-by-step explanation:

To find the area of a rectangle, times the length and the breadth together. So, it would be 16×5=80. option C is 80.

4 0
3 years ago
Read 2 more answers
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