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taurus [48]
3 years ago
10

the rop of a table is in the shape of a trpezoid.it has height 1.5 feet and two parallel bases measure 3 feet and 5 feet.what is

the area of the top of the table?
Mathematics
1 answer:
alexandr1967 [171]3 years ago
7 0
A_{trapezoid} = \dfrac{(b_1 + b_2)h}{2}

A_{trapezoid} = \dfrac{(3~ft + 5~ft)(1.5~ft)}{2}

A_{trapezoid} = 6~ft^2
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Sophia spent $27.16 on four sandwiches. If each sandwich cost the same amount, how much does one sandwich cost?
HACTEHA [7]

Answer:

6.79

Step-by-step explanation:

you just divide 27.16 (the cost) by 4 (how many sandwiches were purchased)

5 0
2 years ago
If 2k, 5k-1 and 6k+2 are the first 3 terms of an arithmetic sequence, find k and the 8th term​
Klio2033 [76]

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a_{2} - a_{1} = a_{3} - a_{2}

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

--------------------------------------------------------

The n th term of an arithmetic sequence is

a_{n} = a_{1} + (n - 1)d

a_{1} = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

a_{8} = 4 + (7 × 5) = 4 + 35 = 39

4 0
3 years ago
Drag each set of column entries to the correct location in the matrix equation. Not all sets of entries will be used. A biker ne
ANEK [815]

Answer:

The matrix equation is \left[\begin{array}{ccc}1&1&1\\1&-1/2&0\\0&2&-1\end{array}\right]=\left[\begin{array}{c}120&35&20\end{array}\right]

Step-by-step explanation:

* Lets change the story problem to equations

- The distance between the starting point and checkpoint 1 is x

- The distance between checkpoint 1 to checkpoint 2 is y

- The distance between checkpoint and the finish line is z

- The total distance for the race is 120 miles

∴ x + y + z = 120 ⇒ (1)

-The distance from the starting point to checkpoint 1 is 35 miles

 more than half the distance from checkpoint 1 to checkpoint 2

∵ The distance from the starting point to checkpoint 1 is x

∵ The distance from checkpoint 1 to checkpoint 2 is y

- x is more than half y by 35

∴ x = 35 + (1/2) y ⇒ subtract (1/2) y from both sides

∴ x - (1/2) y = 35 ⇒ (2)

- The distance from checkpoint 2 to the finish line is 20 miles less

 than twice the distance from checkpoint 1 to checkpoint 2

∵ The distance from checkpoint 2 to the finish line is z

∵ the distance from checkpoint 1 to checkpoint 2 is y

- z is less than twice y by 20

∴ z = 2y - 20 ⇒ add 20 to both sides

∴ z + 20 = 2y ⇒ subtract z from both sides

∴ 2y - z = 20 ⇒ (3)

* Now lets write the three equations

# x + y + z = 120 ⇒ (1)

# x - (1/2) y = 35 ⇒ (2)

# 2y - z = 20 ⇒ (3)

- Now lets write the matrix equation that models this situation

∴ \left[\begin{array}{ccc}1&1&1\\1&-1/2&0\\0&2&-1\end{array}\right]=\left[\begin{array}{c}120&35&20\end{array}\right]

6 0
2 years ago
Read 2 more answers
Identify the coefficients in the expression below.<br><br> -6x+5y+4x+9
Montano1993 [528]

Answer:

3 coefficients in this expression are: -2x, 5y and 9 (natural number)

Step-by-step explanation:

-6x + 5y + 4x + 9

= -6x + 4x + 5y + 9

= -2x + 5y + 9

3 coefficients in this expression are: -2x, 5y and 9 (natural number)

Hope this help you :3

5 0
2 years ago
Read 2 more answers
Which circle is the graph of the equation (x + 4)2 + (y – 5)2 = 4?
garri49 [273]

Answer: CIRCLE C

Step-by-step explanation:

8 0
2 years ago
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