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2 years ago

Which of the following is most likely the next step in the series

Mathematics

1 answer:

alukav5142 [94]2 years ago

7 0

Answer:

Step-by-step explanation:

The pattern is quadrilateral (4-gon), pentagon (5-gon), and hexagon (6-gon). Therefore the next figure would be a heptagon (7-gon).

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The perimeter of a rectangle must be less than 170170 feet. If the length is known to be 4444 feet, find the range of possible w

katrin [286]

Answer:

$w \in (0,41)$

where w is width of rectangle.

Step-by-step explanation:

We are given the following in the question:

The perimeter of a rectangle must be less than 170 feet.

Length of rectangle = 44 feet

Perimeter of rectangle =

$2\times (\text{Length + Width})$

Let w be the width of rectangle.

According to the question,

$P < 170\\2(44 + w)$

Thus, the width of triangle should be less than 41. Since w cannot take negative values, we can express value of w in interval notation as,

$w \in (0,41)$

4 0

3 years ago

Solve the system of equations by finding the reduced row echelon form of the augmented matrix. Write the solutions for x and y i

Gwar [14]

Answer:

The solutions for the given system of equations are:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

Step-by-step explanation:

Given the equation system:

$\left \{ {{3x+y+4z=-3} \atop {-x+y+4z=17}} \right.$

We obtain the following matrix:

$\left[\begin{array}{cccc}3&1&4&-3\\-1&1&4&17\end{array}\right]$

Step 1: Multiply the fisrt row by 1/3.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\-1&1&4&17\end{array}\right]$

Step 2: Sum the first row and the second row.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&\frac{4}{3} &\frac{16}{3}&16\end{array}\right]$

Step 3: Multiply the second row by 3/4.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&1 &4&12\end{array}\right]$

Step 4: Multiply the second row by -1/3 and sum the the first row.

$\left[\begin{array}{cccc}1&0 &0&-5\\0&1 &4&12\end{array}\right]$

The result of the reduced matrix is:

$\left \{ {{x=-5} \atop {y+4z=12}} \right.$

This is equal to:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

These are the solutions for the system of equations in terms of z, where z can be any number.

6 0

2 years ago

Benny was told to practice playing piano for 4/11 of an hour per day. Benny has already played 3/14 of an hour today. How many h

alekssr [168]

Solution:

4/11 = 0.36

3/14 = 0.21

He still needs to play 0.15 of an hour or 3/20 of an hour.

Given facts - Amount he has to play, and the amount he played.
Question - For how long does he need to practice to meet the required time.
Hidden question - There is nothing hidden
Operations used - divisions (not necessary), subtractions and conversion (only if used division).
Number sentence - 4/11 - 3/14 = x
Answer - 3/10 of an hour.

Hope it helped,

Happy homework/ study/ exam!

5 0

2 years ago

Determine whether the following sequence is geometric. If so, find the common ratio.

Shtirlitz [24]

Answer:

a) r = 5

b) false

Step-by-step explanation:

study about GP

8 0

3 years ago

The complement of an angle is 25 less than 3 times the angles itself. Find the measure of each

Semenov [28]

Answer: 28.75° and 61.25°

Step-by-step explanation:

A complementary angle equals 90°.

Let the measure of the angle be a

Therefore, its complement will be:

= 90-a.

The complement of an angle is 25 less than 3 times the angles itself can be written as:

90-a = 3a - 25

90 + 25 = 3a + a

115 = 4a

a = 115/4

a= 28.75

Since the angle is 28.75°, the complement will be:

= 90° - 28.75°

= 61.25°

The angles are 28.75° and 61.25°

6 0

3 years ago