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3 years ago

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Mathematics

1 answer:

raketka [301]3 years ago

8 0

Answer:

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Is the sequence arithmetic if so identify the common difference 13 20 27 34?

Anastasy [175]

Answer:

Yes, The given sequence is Arithmetic with common difference is 7.

Step-by-step explanation:

The given sequence is Arithmetic Sequence.

Generally, we study about two types of sequences which are:

Arithmetic Sequence is a sequence in which every two neighbor digits have equal distances.

Geometric Sequence is the sequence in which every digit is the same multiplier of its previous digit.

The given sequence is: 13, 20, 27, 34,...

Here, First term(a) = 13, Second term(b) = 20

Common difference (d) = b - a = 20 - 13 = 7

Hence, Common difference is 7.

5 0

3 years ago

Read 2 more answers

Find a third-degree polynomial equation with the rational coefficients that has roots -3 and 1+i

jolli1 [7]

Answer:

x³ + x² − 4x + 6 = 0

Step-by-step explanation:

Imaginary roots come in conjugate pairs. So if 1+i is a root, then 1−i is also a root.

(x − (-3)) (x − (1+i) (x − (1−i)) = 0

(x + 3) (x² − (1+i) x − (1−i) x + (1+i) (1−i)) = 0

(x + 3) (x² − x − ix − x + ix + 1 − i²) = 0

(x + 3) (x² − 2x + 2) = 0

x (x² − 2x + 2) + 3 (x² − 2x + 2) = 0

x³ − 2x² + 2x + 3x² − 6x + 6 = 0

x³ + x² − 4x + 6 = 0

3 0

3 years ago

Mom baked a Dutch apple pie in a 9-inch pie pan. She cut the pie into 6 equal pies so that

Hatshy [7]

The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

<h3>How can the pie pieces dimensions be evaluated?</h3>

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = $\dfrac{360^{\circ}}{6}$ = 60°

Therefore;

The central angle of two pie pieces = 2 × 60° = <u>120°</u>

b. Area of circular pie = π·r²

Where;

$r = \mathbf{\dfrac{d}{2}}$

Therefore;

$r = \dfrac{9}{2} = \mathbf{ 4.5}$

$The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}$

The area covered by each pie piece is approximately <u>10.6 square inch</u>

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ <u>28.3 in.</u>

d. Let the arc length of the pie piece = 7 inches

$\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8$

The area of the pie piece is approximately <u>15.8 in.²</u>

<u />

<u /> $The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}$

Learn more about circumference, area and sector of a circle here:

brainly.com/question/12985985

5 0

2 years ago

The product of a number and five is eight

artcher [175]

Answer:

Assuming x is the number, then $x=1.6$

Step-by-step explanation:

If the product of a number and 5 is 8, the equation becomes:

$5x=8$ (assuming x is the unknown number).

We can isolate the variable x by dividing both sides by 5.

$5x\div5 = 8\div5\\x = 1.6$

Hope this helped!

3 0

3 years ago

If y = 80 when x= 32, what is the value of y when x = 5?

REY [17]

Answer: 12.5

Step-by-step explanation:

32 divided by 5= 6.4

80 divided by 6.4= 12.5

7 0

3 years ago

Read 2 more answers