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Mazyrski [523]
3 years ago
6

Write an equation for the nth term of the arithmetic sequence. 17, 12, 7, 2, ... an=

Mathematics
1 answer:
Lorico [155]3 years ago
5 0

Answer:

An equation for the nth term of the arithmetic sequence 17, 12, 7, 2 is 17-5n.

Step-by-step explanation:

Given,

first term(a)=17

common difference (d)=t2-t1

=12-17

=-5

nth term of the arithmetic sequence = a+n×d

=17+n×-5

=17-5n

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Use algebra ,What number exceeds y by 4 less than x?
andriy [413]

Answer:

y + (x-4)

Step-by-step explanation:

4 less than x= x-4

y exceeds 4 less than x = y + (x-4)

6 0
3 years ago
The coordinates of the vertices of a polygon are (-2, 1). (-3, 3), (-1, 5), (2, 4), and (2, 1). What is the perimeter of the pol
kobusy [5.1K]

Answer:

15.2\ units

Step-by-step explanation:

step 1

Plot the vertices of the polygon to better understand the problem

we have

A(-2, 1). B(-3, 3), C(-1, 5), D(2, 4),E(2, 1)

using a graphing tool

The polygon is a pentagon (the number of sides is 5)

see the attached figure

The perimeter is equal to

P=AB+BC+CD+DE+AE

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 2

<em>Find the distance AB</em>

A(-2, 1). B(-3, 3)

substitute in the formula

d=\sqrt{(3-1)^{2}+(-3+2)^{2}}

d=\sqrt{(2)^{2}+(-1)^{2}}

d_A_B=\sqrt{5}=2.24\ units

step 3

<em>Find the distance BC</em>

B(-3, 3), C(-1, 5)

substitute in the formula

d=\sqrt{(5-3)^{2}+(-1+3)^{2}}

d=\sqrt{(2)^{2}+(2)^{2}}

d_B_C=\sqrt{8}=2.83\ units

step 4

<em>Find the distance CD</em>

C(-1, 5), D(2, 4)

substitute in the formula

d=\sqrt{(4-5)^{2}+(2+1)^{2}}

d=\sqrt{(-1)^{2}+(3)^{2}}

d_C_D=\sqrt{10}=3.16\ units

step 5

<em>Find the distance DE</em>

D(2, 4),E(2, 1)

substitute in the formula

d=\sqrt{(1-4)^{2}+(2-2)^{2}}

d=\sqrt{(-3)^{2}+(0)^{2}}

d_D_E=\sqrt{9}\ units

d_D_E=3\ units

step 6

<em>Find the distance AE</em>

A(-2, 1).E(2, 1)

substitute in the formula

d=\sqrt{(1-1)^{2}+(2+2)^{2}}

d=\sqrt{(0)^{2}+(4)^{2}}

d_A_E=\sqrt{16}\ units

d_A_E=4\ units

step 7

Find the perimeter

P=AB+BC+CD+DE+AE

substitute the values

P=2.24+2.83+3.16+3+4=15.23\ units

Round to the nearest tenth of a unit

P=15.2\ units

6 0
3 years ago
Check for understanding:
solniwko [45]

Answer:

<em>Daniel does have enough money to make this car payment</em>

Step-by-step explanation:

<u>Addition and Subtraction</u>

Daniel has an initial balance of $460.63 on this checking account.

He must pay $85.23 for groceries.

The new balance is $460.63 - $85.23 = $375.40

He then pays $81.34 for his cell phone bill. The balance is now $375.40 - $81.34 = $294.06.

He receives a shopping refund of $52.13 that adds up to this balance that now is: $294.06 + $52.13 = $346.19.

Daniel has to make his $264 car payment. The balance is $346.19, thus:

Daniel does have enough money to make this car payment

6 0
2 years ago
A traveler is walking on a moving walkway in an airport The Traveler must walk back on the walkway to get a bag he forgot the Tr
hichkok12 [17]
Let the speed off the walk way be x and speed of the walkway be y
x+y=6....i
x-y=2....ii
adding the above equation we get:
2x=8
thus
x=4 ft/s
and
y=6-4=2 ft/s
thus the speed off the walk way is 4 ft/s
the speed of the moving walkway is 2 ft/s

6 0
3 years ago
Angle A and Angle B are vertical angles. If m
damaskus [11]

Answer:

∠B = 17°

Step-by-step explanation:

Vertical angles are congruent, thus

5x + 7 = x + 15 ( subtract x from both sides )

4x + 7 = 15 ( subtract 7 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

Hence

∠B = 5x + 7 = (5 × 2) + 7 = 10 + 2 = 17°

3 0
3 years ago
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