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3 years ago

An arithmetic sequence has a first term of 10 and a sixth term of 40. What is the 20th term of this sequence?

2 answers:

6 0

In An arithmetic sequence will add or subtract the same thing each time to find the next term. In this case we start with 10 and need to get to 40 on the 6th term. This is a difference of 30 that needs to be divided by 5 open spaces. You are adding 6 each time.

10, 16, 22, 28, 34, 40, _,_,_,_, 70, _,_,_,_,100,_,_,_, 124.

Another way to do this would be to look at the 5th term and multiply it by 4 to get to the 20th term. 34 x 4 = 124.

goldfiish [28.3K]3 years ago

3 0

Answer:124

Step-by-step explanation:

This is an arithmetic sequence

The nth term of an arithmetic sequence is Tn = a + (n-1)d

a is the first term.

n is the number of terms

d is the common difference

a is 10

The sixth term T6 = 10 + (6-1)d = 40

T6 = 10 - 5d = 40

5d = 40 - 10

5d = 30

d = 6

To get the 20th term T20

T20 = 10 + (20-1)6

T20 = 10 + 19(6)

T20 = 10 + 114

T20 = 124

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FrozenT [24]

Hello!

The statement that is true about the three quadrilaterals is the first one:

$\boxed{ \bf D~and~E~are~similar~but~not~congruent.}$

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Option #2 is incorrect because although E and F are similar, they are not congruent. They do not have the same size.

Option #3 is also incorrect because, again, D and E are similar, but they are not congruent.

Option #4 is not correct because it says that "F and D are similar but not congruent." This is not true since they are the same shape and size. Only their orientation is different, which makes them congruent.

4 0

4 years ago

Find the height "h" so that its area is equal to 400 square cm.

jenyasd209 [6]

Answer:

h = 20 cm

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) *h

where b1 and b2 are the two bases

We are given a =400 and b1 =27 and b2 =13

400 = 1/2 (27+13) *h

400 = 1/2 (40) *h

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400/20 = 20h/20

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8 0

3 years ago

ipn [44]

Answer:

50 soldiers must be transferred elsewhere.

Step-by-step explanation:

We solve this question by proportions, using a rule of three.

As the number of soldiers decrease, the provisions last for more time. This means that the measures are inversely proportional, and we have an inverse rule of three, using line multiplication, instead of cross.

30 days of provisions - 200 soldiers

40 days of provisions - x soldiers

$40x = 200*30$

Simplifying by 40

$x = 5*30 = 150$

The provisions will last for 40 days with 150 soldiers, which means that 200 - 150 = 50 soldiers must be transferred elsewhere.

4 0

3 years ago

Find the measurement of the angle

Shalnov [3]

Answer:

∠ 1 = 120°

Step-by-step explanation:

Note that ∠ Q and ∠ R are congruent, that is both 30°, thus

∠ 1 = 180° - (30 + 30)° = 180° - 60° = 120°

6 0

4 years ago

If f(x) = x2 and g(x) = 3x + 1, then g(f(2))= ?

andreyandreev [35.5K]

Answer:

The value of g[f(2)] = 13

Step-by-step explanation:

Given functions:

f(x) = x²

g(x) = 3x + 1

Find:

The value of g[f(2)]

Computation:

f(x) = x²

By putting x = 2 in f(x)

f(x) = x²

f(2) = 2²

f(2) = 2 × 2

f(2) = 4

So the value of f(2) = 4

Value of f(2) putting in g(x)

g(x) = 3x + 1

g[f(2)] = 3[f(2)] + 1

We know that f(2) = 4

So,

g[f(2)] = 3[f(2)] + 1

g[f(2)] = 3[4] + 1

g[f(2)] = 12 + 1

g[f(2)] = 13

The value of g[f(2)] = 13

8 0

3 years ago