What’s 9 + 10? Really struggling :(

Is 1/3, 2/3, 4/3, 8/3, 16/3 arithmetic sequence

The given sequence is not arithmetic sequence

Solution:

Given sequence is:

$\frac{1}{3} , \frac{2}{3} , \frac{4}{3} , \frac{8}{3} , \frac{16}{3}$

We have to find if the above sequence is arithmetic sequence or not

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

Here in the given sequence

$\text{ first term } = a_1 = \frac{1}{3}\\\\\text{ second term } = a_2 = \frac{2}{3}\\\\\text{ third term } = a_3 = \frac{4}{3}\\\\\text{ fourth term } = a_4 = \frac{8}{3}\\\\\text{ fifth term } = a_5 = \frac{16}{3}$

Let us find the difference between terms

$a_2 - a_1 = \frac{2}{3} - \frac{1}{3} = \frac{1}{3}$

$a_3 - a_2 = \frac{4}{3} - \frac{2}{3} = \frac{2}{3}$

$a_4 - a_3 = \frac{8}{3} - \frac{4}{3} = \frac{4}{3}$

$a_5 - a_4 = \frac{16}{3} - \frac{8}{3} = \frac{8}{3}$

Thus the difference between terms is not constant

So the given sequence is not arithmetic sequence

5 0

3 years ago

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, = 6 centime

Bingel [31]

Answer:

Part A) see the explanation

Part B) see the explanation

Part C) The perimeter of trapezoid ABCD is 32 centimeters and the perimeter of trapezoid EFGH is 48 centimeters

Step-by-step explanation:

The complete question is

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

Part A) Write a similarity statement for each of the four pair of corresponding sides

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

The corresponding sides are

AB and EF

BC and FG

CD and GH

AD and EH

so

$\frac{AB}{EF}=\frac{BC}{FG}=\frac{CD}{GH}=\frac{AD}{EH}$

Part B) Write a congruence statement for each of the four pair of corresponding angles.

we know that

If two figures are similar, then its corresponding angles are congruent

The corresponding angles are

∠A and ∠E

∠B and ∠F

∠C and ∠G

∠D and ∠H

so

∠A ≅ ∠E

∠B ≅ ∠F

∠C ≅ ∠G

∠D ≅ ∠H

Part C) Determine the perimeter for each of the isosceles trapezoids

we have

The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

step 1

Find the measure of CD

Remember that

The ratio between corresponding sides is proportional and this ratio is the scale factor

Let

z ----> the scale factor

$z=\frac{2}{3}$

so

$\frac{2}{3}=\frac{CD}{GH}}$

we have

$GH=6\ cm$

substitute

$\frac{2}{3}=\frac{CD}{6}}\\\\CD=4\ cm$

step 2

Find the measure of AB

Remember that

AB is three times the length of DC

so

$AB=3DC$

$DC=CD=4\ cm$

substitute

$AB=3(4)=12\ cm$

step 3

Find the measure of BC

Remember that in an isosceles trapezoid, the legs are equal

so

BC=AD

we have

$AD=8\ cm$

therefore

$BC=8\ cm$

step 4

Find the perimeter of trapezoid ABCD

$P=AB+BC+CD+AD$

substitute the values

$P=12+8+4+8=32\ cm$

step 5

Find the perimeter of trapezoid EFGH

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ---> the scale factor

x ----> the perimeter of trapezoid ABCD

y ----> the perimeter of trapezoid EFGH

so

$z=\frac{x}{y}$

we have

$z=\frac{2}{3}$

$x=32\ cm$

substitute

$\frac{2}{3}=\frac{32}{y}$

$y=32(3)/2=48\ cm$

therefore

The perimeter of trapezoid EFGH is 48 centimeters

3 0

3 years ago

What is the answer for this express

kotykmax [81]

12, 2, 4, and 7. The coefficients in the expression 12xy³+2x⁵y+4x⁵y²+7x⁵y are 12, 2, 4, and 7.

In order to solve this problem we have to know that the coefficients is a factor linked to a monomial. For example, the first monomial of the equation is 12xy³ the coeffcient of xy³ is 12.

8 0

3 years ago

Read 2 more answers

Given f(x)=1/4(5-x)2 what is the value of f(11)

iren [92.7K]

Answer:

f(x)=1/4(5-x)²

Step-by-step explanation:

f(11)=1/4(5-11)²

1/4(-6)²

1/4(36)

=9