All categories

3 years ago

I attatched the problem

Mathematics

2 answers:

Lorico [155]3 years ago

8 0

Heya!

--------------------

Things to know before we solve:

The "6" at the top means that the the sequence only goes to the 6th term.

k = 3 represents that the sequence starts with the 3rd term.

(-2k + 5) represents the rule of the sequence, we can substitute 3, 4, 5, and 6 to solve for the terms of the sequence.

--------------------

Solving for each term:

3rd term:

-2(3) + 5

-6 + 5

-1

4th term:

-2(4) + 5

-8 + 5

-3

5th term:

-2(5) + 5

-10 + 5

-5

6th term:

-2(6) + 5

-12 + 5

-7

--------------------

Simplifying:

Write these terms in expanded form:

(-1) + (-3) + (-5) + (-7)

Find the sum of the series:

(-1) + (-3) + (-5) + (-7) = -16

--------------------

Answer:

The sum of the series is -16

--------------------

Best of Luck!

DanielleElmas [232]3 years ago

6 0

Answer:

-16

Step-by-step explanation:

k = 3

-2(3) + 5 = -1

k = 4

-2(4) + 5 = -3

k = 5

-2(5) + 5 = -5

k = 6

-2(6) + 5 = -7

(-1) + (-3) + (-5) + (-7)

= -16

You might be interested in

Charlie needs to drive to Dallas which is 240 miles. If he drives 60 miles

Eduardwww [97]

Answer:

Step-by-step explanation:

Since the question is asking how long will it take him if he has to drive 240 miles and he drives 60 mph, this can be interpreted as division.

Now that we have converted the words into math, we are really solving 240 ÷ 60 or $\frac{240}{60}$ .

240 divided by 60 is the same as 24 divided by 6 because we can cancel the 0's.

Solving:

24 ÷ 6 = 4.

Thus, our answer is that it will take Charlie 4 hours to get to Dallas.

7 0

3 years ago

The net of a solid figure is shown below:

TiliK225 [7]

The answer is 6*4*4 square inches where 4*4 gives us the area of one square and multiplying by 6 gives you the total surface area.

8 0

3 years ago

Read 2 more answers

Which of the following sets are subspaces of R3 ?

Ratling [72]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

for point A:

$\to A={(x,y,z)|3x+8y-5z=2} \\\\\to for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)$

$=3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)$

The set A is not part of the subspace $R^3$

for point B:

$\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)$

$=-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0$

$\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon B$

The set B is part of the subspace $R^3$

for point C: $\to C={(x,y,z)|x$

In this, the scalar multiplication can't behold

$\to for (-2,-1,2) \varepsilon C$

$\to -1(-2,-1,2)= (2,1,-1)$ ∉ C

this inequality is not hold

The set C is not a part of the subspace $R^3$

for point D:

$\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)$

The scalar multiplication s is not to hold

$\to for (-4, 1,2)\varepsilon D\\\\\to -1(-4,1,2) = (4,-1,-2)$ ∉ D

this is an inequality, which is not hold

The set D is not part of the subspace $R^3$

For point E:

$\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\$

The $x_1, x_2$ is the arbitrary, in which $ax_1+bx_2$ is arbitrary

$\to a(x_1,0,0)+b(x_2,0,0) \varepsilon E$

The set E is the part of the subspace $R^3$

For point F:

$\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon F \\\\\to a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))$

The $x_1, x_2$ arbitrary so, they have $ax_1+bx_2$ as the arbitrary $\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F$

The set F is the subspace of $R^3$

5 0

3 years ago

Triangle EFG is an isosceles triangle with EG=EF. What is the approximate length of EF, and what is the approximate perimeter of

sineoko [7]

Answer:

B. The approximate length of EF is 4.47 units, and the approximate perimeter of triangle EFG is 12.94 units.

Step-by-step explanation:

First step is to determine the length of EF, since that will give us 2 sides of the triangle (since EG = EF).

From the diagram, we can easily make a rectangle triangle by dropping a vertical line from vertex E, let's name Z the meeting point of that line with the segment GF. Then we have a rectangle triangle EZF with a height of 4 and a base of 2, of which EF is the hypotenuse. So...

EF² = 4² + 2² = 16 + 4 = 20

EF = √20 = 4.47

Now that we have EF, we also have EG:

EF = 4.47

EG = 4.47

GF = 4 (visible on the graph)

Perimeter = 4.47 + 4.47 + 4 = 12.94 units.

7 0

3 years ago

Read 2 more answers

Why does -6 - (-2) equal -4?

lukranit [14]

Answer:

when you subtract a negative number the two negative signs cancel out and it turns to a positive number

Step-by-step explanation:

in -6 - (-2)

the two - signs cancel out so it ends up being

-6+2 which is why it equals -4

8 0

3 years ago

Read 2 more answers