Find the fifth term in the sequence
that is defined as follows:
an = 3n - 5

-3 (2.5 + k) + 0.5 (7 + 8k)

Apply distributive property.

-7.5 - 3k + 3.5 + 4k

Add like terms.

-4 + k

k - 4

k - 4 is your answer. I hope this helps you! Let me know if I got anything wrong.

Answer: if you are simplifying it the answer is k-4

Step-by-step explanation:

Answer:

The simplest form of 42/18 is 7/3 or 2 1/3

Step-by-step explanation:

Answer:

7/3 or 2 and 1/3

Step-by-step explanation:

So first you have to find what is GCF of 42 and 18, which is 6 so divide 42 and 18 by 6 and you get 7/3 which is your simplified fraction but you can make this into a mixed number which would be 2 and 1/3

Answer:

14%

Step-by-step explanation:

42 ÷ 300 = 0.14 = 14%

or

subtract 42 from 300 which gives you 258

258 is 86% of 300

86-100 is 14 so 14%

Answer:

Electric force = 8.20x10⁻⁸ N

Gravitational force = 3.61x10⁻⁴⁷ N

Step-by-step explanation:

1. The electric force can be found using the following equation:

[tex] F_{e} = \frac{Kq_{e}q_{p}}{d^{2}} [/tex]

Where:

K: is the Coulomb's constant = 9x10⁹ N.m²/C²      

[tex]q_{p}[/tex]: is the charge of the proton = 1.6x10⁻¹⁹ C

[tex]q_{e}[/tex]: is the charge of the electron = -1.6x10⁻¹⁹ C

d: is the distance = 5.3x10⁻¹¹ m

Hence, the magnitude of the electric force is:

[tex] |F_{e}| = \frac{9\cdot 10^{9} N.m^{2}/C^{2}*(-1.6\cdot 10^{-19} C)*1.6 \cdot 10^{-19} C}{(5.3 \cdot 10^{-11} m)^{2}} = 8.20 \cdot 10^{-8} N [/tex]                

2. The gravitational force can be calculated as follows:

[tex] F_{g} = \frac{Gm_{e}m_{p}}{d^{2}} [/tex]

Where:

[tex]m_{e}[/tex]: is the electron's mass = 9.1x10⁻³¹ kg

[tex]m_{p}[/tex]: is the proton's mass = 1.67x10⁻²⁷ kg

G: is the gravitational constant = 6.67x10⁻¹¹ N.m²/kg²

Therefore, the gravitational force is:

[tex] F_{g} = \frac{6.67 \cdot 10^{-11} N.m^{2}/kg^{2}*9.1 \cdot 10^{-31} kg*1.67 \cdot 10^{-27} kg}{(5.3 \cdot 10^{-11} m)^{2}} = 3.61 \cdot 10^{-47} N [/tex]

As we can see, the gravitational force is much less than the electric force.

I hope it helps you!                                                      

Answer:

x=112

Step-by-step explanation:

[tex]\frac{x}{7} =16[/tex]

x=16*7

x=112

Answer: x = 112

Step-by-step explanation: To solve this equation for x,

I would first change x ÷ 7 to x/7 to make it easier to visualize.

So we have [tex]\frac{x}{7} = 16[/tex].

Since x is being divided by 7, we multiply both sides by 7.

On the left, hat gives us x and on the right, 16 x 7 is 112.

So we have x = 112.

Answer:

25m

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The length of the paper , x, can be obtained using Pythagoras :

Width = 12 ; length = 15

x² = 15² - 12²

x² = 225 - 144

x² = 81

x = sqrt(81)

x = 9

Hence, length of the paper = 9 inches

Step-by-step explanation:

3 is being multiplied by the numbers in the bracket so

18-(3x1+3x5)

18-(3+15)

18-(18)

answer is 0

Answer:

y=1/3x-3

m1=1/3

from,m1m2=-1

1/3m2=-1

m2=-3

again, from

m=(y-y1)/(x-x1)

-3=(y-2)/(x-3)

y-2=-3(x-3)

y-2=-3x+9

y=-3x+9+2

y=-3x+11

9514 1404 393

Answer:

  D.  52 ÷ 3 =17, with a remainder of 1

Step-by-step explanation:

There are only two answer choices that make a true statement: A and D. Of these, comparison with the diagram shows that you're looking for a statement where 17 and a remainder of 1 are involved. That's choice D.

Answer:

200.08

Step-by-step explanation:

Step-by-step explanation:

We need to use the binomial theorem/Pascal's triangle here.

(a+b)^5 = (5 choose 0)a^5 + (5 choose 1)a^4*b + (5 choose 2)a^3*b^2 + (5 choose 3)a^2*b^3 + (5 choose 4)a*b^4 + (5 choose 5)b^5.

5 choose 0 = 1

5 choose 1 = 5

5 choose 2 = 10

5 choose 3 = 10

5 choose 4 = 5

5 choose 5 = 1

And 1, 5, 10, 10, 5, 1, is the (5+1) = 6th row of pascal's triangle.

Therefore we get

g^5 + 5g^4*2 + 10g^3*2^2 + 10g^2*2^3 + 5g*2^4 + 2^5

which is

g^4 + 10g^4 + 40g^3 + 80g^2 + 80g + 32

Or, you could do the slow way, by just doing (g+2)(g+2)(g+2)(g+2)(g+2)

A) 5x + 4y = 120

3x + 5y = 98

B) To solve this, we must solve the equation.

5x + 4y = 120

3x + 5y = 98

STEP ONE:

Divide

x + 4/5y = 24

STEP TWO:

Substitute the variable

x = 24 - 4/5y

STEP THREE:

Substitute the value of the variable

3(24 - 4/5y) + 5y = 98

STEP FOUR:

Multiply

72 - 12/5y + 5y = 98

STEP FIVE:

Subtract 72 from both sides

-12/5y + 5y = 26

STEP SIX:

Add

Turn 5y into 25/5y

-12/5y + 25/5y = 26

13/5y = 26

2.6y = 26

STEP SIX:

Divide 2.6 from both sides

26/2.6 = 10

y = 10

Each Hip-Hop CD Costs $10

(We will save this for later, because the question asked about rock CDs.)

STEP SEVEN:

Find x

x = 24 - 4/5(10)

4/5 = 0.8

0.8(10) = 8

x = 24 - 8

x = 16

Therefore, each Rock CD costed $16.

C) We found this earlier, each Hip-Hop CD costs $10.

Sorry this was a little lengthy, but I hope this helped!

Answer:

y² = 9² + 19² - 2(9)(19)Cos (41°)

Step-by-step explanation:

Triangle X Y Z is shown.

The length of X Y is 9,

the length of Y Z is 19, and the length of X Z is y. Angle X Y Z is 41 degrees.

Law of cosines is given as:a²= b² + c² – 2bccos(A)

Applying this to Triangle XYZ, and since we are Solving for y

y² = x² + z² - 2xzCos Y

The length of X Y = x is 9,

the length of Y Z = y is 19

y²= 9² + 19² - 2(9 × 19)Cos (41°)

= y² = 9² + 19² - 2(9)(19)Cos (41°)

Option d is correct

Answer:

Choice D is correct

Step-by-step explanation:

Just took the test

Answer:

the magnitude of a real number without regard to its sign.

Step-by-step explanation:

Answer:

the magnitude of a real number without regard to its sign

Step-by-step explanation: or something like that