Really Easy Points!!!
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Define potential

Step-by-step explanation:

with the introduction of fractions it is clear we are multiplying things to get the sequence.

that makes this a geometric sequence, meaning that every new term is created by multiplying the previous term by a certain constant number, the ratio r.

what do we have to multiply with the first term (6) to get -4 ?

6×r = -4

r = -4/6 = -2/3

to check we use the same factor with the second term and see, if we get the predefined third term :

-4 × -2/3 = 8/3

correct, perfect.

so,

a0 = 6

an = an-1 × -2/3 = a0 × (-2/3)^(n-1) = 6 × (-2/3)^(n-1)

for the sum of a finite number of terms of a geometric sequence the formula is :

Sn = a0×(r^n - 1) / (r - 1) if |r| > 1

Sn = a0×(1 - r^n) / (1 - r) if |r| < 1

Sn = a0×n if r = 1

in our case : |-2/3| = 2/3 < 1

S8 = 6×(1 - (-2/3)⁸) / (1 - (-2/3)) =

= 6×(1 - 256/6561) / (3/3 - -2/3) =

= 6×(6561/6561 - 256/6561) / (5/3) =

= 6×(6305/6561) × (3/5) = 2×(6305/2187) × (3/5) =

= 2×(1261/2187) × 3 = 2×(1261/729) =

= 2522/729 = 3.459533608...

≈ 3.46

Answer:

(a) Yes Yes No No

(b) Yes No No Yes

Step-by-step explanation:

(a) [tex]\frac{-9}{10}=-\frac{9}{10}[/tex]

[tex]\frac{9}{-10}=-\frac{9}{10}[/tex]

[tex]\frac{-9}{-10}=\frac{9}{10}[/tex]

[tex]\frac{9}{10}=\frac{9}{10}[/tex]

(b) [tex]\frac{-3}{8}=\frac{3}{-8}[/tex]

[tex]\frac{3}{8}=\frac{3}{8}[/tex]

[tex]\frac{-3}{-8}=\frac{3}{8}[/tex]

[tex]-\frac{3}{8}=\frac{3}{-8}[/tex]

Logarithmic function is the inverse of the exponential function. The logarithmic function that is equivalent to 2⁵ = 32 is log₂32=5.

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c =b[/tex]

can be written as

[tex]\rm{log_ab=c[/tex]

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

Given to us

2⁵ = 32

As we know that we can convert a number powered to another number therefore exponential function into a log function, thus,

[tex]2^5 = 32\\\\\rm log_2 32 = 5[/tex]

Hence, the logarithmic function that is equivalent to 2⁵ = 32 is log₂32=5.

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Answer:

0.750 kg

Step-by-step explanation:

Hi there ,

As you know 1 kg = 1000g

So when we convert g to kg then we divide the given value of grams by 1000.

So in this case we have 750 grams, changing it we have :

[tex]\frac{750}{1000}[/tex]

Since there are 3 zeroes in 1000 we move the decimal point by 3 places to the left leaving the answer as : 0.750 kg or [tex]\frac{750}{1000}[/tex] kg

Please mark me as brainliest if you found the above answer helpful

Step-by-step explanation:

Slope formula:

[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]

m = slope

Substitute the points into the formula format:

[tex] \frac{7.5}{3} - \frac{5}{6} = m[/tex]

Solve:

[tex] \frac{ 7.5}{3} - \frac{5}{6} = \frac{2.5}{ - 3} [/tex]

[tex] \frac{ 2.5}{ - 3} = - \frac{5}{6} [/tex]

The slope equals -5/6.

(fog)(3) = 22

Step-by-step explanation:

f(x + 3x - 5; g(x)=x²9(3)=3²=9

(fog)(3) = f(g(3)) = f(9)=3-9-5=27

-5-22 [Ans]

Coterminal angles are measured from the positive x-axis. The coterminal angle for angle 45° is (270°+45°).

Coterminal angles are angles that are made by the positive x-axis of the coordinate plane.

Given to us

θ = 45°

We know that coterminal angles are those angles that are measured from the positive x-axis of the coordinate plane.

In order to find the angle coterminal with a 45° angle, we will deduct θ from 360°, therefore we will measure the from positive x-axis but in the clockwise direction.

[tex]\theta _1 = 360^o - \theta\\\\\theta _1 = 360^o - 45^o\\\\\theta _1 = 315^o\\\\\theta _1= 270^o + 45^o[/tex]

Hence, the coterminal angle for angle 45° is (270°+45°).

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Answer:

c.45° + 270°

Step-by-step explanation:

Answer:

3500[tex]\pi[/tex] = 10995.57 in³ (nearest hundredth)

Step-by-step explanation:

area of a circle = [tex]\pi r^2[/tex]

⇒ area of a semicircle = [tex]\frac{1}{2}\pi r^2[/tex]

⇒ area of a quarter circle = [tex]\frac{1}{4}\pi r^2[/tex]

total area = 5 circles + 10 semicircles + 100 quarter circles

⇒ total area = [tex]5\pi r^2 +(10\times \frac{1}{2}\pi r^2)+(100 \times \frac{1}{4}\pi r^2)[/tex]

⇒ total area = [tex]35\pi r^2[/tex]

If r = 10 inches

⇒ total area = [tex]35\pi \times 10^2=3500\pi =10995.57 \ \textsf{in}^2 \ \textsf{(nearest tenth)}[/tex]

Answer:

28.26 units³

Step-by-step explanation:

gi solved kopo yan

Answer:For example, choice A is incorrect because if the value of 10x + 3 were 4, then it would follow that x = 0.1, and the value of 5x + 6 would be 6.5, not 10.

Step-by-step explanation:

The answer is

3a + 5 = 12

subtract 5 from both sides

3a = 7

divide by 3 on both sides to isolate "a"

a = 7/3

Substitute 7/3 for "a" in the second equation

6(7/3) + 14

6 multiplied by 7/3 = 42/3 = 14

14 + 14 = 28

Answer:

17.39

Step-by-step explanation:

48+a = 90

x= 42

sin 42 = x / 26

x = 17.39

Number 1

________________

Supplementary - either of two angles whose sum is 180°.

Complementary - either of two angles whose sum is 90°.

________________

Since we know that supplementary angles are angles that add up to 180° we can make an equation

________________

[tex]65+x=180\\x=115[/tex]

________________

Number 2

Since we know that complementary angles are angles that add up to 90° we can make an equation

________________

[tex]65+x=90\\x=25[/tex]

________________

[tex]{\huge{\boxed{\mathfrak{Answer}}[/tex]

Answer:

Step-by-step explanation:

Take the six cantaloupes divide it by 32 pieces 6 divided by 32 is 0.1875

The amount of the cantaloupe in each portion will be;

⇒ 5.33

What is mean by Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Six cantaloupes are cut into 32 equal portions for a catering event.

Now,

Since, Six cantaloupes are cut into 32 equal portions.

Hence,

In each portion, the amount of cantaloupe = 32 ÷ 6

                                                                   = 32 / 6

                                                                   = 5.33

Therefore,

The amount of the cantaloupe in each portion will be;

⇒ 5.33

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Answer: 20

Step-by-step explanation:

You do 40➗2 which you would get 20.

    Then you would round 20 to the nearest tenth, then you get 20.  

Because if the number on the left/right is between 0 and 4, the whole number stays the same.

Note: 0-4 stays the same   5-9 higher number.

    For example: Rounding 164 to the nearest tenth will become 160.

Answer:

5

Step-by-step explanation:

[tex]g(x)=\frac{32}{x+3}\\\\\implies g^{-1}(x)=\frac{32}{x}-3\\\\g^{-1}o \ g=[g(g^{-1}(x))]=\frac{32}{\frac{32}{x}-3+3}=x\\\\\implies (g^{-1}o \ g)(5)=5[/tex]

Answer:

$76

Step-by-step explanation:

Regular price: $95

Discount %= 80%

What is 80% of 95

=) [tex]\frac{80}{100}[/tex]×[tex]\frac{95}{1}[/tex]=  76

So, $76 are discounted

Hope this helps!

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

To find volume of sphere first we have to convert Diameter into radius .

Diameter = 2 radius

So:-

⇢Diameter = 2 radius

[tex]\\[/tex]

⇢Radius = Diameter/2

[tex]\\[/tex]

⇢Radius = 8/2

[tex]\\[/tex]

⇢Radius = 2 × 2 × 2/2

[tex]\\[/tex]

⇢Radius = 2 × 2/1

[tex]\\[/tex]

⇢Radius = 4/1

[tex]\\[/tex]

⇢Radius = 4 mm.

[tex]\\[/tex]

Now Finally Let's find volume of sphere.

We know:-

[tex]\\[/tex]

[tex]\star\boxed{\rm Volume~of~sphere=\frac{4}{3}\pi r^3}[/tex]

so:-

[tex]\\\\[/tex]

[tex]\dashrightarrow \sf Volume~of~sphere=\frac{4}{3}\times 3.14 \times 4^3\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 4^3\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 4\times 4\times 4\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow \sf Volume~of~sphere=\dfrac{4}{3}\times \dfrac{314}{100} \times 64\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow \sf Volume~of~sphere=1.33\times \dfrac{314}{100} \times 64\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow \sf Volume~of~sphere= \dfrac{1.33\times314 \times 64}{100}\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow \sf Volume~of~sphere= \dfrac{26,727.68}{100}\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow \sf Volume~of~sphere=26,7.28 (approx)\\[/tex]

[tex]\\\\[/tex]

[tex] \therefore \underline{ \textbf{ \textsf{Volume~of~sphere = \red{26,7.28(approx)}}}}[/tex]

Answer:

see below

Step-by-step explanation:

1. At least 2 points create a line
2. At least 3 points determine a plane
3. The intersection of two distinct planes is a line

3. The intersection of 2 coplanar lines is a point
5. A Plane can contain a line and a point not on the line

Answer:

C

Step-by-step explanation:

1 + 0.02 means the 2% growth every month, power 12 means for 12 month, and power of 2 mean 2 years.

Answer:

1) Slope = -1, y-intercept = 3

2) Slope = 1, y-intercept = -3

3) Slope = -3, y-intercept = 1

4) Slope = 3, y-intercept = -1

Step-by-step explanation:

In order to identify slope and y-intercept, you must find where each variable hits each axis when the other is 0.

For example, to find the y intercept of y=2x-4, you would substitute 0 in for x and solve for y.

y = 2(0)-4  --> y = -4

Thus, the point is (0, -4) with slope of 2. (The slope can be found by identifying the number, m, in front of 'x' from the equation y = mx + b.

Answer:

A. y = 3x-1; slope is 3 and y-intercept is -1

B. -x+3 = y; slope is -1 and y-intercept is 3

C. x-3 = y; slope is 1 and y-intercept is -3

D. y = 1-3x; slope is -3 and y-intercept is 1

Step-by-step explanation: woof

Answer:

yes

Step-by-step explanation:

no

Answer:

114 books.

Step-by-step explanation:

I'm pretty sure what you have to do is just subtract 16 from 130. (130-16).  

When you do that you get 114 books.  (sorry for basically no explanation.)

Answer:

4x-8u+10

Step-by-step explanation:

You take the -2 inside the brackets to remove the brackets. (parenthesis=brackets)

-2×-2x=4x

-2×+4u=-8u

-2×-5=10

4x-8u+10

Answer:

11. 130°, obtuse angle

12. 40°, acute angle

13. 90°, right angle

14. 110°, obtuse angle

15. same as 14, I guess?

Step-by-step explanation:

questions 11, 14, 15 - an obtuse angle is an angle greater than 90° but less than 180°

question 12 - an acute angle is an angle that is less than 90°

question 13 - a right angle is exactly 90°

in question 14 the angle starts at 30° and ends at 140° so you subtract 30 from 140

hope this helps :)

Answer:

There is no way that 4/5 can equal a thing with 3 as a denominator

Step-by-step explanation:

4/5 is already simplified, but it does equal 8/10 or 12/15

Answer:

Not the solution tp the system because the ordered pair should be true for both equations. However the last equation is not true.

Step-by-step explanation:

(-1,-2) is the solution of the system. x + y =-3 and 2x - y = -4*

x + y =-3 :

(-1)+ (-2) = -3

-1-2 =-2   -3=-3

2x - y = -4:

2(-1)-(-2)=-4

(-2) -(-2)= -4

0=-4

Answer:

190 pages

Step-by-step explanation:

To solve the # of pages he would read in 5 hours, let's first find the number of pages he reads in one hour.

Next, we multiply 38 by 5.

Therefore, the answer is 190 pages.

Answer:

190 pages

Step-by-step explanation:

Given the following question:

Erin read 76 pages in 2 hours...
How many pages would he have read in 5 hours?

In order to find the answer, we divide the number of pages he read in two hours by two. To find the number of pages he reads in 1 hour, then just multiply that answer by five.

[tex]2h=76p[/tex]
[tex]4h=76+76=152p[/tex]
[tex]76\div2=38[/tex]
[tex]152+38=190[/tex]
[tex]5h=190p[/tex]

In five hours, Erin would have read "190 pages" of his book.

Hope this helps.

Answer:

6 in

Step-by-step explanation:

The angle bisector divides the opposite side into segments that are proportional to the other 2 sides.

let the third side of the triangle be x , then

[tex]\frac{9}{x}[/tex] = [tex]\frac{6}{4}[/tex] ( cross- multiply )

6x = 36 ( divide both sides by 6 )

x = 6

The third side of the triangle is 6 in

Answer:

[tex]x = \frac{-1}{4}[/tex]

Step-by-step explanation:

[tex]\frac{2}{x} = -8[/tex]

[tex]2 = -8x[/tex]

[tex]x = \frac{-2}{8}[/tex]

[tex]x = \frac{-1}{4}[/tex]

Answer:

[tex]\sf x=-\cfrac{1}{4}[/tex]

Step-by-step explanation:

[tex]\sf \cfrac{2}{x}=-8[/tex]

[tex]\sf \cfrac{2}{x}x=-8x[/tex]

[tex]\sf 2=-8x[/tex]

[tex]\sf \cfrac{-8x}{-8}=\cfrac{2}{-8}[/tex]

[tex]\sf x=-\cfrac{1}{4}[/tex]