What is the common ratio of this sequence: 4, 20, 100...?

pls

Answer:

Example 1:

Find the common denominator of the fractions.

16 and 38

We need to find the least common multiple of 6 and 8 . One way to do this is to list the multiples:

6,12,18,24−−,30,36,42,48,...8,16,24−−,32,40,48,...

The first number that occurs in both lists is 24 , so 24 is the LCM. So we use this as our common denominator.

Listing multiples is impractical for large numbers. Another way to find the LCM of two numbers is to divide their product by their greatest common factor ( GCF ).

Example 2:

Find the common denominator of the fractions.

512 and 215

The greatest common factor of 12 and 15 is 3 .

So, to find the least common multiple, divide the product by 3 .

12⋅153=3 ⋅ 4 ⋅ 153=60

If you can find a least common denominator, then you can rewrite the problem using equivalent fractions that have like denominators, so they are easy to add or subtract.

Example 3:

Add.

512+215

In the previous example, we found that the least common denominator was 60 .

Write each fraction as an equivalent fraction with the denominator 60 . To do this, we multiply both the numerator and denominator of the first fraction by 5 , and the numerator and denominator of the second fraction by 4 . (This is the same as multiplying by 1=55=44 , so it doesn't change the value.)

512=512⋅55=2560215=215⋅44=860

512+215=2560+860                 =3360

Note that this method may not always give the result in lowest terms. In this case, we have to simplify.

=1130

The same idea can be used when there are variables in the fractions—that is, to add or subtract rational expressions .

Example 4:

Subtract.

12a−13b

The two expressions 2a and 3b have no common factors, so their least common multiple is simply their product: 2a⋅3b=6ab .

Rewrite the two fractions with 6ab in the denominator.

12a⋅3b3b=3b6ab13b⋅2a2a=2a6ab

Subtract.

12a−13b=3b6ab−2a6ab                   =3b − 2a6ab

Example 5:

Subtract.

x16−38x

16 and 8x have a common factor of 8 . So, to find the least common multiple, divide the product by 8 .

16⋅8x8=16x

The LCM is 16x . So, multiply the first expression by 1 in the form xx , and multiply the second expression by 1 in the form 22 .

x16⋅xx=x216x38x⋅22=616x

Subtract.

x16−38x=x216x−616x                  =x2 − 616x\

Answer:

There are 6hrs and 38 minutes between 8:15 am and 2:53 pm

Step-by-step explanation:

8:15 a.m- 9:15 am= 1 hr

9:15 am- 10:15 am= 1 hr

10:15 am-11:15 am=1 hr

11:15 am- 12:15 pm= 1 hr

12:15 pm- 1:15 pm= 1 hr

1:15 pm- 2:15 pm= 1hr

2:15 pm-2:53 pm= 53-15= 38 min

Answer:

3.5

Step-by-step explanation:

7/3= 3.5 or 3 1/2

Answer:

4.6538474e+15

Step-by-step explanation:

The direct distance between Centerville and Capital City round to the nearest kilometer is 1,336 kilometers.

The distances between Centerville, Springfield, and Capital City form a right triangle in geography.

The distance between Centerville and Springfield is 913 kilometers, and the distance between Springfield and Capital City is 976 kilometers.

Let x be the direct distance between Centerville and Capital City using the formula

By Pythagorean theorem, we get

                                      913² + 976² = x²

                         833,569 + 952,576 = x²,

                                                      x² = 1786145

                                                       x = √1786145

                                                       x = 1336.46736

Hence, we get x = 1,336.46736 rounding to the nearest tenth is 1,336 kilometers.

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The conclusion that we now make about the result of adding a rational and an irrational number is that the sum of any rational number and any irrational number will always be an irrational number.

Irrational numbers cannot be stated as a fraction, although rational numbers can be expressed as ratios (such as P/Q and Q). However, both of the numbers are genuine and can be shown on a number line.

It should be noted that the conclusion that we now make about the result of adding a rational and an irrational number is that the sum of any rational number and any irrational number will always be an irrational number.

For example, we can conclude that ½+√2 is irrational.

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Answer: 8.65*103

Step-by-step explanation:

Using scientific notation, it is found that the amount raised by the West, in dollars, is of:

[tex]8.65 \times 10^3[/tex]

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

Combined, the amount raised by the North, South and East is:

[tex]2.38 \times 10^4 + 6.75 \times 10^3 + 1.46 \times 10^4[/tex]

To add numbers, they need to have the same exponent, hence:

[tex]6.75 \times 10^3 = 0.675 \times 10^4[/tex]

To add the numbers, we add the bases and keep the exponents, hence:

[tex]2.38 \times 10^4 + 0.675 \times 10^4 + 1.46 \times 10^4 = 2.38 + 0.675 + 1.46 \times 10^4 = 4.515 \times 10^4[/tex]

The total amount is given in the problem, hence the amount raised by the West is:

[tex]5.38 \times 10^4 - 4.515 \times 10^4 = 0.865 \times 10^4 = 8.65 \times 10^3[/tex]

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Answer:5 Hours

Step-by-step explanation:

160/4 = 40 miles per hour

200/40 = 5

Answer:

8 hours

Step-by-step explanation:

there are 360 miles total because it already covered 160 and there are 200 left.  160 / 4 = 4 hours per 40 miles.  200 is 40 more miles than 160.  This means that it is the 4 hours of 160 miles in that 200 + 4 more hours for 40 miles.  Add them together and you get 8 hours.

Answer:

b and m or known the y-intercept and slope

Step-by-step explanation:

you first place your point of y-intercept which is b in the equation its always got a x value of 0 paired with it.

then from there you place points using the m in the equation which is you rise over run for all your folling points on the graph.

hope that helps

Answer:

1.7 miles

Step-by-step explanation:

Pythagoras' Theorem sets the relation between three sides of a right-angled triangle. The distance between Raoul's home and the library is 1.3 miles.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|² = |AB|² + |BC|²    

where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).

The school is located 0.5 miles east of Raoul's house. The library is located 1.2 miles south of the school. Therefore, the distance between the home and the library is the hypotenuse of the triangle formed.

AC² = AB² + BC²

AC² = 0.5² + 1.2²

AC = 1.3 miles

Hence, the distance between Raoul's home and the library is 1.3 miles.

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Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

To find the slope you can use the slope equation:

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

Let's define the terms in the equation:

y2 = 5

y1 = 7

x2 = 4

x1 = 8

Now, let's put these into the equation and solve:

[tex]slope = \frac{5 - 7}{4 - 8} = -\frac{2}{4} = -\frac{1}{2}[/tex]

Therefore, the slope is -1/2.

I hope this helps!!

- Kay :)

A segment addition problem with three points is: DE + EF = DF, which is 2x + 3x = 100. The solution is, x = 20.

Assuming point E is located between points D and F on a straight line, points D, E, and F are collinear, and based on the segment addition postulate, we have the equation that is true:

DE + EF = DF.

Let's assume that we have the following lengths:

DE = 2x

EF = 3x

DF = 100

Therefore, we would have the following:

2x + 3x = 100

5x = 100

5x/5 = 100/5

x = 20.

Therefore, a segment addition problem with three points is: DE + EF = DF, which is 2x + 3x = 100. The solution is, x = 20.

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Answer:

81 pounds

Step-by-step explanation:

Given that:

Peanut per pound = $6.75

Cashew per pound = $9.50

Let

Number of cashews sold = x

Number of peanuts sold = x + 32

Total sales made = $1,012.25

(Number of caahew sold * cost of cahew) + (Number of peanut sold * cost of peanut) = total sales made

(x * 9.50) + [(x + 32) * 6.75)] = 1012.25

9.50x + 6.75x + 216 = 1012.25

16.25x = 796.25

x = 796.25 / 16.25

x = 49

Number of peanuts sold = x + 32 = 49 + 32 = 81

Answer: A

Step-by-step explanation:

Miguel started running, and he runs 1 mile in the first week, then the equation will be y = 2x + 1. Hence, option A is correct.

Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given information in the question,

Miguel runs for 1 mile in the first week.

Then, his goal is to run 2 miles farther than his distance for the previous week.

Then the equation will be: y = 2x + 1

Here, y is the total distance and x is the number of miles.

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Answer:

B. (-5,7) → (-11,3)

T. (0,0) → (-7,2)

F. (0,2) → (5,-2)

A. (4,6) → (1,-3)

L. (-4,-4) → (-8,-2)

Step-by-step explanation:

B. -5 - 6 = -11

    7 - 4 = 3

T. 0 - 7 = -7

   0 + 2 = 2

F. 0 + 5 = 5

   2 - 4 = -2

A. 4 - 3 = 1

   6 - 9 = -4

L. -4 - 4 = -8

   -4 + 2 = -2

Greetings from Brasil...

Translations

Just add or subtract an m value for all X coordinates as well as add or subtract an n value for all Y coordinates of the figure.

If the figure has 3 points (A, B and C), we would be left with:

A(X, Y) ; B(X₂; Y₂) ; C(X₃; Y₃)

A(X, Y) → A'(X ± m; Y ± n)

B(X₂; Y₂) → B'(X₂ ± m; Y₂ ± n)

C(X₃; Y₃) → C'(X₃ ± m; Y₃ ± n)

in our example - see attached figure - let

m = 4

n = - 1

(these values of m=4 and n=-1 were chosen by me arbitrarily)

A(1; 2) → A'(1 + 4; 2 - 1) ⇒ A'(5; 1)

B(2; 3) → B'(2 + 4; 3 - 1) ⇒ B'(6; 2)

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

Rotations

The expression (formula) for rotation will be:

P(X; Y) → P'(Xcos θ - Ysen θ; Xsen θ + Ycos θ)

Let rotate 90° (counter-clockwise): cos 90 = 0 and sen 90 = 1, then

in our example - see attached figure

A(1; 2) → A''(-2; 1)

B(2; 3) → B''(-3; 2)

______________________________

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Answer:

t(s(2)) where s(x) = -x + 1, t(x) = -x^2 - 1 = -2

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

The difference between each term is 4.

-2 - (-6) = 4

2 - (-2) = 4

6 - 2 = 4

10 - 6 = 4

d. 4

here, -2-(-6)= -2+6=4

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

6- 2 = 4

10-6 = 4

so the common difference of them is 4.

Answer:

m=y8+2x

Step-by-step explanation:

Answer:

arc tan (angle) = 1,119 / 173

arc tan (angle) = 6.4682080925

angle = 81.212 Degrees

Step-by-step explanation:

Answer: x= -12.5

Step-by-step explanation:

Start with distributing-5(x+4) or you get

x-5x-20=30

Add x and -5x to get -4x

Thank you add 20 to each side and get

-4x = 50

Divide by -4 on each side to get x=-12.5

Answer:

x=-25/2 is the answer.

Step-by-step explanation:

Below are the steps for solving the equation:

Step 1: Simplify, combine like terms, and distribute:

x−5(x+4)=30

x+(−5)(x)+(−5)(4)=30

x+−5x+−20=30

(x+−5x)+(−20)=30

−4x+−20=30

−4x−20=30

Add 20 to each side:

−4x−20+20=30+20

−4x=50

Divide each side by -4:

-4x/-4=50/-4

x=-25/2, which is -12.5 as a decimal.

So, your answer is x=-25/2 as a fraction, which is also -12.5 as a decimal.

Answer:

the lowest amount mia can spend is $75

Step-by-step explanation:

3x12=36

12x3+15 this is for the noise makers

9 x 4= 36

15 x 4 = 60

60+15=75

she will spend 75 dollars on party suplies

Answer:

17

Step-by-step explanation: