Lily was building towers with her Legos. The first tower that she built had only one LEGO. The second tower had 4 LEGO’s. The towers she built after that had 9 and then 16 LEGO’s. How many LEGO’s would Lily’s 100th tower have?

the LCM of 21 and 105 is 105.

Answer:

The answer to your question is 105

Step-by-step explanation:

To get the least common factor dividing both numbers by the prime numbers starting from 2.

But these numbers are not multiples of 2, try 3

                                                           21   105   3

These numbers are not multiples of 3 let's try 5                                                                    

                                                            7     35  5  

These numbers are multiples of 7     7       7   7

                                                            1        1

The LCM is the product of the prime numbers = 3 x 5 x 7 = 105

Option E

The sum of all possible values of y is 20

Solution:

Given that,

6x + 2y = 25

Where, xy > 0

We have to find the sum of all possible values of y if x is a positive integer

We can use values of x = 1, 2, 3, 4

For x = 5 and above, y will be negative

Substitute x = 1 in given equation

6(1) + 2y = 25

6 + 2y = 25

2y = 25 - 6

2y = 19

Divide both the sides of equation by 2

[tex]y = \frac{19}{2}[/tex]

Substitute x = 2 in given equation

6(2) + 2y = 25

2y = 25 - 12

2y = 13

Divide both the sides of equation by 2

[tex]y = \frac{13}{2}[/tex]

Substitute x = 3 in given equation

6(3) + 2y = 25

2y = 25 - 18

2y = 7

Divide both the sides of equation by 2

[tex]y = \frac{7}{2}[/tex]

Substitute x = 4 in given equation

6(4) + 2y = 25

24 + 2y = 25

2y = 25 - 24

2y = 1

Divide both the sides of equation by 2

[tex]y = \frac{1}{2}[/tex]

Now add all the values of "y"

[tex]\text{Sum of possible values of y } = \frac{19}{2} + \frac{13}{2} + \frac{7}{2} + \frac{1}{2}\\\\\text{Sum of possible values of y } = \frac{19+13+7+1}{2}\\\\\text{Sum of possible values of y } = \frac{40}{2}=20[/tex]

Thus sum of all possible values of y is 20

Answer:

Step-by-step explanation:

think of any number : x

add 3 : x+3

double that : 2(x+3)

subtract 4 : 2(x+3)-4

cut in half (divide by 2) : (2(x+3)-4)/2

subtract original number : (2(x+3)-4)/2-x

if you simplify, you will end up with 1

Step by Step simplification

2(x+3) = 2x+6   double that

2x+6-4=2x+2    subtract 4 : 2(x+3)-4

(2x+2)/2 = x+1     cut in half (divide by 2)

x+1-x = 1      subtract original number

Answer: slope = 0

Step-by-step explanation:

The formula for calculating slope is given as :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = 2

[tex]x_{2}[/tex] = 1

[tex]y_{1}[/tex] = 0

[tex]y_{2}[/tex] = 0

Substituting into the formula , we have

m = [tex]\frac{0}{-1}[/tex]

m = 0

The slope of the line passing through (2, 0) and (1, 0) is 0, indicating that the line is horizontal.

The slope of a line that passes through the points (2, 0) and (1,0) can be determined using the formula for slope, which is (y2 - y1) / (x2 - x1).

Plugging in the coordinates, we get (0 - 0) / (1 - 2), which simplifies to 0/-1.

The slope of this line is 0. This indicates that the line is horizontal because there is no change in the y-value as the x-value changes.

Answer:

6/10

Step-by-step explanation:

Answer:

It would be 4 to 80

Step-by-step explanation:

Answer:

28 boys

Step-by-step explanation:

For every 7 boys there are, there are 20 girls. It is given to us that there are 80 girls. To solve, divide 80 with 20:

80/20 = 4

Next, multiply 4 with 7:

4 x 7 = 28

There are 28 boys at the school dance.

Answer:

9/16

Step-by-step explanation:

18522/32928= 0.5625 which can be reconverted to a fraction, which in this case that fraction is 9/16

Answer:

1451/31914

Step-by-step explanation:

hope this helps :) have a nice day

Answer: D. Point B

Step-by-step explanation: the tangent line is the line outside the circle.

Answer:

12 meter = 129.167

48 = 516.668

121  =1302.43

144 =1550

169 = 1819.1

Step-by-step explanation:

Final answer:

The area of a 12 meter square is calculated by squaring the length of the side, which results in 144 square meters.

Explanation:

The area of a square can be found by squaring the length of one of its sides. Since the given square has a side length of 12 meters, the area can be calculated as follows:

Area = side length * side length

Area = 12 m * 12 m

Area = 144 square meters

Answer:

The equation of the line is y= x + 2

Step-by-step explanation:

The general representation of equation of line is y= ax + b

where a is the slope and b is the y intercept. Here slope of the line is 1 and why is point where two lines intersect hence, it is the intercept.

So, the equation of the other line is y= x + 2

Answer:

The equation of the line is y= x + 2

Step-by-step explanation:

The general representation of the equation of a line is y= ax + b

where a is the slope and b is the y-intercept. Here slope of the line is 1 and why is the point where two lines intersect hence, it is the intercept.

So, the equation of the other line is y= x + 2

Answer:

B= [tex]\frac{2A}{H}[/tex]

Step-by-step explanation:

If you noticed, A= [tex]\frac{1}{2}[/tex]BH is the formula for finding the area for a triangle. Your goal is to get B by it's self. Your first step will be to clear of the fraction first, so you will multiply both sides by 2.   2(A)=2([tex]\frac{1}{2}[/tex]BH).    On the left, you have 2×A= On the right side, you have     2([tex]\frac{1}{2}[/tex]BH),     but since you have a number in the equation, you will only use 2×[tex]\frac{1}{2}[/tex]. To solve  2×[tex]\frac{1}{2}[/tex], you will cnacel out both 2's and you have 1. 1×BH will still equal BH, so you are now left will B×H.

(Your new equation looks like this by the way).    2A=BH

Since you need to get B by its self, the way to clear the H away from the B is by dividing.  You will now divide the B and H aswell as 2A and H. (It will look like this) [tex]\frac{2A}{H} = \frac{BxH}{H}[/tex] . (Again when you have the same number or letter, you cross it out. When you divide, you won't change anything on the left side, and all you have to do on the right id to cross out the H next to the B and cross out the H on the bottom of the equation). You should be left with [tex]\frac{2A}{H}[/tex] = B. Now you can turn it around for your final answer. B= [tex]\frac{2A}{H}[/tex].

Please let me know if i helped, how I did, and if you have any questions.

Answer:

B C D i believe

Step-by-step explanation:

Answer:

Using the formula, write in standard form.

=

−

0.0014

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

1.4

×

10

−

3

Step-by-step explanation:

The decimal number 0.0014 can be written in standard form (also known as scientific notation) as 1.4 x 10^-3. This is done by shifting the decimal place so that you have a number between 1 and 10, and then indicating how many places you moved the decimal in the exponent of ten.

The student asked to convert the decimal 0.0014 into standard form. The standard form for representing decimal numbers involves using the scientific notation which means expressing numbers as a number between 1 and 10, multiplied by the power of ten. So, 0.0014 can be written as 1.4 x 10^-3 in standard form.

This can be done through the following steps:

https://brainly.com/question/37011468

#SPJ3

Answer:

Question 1: A. 2

Question 2: C. [tex]x>90[/tex]

Step-by-step explanation:

Question 1:

Amount to be spend = $625

Cost to rent the ball room for 3 hrs = $350

Cost of each additional hour = $125

Ms Jensen wrote the Inequality as,

[tex]625>350+125h[/tex]

h⇒ Number of additional hours.

We need to find the value of 'h'.

Solution:

[tex]625>350+125h[/tex]

Now Subtracting both side by 350 using subtraction property of Inequality we get;

[tex]625-350>350+125h-350\\\\275>125h[/tex]

Dividing both side by 125 using Division property of Inequality we get;

[tex]\frac{275}{125}>\frac{125h}{125}\\\\2.2>h[/tex]

Hence The value of 'h =2' make the Inequality true.

Question 1:

Given:

[tex]20+2<\frac{x}{3}-8[/tex]

We need to find the solution for Inequality.

Solution:

First we will add the like terms we get;

[tex]22<\frac{x}{3}-8[/tex]

Now Adding both side by 8 using addition property of Inequality we get;

[tex]22+8<\frac{x}{3}-8+8\\\\30<\frac{x}{3}[/tex]

Now multiplying both side by 3 Using multiplication property of Inequality we get;

[tex]30\times3<\frac{x}{3}\times 3\\\\90<x[/tex]

Hence The solution to given Inequality is [tex]x>90[/tex].

Answer:

im not sure sure but by the looks of it i think thats 3,6

Step-by-step explanation:

Answer:

slope of the given straight line in graph is -2

Step-by-step explanation:

Explanation:-

in given graph we have to choose points are A(0,3) on y-axis and B(1.5 , 0) on x- axis

let m be the slope of a line

by using slope formula is

[tex]m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

m = [tex]\frac{0-3}{1.5-0}[/tex]

m= -2

another points we have choose

in given graph we have to choose points are A(0,3) on y-axis and B(2.5 , -2)

slope of a line :-

let m be the slope of a line

by using slope formula is

[tex]m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

[tex]m = \frac{-2-3}{2.5-0}[/tex]

m= -2

where ever you will take point the slope of given straight line is

m = -2

Answer:

cirrus clouds

Step-by-step explanation:

cirrus clouds are very thin so they can't hold much water so the answer is Cirrus

P.S: Please give me brainlest i just need 2 more plz plz plz  

ANSWER

Cirrus clouds

Explanation:

Because the cirrus clouds are more thin then most, therefor it cant hold as much water as other clouds. becuase its thinner it cant hold lots of water. So it is the least effective weather cloud.

Answer:

C

Step-by-step explanation:

Given the logarithmic equation

[tex]\log_4x+\log_4(x-3)=\log_4(-7x+21)[/tex]

First, notice that

[tex]x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x<21\ x<3[/tex]

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

[tex]\log_4x+\log_4(x-3)=\log_4x(x-3),[/tex]

then

[tex]\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3[/tex]

Hence, [tex]x=3[/tex] and [tex]x=-7[/tex] are extraneous solutions

Answer:

2/5

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

40%=40/100=4/10=2/5

Answer:

Step-by-step explanation:

[tex]x^2+5x-4=3x-1\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\x^2+5x-3x-4=3x-3x-1\\\\x^2+2x-4=-1\qquad\text{add 1 to both sides}\\\\x^2+2x-4+1=-1+1\\\\x^2+2x-3=0\\\\x^2+3x-x-3=0\\\\x(x+3)-1(x+3)=0\\\\(x+3)(x-1)=0\iff x+3=0\ \vee\ x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x+3-3=0-3\\\boxed{x=-3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x-1+1=0+1\\\boxed{x=1}[/tex]

Answer:

C both

Step-by-step explanation:

There is a graph

Answer:

c= 9

Step-by-step explanation:

first you would need to get the variable alone

next you would take the one and since it is subtraction you would do the opposite addition

then you would add one to each side and the two ones cancel each other out so the you add 8 and 1 and get nine so c would equal 9

Steps to solve:

c - 1 = 8

~Add 1 to both sides

c - 1 + 1 = 8 + 1

~Simplify

c = 9

Best of Luck!

Answer:

(2, - 3 )

Step-by-step explanation:

Given the 2 equations

2x - 3y = 13 → (1)

x + 2y = - 4 → (2)

Rearrange (2) expressing x in terms of y by subtracting 2y from both sides

x = - 4 - 2y → (3)

Substitute x = - 4 - 2y into (1)

2(- 4 - 2y) - 3y = 13 ← distribute and simplify left side

- 8 - 4y - 3y = 13

- 8 - 7y = 13 ( add 8 to both sides )

- 7y = 21 ( divide both sides by - 7 )

y = - 3

Substitute y = - 3 into (3) for corresponding value of x

x = - 4 - 2(- 3) = - 4 + 6 = 2

Solution is (2, - 3 )

Answer:

17/25

Step-by-step explanation:

Answer:

Part A) [tex]A_s=\frac{\pi r^{2}}{360^o}{\theta}[/tex]

Part B) option 1,option 4

Step-by-step explanation:

Part A) Derive the formula for the area of a sector

we know that

The area of circle is equal to

[tex]A=\pi r^{2}[/tex]

The area of circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector  [tex]A_s[/tex]  by a central angle of ∅ degrees

[tex]\frac{\pi r^{2}}{360^o}=\frac{A_s}{\theta}[/tex]

[tex]A_s=\frac{\pi r^{2}}{360^o}{\theta}[/tex]

Part B) Verify each case

case 1) we have

radius = 5 cm

angle = 120°

area = 26.2 cm 2

Find the area of the sector and then compare with the value of the given area

assume

[tex]\pi=3.14[/tex]

substitute the given values

[tex]A_s=\frac{(3.14)(5)^{2}}{360^o}{120^o}[/tex]

[tex]A_s=26.2\ cm^2[/tex]

so

The given value of area is correct

case 2) we have

radius = 4 cm

angle = 105°

area = 16.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

[tex]\pi=3.14[/tex]

substitute the given values

[tex]A_s=\frac{(3.14)(4)^{2}}{360^o}{105^o}[/tex]

[tex]A_s=14.7\ cm^2[/tex]

so

The given value of area is not correct

case 3) we have

radius = 6 cm

angle = 85°

area = 23.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

[tex]\pi=3.14[/tex]

substitute the given values

[tex]A_s=\frac{(3.14)(6)^{2}}{360^o}{85^o}[/tex]

[tex]A_s=26.7\ cm^2[/tex]

so

The given value of area is not correct

case 4) we have

radius = 7

angle = 75°

area = 32.1 cm 2

Find the area of the sector and then compare with the value of the given area

assume

[tex]\pi=3.14[/tex]

substitute the given values

[tex]A_s=\frac{(3.14)(7)^{2}}{360^o}{75^o}[/tex]

[tex]A_s=32.1\ cm^2[/tex]

so

The given value of area is correct

Answer:

It could be 9 or 23. It could also be many other things.

Step-by-step explanation:

The other side of the triangle has to be greater than 15 when added to 7 or greater than both when they are added together.

Answer:

The answer is: [tex]$ \frac{\textbf{1}}{\textbf{216}} $[/tex]

Step-by-step explanation:

Rule of Exponents:

[tex]$ x^a . x^b \hspace{2mm} = \hspace{2mm} x^{a + b} $[/tex]

[tex]$ \frac{x^a}{x^b} = x^{a}.x^{-b} = x^{a - b} $[/tex]

Here, it is given:

[tex]$ \frac{6^2}{6^5} = 6^{2 - 5} $[/tex]

[tex]$ = 6^{-3} $[/tex]

[tex]$ = \frac{1}{6^3} $[/tex]

[tex]$ = \frac{\textbf{1}}{\textbf{216}} $[/tex]

Hence, the answer.

Answer:

no

Step-by-step explanation:

3=5(3)

3=15

false

Answer:

no

Step-by-step explanation: