11. Mark builds 3 Lego towers. Each tower is made of 5 square layers
which have a width and length of 5 Lego pieces. Suddenly, Mark's little
brother breaks one and runs off with 45 pieces. Use the expression to show
how many pieces Mark is left with.
Answer:
Step-by-step explanation:
A well is 20ft deep. A snail at the bottom of the well climbs upto 4ft each day and slips back 2ft every night.how many days the snail to reach the too
Answer:
10 days
Step-by-step explanation:
4ft-2ft= so the snail moves 2ft every 24hrs
20ft÷2ft= takes the snail 10 days
Answer:
Defining Variables:
Let the number of days the snail takes to climb = x days
Total distance climbed in x days = x*4
Total distance slipped in x days = 2*x
Solving for the number of days:
Since the total distance the snail climbs is 20ft (depth of well)
The total distance climbed - total distance slipped = 20
replacing the variables
4x - 2x = 20
2x = 20
x = 10
Therefore, it will take the snail 10 days to reach the top
How do you do this question?
Exact value: [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]
Approximate value: c = 0.08387
Round the approximate value however you need to
==============================================
Work Shown:
Let x = 1+c
[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]
We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.
Each new term is found by multiplying the previous term by 1/x.
Assuming -1 < r < 1 is true, the infinite geometric sum is
[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]
Plug in S = 11 and solve for x
[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]
Use the quadratic formula to find the two solutions
[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]
Using these x values, we find that the corresponding r values are
r = 1/x = 1/(1.08387) = 0.92262
r = 1/x = 1/(-0.08387) = -11.92321
The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387
----------------------------------------------
Using the solution that corresponds to x = 1.08387, we find the value of c is
[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]
FIRST ANSWER GETS BRAINLIEST!!!
Describe how to model -3x + 7 = 28 with algebra tiles.
Answer:
-7
Step-by-step explanation:
-3x+7=28
-7=28
-7
-3x/21
x=-7
Identify the independent and dependent variables: The cost to gift wrap an order is $ 3 plus $1 per item wrapped
Answer: Indep. is: $3 and the dependent is $1
Step-by-step explanation:
Every item is $3, but if you add more then you also add $1
Given the linear function 2x - y= 5 what is the slope? And As x increase does y increase or decrease and as x decreases does y increase or decrease
Answer:
The slope is 2. As x increase y is increase and as x decrease y decrease
Simplify the expressions by distributing and combining like terms 5/8x-2(7-1/4x)
Carlos cut Start Fraction 5 Over 12 End Fraction of a yard of cloth into 5 pieces of equal length. What was the length of each piece of cloth?
Start Fraction 1 Over 60 End Fraction of a yard
Start Fraction 1 Over 25 End Fraction of a yard
Start Fraction 1 Over 12 End Fraction of a yard
One-fifth of a yard
Answer:
C.1/12
Step-by-step explanation:
Divide 5/12 by 5 since he cut it into 5 equal pieces
Jose is riding his bicycle. He rides at a speed of 12 kilometers per hour fore 38.4 kilometers. For how many hours does he rides
Answer:
3.2 hours
Step-by-step explanation:
Find the value of x
(4x-20)°
Answer:
Bro this has no solution
Answer: 4(x−5)
Step-by-step explanation: I think this is right. If it’s not Im sorry. But if it is hope this helps!
A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.
What are the measures of the angles in triangle ABC?
m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90°
m∠A ≈ 73.0°, m∠B ≈ 17.0°, m∠C ≈ 90°
m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°
Answer:c
Step-by-step explanation:
The measures of the angles in triangle ABC are; m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
How to find the measures of angles in triangle ABCIt follows that the right angle is between the two shorter sides;
Hence, the angle measure, m∠C ≈ 90°.On this note, the angle, m∠A is opposite side BC;
Therefore, from sine formula;
Sin m∠A ≈ 24/25Sin m∠A ≈ 0.96m∠A ≈ sin-¹(0.96)m∠A ≈ 73.7°
And from sum of angles in a triangle;
m∠A ≈ 16.3°
Read more on right triangle;
https://brainly.com/question/2437195
Find a and b: (10-4i)-(a+bi)=(6-6i)
Answer:
look at attached image, hope this helps! :)
5.) You are working for a car dealership. You are doing an inventory of the lot. You counted 34
trucks. 15 cars, and 8 SUVs. What is the ratio of SUVs to total vehicles on the lot?
Answer: 8 SUVs to 57 total
Step-by-step explanation: You add 34 + 15 + 8 which gives you 57 Then you see there are 8 SUVs. So the answer is 8 to 57.
Sorry. I kinda got ahead of myself and excited. Guess mistakes happen. I was right the first time. I'm just so tired right now
I will give you branilest!
What does the constant of proportionality represent?
Answer:
The constant of proportionality is the ratio between two directly proportional quantities
Step-by-step explanation:
Two quantities are directly proportional when they increase and decrease at the same rate.
Answer:The constant of proportionality is the constant value of the ratio of two proportional quantities x and y, typically the equation is Y=KX.
Step-by-step explanation:
3/4 (x + 18) = 15 What is x equal to
Answer:
x=2
Step-by-step explanation:
hope it helps
please mark as Brainliest
Answer:
x = 2
Step-by-step explanation:
For me it's easier to work with decimals than fractions, so I converted 3/4 to .75
.75(x + 18) = 15
.75x + 13.5 = 15
That was just distributing the .75 but here is where it gets a bit confusing.
.75x + 13.5 = 15
-13.5 -13.5
.75x = 1.5
Divide both sides by .75 to isolate the variable.
x = 2
Hope that helps and have a great day!
Please help what is -0.5 divided by -1/5
A couch and coffee table cost a total of $1156. The cost of the couch is three times the cost of the coffee table find the cost of each item.
Answer:
The couch is 867 and the coffee table is 289
Step-by-step explanation:
The question states that the couch is 3 times the cost of the coffee table. This means this includes the cost of the couch and the coffee table. So I would do 1156= x+3x, which equals 1156=4x. X is the cost of the coffee table. 3x is the cost of the couch. I'd divide 1156 by 4 and get 289. Now you take 289 and plug it in the equation, 1156=x+3x. X would equal to 289, and 3x would equal to 867.
i need your help and to try this out so can you please answer dis
-2(x+6)
Answer:
12x - 12
Step-by-step explanation:
-2(x + 6)
open the parenthesis
-2 * x + -2 * 6
-2x - 12
-2x - 12
Find the equation of a line that passes through the points (1, 2) and (5,8).
1: y= 3/2 + 1/2
2: y= 3/2 + 1
3: y= 3/2 + 2
Answer:
1: y = 3/2 + 1/2
Step-by-step explanation:
y1 -y2/x1 - x2
8-2 / 5-1
6/4 = 3/2
y-2=3/2(x-1)
y-2=3/2x - 3/2
y-2 +2= 3/2x - 3/2 +2
y=3/2x + 1/2
(3.1 · 10² ) (2 · 10³) Write in Scientific Notation.
Answer:6.03*10^3
Step-by-step explanation:
(3.1 *10^2)(2*10^3)
2*10^3=20*10^2
(3.1*10^2)(20*10^2)
(60.3*10^2)=
6.03*10^3
If he drank 80% of his water on his entire hike, how much did he drink?
Not enough information is given to answer this question. If there was 100% water at the beginning of the hike and now there is 80% it would be 20% but without the information, you cant know.
Kia Read for a total of 60 minutes on Monday and Tuesday. He read for 60 minutes on Tuesday. How many minutes did he read on Monday?
(Graph attached)
Please show work
What is the average speed of the runner at 4 seconds
have a random argument with yourselves
Answer:
ok
Step-by-step explanation:
If the odds for a certain event are 5 to 12, what is the probability of the event occuring? Write your answer
as a simplified fraction.
Answer:
5/12
Step-by-step explanation:
Isn't this just a ratio?
8 Determine if the product of 32 and 8V 18 is
rational or irrational. Explain your answer.
Answer: It is irrational.
Step-by-step explanation:
√18 is an irational number. Multiplying most rational numbers by an irrational number results in an irrational number.
The area of a square sports arena is 10,000 m² what are the dimensions of the sports arena on the map.
Answer:
Step-by-step explanation:10,000square you have to multiply them my all squares to get the answer
Is 2|12 true or false
Answer:
true
Step-by-step explanation:
Because it is
Calculate the area of the triangle: A =
Answer:
27
Step-by-step explanation:
The area of the triangle is 30.9 square units.
We have,
From the figure,
Height = Distance between (-2, 6) and (-2, 0).
Base = Distance between (-2, 0) and (7, -5).
To find the distance between two points in a Cartesian coordinate system, use the distance formula:
Distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
Height:
Distance = √((-2 - (-2))² + (0 - 6)²)
Distance = √(0² + (-6)²)
Distance = √(0 + 36)
Distance = √36
Distance = 6
Base:
Distance = √((7 - (-2))² + (-5 - 0)²)
Distance = √((7 + 2)² + (-5)²)
Distance = √(9² + (-5)²)
Distance = √(81 + 25)
Distance = √106
Distance ≈ 10.3
Now,
The area of the triangle.
= 1/2 x base x height
= 1/2 x 10.3 x 6
= 10.3 x 3
= 30.9 square units
Thus,
The area of the triangle is 30.9 square units.
Learn more about triangles here:
https://brainly.com/question/25950519
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