The first three towers in a sequence are shown. The nth tower is formed by stacking n blocks on top of an n times n square of blocks. How many blocks are in the 99th tower?
Answer:
The 99th tower contains 9900 blocks.
Step-by-step explanation:
From the question given, we were told that the nth tower is formed by stacking n blocks on top of an n times n square of blocks. This implies that the number of blocks in n tower will be:
n + n²
Now let us use the diagram to validate the idea.
Tower 1:
n = 1
Number of blocks = 1 + 1² = 2
Tower 2:
Number of blocks = 2 + 2² = 6
Tower 3:
Number of blocks = 3 + 3² = 12
Using same idea, we can obtain the number of blocks in the 99th tower as follow:
Tower 99:
n = 99
Number of blocks = 99 + 99² = 9900
Therefore, the 99th tower contains 9900 blocks.
Evaluate (-B)2 for A= 5, B = -4, and C = 2.
Answer:
8
Step-by-step explanation:
Expression:
(-B)2
Let's substitute the value of B into this expression:
B = -4
(-B)2
[-(-4)]2
Notice how there are two negative signs int this expression:
[-(-4)]2
Well, there is an invisible 1 behind the first negative sign.
[-(-4)]2
[-1(-4)]2
All we have to do now is multiply:
[-1(-4)]2
(4)2
(4)2
= 8
Therefore, the value of the expression is 8.
Please help, having trouble figuring out this word problem. Thanks if you do :)
Answer:
-21. -19.-17
Step-by-step explanation:
Let x be the smallest
x+2 next smallest
x+4 be the largest
4*(x) = 18+6(x+4)
Distribute
4x = 18+6x+24
Combine like terms
4x = 42+6x
Subtract 6x from each side
-2x = 42
Divide by -2
-2x/-2 = 42/-2
x = -21
x+2 = -19
x+4 = -17
Answer:
- 21, - 19, - 17
Step-by-step explanation:
Let y be the smallest no.
& y + 2 next smallest no.
& y + 4 be the largest no.
= 4 * (y) = 18 + 6 * (y + 4)
4y = 18 + 6y + 24
4y - 6y = 42
- 2y = 42
= - 21
The other 2 numbers are:
y + 2
= - 19
y + 4
= - 17
Hope this helps!
f(x) = (x + 3)(x + 5).
Answer:
Step-by-step explanation:
Answer:y=x+8x+15
Step-by-step explanation:
determine the angle of elevation if a 7-metre tree has a 12-metre shadow
Answer:
about 30.26
Step-by-step explanation:
tan-1 7/12 = 30.26
solve
−2(x−7)+3(x+5)=x+9
Answer:
no solutions
Step-by-step explanation:
−2(x−7)+3(x+5)=x+9
Distribute
-2x +14 +3x +15 = x+9
Combine like terms
x + 29 = x+9
Subtract x from each side
x+29 -x = x+9-x
29 = 9
This is never true so there are no solutions
Answer:
It is wrong Problem
Step-by-step explanation:
-2x+14+3x+15=x+9
x+29=x+9
????
PLEASE PLEASE HELP ME IM SOOO CONFUSED!!!!!
( show the work MANDATORY)
WRITE EACH FRACTION AS A DECIMAL. USE A BAR TO SHOW REPEATING DECIMAL.
1.) 7/10
2.) 1/4
3.)-3/10
4.)1/8
5.) 7/30
6.) 7/11
7.)-3/5
Answer:
1=0.70 2=0.25 3=-0.30 4=0.125 5=0.233333333 6=0.636363636 7=-0.6
Step-by-step explanation:
Calculator and anything over 10, just move the decimal back one space!
Find the perimeter of the following figure.
x + 13
3x + 2
8
2
X + 5
Answer:
5x+30
Step-by-step explanation:
simply add each side together:
(x+13)+(3x+2)+8+2+(x+5)
=5x+30
Which explains how to find the quotient of the division below? Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction Write Negative 3 and one-third as Negative StartFraction 13 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 13 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 9 and three-fourths. Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 7 and StartFraction 6 over 12 EndFraction = Negative 7 and one-half. Write Negative 3 and one-third as Negative StartFraction 9 over 3 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 9 over 3 EndFraction times StartFraction 4 over 9 EndFraction. The quotient is Negative 1 and one-third. Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 4 over 9 EndFraction. The quotient is Negative 1 and StartFraction 13 over 27 EndFraction = Negative 1 and StartFraction 13 over 27 EndFraction.
Answer:
(B) Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 7 and StartFraction 6 over 12 EndFraction = Negative 7 and one-half.
Step-by-step explanation:
To find the quotient of the division:
[tex]-3\dfrac13 \div \dfrac49[/tex]
Step 1: [tex]\text{Write}$ $ -3\dfrac13$ as $ -\dfrac{10}{3}[/tex]
[tex]-3\dfrac13 \div \dfrac49 = -\dfrac{10}{3} \div \dfrac49[/tex]
Step 2: Find the reciprocal of [tex]\dfrac94[/tex]
[tex]-\dfrac{10}{3} \times \dfrac94\\=-7\dfrac12[/tex]
Answer:
b
Step-by-step explanation:
Find the volume of the rectangular prism. Express your answer as a simplified mixed number.
Answer:
414 9/16 m³
[tex]414\frac{9}{16}m^{3}[/tex]
Step-by-step explanation:
The volume of a Rectangular prism is calculated as Length × Width × Height
From the attached diagram,we can see that
The length = 8 3/8 m
The width = 6 m
The height =8 1/4 m
Converting the mixed fraction to improper fraction in other to simplify it better
The length = 67/8 m
The height = 33/4 m
The volume of the rectangular prism =
67/8 m × 6m × 33/4m
= (13266/32)m³
= 6633/16 m³
= 414 9/16 m³
= [tex]414\frac{9}{16}m^{3}[/tex]
3.) The length of a midsegment of a trapezoid is the blank
lengths of the bases. *
Your answer for blank!
Answer:
Average
Step-by-step explanation:
If a and b are the lengths of the bases, then a+b/2 is the length of the midsegment of the trapezoid.
La mama de maximo le pidio que fuera a la tienda dijo que comprara 0.5 litros de leche, el dueño de la tienda le dijo que solo tenia leche en envases de ½ litros ¿Es mas, menos o igual a la capacidad que le pidió su mama?
Answer:
1/2 litros es igual a la capacidad que le pidió su mamá.
Step-by-step explanation:
Para encontrar la respuesta debes escribir 0.5 como fracción. Para hacerlo, el numerador es el número original sin el punto decimal y para definir el denominador debes determinar cuántos digitos decimales tienes. En este caso, el número tiene un dígito decimal, por lo cual el denominador es 10. De acuerdo a esto:
0.5 se escribiría como [tex]\frac{5}{10}[/tex] y esta fracción se puede simplificar porque los dos números son divisibles entre 5:
5/5= 1
10/5= 2
Por esto, 0.5= [tex]\frac{1}{2}[/tex]
Esto significa que 1/2 litros es igual a la capacidad que le pidió su mama.
Will mark brianliest !!!!!!!!!!!!! Please answer correctly !!!!!!!!!!!!!
Answer:
9 is the greater x and 2 is the lesser x
Step-by-step explanation:
I really don't know how to explain without simply writing it out for you, which I really can't do. But there's the answer lol
Answer:
x = 2, x = 9
Step-by-step explanation:
Given
x² - 11x + 18 = 0
Consider the factors of the constant term (+ 18) which sum to give the coefficient of the x- term (- 11)
The factors are - 9 and - 2 , since
- 9 × - 2 = + 18 and - 9 - 2 = - 11 , thus
(x - 9)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2 ← lesser value
x - 9 = 0 ⇒ x = 9 ← greater value
Simplify 3(x - 2) + 5x
Solve the following:
A) 4x-1/2=x+7
B) 3x+2=2x+13/3
C) 2x-7/4=3+x/3
Answer:
a. 2.5
b. 2.333
c. 2.85
Step-by-step explanation:
A) 1. subtract -x on both sides 2. to get 3x-1/2=7
3. Add 1/2 on both sides 4. to get 3x=7.5
5. divide 3 on both sides 6. To get... x=2.5
B)1. Same process. 2. x+2=13/3
3. x=13/3-2 4. x= 2.33(repeating)
C) 1. same process. 2. 2x-x/3=3+7/4
3. 2x-x/3=4.75 4. Isolate -x/3
5.-x/3=4.75-2x 6. multiply both sides by 3
7. -x=14.25-6x 8. 5x=14.25
9. x= 2.85
* remember to distribute the 3 to each variable.
Question 1 of 10
2 Points
If f(x)= 2(x)2 +5W/(x+2), complete the following statement:
f(2)=
Answer:
8 + (5W)/ 4
Step-by-step explanation:
Plug in 2 for x
2 * 2 * 2 + (5W)/(2 + 2)
8 + (5W)/ 4
What do I do in this question
Step-by-step explanation:
X × 3 + 4 = 22
X × 3 = 22 - 4
X × 3 = 18
X = 18 /3
X = 6
The picture below has all the questions I need assistance with.
Answer:
11) D, 12) D
Step-by-step explanation:
if you do the math it works
Krutika and Natasha are marking exam papers. Each set takes Krutika 72 minutes and Natasha 1 hour. Express the times Krutika and Natasha take as a ratio. Give your answer in its simplest form.
Answer:
6 : 5
Step-by-step explanation:
Each set takes Krutika 72 minutes.
Each set takes Natasha 1 hour.
Let us convert that to minutes:
1 hour = 60 minutes
Therefore, expressing the times it takes Krutika and Natasha as a ratio:
72 : 60
Divide by 6
12 : 10
Divide by 2
6 : 5
The ratio is 6 : 5
(1 1/6 − 7/18 )÷2.8/0.5+ 1/18 =
Dr. Karuza would like to send some classes on a trip to Disneyland. She explains that in order for any classses to go, 25% of the passengers must be teachers. Aniyah explains that if 4 teachers chose 24 students from 1 class to go then the teachers will be 25% of the passengers.
Do you agree or disagree with her answer?
Answer:
No, if 4 teachers chose 24 students from 1 class to go then the teachers will not be 25% of the passengers.
Step-by-step explanation:
Given: If 4 teachers chose 24 students from 1 class to go then the teachers will be 25% of the passengers.
To find: if the given statement is correct or not
Solution:
Total number of teachers = 4
Total number of students = 24
Total number of passengers = Total number of teachers + Total number of students = 4 + 24 = 28
Here,
25% of Total number of passengers = [tex]\frac{25}{100}(28)=7\neq 4[/tex]
So, if 4 teachers chose 24 students from 1 class to go then the teachers will not be 25% of the passengers.
What is the next number in the pattern
2,4,8,16,32....
Answer:64
Step-by-step explanation: because 2 multiplied by 2 is 4 four multiplied by 2 is eight as the pattern continues 32 multiplied by 2 is 64.
Answer:
2+2=4
4+4=8
8+8=16
16+16=32
32+32=64
Ms.Thomas took her family and friends to the movies. There were a total of 16 people. Children tickets cost $6 and adult tickets costs $9. She spent a total of $129. How many adults went to the movies?
Answer: ijiijijijijijijiijij
Step-by-step explanation:
okjopunnounpoino
please help for brainliest
Answer:
f = 6, g = 8
Step-by-step explanation:
The area of Δ ADE = 60 - 48 = 12 cm²
Thus
[tex]\frac{1}{2}[/tex] AD × 4 = 12, that is
2AD = 12 ( divide both sides by 2 )
AD = 6 = f
The area of ABCD = 48 cm² , thus
fg = 48 , that is
6g = 48 ( divide both sides by 6 )
g = 8
Thus f = 6 and g = 8
Seaside Bike Rental Shop charges a $13 fee plus $7 per hour to rent a bike. Chris paid $62 to rent a bike. How many hours did he pay for?
Answer:
7 hours
Step-by-step explanation:
(62-13)/7=7
Solve for w. 5w + 9z = 2z + 3w w = w equals negative StartFraction 7 Over 2 EndFraction z.Z w = w equals negative StartFraction 2 Over 7 EndFraction z.Z w = –2z w = –7z
Answer:
w = -7z/2
Step-by-step explanation:
We need to solve for w in terms of z.
The equation given is:
5w + 9z = 2z + 3w
Collect like terms:
5w - 3w = 2z - 9z
2w = -7z
w = -7z/2
Answer:
option A (-7/2z)
Step-by-step explanation:
What is the area of a circle with a radius of 6 inches?
9 st in?
12 x in.2
36 x in 2
81 x in 2
Answer:
A≈113.1in²
Step-by-step explanation:
Radius: 6in
Solved for area
Shape: Circle
Formula: A=πr2
1: Use the formula πr (r) to calculate the the area.
2: We are looking for the area.
3: 6 inches for radius to find the area
Answer: A≈113.1in²
Hope this helps.
A sports club charges an initiation fee and a monthly fee. At the end of the 5 months, a member had paid a total of $450. At the end of the 10 months, she had paid a total of $500.
a) Write a linear system to model the situation
b) Solve the linear system by substitution to solve the related problem: What are the initiation fee and the monthly fee?
Answer:Initiation fee is $400 while monthly fee is $10
Step-by-step explanation:
Let the initial fee be x which is fixed while the monthly fee be y
At the end of 5 months, 450 was paid
This means that;
x + 5y = 450 ••••••••(i)
At the end of 10 months, $500 was paid
Mathematically, this means that;
x + 10y = 500•••••••••••(ii)
now we solve both equations simultaneously to get the value of x and y
our equation ii can be rewritten as;
x + 5y + 5y = 500
we can now insert equation i directly into this
450 + 5y = 500
5y = 500-450
5y = 50
y = 50/5
y = $10
From x + 5y = 450
let’s insert the calculated value of y
x + 5(10) = 450
x + 50 = 450
x = 450-50
x = $400
Entre Amaya y Alberto tienen 5€ entre Alberto y Rosa tienen 10€ sabiendo que Amaya tiene 2,70€ ¿cuanto tiene Rosa?
Ani will put this in a translator
Step-by-step explanation:
The table gives some information about the heights of 30 plants.
Height, h in cm
Frequency
0<h < 10
1
10 <h < 20
9
20 <h < 30
7
30 <h < 40
13
Which class interval contains the median?
Select your answer.
osh <10 10 sh< 20 20 sh < 30 30 sh<40
А
B
C
D
Answer:
2,8,8
Step-by-step explanation:
The class interval 20 <h < 30 contains the median.
Median :To find the interval in which median is lies, first we have to find the cumulative frequency.
The table is,
Height range frequency Cumulative frequency
0<h < 10 1 1
10 <h < 20 9 1 + 9 = 10
20 <h < 30 7 10 + 7 = 17
30 <h < 40 13 17 + 13 = 30
Sum = 30
Since, the sum of frequency is even. So that the median is ,
[tex]\frac{\frac{n}{2} th +(\frac{n}{2} +1)th}{2} =\frac{15th +16th}{2}[/tex]
From observing table, 15th and 16th term lies in cumulative frequency of 17.
Thus, the class interval 20 <h < 30 contains the median.
Learn more about the class interval here:
https://brainly.com/question/7587748