The cost of the room before the tax is X.
To get the total cost they multiply the cost of the room x by 1 + sales tax rate.
Total cost would be x(1.05)
To find x divide total cost by 1.05:
Cost of room before tax: 172.20/1.05
Cost: $164
solve by completing the square pls show work i will mark brainliest
Answer:
[tex]3(x-1)^2 +6[/tex]
Step-by-step explanation:
Write [tex]3x^2-6x+9[/tex] in the form: [tex]x^2 + 2ax + a^2[/tex].
Factor out 3.
[tex]3(x^2 -2x+3)[/tex]
Add and subtract [tex]\left(-1\right)^2\:[/tex].
[tex]3\left(x^2-2x+3+\left(-1\right)^2-\left(-1\right)^2\right)[/tex]
You dont have to write this section down but its for notes:
[tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]
[tex]x^2-2x+\left(-1\right)^2=\left(x-1\right)^2[/tex]
Continue writing this down to show work:
Complete the square
[tex]3\left(\left(x-1\right)^2+3-\left(-1\right)^2\right)[/tex]
Simplify
[tex]3\left(x-1\right)^2+6[/tex]
Which expression represents the number of sides in the polygon for the nth member of the sequence?
A) n+2
B) 2n + 1
C) 4n-3
D) 3n+2
Answer:
The answer is n+2.Step-by-step explanation:
I hope U like my answer and my answer helped U....Answer:
n+2 represemts the number of sides in the polygon for the nth member of the sequence
18/73 and 4/16. Proportional or Not Proportional
Answer:
not proportional
Step-by-step explanation:
We can check using cross products
18/73 = 4/16
18*16 = 73*4
288=292
Since this is not equal, this is not proportional
A cookie company expanded its standard package of 36 cookies to include 4 extra cookies of a brand new flavor. If all of the cookies from an expanded package were put in a container and one were selected at random, what is the probability that it will be a cookie of the new flavor?
Answer:
1/9 probability
Step-by-step explanation:
The total cookies are 36 and the new flavors are 4, if you simplify 4/36, it equals 1/9
please help me is for my homework
Answer:
35/100 if I remembered correctly, XD
Answer:
[tex]\frac{35}{100}[/tex]
Step-by-step explanation:
if you want to convert decimal to fraction you first have to observe the decimal point
here the decimal point is after 2 numbers so
u will take 100 to be divided with
[tex]\frac{35}{100}[/tex]
Round
63.999
to two decimal places?
Answer:
64.00
Step-by-step explanation:
64.00 is the correct answer.
63.999 rounded to 2 decimal places is 64.00
What is the 5 rounding rule?In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be increased by 1 if that last figure is odd.
For example, if only two decimals are to be kept, then 6.755000 becomes 6.76.
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Jocelyn is going to the amusement park, where she has to pay a set price of admission
and another price for tickets to go on each of the rides. The total amount of money
Jocelyn will spend is given by the equation y 3.5x + 28, where y represents the
total amount of money, in dollars and cents, and x represents the number of rides
Jocelyn goes on. What could the number 28 represent in the equation?
Can you answer this, please?
Answer: C) 3
Explanation:
The degree of a single variable polynomial is the largest exponent, which in this case is 3.
A gas has a density of 0.824 g/L and occupies a volume of 3.00 liters. What is the mass in grams?
Density is mass per unit volume,
ρ = m/v
Solving for mass gives
m = ρv
so that a gas with density 0.824 g/L that occupies 3.00 L has a mass of
m = (0.824 g/L) (3.00 L) = 2.47 g
identity the value for a, b, and c.
2x^2=-7x-9
Problem 11
Six friends who enjoy tennis decide to play a game of singles and a game
of doubles every day of the 7-week school holidays.
(a) Show that at least four of the games of singles will be between friends
playing each other for the fourth time.
(b) Show that at least four of the games of doubles will be between pairs
playing the same opposing pair for the second time.
Number combination can be used to find the number of selecting n items from m items
The known parameters are;
Number of days the six friends play a game of tennis = Every day = 7 days
Number of weeks the six friends the friends play for = 7 weeks
Therefore the total number of days = 7 × 7 days = 49 days
Required:
(a) The number of ways the friends can play with each other once is given as follows;
[tex]The \ number \ of \ 2 \ combinations \ in \ 6 \ options, C_6^2 = \dfrac{6!}{2!\times (6-2)!} = 15[/tex]
The number of ways the six friends can play with each other once is 15 ways
Therefore, minimum number of singles games that will be between the same friends playing each other is given as follows;
[tex]\mathbf{Number \ of \ games = \dfrac{7 \times 7}{C_6^2} }=3.2\overline 6[/tex]
Therefore, more than 3 of the games or four games will be between pairs playing the game more than four times together, and when at least four of the games of singles are counted it will be between friends playing each other for the fourth time
(b) The number of ways the friends can play game of doubles is given as follows;
[tex]C_6^4 = \dfrac{6!}{4! \times (6 - 4)!} = 15[/tex]
The number of pairs = ₆C₂ = 15
The number of games of doubles = 49
In 49 games, we have;
The number of times the same opposing will play a game of doubles where a member of the pair can be on either side of the court will given as follows;
[tex]\mathbf{Number \ of \ games \ of \ doubles \ between \ same \ pair} = \dfrac{7 \times 7}{15 } =3.2\overline 6[/tex]
Therefore, at least four of the of the games of doubles will be between the same set of four friends playing for the 4th time, which gives; at least four games of doubles between the same set of four friends, two of which are playing (as a pair) the same opposing pair for the 4/2 = second time
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What numbers are 3 units from -2 on a number line?
A number line ranging from negative 10 to positive 10
Select from the drop-down menus to correctly complete the statements.
______is 3 units left from -2 on a number line.
______- is 3 units right from -2 on a number line.
The answers are
-1
-5
1
5
please hurry
Answer:
___-5___is 3 units left from -2 on a number line.
___1___- is 3 units right from -2 on a number line
Someone help pleasee
Answer:
a horizontal translation 3 units to the right because-3 has been added to the exponent
How many solutions are there to the equation below?
9x + 16 = 4x
A. infinitely many
B. 1
C. 0
Step-by-step explanation:
Infinitely many solutions are there....
hope it helps
HELP ASAP will give BRAINLIEST
Hey there! I'm happy to help!
The question tells us that m∠JKL is 54. We see from the diagram that this is the combination of the angles m∠JKM and m∠MKL. So, we can combine their values, which are equal to 54 to find x.
13x+1+5x+4=54
We combine like terms
18x+5=54
We subtract 5 from both sides.
18x=49
We divide both sides by 18.
x=2.7222222....
Now, we want to find the measure of m∠MKL. We plug our x value into the value of this angle and evaluate.
5(2.722....)+4=17.61111....... or 17 11/18.
Have a wonderful day and keep on learning! :D
Multiply. Write your answer as a fraction in simplest form. −1/4×(−4/3)=
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given
- [tex]\frac{1}{4}[/tex] × - [tex]\frac{4}{3}[/tex] ( negative times negative = positive )
= [tex]\frac{1}{4}[/tex] × [tex]\frac{4}{3}[/tex] ( cancel the 4 on the numerator and denominator )
= [tex]\frac{1}{3}[/tex]
when is it hard to show if a set is closed or not closed?
What is the smallest integer greater than the square root of 325
Answer:
19
Step-by-step explanation:
√325 ≈ 18.02
The next greatest integer is 19.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Let x represent the side length of a square. Find a regular polygon with side length x whose perimeter is twice the perimeter of the square. Find a regular polygon with side length x whose perimeter is three times the length of the square
Answer:
Step-by-step explanation:t55
An octagon has 8 sides. If each of them has a length of x, then the perimeter is 8x which is twice the perimeter of the square. (The square has a perimeter of 4x)
A dodecagon is a 12 sided regular polygon. It will have 12 sides all of which are equal to x. Since the square has a perimeter of 4x and the dodecagon has a perimeter of 12x the perimeter of the dodecagon is 3 times that of the given square.
calculate Z
z = 81
z = 30
z = 15
z = 20
choose the only correct answer
The product of 4 and a number x
Answer:
you can`t multiply an integer with a variable unless the variable represents something
ex: if x = 10 then the product of 4 and x is 40
Answer:
4x
Step-by-step explanation:
'Product' refers to multiplication.
What is the solution to the equation 1/4x - 1/8 = 7/8 + 1/2x ?
A. x = -5
B. x = -4
C. x = 4
D. x = 5
Hey there! I'm happy to help!
We want to get all of the variables on the left side and all of the numbers on the right side. This will allow our variable to be isolated so we can see what it is equal to.
1/4x - 1/8 = 7/8 + 1/2x
We add 1/8 to both sides.
1/4x=1+1/2x
We subtract 1/2x from both sides.
-1/4x=1
We divide both sides by -1/4 (same thing as multiplying -4).
B. x=-4
Have a wonderful day and keep on learning! :D
Help me with this math question plss
Answer:
C. 8/17
Step-by-step explanation:
PM = 16+14 = 30 cm
KP= LN = 16×tan45° = 16×1 = 16cm
by using pythagorean theorem, we find :
KM² = PM²+KP²
= 30²+16²
= 900+256
= 1156
=> KM =√1156 = 34cm
so, cos theta = KP/KM = 16/34 = 8/17
(Please help) Solve.
-4+4(-8+2n) = -37+8n
Answer:
No solutions for n
Step-by-step explanation:
Distribute the 4 to the -8 and the 2n
-4 + 4*-8 + 4*2n = -37 + 8n
Multiply
-4 - 32 + 8n = -37 + 8n
Subtract 8n on both sides
-4 - 32 = -37
Subtract on the left
-36 = -37
No solutions because -36 does not equal -37
Answer:
No solution
Step-by-step explanation:
-4 + 4(-8 + 2n) = -37 + 8n
-4 - 32 + 8n = -37 + 8n
-36 + 8n = -37 + 8n
8n - 8n = -37 + 36
0 = -1
Since 0 does not equal 1, this is a “No Solution”
Help please.
Simplify: 5i/ 3 + 2i
Answer:
10+15i/13
Step-by-step explanation:
This question is about complex numbers.
so,
in this type of questions we have to multiply this fraction by the conjugate of the denominator
conjugate of the denominator is 3-2i
1) 5i(3-2i)/(3+2i)(3-2i)
2) 15i-10i^2/9-4i^2 ( we know that i^2 = -1 )
3) 15i+10/9+4
4) 15i+10 / 13
order of operations. please help!
5. Classify the number 15.
O Whole, integer, rational, real
Integer, rational, real
O Natural, whole, integer, rational, real
O rational, real
Answer:
O Natural, whole, integer, rational, real
Step-by-step explanation:
it can be expressed as a fraction of 45/3, which means that it is rational.
it is a whole number because it does not contain a fraction or decimal.
it is a real number because it is a number we normally use such as 1, -0.1, 3/4, etc
it is a natural number because it is a positive integer.
and it is an integer because it does not contain a decimal.
Answer: Natural, whole, integer, rational, real
Find type of angle and solve for x.Please help.
Step-by-step explanation:
72° and a° is the angle of a straight line so
a+72°=180
a=180-72
a=108°
By using alternate exterior angle definition:
7x+24=180
7x=108-24
7x=84
x=84/7
x=12
Subtract.
−135−(−258)
Enter your answer as a simplified fraction by filling in the boxes.
[ ]
[ ]
Answer:
123/1
Step-by-step explanation:
-135- (-258)
123
123/1
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A 180-inch pipe is cut into two pieces.one piece is three times the length of the other.find the length of the shorter piece.
The length of the shorter piece is 45 inches.
How to determine the length of the shorter piece.Let's represent the length of the shorter piece as "x" inches.
According to the information given, the length of the longer piece would be three times the length of the shorter piece, which means it's 3x inches.
Since the total length of the pipe is 180 inches, we can set up an equation:
x (shorter piece) + 3x (longer piece) = 180
Now solve for x:
4x = 180
x = 45
Therefore, the length of the shorter piece is 45 inches.
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