By solving a system of equations we will see that the charge on the first city was $5,000, and on the second city, $4,000.
How much was the hotel charge in each city?
Let's define the variables:
C₁ = charge in the first city.C₂ = charge on the second city.We know that:
C₂ = C₁ - $1000
And we also know that the total tax is $455, then we can write:
0.035*C₁ + 0.07*C₂ = $455
(this says that the total tax is $455)
So we have a system of equations:
C₂ = C₁ - $1000
0.035*C₁ + 0.07*C₂ = $455
We can replace the first one into the second to get:
0.035*C₁ + 0.07*(C₁ - $1000) = $455
0.105*C₁ - $70 = $455
C₁ = ($455 + $70)/0.105 = $5,000
And:
C₂ = C₁ - $1000 = $5,000 - $1,000 = $4,000
The charge in the first city is $5,000 and in the second city was $4,000.
If you want to learn more about systems of equations, you can read:
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A polygon that undergoes a series of transformations such that the image has the corresponding sides and angles of equal measure to those of the original, it can be said that the original and the image are congruent. true or false
Yes the pre image and image are congruent always
See
They are transformed through a constant scale factor so they ought to be same .
And
If there angles of one triangle (pre image) are congruent to rest three(image) then triangles are congruent by AAA congruence
Help
Need the steps >.
Answer:
x = 3
Step-by-step explanation:
using the rule of exponents
[tex]4^{x}[/tex] = [tex](\frac{1}{2}) ^{x-9}[/tex]
[tex](2^2)^{x}[/tex] = [tex](2^{-1}) ^{x-9}[/tex]
[tex]2^{2x}[/tex] = [tex]2^{-1(x-9)}[/tex] = [tex]2^{9-x}[/tex]
suince the bases on both sides are equal, then equate the exponents
2x = 9 - x ( add x to both sides )
3x = 9 ( divide both sides by 3 )
x = 3
through (-2,5)
and (2, 1)
Answer:
x + y = 3
Step-by-step explanation:
The equation of a line through two points can be found using the 2-point form for the equation of a line:
y -y1 = (y2 -y1)/(x2 -x1)(x -x1) . . . . . line through points (x1, y1) and (x2, y2)
__
y -5 = (1 -5)/(2 -(-2))(x +2) . . . . using points (-2, 5) and (2, 1)
y -5 = (-4/4)(x +2)
y -5 = -(x +2) . . . . . . equation in point-slope form
y -5 = -x -2
y = -x +3 . . . . . . . . . equation in slope-interept form
x + y = 3 . . . . . . . . . equation in standard form
437.683
Write a number with a 7 in it that is 1/10 the size of the 7 in the number above.
Step-by-step explanation:
find the egn of the line through (a.b)and perpendicular to the lime passing through (a.2b)and (b.2a)for a#b?
It takes 4/5 of an hour to paint 2/5 of a room, how long does it take to paint one room?
Answer:
It should be 2/5 hours. 4/5 - 2/5 is 2/5.
Step-by-step explanation:
Which statement describes the relationship between x and y PLEASE HELP
As x increases, y decreases.
Use the graph to determine which statement describes f(x).
AY
5
y = f(x)
5
A
O A. R(x) does not have an inverse function, because its graph fails the
vertical line test
B. f(x) does not have an inverse function, because its graph fails the
horizontal line test
O C. Rx) has an inverse function, because its graph passes the vertical
line test
OD. Rx) has an inverse function, because its graph passes the
horizontal line test.
Answer: B
Step-by-step explanation:
The solution is : B. f(x) does not have an inverse function, because its graph fails the horizontal line test.
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
here, we have,
In the graph, we can see two asymptotes at x = 1.
This means that the denominator is equal to 0 when x = 1, then we can write:
f(x) = A/(x - 1)
Where we can start thinking that A is a constant.
Now we also can see that when x = 2, f(2) is equal to 1, or:
f(2) = 1.
Then:
f(2) = 1 = A/(2 - 1) = A/1
Then we have A = 1.
Then our function is:
f(x) = 1/(x - 1)
Hence, The solution is : B. f(x) does not have an inverse function, because its graph fails the horizontal line test.
To learn more on graph click:
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Suppose you take a sample of 15 pieces of colored fruit snacks and a sample of 60 pieces of colored fruit snacks from one day's production. Which sample is more likely to give you a prediction closer to the actual number of each color? Explain
Answer:
The sample of 15 pieces of colored fruit snacks
Step-by-step explanation:
The sample of 15 pieces of colored fruit snacks. The 60 pieces are from ONE day which means it can be heavily biased. It might be like "BLUE RASPBERRY SPECIAL DAY!" or "PRESIDENTS DAY!! RED BLUE AND WHITE!!". However, 15 pieces, whilst having less of a population, is probably more spaced out.
find the ninth term of the geometric sequence, given the first term and the common ratio: a1=1, r=-1/3
Answer:
1(-1/3)^8
Answer: 1/6561
hope this is better
Create a table of values and graph the function g(x)=|x-4|
Table of values
4 0
5 1
6 2
7 3
The area of a triangle is 12 square feet. If the base is 6 feet, what is the height of the triangle?
Options:
2 feet
1 feet
6 feet
4 feet
Answer:
4 feet
Step-by-step explanation:
A=hbb
2
Solving forhb
hb=2A
b=2·12
6=4ft
The Coolmathz family is ordering pizza. They order two pizzas. One is $15, and the other is $12. They use a coupon for 5% off the whole order. They then tip 18% of the cost after the coupon. How much did the Coolmathz family spend in total? Show your work
Answer:
30.51$
Step-by-step explanation:
15+12=27$
5% of 27$=1.35$
18% of 27=4.86
Do the math: 27+4.86-1.35=30.51
Mary did not pay last month's credit card bill in full. Below is a list of Mary's daily balances for his last billing cycle.
For 6 days she owed $500.00
For 4 days she owed $350.26
For 7 days she owed $568.45
For 8 days she owed $480.34
For 6 days she owed $649.90
Type your answer.
500+350.26+568.45+480.34+649.90 = $2548.95
hope it really helps...!!!
A Diameter of a circle has endpoints P(-10, -2) and Q(4, 6)
a. Find the center of the circle.
b. find the radius. If your answer is not an integer, express in in radical form.
c. write an equation for the circle
PLS HELP FAST!
Will Give Brainiest if answered properly!
Answer:
see explanation
Step-by-step explanation:
(a)
the centre of the circle is at the midpoint of the endpoints.
using the midpoint formula
centre = ( [tex]\frac{-10+4}{2}[/tex] , [tex]\frac{-2+6}{2}[/tex] ) = ([tex]\frac{-6}{2}[/tex] , [tex]\frac{4}{2}[/tex] ) = (- 3, 2 )
(b)
the radius r is the distance from the centre to either of the endpoints
using the distance formula to find r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = Q (4, 6 )
r = [tex]\sqrt{(4-(-3))^2+(6-2)^2}[/tex]
= [tex]\sqrt{(4+3)^2+4^2}[/tex]
= [tex]\sqrt{7^2+16}[/tex]
= [tex]\sqrt{49+16}[/tex]
= [tex]\sqrt{65}[/tex]
(c)
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius , then
(x - (- 3) )² + (y - 2)² = ([tex]\sqrt{65}[/tex] )² , that is
(x + 3)² + (y - 2)² = 65
Answer:
Step-by-step explanation:
a) Use midpoint formula to find the center.
[tex]\sf \boxed{Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]
P(-10 ,-2) ⇒x₁ = -10 & y₁ = -2
Q(4,6) ⇒ x₂=4 & y₂ = 6
[tex]\sf midpoint = \left(\dfrac{-10+4}{2},\dfrac{-2+6}{2}\right)[/tex]
[tex]=\left(\dfrac{-6}{2},\dfrac{4}{2}\right)\\\\=\left(-3,2\right)[/tex]
b) To find the radius, use the distance formula
[tex]\boxed{distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
Q(4,6) & O(-3,2)
[tex]r=\sqrt{(-3-4)^2+(2-6)^{2}}\\\\=\sqrt{(-7)^{2}+(-4)^2}\\\\=\sqrt{49+16}\\\\= \sqrt{65}[/tex]
radius = √65
c) Equation of circle : (x - h)² +(y -k)² = r²
Where (h,k) is the coordinates of the center and r is the radius
(x -[-3])² + (y - 2)²= (√65)²
(x + 3)² + (y -2)² = 65
Plss some help!!
Its easy just not for me. lol
Answer:729
Step-by-step explanation: volume is base area × height
Base area = 9×9
Volume =9×9×9
6. Find the value of x to the nearest tenth. Volume of the
cylinder is 602.88 cm3.
Volume: 602.88 cm3
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=x\\ h=12\\ V=602.88 \end{cases}\implies \begin{array}{llll} 602.88=\pi (x)^2(12)\implies \cfrac{602.88}{12\pi }=x^2 \\\\\\ \sqrt{\cfrac{602.88}{12\pi }}=x\implies 4.0\approx x \end{array}[/tex]
How many molecules of hydrogen chloride would there be in 100. 00 grams of this gas? please help
Answer:
9.5 * 10^23 molecules of HCl
Step-by-step explanation:
just a note this might be better to put in the chem section next time since this is a stoichiometry question
the molar mass of HCL is 1.007 + 35.45 = 65.457 g/mol
to find the number of moles, divide 100 by 65.457
then multiply the number of moles by 6.22 * 10^23 to get the number of molecules
[tex]100.00g * \frac{1 mol}{65.457g} * \frac{6.22 * 10^{23} molecules }{1 mol} = 9.502 * 10^{23} molecules[/tex]
3. 4g (2) + 7g - h
A. g-h
B. 159 - h
Answer:
15g-h is the answer......
A student prepares 150.0 ml of 1.40 m hcl using 35.0 ml of a stock solution. what is the concentration of the stock solution? use m subscript i v subscript i equals m subscript f v subscript f.. 0.327 m 4.29 m 6.00 m 7.35 m
Answer:
(c) 6.00 M
Step-by-step explanation:
The given equation can be solved for the unknown concentration.
__
[tex]m_iv_i=m_fv_f\\\\m_i(35.0\text{ ml})=(1.40\text{ M})(150.0\text{ ml})\\\\m_i=\dfrac{(1.40\text{ M})(150.0\text{ ml})}{35.0\text{ ml}}\\\\\boxed{m_i=6.00\text{ M}}[/tex]
The concentration of the stock solution is 6 M.
Answer: c- 6.00 m
Step-by-step explanation:
got it right on edge
The inequality 10w + 40 < 450 represents the maximum number of ten-pound weights, w, a weight bench can hold if the maximum weight capacity of the bench is less than 450 pounds. The table shows the steps a trainer takes to solve the inequality.
Hey there!
10w + 40 < 450
SUBTRACT 40 to BOTH SIDES
10w + 40 - 40 < 450 - 40
SIMPLIFY IT!
10w < 450 - 40
10w < 410
DIVIDE 10 to BOTH SIDES
10w/10 < 410/10
SIMPLIFY IT!
w < 410/10
w < 41
(Your graph is shown below)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
#5 The MAC is 4 centimeters. Find the circumference of B. Round your answer to the hundredths.
Answer:
C ≈ 11.71 cm
Step-by-step explanation:
using the ratio arc AC : circumference C = angle at centre of sector : 360°
[tex]\frac{AC}{C}[/tex] = [tex]\frac{123}{360}[/tex] , that is
[tex]\frac{4}{C}[/tex] = [tex]\frac{123}{360}[/tex] ( cross- multiply )
123 × C = 4 × 360 = 1440 ( divide both sides by 123 )
C = [tex]\frac{1440}{123}[/tex] ≈ 11.71 cm ( to the nearest hundredth )
please help, thank you so much
Step-by-step explanation:
a) 3×2×t=6t
b)500 years
PLS HELPPPPPP IT'S LOCUS AND I HAVE NO IDEA HOW TO DRAWWWW
40 POINTS WILL BE REWARDED
THANKS A LOT
Answer:
im not really good at drawing but Can I ask a question can I help you with other questions?
Step-by-step explanation:
xy and 5x²y are like terms. *
1 point
True
False
Like terms are polynomials that have the same variables with their exponents. *
1 point
True
False
The product obtained in square of binomial is the difference of two squares. *
1 point
True
False
The sum of x and 3x is 4x *
1 point
True
False
In the acronym FOIL Method, O means opposite. *
1 point
True
False
Expression 10 + k has two terms 10 and k. *
1 point
True
False
– 7xy and 27xyz are unlike terms. *
True
False
8z has two terms 8 and z. *
True
False
xy and – xy are like terms *
True
False
Option 3
The answer obtained in multiplying two binomial is a monomial. *
True
False
Answer:
now let's answer this question:
Step-by-step explanation:
1) False
the power 2 spoiled everything.
2) False
like therms aren't always polynomials.
3)False
it's doesn't always come out as diff. of two squares.
4)True
1x+3x =4x ( imagine 1 + 3 = 4 s) ( sum means "add up").
5)False
the O in FOIL means "outer" or "outside" (tip: FOIL means "First", "Outside", "Inside", "Last").
6) True
we can't add them together, they're "unlike terms".
7)True
"Z" is missing in the first term
8) False
they're were multiplied which means they become one term now.
9)Trueeee
having a negative symbol doesn't change nothing
10)False
it's will still take the power it came with which is "2"
e.g 3^2 x 4^2 = 12^2 ( not 12^1 ).
Hope it helps...
thanks
what 3x to the 5th power and 3x to the ninth power
Answer: 19926
this is the answer
HELP ME PLS FOR 90 PTS
In the number 1.1084, how does the value of the 1 in the ones place compare to the value of the 1 in the tenths place?
a The value of the 1 in the ones place is 1/10 the value of the 1 in the tenths place.
b The value of the 1 in the ones place is 10 times the value of the 1 in the tenths place.
c The value of the 1 in the ones place is 1/100 the value of the 1 in the tenths place.
d The value of the 1 in the ones place is 100 times the value of the 1 in the tenths place.
Answer:
a
Step-by-step explanation:
The value of the 1 in the ones place is 1/10 the value of the 1 in the tenths place.
Find the 8th
term of the geometric sequence 8, 16, 32. ..
the 8th term of the geometric sequence 8, 16, 32 is 1024
first we have to find the ratio
r=2
then, we have to find the 8th term
U8=1024
How many ways are there to seat six boys and seven girls in a row of chairs so that none of the girls sit together. A detailed explanation would be most appreciated.
Answer:
5040 ways
Step-by-step explanation:
There will be 13 chairs altogether.
Since there are 7 girls who cannot sit together, the pattern will be alternate.
→ G, B, G, B, G, B, G, B, G, B, G, B, G
Means the ways of girls seated = 7!No. of ways of boys seated = 6!Total Ways
7! x 6!6! (7 x 1)6 x 5 x 4 x 3 x 2 x 1 x 7720 x 75040 waysPlease help me with this
It would be C because that is the one that make the most sense
Help pls i rly need help
Step by step explanation :
[tex] \frac{x}{2} - 1 = \frac{3 - x}{5} [/tex]Taking LCM in Left Hand Side
[tex]⇢ \frac{x - 2}{2} = \frac{3 - x}{5} [/tex]Now, By cross multiplying ,we get. ..
[tex]⇢5(x - 2) = 2(3 - x)[/tex]
[tex]⇢5x - 10 = 6 - 2x[/tex]
[tex]⇢5x + 2x = 6 + 10[/tex]
[tex]⇢7x = 16[/tex]
[tex]⇢ \boxed{ x = \frac{16}{7} }[/tex]
Answer:
x = 16/7
Step-by-step explanation:
Given
x/2 - 1 = 3 - x / 5Solving
#1) Find the LCM.
Product of denominator values2 x 5 = 10#2) Multiply both sides by 10.
10(x/2 - 1) = 10(3 - x / 5)5x - 10 = 2(3 - x)5x - 10 = 6 - 2x#3) Bring x terms to the left and numbers to the right.
5x + 2x = 6 + 107x = 16x = 16/7