7 x² + 7 y² - 28 x + 42 y - 35 = 0 /: 7
x² + y² - 4 x + 6 y - 5 = 0
( x² - 4 x + 4 ) + ( y² + 6 y + 9 ) - 4 - 9 - 5 = 0
The equation in the standard form is:
( x - 2 )² + ( y + 3 )² = 18
The center is at the point ( 2, - 3 ).
Its radius is: √18 = 3√2 units.
Answer:
A. (x - 2)^2 + (y + 3)^2 = 18.
B. (2, -3)
C. 3(2^(1/2))
Step-by-step explanation:
The equation of this circle in standard form is (x - 2)^2 + (y + 3)^2 = 18. The center of the circle is at the point (2, -3), and its radius is 3(2^(1/2)) units.
A bicycle has a listed price of $660.95 before tax. If the sales tax rate is 7.25%, find the total cost of the bicycle with sales tax included.
Round your answer to the nearest cent, as necessary
9514 1404 393
Answer:
$708.87
Step-by-step explanation:
The price with tax included is ...
660.95 + 0.0725×660.95 = 660.95(1 +0.0725) = 708.87
The total cost of the bicycle with tax is $708.87.
Answer:
$ 708.87
Step-by-step explanation:
Think that, a bicycle has listed price of $ 100,
Listed price Tax rate Total cost of the bicycle with sales tax
$ 100 7.25 107.25
$ 660.95 x
Let the Total price of the bicycle be x
Now you can create a equation like this,
[tex]\frac{100}{660.95}=\frac{107.25}{x}[/tex]
Use cross multiplication, and find out the total cost of the bicycle with sales tax.
[tex]100x=660.95*107.25[/tex]
[tex]100x=70886.8875[/tex]
[tex]\frac{100x}{100} =\frac{70886.8875}{100} \\[/tex]
[tex]x=708.8688[/tex]
Therefore, the total cost of the bicycle with sales tax is,
≈ $ 708.87
Hope this helps you.
Let me know if you have any other questions :-)
Complete the equivalent fraction.2/1= /18
Use Pythagoras Theorem to determine which of the following shapes are rectangles. please awnser
Answer:
(a) - no, (b) - yesStep-by-step explanation:
Use equation and compare results:
d² = a² + b²(a)
10.15² = 8.1² + 6.3²103.0 ≠ 105.3, no(b)
15.31² = 14.4² + 5.2²234.4 = 234.4, yes#a
[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]
[tex]\\ \sf\longmapsto (10.15)^2=(8.1)^2+(6.3)^2[/tex]
[tex]\\ \sf\longmapsto 103=65.61+39.69[/tex]
[tex]\\ \sf\longmapsto 103\neq 105.3[/tex]
No
#b
[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]
[tex]\\ \sf\longmapsto (15.31)^2=(14.4)^2+(5.2)^2[/tex]
[tex]\\ \sf\longmapsto 234.4=207.3+27.1[/tex]
[tex]\\ \sf\longmapsto 234.4\neq 234.4[/tex]
Yes
Sabrina has eight boxes of crayons, with ten crayons in each box. She uses twelve crayons. How many crayons does she
have left?
Answer:
68
Step-by-step explanation:
8 boxes. 10 per one box. 8×10=80
80-12= 68
should I buy a new gold ring today
Answer: go for it!
Step-by-step explanation:
La probabilidad de que julio salga con carla es 0.75 , y la probabilidad de que salga con marisol es de 0.50. Si la probabilidad de que salga con carla o marisol es 0.85; calcular la probabilidad de que salga con ambas a la vez
La probabilidad de que Julio salga con Marisol y Carla al mismo tiempo es 0.40
What is the addition rule of probability for two events?For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
This can be written symbolically as:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Given that;
The probability that Julio goes out with Carla is 0.75, and
the probability that he goes out with Marisol is 0.50.
The probability that he goes out with Carla or Marisol is 0.85
To find:
The probability that he will date both at the same time.
Let we take:
A = event that Julio goes with Carla
B = event that Julio goes with Marisol, then, the given expression is symbolically represented as:
[tex]P(A) = 0.75\\[/tex][tex]P(B) = 0.50[/tex][tex]P(A \cup B) = 0.85[/tex]To find: [tex]P(A \cap B)\\[/tex]
Using the addition rule, we get:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)\\0.85 = 0.75 + 0.50 - P(A \cap B)\\P(A \cap B) = 1.25 - 0.85 = 0.40[/tex]
Thus, the probability that Julio will date Marisol and Carla at the same time is 0.40
Learn more about probability here:
brainly.com/question/1210781
The probability that Julio will date Marisol and Carla at the same time is 0.40.
Here, we have, For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
This can be written symbolically as:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Given that;
The probability that Julio goes out with Carla is 0.75, and
the probability that he goes out with Marisol is 0.50.
The probability that he goes out with Carla or Marisol is 0.85
To find:
The probability that he will date both at the same time.
Let we take:
A = event that Julio goes with Carla
B = event that Julio goes with Marisol, then, the given expression is symbolically represented as:
P(A) = 0.75
P(B) = 0.50
P(A∪B)= 0.85
To find: P(A ∩ B)
Using the addition rule, we get:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.85 = 0.75 + 0.50 - P(A ∩ B)
P(A ∩ B) = 0.40
Thus, the probability that Julio will date Marisol and Carla at the same time is 0.40.
Learn more about probability here:
brainly.com/question/1210781
#SPJ3
complete question:
The probability that Julio dates Carla is 0.75, and the probability that he dates Marisol is 0.50. If the probability that he goes out with carla or marisol is 0.85; Calculate the probability that he will date both at the same time.
i need help with #5
Answer:
<1 = 50
<2 = 130
Step-by-step explanation:
<1 and 130 are supplementary angles
<1 + 130 = 180
<1 =180-130
<1 = 50
130 and <2 are corresponding angles and corresponding angles are equal when the lines are parallel
<2 = 130
Step-by-step explanation:
Well first we can say measure angle 2 equals 130° because they are S.s.int.ext angles, (same side interior angles and exterior). Or also corresponding
Now with measure angle 1, it is a supplementary angle
Let 1 stand for measure angle 1
[tex]130 + m1 = 180[/tex]
Subtract 130° from both sides
[tex]m1 = 50[/tex]
Have a good day :)!Mrs.Thomas sells online math and reading games. His revenue for each game (in dollars) is modeled by the given equations, where x is the number of days since the games went on sale.
Math Game: M(d)=2x^2+8x+2
Reading Game: R(d)=3x+5
Solve the system algebraically. After how many days is the revenue for each game the same? Show your work and explain your answer.
Graph this system to show the solutions. Label each axis appropriately.
Mr. Thomas would take 0.5 (half) day for the revenue for each game to be the same.
Revenue is the total amount of money made from selling a particular number of items.
The revenue for math game is:
M(d)=2x² + 8x + 2
While the revenue for Reading Game is:
R(d)=3x+5
For the revenue of each game to be the same, hence:
M(d) = R(d)
2x² + 8x + 2 = 3x + 5
2x² + 5x - 3 = 0
x = -3 or x = 0.5
Since the number of days cannot be negative, hence it would take 0.5 (half) day for the revenue for each game to be the same.
Find out more at: https://brainly.com/question/8645356
Need help from mathematics only ?
9514 1404 393
Answer:
8. 50 yards
9. 9%
Step-by-step explanation:
In each case, we fill in the given values in the formula, then divide both sides of the equation by the coefficient of the variable.
8)The missing formula is ...
A = LW . . . . where A is area, L is length, W is width
6000 yd² = (120 yd)W
W = (6000 yd²)/(120 yd) = 50 yd . . . the width of the field
__
9)The missing formula is ...
I = Prt . . . . where I is the interest on principal P at rate r for t years
1800 = 5000(r)(4)
r = 1800/20000 = 0.09 = 9% . . . interest rate on the investment
Theresa ran 7.56 miles this week. Write her distance as a mixed number and as an improper fraction.
Answer:
Mixed=7 14/25 improper=189/25
Step-by-step explanation:
)Of the people in the theater, 5% have seen the movie before. If there are 8 people who have seen the movie before, how many people are in the theater?
Answer: 160
Step-by-step explanation: 5% of x = 8
In other words, x * 0.05 = 8. To find what x is, we need to work backwards.
x * 0.05 = 8
x = 8/0.05
x = 160
Would appreciate a brainly <3
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.07 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Answer:
93.684
Step-by-step explanation:
They just give a 5% bonus to the price of the lunch
geomtry plzzzzz help. me
Answer:
N=3.5
Step-by-step explanation:
it is 3.5 because it said line p is the perendicular bisector so the triangle has to be equal. so the line ZY=XY
14/4=3.5
Juwan went on a bike ride of 36 miles. He realized that if he had gone 15 mph faster, he would have arrived
10 hours sooner. How fast did he actually ride?
Step-by-step explanation:
Distance = (Rate)(Time) So, Time = (Distance)/(Rate)
Time at slower speed = Time at faster speed + 3
36/x = 36/(x+6) + 3
Multiply the equation by the LCD, x(x+6) to obtain:
36(x+6) = 36x + 3x(x+6)
36x + 216 = 36x + 3x2 + 18x
3x2 + 18x - 216 = 0
x2 + 6x - 72 = 0
(x + 12)(x - 6) = 0
x = -12 or x = 6
Since x can't be negative, x = 6 mph
How to solve this question? Adding algebraic fractions
Answer:
it should be 2/12 and 9/11
Step-by-step explanation:
A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches. What is the scale of inches in the drawing to inches in the actual room?
Enter the correct answer in the box.
Answer:
The scale is 1:18 for the entire room, 1 inch in the diagram for 18 inches IRL
Step-by-step explanation:
12 inches = 1 foot
Convert the feet to inches, then divide both sides of the ratio by the # of inches in the diagram
So for length:
10:(15*12)
10:180
1:18
And for width:
8:12(12)
8:144
1:18
Answer:
18 inches
Step-by-step explanation:
The question asks for scale of inches in the drawing and the actual room, so first convert 15 ft and 12 ft into inches.
1 foot= 12in x 1ft= 12 inches
15 feet= 12in x 15ft = 180 inches
12 feet= 12in x 12ft = 144 inches
The room is 180 inches long and 144 inches wide.
To find the scale, set up a proportion to the drawing to the room.
[tex]\frac{10}{8} =\frac{180}{144}[/tex]
You can see that the scale is 18 inches because to get from 180 to 10, you multiply by 18, and the same thing as 8, you would multiply 8 by 18 to get to 144.
the odds against your bet are to 3. if you bet $27 and win. how much you win
what is the slope intercept form of 12x+4y=-12
Answer:
y=-3-3x
Step-by-step explanation:
Transpose the equation for y
y=-12/4-12x/4
y=-3-3x
9.
Use vertex form to write the equation of the parabola.
A. y = (x + 3)^2 - 3
B. y = 2(x - 3)^2 - 3
C. y = 2(x - 3)^2 + 3
D. y = 2(x + 3)^2 - 3
Answer:
Step-by-step explanation:
hmm
Which linear equation would produce a y-intercept of (0,-7) and a slope of 5?
how to find the circumference with a diameter?
Answer:
Multiply the diameter by pie which 3.14
Step-by-step explanation:
Pls help I will mark brainless
Answer:the answer is 1/5
Step-by-step explanation:
pls say the answer to me
Answer:
Sohan has read more pages and Sonali was more faster
)) Fill in the missing number.
()) 70% of
=
56
Answer: x=80
Step-by-step explanation: multiplying both sides by 100 and dividing both sides by 70 then we have x=56 x 100/70 then your answer is x=80. If you're using a calculator, simply enter 56x100 divided by 70 which will give you the answerLet that be x
70% of x=567/10 × x=56x=56×10/7x=8(10)x=80WILL MARK BRAINLIEST AND GIVE 75 POINTS!!!
Summer is thinking about buying a car for $45,000. The table below shows the projected value of two different cars for three years.
Number of years 1 2 3
Car 1 (value in dollars) 40,500 36,450 32,805
Car 2 (value in dollars) 42,000 39,000 36,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)
Part C: Summer wants to purchase a car that would have the greatest value in 13 years. Will there be any significant difference in the value of either car after 13 years? Explain your answer, and show the value of each car after 13 years. (4 points)
Answer:
A) 1: exponential; 2: linear
B) 1: f(x) = 45000·0.9^x; 2: f(x) = -3000x+45000
C) The difference is significant. 1: $11,348; 2: $6,000
Step-by-step explanation:
Part AThe values for Car 1 have a common ratio of 40500/45000 = 0.9. An exponential function is used to describe a sequence where the terms have a common ratio.
The values for Car 2 have a common difference of 42000-45000 = -3000. A linear function is used to describe a sequence where the terms have a common difference.
__
Part BAn exponential function can be written as ...
f(x) = (initial value)·(common ratio)^x
A linear function can be written as ...
f(x) = (common difference)x + (initial value)
The functions are ...
Car 1: f(x) = 45000·0.9^x
Car 2: f(x) = -3000x +45000
___
Part CThe formulas for the different car values after 13 years give ...
Car 1: f(13) = 45000·0.9^13 ≈ 11,348
Car 2: f(13) = -3000(13) +45000 = 6,000
The value of Car 1 will be almost double the value of Car 2 after 13 years. Yes the difference in value is significant.
A water bottling facility has a mean bottling rate of 33.5 thousand bottles per hour with a standard deviation of 1.92 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 26.2 thousand bottles per hour with a standard deviation of 1.42 thousand bottles. One Wednesday from noon to 1:00 p.m., the water bottling facility bottled 34.9 thousand bottles of water, and the cola bottling facility bottled 26.8 thousand bottles of cola. Which facility increased their efficiency more during that hour
Using z-scores, we have that due to the higher z-score, the water bottling facility increased their efficiency more during that hour.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean.In this problem, the facility with the higher z-score increased their efficiency more during that hour.
For the water bottling facility, we have that [tex]\mu = 33.5, \sigma = 1.92, X = 34.9[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{34.9 - 33.5}{1.92}[/tex]
[tex]Z = 0.73[/tex]
For the cola bottling facility, we have that [tex]\mu = 26.2, \sigma = 1.42, X = 26.8[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{26.8 - 26.2}{1.42}[/tex]
[tex]Z = 0.42[/tex]
Due to the higher z-score, the water bottling facility increased their efficiency more during that hour.
A similar problem is given at https://brainly.com/question/24663213
Can someone please help me with #14 and #15?
14.Given y=2(x - 10)+3, write an equation in point slope and slope intercept form that is:
a) Parallel and goes through (-4,1).
b) Perpendicular and goes through (-4,1).
15.Given 5x+2y=7
a.Find an equation parallel to the equation and through (0,10).
b.Find an equation perpendicular to the equation and through (0,10).
This picture is an example of what the answers should look like.
Problem 14, Part (a)
The given equation y = 2(x-10)+3 has a slope of m = 2. Anything parallel to this will also have the same slope, but a different y intercept.
Let's find the point slope form of the parallel line through (-4,1)
[tex]y-y_1 = m(x - x_1)\\\\y-1 = 2(x - (-4))\\\\y-1 = 2(x + 4)\\\\[/tex]
The point slope form is: y-1 = 2(x+4)Now solve for y to get the slope intercept form.
[tex]y-1 = 2(x + 4)\\\\y = 2(x + 4)+1\\\\y = 2x + 8+1\\\\y = 2x + 9\\\\[/tex]
The slope intercept form is: y = 2x+9============================================================
Problem 14, Part (b)
The original slope is m = 2. Apply the negative reciprocal to go from 2/1 to -1/2. The perpendicular slope is -1/2.
Using the same point (-4,1), we find that the point slope form is...
[tex]y-y_1 = m(x - x_1)\\\\y-1 = -\frac{1}{2}(x - (-4))\\\\y-1 = -\frac{1}{2}(x+4)\\\\[/tex]
The point slope form is: y-1 = (-1/2)*(x+4)Now solve for y
[tex]y-1 = -\frac{1}{2}(x+4)\\\\y = -\frac{1}{2}(x+4)+1\\\\y = -\frac{1}{2}x-2+1\\\\y = -\frac{1}{2}x-1\\\\[/tex]
The slope intercept form is: y = (-1/2)x - 1============================================================
Problem 15, Part (a)
Anything parallel to Ax+By = C will be in the form Ax+By = D. The only thing changes is the C becomes D, where [tex]C \ne D[/tex]. If C = D, then we'd be talking about the exact same line rather than two parallel lines.
We're given 5x+2y = 7. The answer is in the form 5x+2y = D. Plug in (x,y) = (0,10) to find the value of D
5x+2y = D
D = 5x+2y
D = 5(0)+2(10)
D = 20
The equation 5x+2y = D updates to 5x+2y = 20
Answer: 5x+2y = 20============================================================
Problem 15, Part (b)
If you are given Ax+By = C, then anything perpendicular to this is Bx-Ay = D. Here it's possible that C = D; however, it's likely that they'll be different.
The given equation 5x+2y = 7 is perpendicular to anything of the form 2x-5y = D. We'll plug in the given point to find D.
2x-5y = D
D = 2x-5y
D = 2(0)-5(10)
D = -50
Answer: 2x-5y = -50A Gardner has 1 1/4 cubic feet of soil available for filling pots. Each pot will need 2/5 cubic foot to be filled. What is the greatest number of pots that the gardener fill
The greatest number of pots that can be filled is 3.
In order to determine the greatest number of pots that can be filled, the quantity of soil available would be divided by the capacity of each pot.
Number of pots that can be filled = 1 1/4 ÷ 2/5
= 5/4 ÷ 2/5
= 5/4 x 5/2 = 25/8 = 3 1/8
Thus, the greatest number of pots that can be filled is 3.
To learn more, please check: https://brainly.com/question/194007
Help help help math help please
Answer:
x + 15
Step-by-step explanation:
9x + 25 + x + 5 = 180
9x + x + 25 + 5 = 180
10x + 30 = 180
10x = 180 - 30
10x = 150
x = 150÷10
x = 15.
Rodolfo has 15 toys in a toy box, and he adds 2 new toys every month. Based on this information , which representation best shows this relationship between the number of toys Rodolfo has in his toy box, y, and the number of months that have passed, x?
Answer: The image listed below. It's the only valid answer that best shows the numbers of toys Roldlfo has in his toy box, y, and the number of months that have passed, x.