The equation of the circle is given by (C) (x-3)² + (y + 4)² = 9
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its center.
The equation of the circle in the general form is given by the
(x-a)²+(y-b)²=r²
Where (a,b) is the co-ordinates of the center of the circle and the radius is r.
Now the center of the circle is given at (3,-4) and the radius is r.
We know that the general equation of a circle is [tex]{\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}[/tex]
Substituting the values in the equation we get:
(x-3)²+(y-(-4))²=(3)²
or, (x-3)²+(y+4)²=9
Hence the equation of the circle is (x-3)² + (y + 4)² = 9.
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HELP PLEASE PLEASE HELP SHOW WORK HELP PLS PLS PLS
Answer:
A = 8x, B = -a^2-2a-2
Step-by-step explanation:
Evaluate [tex]8^{10/}[/tex][tex]8^{2}[/tex] using the quotient of exponents property.
Answer:
16777216
Step-by-step explanation:
1) [tex]\frac{8^{10} }{8^2} = 8^{10-2}[/tex]
2) [tex]8^{10-2} = 8^8[/tex]
3) [tex]8^8[/tex] = 16777216
Let q = a / b and r = c / d be two rational numbers written in lowest terms. Let s = q + r and s = e / f be written in lowest terms. Assume that is not 0. Prove or disprove the following two statements. A.) If b and d are odd, then f is odd. B.) If b and d are even, then f is even.
Both the statements are true.
q = a/b and r = c/d.s = q + rs = a/b + c/ds = (ad + bc)/bde/f = (ad + bc)/bde = ad + bc and f = bda) If b and d are odd, we know that the product of two odd numbers is always odd, so f = b*d is odd.We can prove this because b*d = b*(d-1+1)b*(d-1+1) = b*(d-1) + bSince d is odd, d-1 is even, and therefore b*(d-1) is even. Since b is odd and the sum of an odd number and an even number is always odd, the above product is odd.b) If b and d are even, we know that the product of two even numbers is even, and therefore f = b*d is even.To learn more about numbers, visit :
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A pollster would like to predict the mayoralty winner of a certain town. However, his budget for a quick survey is good only for 30 out of the 110 barangays of that town. Which statistics is more appropriate to use – descriptive or inferential? Justify your answer.
Inferential statistics are a better way to interpret the data.
Inferential statistics are regularly used to evaluate the variations among the remedy corporations. Inferential records use measurements from the pattern of topics within side the test to evaluate the remedy corporations and make generalizations approximately the bigger populace of topics.
There are many sorts of inferential records and every is suitable for a selected studies layout and pattern characteristics. Researchers must seek advice from the numerous texts on experimental layout and records to discover the proper statistical take a look at for his or her test. However, maximum inferential records are primarily based totally at the precept that a take a look at-statistic cost is calculated on the premise of a specific formula. That cost together with the levels of freedom, a degree associated with the pattern size, and the rejection standards are used to decide whether or not variations exist among the remedy corporations. The large the pattern size, the much more likely a statistic is to suggest that variations exist among the remedy corporations.
Therefore, we get that inferential statistics are a better way to interpret the data.
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19/20 divided by 20/30 = 19/20 x ?
A. -30/20
B. 30/20
C. 20/19
D. -20/19
Answer:
19/20*30/20=19/20 x
570/400=19/20 x
57*20=40*19x
1140=760x
x=30/20 or 3/2
A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The
function f(x)-- 5 represents the remaining time in minutes needed to fill the tank. How is the graph of the pare
100
-
X
function f(x)-
-
100
transformed to create the graph of the function f(x)-- X
-5?
The function f(x)-- 5 represents the remaining time in minutes needed to fill the tank in the graph of the pare
Answer:
- Vertically stretching the parent function [tex]f(x) = \frac{1}{x}[/tex] .- A 5 unit right shift of the parent function [tex]f(x) = \frac{100}{x-5}[/tex] .Here are some function transformations:
1. The function is moved up by "k" units if [tex]f(x) + k[/tex].
2. The function is moved down "k" units if [tex]f(x) - k[/tex].
3. The function is moved "k" units to the right if [tex]f(x) - k\\[/tex] .
4. If [tex]f(x) + k[/tex], the function is "k" units to the left.
5. If [tex]bf(x)[/tex] and b>1, the function is b times more vertically stretched.
6. In the event that [tex]bf(x)[/tex] and 0<b<1 the function is vertically compressed by a factor of "b".
The following parent function is provided by the question:
[tex]f(x) = \frac{1}{x}[/tex] .We also know that the transformed function, which denotes the number of minutes still required to fill the tank, is:
[tex]f(x) = \frac{100}{x-5}[/tex] .Therefore, based on the transformations previously described, we can determine that the following produces the graph of the transformed function:
Answer:
- Vertically stretching the parent function [tex]f(x) = \frac{1}{x}[/tex] .- A 5 unit right shift of the parent function [tex]f(x) = \frac{100}{x-5}[/tex] .To learn more about graph please click on the link:
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The complete exercise is: " A 100 gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The function [tex]f(x) = \frac{100}{x-5}[/tex] represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function [tex]f(x) = \frac{1}{x}[/tex] transformed to create the graph of [tex]f(x) = \frac{100}{x-5}[/tex] ?"
what is the ordered pair for -5, 6
The ordered pair for -5, 6 is (-5, 6)
How to determine the ordered pair for -5, 6?The expression is given as:
-5, 6
Ordered pairs are often represented by the parenthesis i.e. ( , )
Where the variables x and y are in the parenthesis
So, the proper representation of an ordered pair is
(x, y)
Substitute -5, 6 for x and y in (x, y)
(-5, 6)
Hence, the ordered pair for -5, 6 is (-5, 6)
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Please answer question 1 in the picture, I will mark brainliest
Answer:
B,
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
12. A summer soccer camp ordered a total of 84 soccer balls and t-shirts for the season. Soccer balls cost $25 each and t-shirts cost $9.50 each. If they payed $1,046 total for the purchase, how many of each item was ordered?
Answer:
16 Soccer balls
68 T-shirts
Step-by-step explanation:
Given information:
Total order = 84 itemsCost of a soccer ball = $25Cost of a t-shirt = $9.50Total bill = $1,046Define the variables:
Let x = the number of soccer balls ordered.Let y = the number of t-shirts ordered.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad x + y = 84[/tex]
[tex]\textsf{Equation 2}: \quad 25x+9.5y=1046[/tex]
Rewrite Equation 1 to make y the subject:
[tex]\implies y=84-x[/tex]
Substitute this into Equation 2 and solve for x:
[tex]\implies 25x+9.5(84-x)=1046[/tex]
[tex]\implies 25x+798-9.5x=1046[/tex]
[tex]\implies 15.5x+798=1046[/tex]
[tex]\implies 15.5x=248[/tex]
[tex]\implies x=16[/tex]
Substitute the found value of x into the rewritten form of Equation 1 and solve for y:
[tex]\implies y=84-16[/tex]
[tex]\implies y=68[/tex]
Solution
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Which is the equation of a hyperbola centered at the origin with focus (-3,0) and vertex (-2,0)
Main answer:[tex]x^{2}[/tex]/4 - [tex]y^{2}[/tex]/5=1
Definition of Hyperbola=a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
Formula=[tex](x-x1)^{2}[/tex]/[tex]a^{2}[/tex] - [tex](y-y1)^{2}[/tex]/[tex]b^{2}[/tex]=1
Given,
origin o(0,0) , focus s(-3,0) , vertex v(-2,0)
and , x1=0, y1=0
then, equation of hyperbola becomes= [tex]x^{2}[/tex]/[tex]a^{2}[/tex]-[tex]y^{2}[/tex]/[tex]b^{2}[/tex]=1
a is the distance between center and the vertex,
distance between o and v = 2
c is the distance between center and the focus,
distance between o and s =3
[tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]
4+[tex]b^{2}[/tex]=9
[tex]b^{2}[/tex]=5
Then the equation of hyperbola becomes=[tex]x^{2}[/tex]/4 -[tex]y{2}[/tex]/5=1
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Sherman has 3 cats and 2 dogs. He wants to buy a toy for eeach of his pets. Sherman has $22 dollars to spend on pet toys. How much can he spend on each pet? Write your answer as a fraction and as amount in dollars and cents.
Answer:
22/5
4 2/5
$4.40
Step-by-step explanation:
Answer:
4 4/10
Step-by-step explanation:
He has 5 pets in all (3 cats, 2 dogs)
Divide 22 with 5
22/5 = 4.4
He can spend $4.40, or in fraction form:
4 4/10 (Mixed fraction)
8. The road transport company of Maldivies keep MVR 950 aside as a wage per day for the hired labourers. The company initially hires 10 laboures. Find out the income of each labourer.
The income of each laborer is MVR 95.
The total amount of money kept aside by the road transport company of Maldives is MVR 950.
Initial hiring of the laborer is 10.
Here we have to have to income of each laborer.
So, Income of each laborer = total income/number of laborer
= 950/ 10
= 95
Therefore the income of each laborer is MVR95.
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If T is the midpoint of SU what are ST, TU, and SU?
Answer:
Step-by-step explanation:
ST=SU
5x=3x+32
5x-3x=32
2x=32
x=32/2=16
ST=5×16=80
TU=80
SU=2×80=160
In a 40 hour work week marcie spends 15 hours answering phones what is the ratio of hours spent answering telephones to hours doing other types of work?
Out of 40 hours that Marcie works, 15 of those hours are spent answering phones. The problem asks that the hours spent answering telephones goes first in the ratio, so that will be the first number.
15 :
The last number is the total number of hours Marcie works.
15 : 40
own to place into her scrapbook. What is the area of each picture?
3 in.
5 in.
3 in.
Answer:
Step-by-step explanation:
3x5=15x3=45
PLEASE HELP!! I NEED THIS ASAP. I WILL GIVE BRAINLY
Answer:On three of the percentage points you improved your average score.
Step-by-step explanation:I hope this helps.
Answer:
75 + 85 + 90 + 90 + 100 + 75 + 80 + 100 + 90 = 785
785/9 = 87.2
85 + 85 + 100 + 90 + 100 + 85 + 80 + 100 + 90 = 815
815/9 = 90.5
90.5 - 87.2 = 3.3
Round 3.3 to the nearest percent = 3%
The difference between two positive numbers is 40 and the ratio of these integers is 1:3.Find the integers.
Answer:
A:B= 1:3
let A=1x,B=3x
A+B = x+3x
x+3x = 40
4x = 40
x=10
A=1(10)=10
B=3(10)=30
Step-by-step explanation:
Dont really know how to explain it well
- 4/7 + 2/7x - 14 + 4/7
Answer: 2x/7 -14
Step-by-step explanation:
- 4/7 + 2/7x - 14 + 4/7=
2/7x - 14 + 4/7 - 4/7=
2/7x - 14 = 2x/7 - 14
Multiply
(2/5)(-5/4)
Enter your answer as a fraction, in simplest form, in the box.
Answer:
-1/2
Step-by-step explanation:
first, we multiply 2 and -5 which is -10, then we multiply 5 and 4 which is 20
so, we get -10/20 then the simplest form is -1/2
MARK ME BRAINLIEST IF IT HELPED :)
Hannah took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.90 plus $3.75 per mile. The total fare was $80.65, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
Answer: y=3.75x+1.9
Step-by-step explanation: the pick up fee would be the y-intercept and the per mile cost would be the slope.
The equation that can be used to determine the number of miles in the taxi ride is 1.90 + 3.75x = 80.65.
The number of miles traveled is 21 miles.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Pick up fee charges = $1.90
Charges per mile = $3.75
Total fare = $80.65
The number of miles traveled = x
We can write an equation as:
1.90 + 3.75x = 80.65
The number of miles traveled:
1.90 + 3.75x = 80.65
Subtract 1.90 on both sides.
1.90 + 3.75x - 1.90 = 80.65 - 1.90
3.75x = 78.75
Divide both sides by 3.75.
x = 21.
Thus,
The equation that can be used to determine the number of miles in the taxi ride is 1.90 + 3.75x = 80.65.
The number of miles traveled is 21 miles.
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does anyone know how to solve this pre cal question Im super confused
Answer:
f(-3) = 3*-3 + 4 = -9 + 4 = -5
f(3) = 2*3 - 2 = 6 - 2 = 4
f(0) = 2*0 - 2 = 0 - 2 = -2
Polygon EFGH is a scaled copy of polygon ABCD.
Select ALL of the true statements.
(Select all that apply.)
The area of EFGH is twice the area of ABCD.
Segment FG is twice as long as segment CD.
Segment EF is twice as long as segment AB.
The scale factor from EFGH to ABCD is 2.
The length of segment AD is 8 units.
The following statements are true and correct:
Segment EF is twice as long as segment AB
The length of segment AD is 8 units
How to interpret dilation transformation?
Since quadrilateral ABCD is scaled to form quadrilateral EFGH, both are similar polygon.
Now, it is known that;
scale factor = ratio of any of their corresponding side
Thus;
Scale factor = GH/CD = 12/6 = 2
This means quadrilateral EFGH is twice the size of quadrilateral ABCD.
The shape of the original polygon remains the same while the size increases.
This implies that, all segments of quadrilateral ABCD increases proportionally times 2 to give us corresponding lengths of the segments of quadrilateral EFGH.
Since shape remains the same, their corresponding angles are congruent and the same in measure.
Therefore, the following statements are true and correct:
Segment EF is twice as long as segment AB; because (EF = AB*scale factor = 3*2 = 6)
The length of segment AD is 8 units because (EH = AD*scale factor = 8*2 = 16)
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A state park has an area of 112 acres. The table shows the estimated park populations for several animals. Find the population density in animals per acre for each animal?
Animal-Population
otter-35
raccoon-186
fox-9
bobcat-3
The population density of otter, raccoon, fox and bobcat is 0.3125, 1.66, 0.0803 and 0.0267 per acre
Total park area of the state park = 112 acres
Number of Otter = 35
Number of Raccoon = 186
Number of Fox = 9
Number of Bobcat = 3
The formula of population density is given by:
Population Density = Number of animals/Area of land
Population density of Otter in the park = 35/112 = 0.3125 Otter per acre
Population density of raccoon in the park = 186/112 = 1.66 Raccoon per acre
Population density of fox in the park = 9/112 = 0.0803 Fox per acre
Population density of bobcat in the park= 3/112 = 0.0267 bobcat per acre
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Norma plans to rent a car for her vacation. The cost to rent the car is $39
plus $0.15 per mile she drives. Write a function rule for the total cost of
the rental.
Answer:
$39 + 0.15x
Step-by-step explanation:
$39 is the flat fee no matter what and x is the number of miles driven times cost per mile.
Find the 8th term of the geometric sequence 6, 18, 54
Answer:
13122
Step-by-step explanation:
Term multiply by 3
First term is 6
Seven terms remain to be defined
then the 8th term is:
6 * 3⁷ = 6*2187
= 13122
Any number besides 0 to the zero power evaluates to 0. True or false?
Answer:
True
Step-by-step explanation:
Because anything multiplied by 0 is equal to 0.
What happens to matter when it is an closed system.
Answer:
In thermodynamics, a closed system can exchange energy (as heat or work) but not matter, with its surroundings. An isolated system cannot exchange any heat, work, or matter with the surroundings, while an open system can exchange energy and matter.
Anyone please solve for me
Answer:
A
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST
Answer:
1302 for the first
-194 for second
Step-by-step explanation:
just do the operation
The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=3.
x=5, y=-4
an equation is y=___
When x=3, y=___
Show work
The equation is y = ₋20/x and when x = 3 then y = ₋ 6.6 .
Given x and y vary inversely.
The relationships between variables that are expressed as y = k/x, where x and y are two variables and k is a constant value, are known as inverse variation. According to this statement, if the value of one item rises, the value of the other quantity falls.
the value of x is = 3, we need to find the value of y.
then when x = 5 and y = ₋4
If y varies inversely as x then:
x × y = k (for some constant c)
If (x,y) = (5,₋4) then:
5 × ₋4 = k
₋20 = k
Therefore, xy = ₋20
then, y = ₋20/x ; is the equation of y.
when x = 3, then:
y = ₋20/3 or y = 6.6
Hence we get the required equation of y and the value of when x = 3 as y=₋20/x and y = ₋20/3 or y = 6.6
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