This is a practice assessment that will not be graded! Just need help finding this answer to understand it overall
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The general structure of the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
h is the x-coordinate of the center of the circle
k is the y-coordinate of the center of the circle
r is the radius of the circle.
Note that the equation has minus signs inside the parentheses, this means that the sign of the coordinates is the opposite as the one shows on the equation.
The first step is to identify the coordinates of the center of the circle in each equation as well as the radius:
Equation 1:
[tex](x-3)^2+(y+2)^2=9[/tex]The x-coordinate of the center is the value inside the first parentheses: h= 3
The y-coordinate of the center is the value inside the second parentheses: k= -2
[tex]center\colon(3,-2)[/tex]To determine the radius you have to calculate the square root of the last number of the equation:
[tex]\begin{gathered} r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Use the same logic for the other three equations:
Equation 2:
[tex](x-3)^2+(y-2)^2=16[/tex]h=3
k=2
[tex]\text{center:(3,2)}[/tex]Radius:
[tex]\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}[/tex]Equation 3
[tex](x+3)^2+(y+2)^2=16[/tex]h=-3
k=-2
[tex]\text{center:(-3,-2)}[/tex]Radius:
[tex]\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}[/tex]Equation 4
[tex](x-3)^2+(y-2)^2=9[/tex]h=3
k=2
[tex]\text{center:(3,2)}[/tex]Radius:
[tex]\begin{gathered} r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Next, you have to determine the center and the radius of each graph:
Circle 1:
Has a radius with a length of 4 units and center (3,2), the equation that corresponds to this circle is the second equation.
Circle 2:
Has a radius with a length of 4 units and the center at (-3,-2), the equation that corresponds to this circle is the third equation.
Circle 3:
Has a radius with a length of 3 units and a center at (3,2), the equation that corresponds to this circle is the fourth equation.
Circle 4:
Has a radius with a length of 3 units and center at (3,-2), the equation that corresponds to this graph is the first equation.
Related Questions
I am thinking of a number. It has two digits. When I reverse the digits and then add the new number to the original number I get 33. What is my number?
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I am thinking of a number. It has two digits. When I reverse the digits and then add the new number to the original number I get 33. What is my number?
Let
the number xy
so
Reverse the digits yx
xy+yx=33
10x+10y=30 ------> equation 1
y+x=3 ----> equation 2
solve the system by graphing
the syste
I'm not entirely sure what I'm supposed to be doing
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The intercept between both lines, represents the solution to the system compounded by the equations for both lines. It means (3,4) is the solution to both lines A and B.
Find quotient of 5,433 % 8
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Find the quotient of 5,433 by 8.
8 | 5,433
Divide 54 by 8. The quotient is 6. 6x8 = 48. 54 - 48 = 6.
6
8 | 5433
-48
-------
63
63 by 8 is 7. 7x8 = 56. 63 - 56 = 7.
67
8 | 5433
-48
-------
63
-56
--------
73
73 by 8 is 9. 9x8 = 72. 73 - 72 = 1. The final step is:
679 <== Quotiet
8 | 5433
-48
-------
63
-56
--------
73
-72
-------------
1 <== Remainder
In a study of 200 students under 25 years old one-fifth have not yet learned to drive. What percentage can drive?
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find the equation of line with points (3, 3) that passes through a slope of 2/3
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hello
the standard equation of a straight line is given as y = mx + b
y = y-coordinate
x = x-coordinate
m = slope
b = intercept
the points given are (3, 3) and the slope = 2 / 3
y = mx + b
y = 3
x = 3
let's substitute in our values and solve for b
[tex]\begin{gathered} y=mx+b \\ 3=\frac{2}{3}(3)+b \\ 3=2+b \\ b=3-2 \\ b=1 \end{gathered}[/tex]since we have the value of the slope, we can simply write the equation from y = mx + b to y = 2/3x + 1
[tex]y=\frac{2}{3}x+1[/tex]this is the equation of the line.
but we can further simplify this by looking for the LCM of the denominators of the independent variables
[tex]\begin{gathered} y=\frac{2}{3}x+1 \\ y=\frac{2x+3}{3} \\ \text{cross multiply both sides} \\ 3y=2x+3 \end{gathered}[/tex]the equation can be rewritten as 3y = 2x + 3
Art wants to calculate the diagonal distance across opposite corners of a rectangular parcel. The parcel is 161’ by 326’ . How long is the diagonal measurement?
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Recall that the formula for the length of the diagonal of a rectangle is:
[tex]l=\sqrt[]{a^2+b^2}.[/tex]Where a, and b are the lengths of the sides of the rectangle.
Substituting a=161´, b=326´ in the above formula we get:
[tex]\begin{gathered} l=\sqrt[]{(161^{\prime})^2+(326^{\prime})^2}, \\ l=363.5890537^{\prime}\text{.} \end{gathered}[/tex]Answer: 363.5890537 ´.
Recommendations Skill plans Math Common Core Fifth grade > * P.7 Guess-and-check problems DAJ Kurt bought 28 stamps at the post office. The number of stamps in each book was 7 times as large as the number of books. How many stamps were in each book? stamps Submit
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28/7 = 4
There were 7 stamps in each book
Please helpWrite 78 percent as fraction In simplest form
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Step 1:
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Step 2:
[tex]\begin{gathered} 78\text{ percent = }\frac{78}{100} \\ To\text{ write to the simplest fraction} \\ \text{Divide both the numerator and the denominator by 2} \\ \frac{78}{100}\text{ = }\frac{39}{50} \end{gathered}[/tex]Final answer
[tex]\frac{39}{50}[/tex]how many people are :9 or younger ?At most 60 years old ?40 to 59 ?
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Given the table represents the ages of people :
We need to find the following:
1. how many people are : 9 or younger ?
As shown in the table : the ages 0 - 9 has a frequency of 8
So, the answer is : 8 people
2. How many people at most 60 years old ?
From the table : the age 60 - 69 the frequency is 10
But there is no information to specify the age 60
The answer is : NEI
3. How many people are : 40 to 59 ?
From the table :
the age 40-49 has a frequency = 9
the age 50-59 has a frequency = 6
So, the answer is 9 + 6 = 15 people
write a ratio that is equivalent to the ratio: 9/12
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the given ratio is
9/12
divide numerator and denominator by 3
[tex]\frac{\frac{9}{3}}{\frac{12}{3}}=\frac{3}{4}[/tex]so the equivalent ratio is 3/4
I have no clue how to graph inequalities and find the solution
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In the graph we can see two line y=2 and y=x.
Also, we know that there is a system of inequalities and the blue area in the graph represent the solutions for the system.
We can see that the blue area is above the line y=2, thats mean one inequality is:
[tex]y\ge2[/tex]So, any points that y-coordinate is greater than or equal than 2 satisfy the inequality.
Also we can see that the blue area is bellow the line y=x and the line is a dotted line, this last means the inequality do not take take value in the line. So, the second inequation is:
[tex]ySo, the points that satisfy the system of inequalities are above the line y=2 and bellow the line y=x and not touch the line y=x.please help me solve this step by step with wrriten explanation. context and words help me
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Find the volume of the rectangular prism O 8 cubic units O 4 cubic units 6 cubic units O 3 cubic units
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Given data:
The given rectangular prism.
The volume of the given prism is,
[tex]\begin{gathered} V=6(\text{volume of a cube)} \\ =\text{ 6(1 cubic-units)} \\ =\text{ 6 cubic-unis} \end{gathered}[/tex]I need help question
Answers
[tex]f(x)=x^2-4x-94[/tex]
The diffrentiated function will be
[tex]2x-4[/tex]RULES FOR DIFFERENTIATION
[tex]\begin{gathered} y=x^n \\ \frac{dy}{dx}=nx^{n-1} \end{gathered}[/tex]Also
[tex]\begin{gathered} y=kx \\ \frac{dy}{dx}=k \end{gathered}[/tex]Also
[tex]\begin{gathered} y=k \\ \frac{dy}{dx}=0 \end{gathered}[/tex]evaluate the following expression 2 * 1 + 2 * 24/4
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using PEDMAS/ BODMAS
division is executed first followed by multiplication then addition
Which choice is equivalent to the quotient shown here when x > 0?A.2xB.2x2C.D.
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Given
[tex]\sqrt{22x^6}\div \sqrt{11x^4}[/tex]Solution
[tex]\begin{gathered} \frac{\sqrt{22x^6}}{\sqrt{11x^4}}=\sqrt{\frac{22x^6}{11x^4}} \\ \\ =\sqrt{\frac{22x^6}{11x^4}} \\ \\ =\sqrt{2x^2} \\ \\ =x\sqrt{2} \end{gathered}[/tex]The final answerOption C[tex]x\sqrt{2}[/tex]You'll have to make a series of transformations to make this parabola fit the bridge. Describethem
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The transformations are as follows:
- There is firstly a vertical reflection
- There is a vertex shift from (0,0) to the (-2, 3) position (approximate)
- There is also a horizontal compression of the parabola.
BD is the perpendicular bisector of ac,ac=10and bc=7 find the length of ad and ab
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Since, BD is the perpendicular bisector of AC. So, AD = 1/2(AC) = 5.
Since, BD is the perpendicular bisector of AC and BC is not equal to AC. So, triangle ABC is an isosceles triangle. Therefore, AB = BC = 7.
Frank's rectangular box of toys has a perimeter of 30 inches. The length is twice as long as the width. Which of the following expressions could be a major step in finding the length? A. Length times Width equals AreaB. 2 times Width plus 2 times Width plus Width plus Width equals 30C. Perimeter equals Width plus Width plus Width plus WidthD. 2 times Length equals Width
Answers
From the given problem,
length is twice as long as the width
length = 2 x width
Note that the perimeter is :
[tex]P=2W+2L[/tex]where W and L are the width and length respectively.
Since L = 2W
Perimeter will be :
[tex]\begin{gathered} P=2W+2(2W) \\ P=2W+4W \\ P=6W \end{gathered}[/tex]Perimeter is equal to 30 inches :
[tex]6W=30in[/tex]From the given choices, only B satisfies this condition.
2W + 2W + W + W = 30
6W = 30
Therefore, the answer is B.
use only commutative property of addition to rewrite the expression 619+59
Answers
Given:
Given the sum 619+59
Required: Another expression using commutative property and the simplified expression
Explanation:
The commutative property says that for any two real numbers,
[tex]a+b=b+a[/tex]So, the expression 619+59 can also be written as 59+619, using commutative property.
Now, find the sum.
So, the sum is 678.
Final Answer: Another expression of 619+59 is 59+619 and its sum is 678.
ring×heart=hathat×2=heartheart-ring=1/4
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Let's begin by identifying key information given to us:
[tex]undefined[/tex]For the following exercises, determine the least possible degree of the polynomial function shown.
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Solution
To determine the least possible degree of the polynomial function
The function has atmost n - intercepts in the horizontal
The graph turns 4 times in the above curve, hence n = 4
[tex]\begin{gathered} n+1 \\ n=\text{ number of turns} \\ 4+1=5 \end{gathered}[/tex]Therefore the least possible degree of the polynomial = 5
Hence it is a 5 possible polynomial function
A cylinder has a height of 44.5 inches and a radius of 22.8 inches. Which of the following measurements is closest to the lateral surface area of the cylinder in square inches? F 6,374.9 in.2 G 145,274.5 in.? H 3,185.8 in. ? J 2,029.2 in.2 2.
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We have the following:
The formula for the lateral surface area of a cylinder is as follows
[tex]LSA=2\cdot\pi\cdot r\cdot h[/tex]replacing:
[tex]\begin{gathered} LSA=2\cdot3.14\cdot22.8\cdot44.5 \\ LSA=6371.7 \end{gathered}[/tex]Therefore the answer is F 6374.9 in ^ 2
Select all the statements below that are true for the following graph
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From the graph given,
It is an absolute function
The following statements are true about the graph
i) The vertex is located at (2, -2)
ii) The graph has two zeros
ii) The range is [-2, ∞)
Please help me with these 2 questions they are both solved problems that go together with one huge problem so please answer both thank you
Answers
1).
r = 11 in
The diameter is twice the radius, so:
d = 2*11 = 22 inches
2).
d = 18 inches
The radius is half the diameter, so:
r = 18/2 = 9 inches
If a car travels at a speed of 45 mi/h fort hours, then travels 65 mi/h for m hours, what does theexpression 45t +65m represent?The expression represents the (select)
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total distance travelled by the car (option D)
Explanation:
When speed = 45mi/h
time = t hours
when speed = 65mi/h
time = m hours
45t +65m means 45mi/h × t + 65mi/h × m
The formula that relates the speed and the time is distance:
speed = distance/time
distance = speed × time
The distance for the first speed and time = 45mi/h × t hours = 45t
The distance for the second speed and time = 65mi/h × m hours = 65m
The sum of the two distance = distance covered by the car = 45t + 65m
Hence, we can say the expression 45t +65m represents the total distance travelled by the car (option D)
The amount of garbage, G produced by a city with population p is given by G = f ( p ) . G is measured in tons per week, and p is measured in thousands of people. The town of Tola has a population of 45,000 and produces 6 tons of garbage each week. Express this information in terms of the function f. f = 6 / 45 f ( 45 ) = 6 f ( 6 ) = 45
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Solution:
Given that the amount of garbage G produced by a city with population p is expressed as
[tex]\begin{gathered} G=f(p) \\ where \\ G\text{ is measured in tons per week} \\ p\text{ is measured in thousands of people} \end{gathered}[/tex]If a town Tola has a population of 45,000 and produces 6 tons of garbage per week, this implies that we substitute these parameters into the above equation.
This gives
[tex]6=f(45)[/tex]Hence, in terms of function f, the information is expressed as
[tex]f(45)=6[/tex]The second option is the correct answer.
please help me 60 points please show all work this is due in 15 minutes5x-(3x-6)=182(3x-4)=102x+7=5x+16x/3-8=-23x – 6 = -12x/-3=8
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a. 20% of 60 is ____ d. 50% of 90 is b. 25% of _____ Is 6 e. 10% of _ is 7c. _____% of 100 is 14 f. 30% of 70 is _
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20% of 60 is 12
25% of 24 is 6
14% of 100 is 14
50% of 90 is 45
10% of 70 is 7
30% of 70 is 21
a. 20% of 60 is 12 because 60x20/100 = 60x0.2 = 12
b. 25% of 24 is 6 because 6x100/25 = 24
c. 14% of 100 is 14 because 100x(14/100) = 14
d. 50% of 90 is 45 is 14 because 90x50/100 = 45
e. 10% of 70 is 7 because 7x100/10 = 70
f. 30% of 70 is 21 because 70x30/100 = 21
n% of m is (n x m)/100
For example: 20% of 60 is (20 x 60)/100 = 1200/100 = 12
grandma has $250000 to invest. she divides her money into two accounts. one account is in ultra-safe treasury bills paying 4% interest, and the other is in riskier corporate bonds paying 6%. if she needs $12,000 per year in income from her investments, how much should she invest in each account
Answers
for the ultra-safe treasury bills:
[tex]\begin{gathered} I_1=PV\cdot r\cdot t \\ I_1=x\cdot0.04\cdot1 \\ I_1=0.04x \\ \text{where:} \\ x=\text{amount 1} \end{gathered}[/tex]For riskier corporate bonds:
[tex]\begin{gathered} I_2=PV\cdot r\cdot t \\ I_2=y\cdot0.06\cdot1 \\ I_2=0.06y \\ \text{Where:} \\ y=\text{amount 2} \end{gathered}[/tex]she needs $12,000 per year, so:
[tex]\begin{gathered} I_1+I_2=12000 \\ 0.04x+0.06y=12000 \end{gathered}[/tex]grandma has $250000 to invest, therefore:
[tex]x+y=250000[/tex]Let:
[tex]\begin{gathered} x+y=250000\text{ (1)} \\ 0.04x+0.06y=12000\text{ (2)} \\ \text{From (1) solve for x:} \\ x=250000-y\text{ (3)} \\ \text{ Replace (3) into (2)} \\ 0.04(250000-y)+0.06y=12000 \\ 10000-0.04y+0.06y=12000 \\ 0.02y=12000-10000 \\ 0.02y=2000 \\ y=\frac{2000}{0.02} \\ y=100000 \end{gathered}[/tex]Replace y into (3):
[tex]\begin{gathered} x=250000-100000 \\ x=150000 \end{gathered}[/tex]Therefore, grandma needs to invest $150000 in ultra-safe treasury bills, and