Writing the equation of a circle centered at the origin given it’s radius or appoint on the circle
Answers
The equation of the circle has the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
(h,k) are the coordinates of the center of the circle
r is the radius of the circle
If the center of the circle is at the origin, (0,0) and it passes through the point (0,-9), since both x-coordinates are equal, the length of the radius is equal to the difference between the y-coordinates of the center and the given point:
[tex]r=y_{\text{center}}-y_{point=}0-(-9)=0+9=9[/tex]The radius is 9 units long.
Replace the coordinates of the center and the length of the radius in the formula:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=9^2 \\ x^2+y^2=81 \end{gathered}[/tex]So, the equation of the circle that has a center in the origin and passes through the point (0.-9) is:
[tex]x^2+y^2=81[/tex]Related Questions
the price of a lounge chair is $140 plus 7.5% sales tax.what is the sales tax on the lunge chair in dollors and cents
Answers
Given that the price is $140 , and the tax rate is 7.5% (0.075 in decimal form)
we can find the amount in taxes by the product :
0.075 times 140
0.075 * 140 = 10.5
so $10.5 is the amount to be paid in taxes
[tex]undefined[/tex]How much will the account be worth in 46 months?
Answers
In the question we are given the following parameters
Principal = $5100
Rate = 16.87% compounded semi-annually
Time = 46 months = 3yrs 10 months = 3 5/6 years
Explanation
We can solve the question using the formula below
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]"nt" is the number of months the principal accrues interest twice a year.
Therefore we have;
[tex]\begin{gathered} A=5100(1+\frac{16.87\div100}{2})^{\frac{23}{6}\times2} \\ A=5100(1+0.08435)^{\frac{23}{3}} \\ A=5100(1.08435)^{\frac{23}{3}} \\ A=9488.62 \end{gathered}[/tex]Answer:$9488.62
1. The sliders for y = ax + b have been set to create the following graph. What are possible values for a and b?
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The slope of the line is m = 2 and the y-intercept b = 2
Therefore, the equation for the graph is
[tex]y=-2|x|+2[/tex]meaning a = -2 and b = 2.
(The negative sign in front of the absolute value drags the graph below the y = 0 )
Hello! I think I'm overthinking this. Could you please help me decipher?
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A scatter plot uses dots to represent values for two different values
(16,15)
(20,12)
(14,20)
(15,18)
(19,14)
(18,21)
Where the x value is boys and the y value is girls
3 ftFind the outer perimeter ofthis figure. Round youranswer to the nearesthundredth. Use 3.14 toapproximate .4 ft5 ft5 ftP = [ ? ] ftNotice that only half of the circle is included in the figure!Enter
Answers
Perimeter = sum of outer lengths
Lenght of the triangle sides = 5ft
perimeter of a semicircle = π d; half = π d / 2
5 ft + 5ft + π r
5 + 5 + (3.14*3) = 19.42 ft
A squirrel is perched in a tree 50 feet above sea level. Directly below the squirrel, a bird is flying 17 feet above sea level. Directly below the bird is a trout, swimming 23 feet below seal level.how far apart are the squirrel and bird?
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Solution
We can do the following operation_
17-50 = -33 ft
And that represent the distance between te heron and the squirrel
And since the actual height is -23 ft
Then the answer would be given by:
17 -(-23) = 40 ft
The distance from the squirrel and the bird is 40 ft
a museum wants to use equal rows to arrange the African baskets. which list shows all the different possible arrangements so that all the rows have the same number. Assume that an arrangement such as 4 x 20 is the same as 20 x 4.
Answers
Answer:
(B)1 x 80,2x 40,4 x 20,5 x 16,8 x 10
Explanation:
The number of African Baskets = 80
The list of all possible arrangements so that all the rows have the same number will be a list that contains all the positive product of factors of 80.
Factors of 80 are: 1,2,4,5,8, 10, 16,20,40,80
The list is, therefore:
[tex]1\times80,2\times40,4\times20,5\times16,8\times10[/tex]The correct choice is B.
The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m^s. Find the dimensions.
Answers
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the formula for total surface area of cuboid
[tex]\begin{gathered} 2(lb+bh+lh) \\ \text{where l is the length} \\ b\text{ is the breadth} \\ \text{h is the height} \end{gathered}[/tex]STEP 2: Get the dimension of the sides
[tex]\begin{gathered} \text{ Since the dimensions of the cuboid are in the ratio 1:2:3} \\ the\text{ dimensions are given as:} \\ x,2x\text{ and }3x \\ \text{lenght}=x \\ \text{breadth}=2x \\ \text{height}=3x \end{gathered}[/tex]STEP 3: Substitute the dimensions into the formula to get the value of x
[tex]\begin{gathered} 2(lb+bh+lh)=88 \\ By\text{ substitution,} \\ 2((x\cdot2x)+(2x\cdot3x)+(x\cdot3x))=88 \\ \Rightarrow2(2x^2+6x^2+3x^2)=88 \\ \text{Divide both sides by 2} \\ \Rightarrow\frac{2(2x^2+6x^2+3x^2)}{2}=\frac{88}{2} \\ \Rightarrow2x^2+6x^2+3x^2=44 \\ 11x^2=44 \\ \text{Divide both sides by 11} \\ \frac{11x^2}{11}=\frac{44}{11} \\ x^2=4 \\ x=\sqrt[]{4}=2 \\ x=2m \end{gathered}[/tex]STEP 4: Get the other dimensions
[tex]\begin{gathered} \text{breadth}=2x \\ \text{substitute 2 for x} \\ \text{breadth}=2(2)m=4m \\ \\ To\text{ get height} \\ \text{height}=3x \\ \text{substitute 2 for x} \\ \text{height}=3(2)m=6m \end{gathered}[/tex]Hence, the dimensions are:
[tex]2m,4m,6m[/tex]what should be done to solve the following e q u a t i o n x + 8 equals 4
Answers
we have the equation
x+8=14
step 1
subtract 8 both sides
x+8-8=14-8
x=6
therefore the answer is the last option
1.) You are buying flower bundles and have
$24 to spend. Rose bundles cost $4. Tulip bundles
cost $6. Write an equation to describe how many
types of each kind of bundle you can buy.
Answers
Answer:
[tex]4r+6t \leq 24[/tex]
Step-by-step explanation:
The cost of money spent on a rose bundle can be represented by 4r, where 4 is the cost of one rose bundle and r is the number of rose bundles purchased.
The cost of money spent on a tulip bundle can be represented by 6t, where 6 is the cost of one tulip bundle and t is the number of rose bundles purchased.
The amount spent on rose bundles added to the amount spent on tulip bundles must be equal to or less than $24, since that's all you have to spend. This can be represented using this equation:
[tex]4r + 6t \leq 24[/tex]
:)
I need help with this practice problem solving It asks to divide
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ANSWER
[tex]-\frac{5}{13}-\frac{14i}{13}[/tex]EXPLANATION
We want to divide the given complex fraction:
[tex]\frac{4+i}{-2+3i}[/tex]To do this, we have to rationalize the denominator of the fraction by multiplying the given fraction by another fraction made up of the conjugate of the denominator of the given fraction:
[tex]\frac{4+i}{-2+3i}\cdot\frac{-2-3i}{-2-3i}[/tex]Simplifying this, we have:
[tex]\begin{gathered} \frac{(4+i)(-2-3i)}{(-2+3i)(-2-3i)} \\ \Rightarrow\frac{-8-12i-2i+3}{4+6i-6i+9} \\ \frac{-8+3-12i-2i}{13}=\frac{-5-14i}{13} \\ \Rightarrow-\frac{5}{13}-\frac{14i}{13} \end{gathered}[/tex]That is the solution of the division.
the difference between the number c and the quotient of a and b in a mathematical expression.
Answers
Answer:
no difference
step by step explanations
because a/b=c
these means c(b) and a(1)
cb=a this means
cb/b=a/b
b cancle by b
and c=a/b
How to solve problem 31? Solve for x y and z using ratios
Answers
The Solution:
Given:
Required:
Find the values for x, y, and z.
By the Similarity Theorem:
[tex]\Delta BAD\cong\Delta CBD[/tex]So,
[tex]\begin{gathered} \frac{x}{36}=\frac{36}{6x} \\ \\ \frac{x}{36}=\frac{6}{x} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} x^2=36\times6 \\ \\ x=\sqrt{36\times6}=6\sqrt{6} \end{gathered}[/tex]Find y by applying the Pythagorean Theorem on the right triangle CBD:
[tex]\begin{gathered} y^2=36^2+(6\sqrt{6)}^2 \\ \\ y=6\sqrt{42} \end{gathered}[/tex]Find z:
By the Pythagorean Theorem:
[tex]\begin{gathered} z^2=(42\sqrt{6})^2-(6\sqrt{42})^2 \\ \\ z=36\sqrt{7} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} x=6\sqrt{6} \\ \\ y=6\sqrt{42} \\ \\ z=36\sqrt{7} \end{gathered}[/tex]which functions are inverses of each other?A. both pair 1 and pair 2B. pair 1 only C. Pair 2 only D. neither pair 1 nor pair 2
Answers
Answer:
The pair one functions are given below as
[tex]\begin{gathered} f(x)=2x-6,g(x)=\frac{x}{2}+3 \\ f(g(x))=2(\frac{x}{2}+3)-6 \\ g(f(x))=\frac{2x-6}{2}+3 \end{gathered}[/tex]Step 1:
From pair 1, substitute the value of x=1 in the
[tex]\begin{gathered} f(x)=2x-6, \\ f(1)=2(1)-6 \\ f(1)=2-6 \\ f(1)=-4 \\ \\ g(x)=\frac{x}{2}+3 \\ g(-4)=-\frac{4}{2}+3 \\ g(-4)=-2+3 \\ g(-4)=1 \end{gathered}[/tex]Step 2:
For pair 2, substitute x=1
[tex]f(x)=7x,g(x)=-7x[/tex][tex]\begin{gathered} f(x)=7x \\ f(1)=7(1) \\ f(1)=7 \\ \\ g(x)=-7x \\ g(7)=-7(7) \\ g(7)=-49 \end{gathered}[/tex]Step 3:
From pair one,
[tex]f(1)=-4,g(-4)=1[/tex]From pair 2,
[tex]f(1)=7,g(7)=-49[/tex][tex]f(x)=y,g(y)=x(\text{inverse)}[/tex]From the above conclusion, we can say that
The final answer is
PAIR 1 ONLY
OPTION B is the right answer
on a trip of 2,300 miles, a missionary went 9 times as far by plane as by car. How for did the missionary travel by plane
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Let the trip by car be c and the trip by plane be p.
The missionary travelled 9 times as far by plane as he did by car. This means if his trip by car is modelled by c, then the trip by plane would be 9c.
Hence, knowing that the entire trip of 2300 miles is by plane and by car;
[tex]\begin{gathered} c+p=2300 \\ \text{When p=9c, then} \\ c+9c=2300 \\ 10c=2300 \\ \text{Divide both sides by 10} \\ c=230 \\ \text{Therefore, his trip by plane would be derived as;} \\ c+p=2300 \\ 230+p=2300 \\ \text{Subtract 230from both sides} \\ p=2070 \end{gathered}[/tex]What is the least common denominator of 1/20 and 7/50
Answers
Considering the given fractions
[tex]\frac{1}{20};\frac{7}{50}[/tex]You have to find the least common denominator between the denominators "20" and "50"
For these values, the least common denominator is the least common multiple between both values:
[tex]20\cdot50=100[/tex]So, the least common denominator is 100.
I need help with his practice problems from my ACT prep guidePlease show your work in steps
Answers
Answer:
[tex]-\sqrt[]{6}+1[/tex]Explanation:
Given the below expression;
[tex]\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)[/tex]Recall that;
[tex]\begin{gathered} \sec x=\frac{1}{\cos x} \\ \sin x=\cos (\frac{\pi}{2}-x) \end{gathered}[/tex]So we can rewrite the expression as;
[tex]\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{\cos(\pi-\frac{7\pi}{4})}-\frac{1}{\cos(-\pi)} \\ \frac{\tan(-\frac{2\pi}{3})}{\cos(-\frac{5\pi}{4})}-\frac{1}{\cos(-\pi)} \end{gathered}[/tex]Also, recall that;
[tex]\begin{gathered} \cos (-x)=\cos x \\ \tan (-x)=-\tan x \end{gathered}[/tex]So we'll have;
[tex]\frac{-\tan (\frac{2\pi}{3})}{\cos (\frac{5\pi}{4})}-\frac{1}{\cos (\pi)}[/tex]From the Unit circle, we have that;
[tex]\begin{gathered} \cos \pi=-1 \\ \cos (\frac{5\pi}{4})=\frac{-\sqrt[]{2}}{2} \\ \tan (\frac{2\pi}{3})=-\sqrt[]{3} \end{gathered}[/tex]Substituting the above values into the expression and simplifying, we'll have;
[tex]\begin{gathered} \frac{-(-\sqrt[]{3})}{\frac{-\sqrt[]{2}}{2}}-\frac{1}{-1}=\frac{\sqrt[]{3}}{\frac{-\sqrt[]{2}}{2}}+1=-\frac{2\sqrt[]{3}\sqrt[]{2}}{\sqrt[]{2}\cdot\sqrt[]{2}}+1 \\ =-\sqrt[]{6}+1 \end{gathered}[/tex]What is the image of the point (-7,-3) after a rotation of 90° counterclockwise about the origin?
Answers
The new point after rotation of point (-7, -3) counterclockwise by 90 degrees will be ( 3, -7).
What is meant by coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x, y).
Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.
Given: the Point A be (-7, -3)
After rotation, this point moves to a unique coordinate (x, y) which exists as point B
Let's say the origin is O
Slope of line segment AO = (-3-0)/(-7-0) = 3/7
Slope of line segment BO = (y - 0)/(x - 0) = y/x
Since both lines exist perpendicular to each other so
Slope AO × Slope BO = -1
3/7 × y/x = -1
⇒ 3y = -7x
If we observe the result then it will be clear that if we put x = 3 then y = -7 will be the new coordinate.
Therefore, the new point after rotation of point (-7, -3) counterclockwise by 90 degrees will be ( 3, -7).
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Divide the polynomial by the monomial (63xy^3+ 56x^2y^4)/(7xy)
Answers
ANSWER
9y² + 8xy³
EXPLANATION
To divide this polynomial by the given monomial, we can distribute the denominator into the sum,
[tex]\frac{63xy^3+56x^2y^4}{7xy}=\frac{63xy^3}{7xy}+\frac{56x^2y^4}{7xy}[/tex]Then, each coefficient simplifies with the coefficient of the monomial, since both are multiples of 7. Also, in the first term, x cancels out, and we have to subtract 1 from the exponent of y. In the second term, we subtract 1 from both the exponents of x and y,
[tex]\frac{63xy^3}{7xy}+\frac{56x^2y^4}{7xy}=9y^2+8xy^3[/tex]Hence, the result is 9y² + 8xy³.
Find the zeros of the following logarithmic function: f(x) = 2logx - 6.
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Determine if the following answers are true or false. If false, justify why it’s not true and find the correct answer(s). If true, justify why they are correct. You must show your step-by-step process to solve each question to receive full credit.
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Given the following inequality
[tex]\begin{gathered} \tan ^2(x)>\sqrt[]{5} \\ x\in\lbrack-\pi,\pi\rbrack \\ \end{gathered}[/tex]We need to check if x=0.981 is a solution.
This value is inside of the range, then, we just need to evaluate.
[tex]\tan ^2(0.981)\approx2.2325919107[/tex]Calculating the square root of 5:
[tex]\sqrt[]{5}\approx2.2360679775[/tex]From this, we know that the statement is false, because
[tex]\tan ^2(0.981)<\sqrt[]{5}[/tex]The local humane society is restocking on cat food to prepare for kitten season. Very young kittens need kitten formula which costs $4.00 per bottle. Older kittens need wet cat food which costs $1.50 per can. Answer numbers 5 and 6. 15) Write an algebraic expression to describe how much the humane society will spend on kitten supplies based on the number of bottles and the number of cans they buy. 16) How much money (before tax) will the humane society spend if they buy 5 bottles of kitten formula and 12 cans of wet cat food? Show your work.
Answers
Lets call B the nuber of bottles they will buy and C the number of cans.
Then, if each bottle cost $4, the cost of all the bottles will be 4B.
If each can cost $1.50, then, the total cost of the cans is 1.5C.
If we add this two costs, we have the expression we need:
[tex]\text{Cost}=4B+1.5C[/tex]If they buy 5 bottles of kitten formula and 12 cans of wet cat food, we have B=5 and C=12, and the cost is:
[tex]\text{Cost}=4B+1.5C=4\cdot5+1.5\cdot12=20+18=38[/tex]They will spend $38.
[tex]4\sqrt[3]{16} /2\sqrt[3]{2}[/tex]
Answers
The expression 4∛16/2∛2 has a value of 4when simplified
How to evaluate the expression?From the question, the expression is given as
4∛16/2∛2
From the above parameter, we can see that the factors of the expression uses the cube root symbol
This means that the expression is a radical expression
Next, we have
4∛16/2∛2 = 4∛16/2∛2
Divide 4 by 2 in the equation
So, we have
4∛16/2∛2 = 2∛16/∛2
Solving further, we combine the cube roots (or radicals)
This is represented as
4∛16/2∛2 = 2∛(16/2)
Evaluate the quotient of 16 and 2
So, we have the following equation
4∛16/2∛2 = 2∛8
Take the cube root of 8
4∛16/2∛2 = 2 x 2
Evaluate the product
4∛16/2∛2 = 4
The expression cannot be further simplified
Hence, the solution to the expression 4∛16/2∛2 is 4
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the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. what is the best point estimate for the mean monthly water bill for all residents of the local apartmemt complex?
Answers
From the information given, the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. The best estimate for the mean monthly water bill is the sample mean. Since 137 dollars is the sample mean, the correct answer is 137
Drag the measurements to the containers to show equal length
Answers
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
What is meant by measurements?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
An equation exists an expression that indicates the relationship between two or more numbers and variables.
1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.
Hence:
15 yd = 15 yd × 36 in per yd = 540 in
195 ft = 195 ft × 12 in per ft = 2340 in
5280 yd = 5280 yd * 3 ft per yd = 15840 ft
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft.
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Following figure shows ABC with silencer the nearest 10th find AB in ABC
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We have to find the length of AB.
We can use the Law of sines the tell us that the quotient between the sine of an angle and the length of the opposite side is constant for each of the three angles.
So we can write:
[tex]\begin{gathered} \frac{\sin(A)}{CB}=\frac{\sin(C)}{AB} \\ \frac{\sin(71\degree)}{6}=\frac{\sin(48\degree)}{AB} \\ AB=\frac{6\cdot\sin(48\degree)}{\sin(71\degree)} \\ AB\approx\frac{6\cdot0.743}{0.946} \\ AB\approx4.7 \end{gathered}[/tex]Answer: AB = 4.7
PLS HELP ASAP I WILL GIVE BRAINLIEST
Answers
Answer: I think the answer is [tex]\frac{2/3}{1}\\[/tex] and [tex]\frac{3}{1}[/tex]
Step-by-step explanation: I hope this helps. Correct me if I am wrong.
Please help and answer this question ASAP! :)
Answers
Answer:
Odd, Even, Even, Neither=========================
The difference between odd and even functions is that:
f(-x) = f(x) for even functions,f(-x) = - f(x) for odd functions.Let's test this property for the given functions.
Function f(x)f(-4) = - f(4) = 8 and f(-2) = - f(2) = 1, so this is an odd functionFunction g(x)g(4) = g(-4) = -4 and g(2) = g(-2) = 2, so this is an even functionFunction j(x)j(2) = j(-2) = 2 and j(1) = (j-1) = - 4, so this is an even functionFunction k(x)k(-4) = 9, k(4) = 1 and k(-2) = 4, k(2) = 0, since each value is different this is neither odd nor even functionFor the function f(x). describe, in words, the effects of each variable alb,h,k on the graph of a*f(bx+h)+k
Answers
Answer:
a: a produces vertical stretch
b: b produces a horizontal stretch
h: h produces a translation to the left of the X-axis
k: k produces a translation on the new function upward of the Y-axis
Step-by-step explanation:
An intermediate function is produced by adding each variable in the following order:
1) f(x) to f(bx):
Effect:
the horizontal stretch of f(x) along the x-axis with stretch factor b
2) f(bx) to f(bx+h):
Effect:
translation of f(bx) to the left of the X-axis by h units
3) f(bx+h) to a*f(bx+h):
Effect:
vertical stretching of f(bx+h) by a factor equal to a
4) Finally, a*f(bx+h) to a*f(bx+h)+k:
Effect:
vertical translation of a*f(bx+h) by h units upwards along the Y-axis.
Blaise M.
A company plans a major investment and theamount of profit is uncertain, but researchersgive the following estimate for the distribution.1.5210Profit(inmillions)Probability0.10.20.40.20.1What is the expected value of the profit?[?] million dollars
Answers
The expected value is the return you expect from some kind of investment/action.
When we are presented with probabilty of an action, we can take the expected value of the whole table [investment] by taking the sum of the products of probability and the action.
Here, we want products of "probability" and "profit". Then we sum it. Shown below:
[tex]\begin{gathered} E=(0.1)(1)+(0.2)(1.5)+(0.4)(2)+(0.2)(4)+(0.1)(10) \\ E=3 \end{gathered}[/tex]Expected value of profit = 3 million dollars