Does the point (3,-1) lie on the circle (x + 1)2 + (y - 1)1)2 = 16?no; the point is not represented by (h, k) in the equationyes; when you plug the point in for x and y you get a true statementno; when you plug in the point for x and y in the equation, you do not get a trueyes; the point is represented by (h, k) in the equation
Answers
We are given an equation of a circle and a point. We are then asked to find if the point lies on the circle. The equation of the circle and the point is given below
[tex]\begin{gathered} \text{Equation of the circle} \\ (x+1)^2+(y-1)^2=16 \\ \text{Given point =(3,-1)} \end{gathered}[/tex]To find if the point lies in the circle, we can use the simple method of substituting the coordinates into the equation of the circle.
This can be seen below:
[tex]\begin{gathered} (3+1)^2+(-1-1)^2=16 \\ 4^2+(-2)^2=16 \\ 16+4=16 \\ \therefore20\ne16 \end{gathered}[/tex]Since 20 cannot be equal to 16, this implies that the point does not lie on the circle.
ANSWER: Option 3
Related Questions
the measure of angle is 15.1 what is measure of a supplementary angle
Answers
we get that measure of the supplemantary angle is:
[tex]180-15.1=164.9[/tex]A circle has a circumference of 10 inches. Find its approximate radius, diameter and area
Answers
Answer:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
Explanation:
The circumference of a circle can be calculated as:
[tex]C=2\pi r[/tex]Where r is the radius of the circle and π is approximately 3.14. So, replacing C by 10 in and solving for r, we get:
[tex]\begin{gathered} 10\text{ in = 2}\pi r \\ \frac{10\text{ in}}{2\pi}=\frac{2\pi r}{2\pi} \\ 1.59\text{ in = r} \end{gathered}[/tex]Then, the radius is 1.59 in.
Now, the diameter is twice the radius, so the diameter is equal to:
Diameter = 2 x r = 2 x 1.59 in = 3.18 in
On the other hand, the area can be calculated as:
[tex]A=\pi\cdot r^2[/tex]So, replacing r = 1.59 in, we get:
[tex]\begin{gathered} A=3.14\times(1.59)^2 \\ A=3.14\times2.53 \\ A=7.94in^2 \end{gathered}[/tex]Therefore, the answer are:
Radius = 1.59 in
Diameter = 3.18 in
Area = 7.94 in²
a box of cereal states that there are 75 calories in a 3/4 serving what is the unit rate for calories cup how many calories are there in 2 cups
Answers
We know that a box of cereal states that there are 75 calories in a 3/4 cup.
To find the unit rate for calories cup we must represent the the situation with an equation
[tex]\frac{75\text{ calories}}{\frac{3}{4}\text{ cup}}=\frac{x\text{ calories}}{1\text{ cup}}[/tex]Then, to find the unit rate for calories we need to solve the equation for x
[tex]x\text{ calories}=\frac{75\text{ calories}\cdot1\text{ cup}}{\frac{3}{4}\text{ cup}}=100\text{ calories}[/tex]Now, to find how many calories there are in 2 cups we must multiply the unit rate for calories by 2
[tex]x\text{ calories=100 calories}\cdot2=200\text{ calories}[/tex]Finally, the answers are:
- The unit rate for calories is 100 calories/cup.
- In 2 cups there are 200 calories.
Subtract. Write fractions in simplest form. 12/7 - (-2/9) =
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You have to subtract the fractions:
[tex]\frac{12}{7}-(-\frac{2}{9})[/tex]You have to subtract a negative number, as you can see in the expression, both negatives values are together. This situation is called a "double negative" when you subtract a negative value, both minus signs cancel each other and turn into a plus sign:
[tex]\frac{12}{7}+\frac{2}{9}[/tex]Now to add both fractions you have to find a common denominator for both of them. The fractions have denominators 7 and 9, the least common dneominator between these two numbers is the product of their multiplication:
7*9=63
Using this value you have to convert both fractions so that they have the same denominator 63,
For the first fraction 12/7 multiply both values by 9:
[tex]\frac{12\cdot9}{7\cdot9}=\frac{108}{63}[/tex]For the second fraction 2/9 multiply both values by 7:
[tex]\frac{2\cdot7}{9\cdot7}=\frac{14}{63}[/tex]Now you can add both fractions:
[tex]\frac{108}{63}+\frac{14}{63}=\frac{108+14}{63}=\frac{122}{63}[/tex]Christian buys a $3500 computer using an installment plan that requires 17% down and a 3.7% interest rate. How much is the down payment?
Answers
1) Gathering the data
$3500 computer
17% down
3.7% interest rate.
2) Since we want to know how much is that down payment, we must turn that 17% into decimal form, then multiply it by the computer value:
17%=0.17
3500 x 0.17 = $595
3) So Christian must pay $595 as the down payment
There is a 50% chance of rain here and a 10% chance of rain on Mars. Therefore, there is a 45% chance that it will rain in neither place.
Answers
The given statement is true.
This is a question of probability.
It is given in the question that:-
Chance of raining here = 50 %
Chance of raining on Mars = 10 %
The given statement is :-
There is a 45 % chance that it will rain in neither place.
Chance of not raining here = 100 - 50 % = 50 % = 1/2
Chance of not raining on Mars = 100 - 10% = 90 % = 9/10
Hence, chance of raining in neither place = (1/2)*(9/10) = 9/20
9/20 = (9/20)*100 = 45 %.
Hence, the given statement "There is a 45% chance that it will rain in neither place" is true.
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3 /17% of a quantity is equal to what fraction of the quantity
Answers
Given:
The objective is to find the fraction of 3/17% of the quantity.
Consider the quantity as x. The fraction of 3/17% of the quantity can be calculated as,
[tex]\begin{gathered} =\frac{3}{17}\frac{1}{100}x \\ =\frac{3}{1700}x \end{gathered}[/tex]Hence, the required fraction of quantity is 3/1700 of x.
If your distance from the foot of the tower is 20 m and the angle of elevation is 40°, find the height of thetower.
Answers
We have to use the tangent of angle 40 to find the height of the tower.
[tex]\text{tan(angle) = }\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]The adjacent side is 20m, and the angle is 40 degrees, then
[tex]\tan (40)\text{ = }\frac{height\text{ of the tower}}{20m}[/tex][tex]\text{height = 20m }\cdot\text{ tan(40) = 20m }\cdot0.84\text{ = }16.8m[/tex]Therefore, the height of the tower is 16.8m
Consider the triangles ADB and EDC. Explain how they are similar.
Answers
Example: Triangles like ABC and EDC are similar by SAS similarity, because angle C is congruent in each triangle, and AC/EC = BC/DC = 2. By the definition of similarity, it follows that AB/DE = BC/EF = AC/DF = 2.
Factor.2n2 + 7n + 5
Answers
The first step to factor this expression is to find its roots (the values of 'n' that makes this expression equals zero)
To find the roots, we can use the quadratic formula:
(Using the coefficients a=2, b=7 and c=5)
[tex]\begin{gathered} n_1=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{-7-\sqrt{49-40}}{4}=\frac{-7-3}{4}=\frac{-10}{4}=\frac{-5}{2} \\ n_2=\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-7+3}{4}=\frac{-4}{4}=-1 \end{gathered}[/tex]So the roots of the expression are -5/2 and -1. Now, we can write the expression in this factored form:
[tex]\begin{gathered} a(n-n_1)(n-n_2) \\ 2(n+\frac{5}{2})(n+1) \\ (2n+5)(n+1) \end{gathered}[/tex]So the factored form is (2n+5)(n+1)
How to write slope intercept form
Answers
Answer:
See below
Step-by-step explanation:
If you are given slope (m) and intercept (b) , then write the line equation like this:
y = mx + b
Use the remainder theorem to find P(-2) for P(x) = x³ + 3x² +9,Specifically, give the quotient and the remainder for the associated division and the value of P(-2).QuotientRemainder =P(-2)=
Answers
Answer:
Quotient:
[tex]x^2+x-2[/tex]Remainder:
[tex]13[/tex]P(-2):
[tex]13[/tex]Step-by-step explanation:
Remember that the remainder theorem states that the remainder when a polynomial p(x) is divided by (x - a) is p(a).
To calculate the quotient, we'll do the synthetic division as following:
Step one:
Write down the first coefficient without changes
Step two:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 3:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 4:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Now, we will have completed the division and have obtained the following resulting coefficients:
[tex]1,1,-2,13[/tex]Thus, we can conlcude that the quotient is:
[tex]x^2+x-2[/tex]And the remainder is 13, which is indeed P(-2)
Find the equation of the line parallel to the line y=-1, going through point (-5,4)
Answers
In this problem, want to find the equation of a line that will be parallel to a given function through a point.
Recall that parallel lines have the same slope.
We are given the line
[tex]y=-1[/tex]and the point
[tex](-5,4)[/tex]Notice that the equations is technically in slope-intercept form, by the value of the slope will be 0:
[tex]y=0x-1[/tex]Therefore, the slope of the line through (-5,4) will also be zero. We can use that information to find the equation.
Using the form
[tex]y=mx+b[/tex]we can substitute the point and the slope to solve for b:
[tex]\begin{gathered} 4=0(-5)+b \\ \\ 4=b \end{gathered}[/tex]So, the equation of our line is:
[tex]y=0x+4\text{ or }\boxed{y=4}[/tex]Ariana is going to invest $62,000 and leave it in an account for 20 years. Assuming
the interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Ariana to end up with $233,000?
Answers
The rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.
What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/f))ⁿ ;
where A = amount that the depositor will receive
P = initial amount that the depositor has invested
R = rate of interest offered to the depositor
f = frequency of compounding offered per year
n = number of years.
Given, Amount that Ariana wants to end up receiving = A = $233,00
Principal amount that Ariana can invest = P = $62,000
Frequency of compounding offered per year = f = 1
Number of years = 20
Let the rate of interest offered to the depositor be = R
Following the formula established in the literature, we have:
233000 = 62000(1 + R)²⁰ ⇒ 3.76 = (1 + R)²⁰ ⇒ 1.07 = 1 + R ⇒ R = 0.07%
Thus, the rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.
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What is the value of the expression below when z6?9z + 8
Answers
Hello!
Let's solve your expression:
[tex]9z+8[/tex]Let's replace where's z by 6, look:
[tex]\begin{gathered} (9\cdot z)+18 \\ (9\cdot6)+18 \\ 54+18 \\ =72 \end{gathered}[/tex]So the value of this expression when z=6 is 72.
Convert do you need to the specified equivalent unit round your answer to the nearest 1 decimal place, if necessary
Answers
Answer:
There are 59251.5 decigrams in 209 ounces.
Step-by-step explanation:
We'll solve this using the rule of three.
We know that there are 28.35 grams in an ounce. This way,
This way,
[tex]\begin{gathered} x=\frac{209\times28.35}{1} \\ \\ \Rightarrow x=5925.15 \end{gathered}[/tex]And since we know there are 10 decigrams in a gram, we'll have that:
This way,
[tex]\begin{gathered} y=\frac{5925.15\times10}{1} \\ \\ \Rightarrow y=59251.5 \end{gathered}[/tex]This way, we can conclude that there are 59251.5 decigrams in 209 ounces.
f(x)A6X-868Which of the given functions could this graph represent?OA. f(t) = (x - 1)(x - 2)(x + 1)(x + 2)O B. f(x) = x(x - 1)(1 + 1)Oc. /(x) = x(x - 1)(x - 2)(x + 1)(x + 2)OD. (r) = x(x - 1)(x - 2)
Answers
The Solution:
Given the graph below:
We are required to determine the function that best describes the above graph.
Step1:
Identify the roots of the function from the given graph.
[tex]\begin{gathered} x=-2 \\ x=-1 \\ x=1 \\ x=2 \end{gathered}[/tex]This means that:
[tex]\begin{gathered} x+2=0 \\ x+1=0 \\ x-1=0 \\ x-2=0 \end{gathered}[/tex]So, the required function becomes:
[tex]f(x)=(x-1)(x-2)(x+1)(x+2)[/tex]Therefore, the correct answer is [option A]
An actor invests some money at 7%, and $24000 more than three times the amount at 11%. The total annual interest earned from the investment is $27040. How much did he invest at each amount? Use the six-step method.
Answers
0.07x+0.11(3x+24000)=27040
we will solve for x
x=61,000 [ investment at 7%]
Investment at 11% = 3x + 24000
= 3(61000)+24000
= 207000 [ investment at 11%]
How long can you lease the car before the amount of the lease is more than the cost of the car
Answers
ANSWER:
48 months
STEP-BY-STEP EXPLANATION:
According to the statement we can propose the following equation, where the price of the car is more than or equal to the amount of the lease. Just like this:
Let x be the number of months
[tex]16920\ge600+340x[/tex]We solve for x, just like this:
[tex]\begin{gathered} 600+340x-600\le16920-600 \\ \frac{340x}{340}\le\frac{16320}{340} \\ x\le48 \end{gathered}[/tex]Therefore, for 48 months, the car rental will be lower
1. Sketch the graph of y = x that is stretched vertically by a factor of 3. (Hint: Write the equation first, then graph) Sketch both y = x and the transformed graph.
Answers
ANSWER and EXPLANATION
We want to stretch the graph of:
y = x
A vertical stretch of a linear function is represented as:
y' = c * y
where c is the factor
The factor from the question is 3.
So, the new equation is:
y' = 3 * x
y' = 3x
Let us plot the functions:
I need help to solve by using the information provided to write the equation of each circle! Thanks
Answers
Explanation
For the first question
We are asked to write the equation of the circle given that
[tex]\begin{gathered} center:(13,-13) \\ Radius:4 \end{gathered}[/tex]The equation of a circle is of the form
[tex](x-a)^2+(y-b)^2=r^2[/tex]In our case
[tex]\begin{gathered} a=13 \\ b=-13 \\ r=4 \end{gathered}[/tex]Substituting the values
[tex](x-13)^2+(y+13)^2=4^2[/tex]For the second question
Given that
[tex](18,-13)\text{ and \lparen4,-3\rparen}[/tex]We will have to get the midpoints (center) first
[tex]\frac{18+4}{2},\frac{-13-3}{2}=\frac{22}{2},\frac{-16}{2}=(11,-8)[/tex]Next, we will find the radius
Using the points (4,-3) and (11,-8)
[tex]undefined[/tex]Find the absolute maximum and minimum values of the following function on the given interval. f(x)=3x−6cos(x), [−π,π]
Answers
Answer:
Absolute minimum: x = -π / 6
Absolute maximum: x = π
Explanation:
The candidates for the absolute maximum and minimum are the endpoints and the critical points of the function.
First, we evaluate the function at the endpoints.
At x = -π, we have
[tex]f(-\pi)=3(-\pi)-6\cos (-\pi)[/tex][tex]\Rightarrow\boxed{f(-\pi)\approx-3.425}[/tex]At x = π, we have
[tex]f(\pi)=3(\pi)-6\cos (\pi)[/tex][tex]\Rightarrow\boxed{f(\pi)\approx15.425.}[/tex]Next, we find the critical points and evaluate the function at them.
The critical points = are points where the first derivative of the function are zero.
Taking the first derivative of the function gives
[tex]\frac{df(x)}{dx}=\frac{d}{dx}\lbrack3x-6\cos (x)\rbrack[/tex][tex]\Rightarrow\frac{df(x)}{dx}=3+6\sin (x)[/tex]Now the critical points are where df(x)/dx =0; therefore, we solve
[tex]3+6\sin (x)=0[/tex]solving for x gives
[tex]\begin{gathered} \sin (x)=-\frac{1}{2} \\ x=\sin ^{-1}(-\frac{1}{2}) \end{gathered}[/tex][tex]x=-\frac{\pi}{6},\; x=-\frac{5\pi}{6}[/tex]
on the interval [−π,π].
Now, we evaluate the function at the critical points.
At x = -π/ 6, we have
[tex]f(-\frac{\pi}{6})=3(-\frac{\pi}{6})-6\cos (-\frac{\pi}{6})[/tex][tex]\boxed{f(-\frac{\pi}{6})\approx-6.77.}[/tex]At x = -5π/6, we have
[tex]f(\frac{-5\pi}{6})=3(-\frac{5\pi}{6})-6\cos (-\frac{5\pi}{6})[/tex][tex]\Rightarrow\boxed{f(-\frac{5\pi}{6})\approx-2.66}[/tex]Hence, our candidates for absolute extrema are
[tex]\begin{gathered} f(-\pi)\approx-3.425 \\ f(\pi)\approx15.425 \\ f(-\frac{\pi}{6})\approx-6.77 \\ f(-\frac{5\pi}{6})\approx-2.66 \end{gathered}[/tex]Looking at the above we see that the absolute maximum occurs at x = π and the absolute minimum x = -π/6.
Hence,
Absolute maximum: x = π
Absolute minimum: x = -π / 6
If the number of college professors is P and the number of students S, and there are 20 times more students as professors, write an algebraic equation that shows the relationship
Answers
Answer
Algebraic equation that shows the relationship is
P = 20S
Explanation
Number of college professors = P
Number of students = S
There are 20 times as many students as professors.
P = (S) (20)
P = 20S
Hope this Helps!!!
write the number 1,900 in scientific notation
Answers
Explanation
[tex]1900[/tex]Calculating scientific notation for a positive integer is simple, as it always follows this notation:
[tex]a\cdot10^b[/tex]Step 1
To find a, take the number and move a decimal place to the right one position.
so
[tex]1900\Rightarrow1.900\text{ }[/tex]Step 2
Now, to find b, count how many places to the right of the decimal.
[tex]1900\Rightarrow1.900\text{ ( 3 places)}[/tex]Step 3
finally,
Building upon what we know above,
a= 1.9
b=3 (Since we moved the decimal to the left the exponent b is positive)
replace
[tex]\begin{gathered} a\cdot10^b \\ a\cdot10^b=1.9\cdot10^3 \end{gathered}[/tex]therefore, the answer i
[tex]1.9\cdot10^3[/tex]I hope this helps you
I had $70 and my mother gave me $10 and my father gave me $30 and aunt and uncle gave me $150 and I had another $7 how much do I have
Answers
Initial money = 70
then add
10 + 30 + 150 + 7 = 197
Now add both results
70 + 197 = 267
Answer is
You have $267
(x^2+9)(x^2-9) degree and number of terms
Answers
ANSWER
Degree: 4
Number of terms: 2
EXPLANATION
Help asp show your work you’ll get brainliest
Answers
The information given in the table on the Value of a Car and the Age of the Car, gives;
First Part;
The dependent variable is; The Value of Car
The independent variable is; The Age of Car
Second part;
The situation is a function given that each Age of Car maps to only one Value of Car.
What is a dependent and a independent variable?A dependent variable is an output variable which is being observed, while an independent variable is the input variable which is known or controlled by the researcher.
First part;
The given information in the table is with regards to how the car's value decreases with time, therefore;
The dependent variable, which is the output variable, or the variable whose value is required is the current Value of the Car (Dollars)The independent variable, which is the input variable, or the variable that determines the value of the output or dependent variable, is the Age of Car (Years)Second part;
A function is a relationship in which each input value has exactly one output.
Given that the Values of the cars are all different, and no two car of a particular age has two values, therefore;
The situation is a functionGiven that the first difference varies depending on the age of the car, the function can be taken as a piecewise function
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which of the following equations represent a line that is perpendicular to y=-3x+6 and passes through the point (3,2)
Answers
Answer:
y = [tex]\frac{1}{3}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 6 ← is in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (3, 2 ) into the partial equation
2 = 1 + c ⇒ c = 2 - 1 = 1
y = [tex]\frac{1}{3}[/tex] x + 1 ← equation of perpendicular line
How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles?
Answers
Using scales, the distance of the two cities on the map would be of:
distance on the map = actual distance/40
What is the scale of a map?A scale on the map represents the ratio between the actual length of a segment and the length of drawn segment, hence:
Scale = actual length/drawn length
In this problem, the scale is of 1 inch to 40 miles, meaning that:
Each inch drawn on the map represents 40 miles.
Then the distance of the two cities on the map, in inches, would be given as follows:
distance on the map = actual distance/40.
If the distance was of 200 miles, for example, the distance on the map would be of 5 inches.
The problem is incomplete, hence the answer was given in terms of the actual distance of the two cities. You just have to replace the actual distance into the equation to find the distance on the map.
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help meeeeeeeeee pleaseee !!!!!
Answers
The composition of the function (g o f)(5) is evaluated as: (g o f)(5) = g(f(5)) = 6.
How to Determine the Composition of a Function?To find the composition of a function, we have to first evaluate the inner function for the given value of x that is given as its input. After that, the output of the inner function would then be used as the input for the outer function, which would now be evaluated for the composition of the function.
Given the functions:
f(x) = x² - 6x + 2
g(x) = -2x
We need to find the composition of the function, (g o f)(5), where the inner function is f(x), and the outer function is g(x).
Therefore:
(g o f)(5) = g(f(5))
Find f(5):
f(5) = (5)² - 6(5) + 2
f(5) = -3
Substitute x = -3 into g(x) = -2x:
(g o f)(5) = -2(-3)
(g o f)(5) = 6
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