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

Answer:

Radius = 1.59 in

Diameter = 3.18 in

Area = 7.94 in²

Explanation:

The circumference of a circle can be calculated as:

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:

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:

So, replacing r = 1.59 in, we get:

Therefore, the answer are:

Radius = 1.59 in

Diameter = 3.18 in

Area = 7.94 in²

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

Hello!

Let's solve your expression:

Let's replace where's z by 6, look:

So the value of this expression when z=6 is 72.

Initial money = 70

then add

10 + 30 + 150 + 7 = 197

Now add both results

70 + 197 = 267

Answer is

You have $267

You have to subtract the fractions:

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:

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:

For the second fraction 2/9 multiply both values by 7:

Now you can add both fractions:

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:

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!!!

Explanation

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

Step 1

To find a, take the number and move a decimal place to the right one position.

so

Step 2

Now, to find b, count how many places to the right of the decimal.

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

therefore, the answer i

I hope this helps you

we get that measure of the supplemantary angle is:

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

Then, to find the unit rate for calories we need to solve the equation for x

Now, to find how many calories there are in 2 cups we must multiply the unit rate for calories by 2

Finally, the answers are:

- The unit rate for calories is 100 calories/cup.

- In 2 cups there are 200 calories.

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,

Hence, the required fraction of quantity is 3/1700 of x.

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

The composition of the function (g o f)(5) is evaluated as: (g o f)(5) = g(f(5)) = 6.

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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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%]

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,

And since we know there are 10 decigrams in a gram, we'll have that:

This way,

This way, we can conclude that there are 59251.5 decigrams in 209 ounces.

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.

This means that:

So, the required function becomes:

Therefore, the correct answer is [option A]

Using scales, the distance of the two cities on the map would be of:

distance on the map = actual distance/40

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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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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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

At x = π, we have

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

Now the critical points are where df(x)/dx =0; therefore, we solve

solving for x gives

on the interval [−π,π].

Now, we evaluate the function at the critical points.

At x = -π/ 6, we have

At x = -5π/6, we have

Hence, our candidates for absolute extrema are

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

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.

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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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

We solve for x, just like this:

Therefore, for 48 months, the car rental will be lower

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)

So the roots of the expression are -5/2 and -1. Now, we can write the expression in this factored form:

So the factored form is (2n+5)(n+1)

Explanation

For the first question

We are asked to write the equation of the circle given that

The equation of a circle is of the form

In our case

Substituting the values

For the second question

Given that

We will have to get the midpoints (center) first

Next, we will find the radius

Using the points (4,-3) and (11,-8)

ANSWER

Degree: 4

Number of terms: 2

EXPLANATION

Answer:

Quotient:

Remainder:

P(-2):

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:

Thus, we can conlcude that the quotient is:

And the remainder is 13, which is indeed P(-2)

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

and the point

Notice that the equations is technically in slope-intercept form, by the value of the slope will be 0:

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

we can substitute the point and the slope to solve for b:

So, the equation of our line is:

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

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.

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;

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;

Given 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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We have to use the tangent of angle 40 to find the height of the tower.

The adjacent side is 20m, and the angle is 40 degrees, then

Therefore, the height of the tower is 16.8m