Identify the center and the radius of a
circle that has a diameter with endpoints at (2, 7)
and (8, 9).

Answer:

Step-by-step explanation:

-4 [tex]\leq[/tex] x [tex]\leq[/tex] 6

x = {-4,-3,-2,-1,0,1,2,3,4,5,6}

Hope I helped...

Answer:479

Step-by-step explanation:470+9=479

We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as →  30x + 80y = 470   and    x + y = 9. The variables used in the system of equations are -

x - Number of times his song played in a commercial

y - Number of times his song played in a movie.

Equation modelling is a method of writing a mathematical relation from a mathematical statement for mathematical analyses of the problem given.

Given is Mason who collects royalties on his songs whenever they are played in commercials or movies.

Assume that his song played in 'x' commercials and 'y' movies.

Cost per song when played in commercial = $30

Then for 'x' commercials, total cost will be = $30x

Cost per song when played in movie = $80

Then for 'y' movies, total cost will be = $80y

Total money earned through both = $470

We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as -

30x + 80y = 470

The total number of commercials and movies combined -

x + y = 9

The variables used in the system of equations are -

x -   Number of times his song played in a commercial

y - Number of times his song played in a movie.

Therefore, We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as →  30x + 80y = 470   and    x + y = 9. The variables used in the system of equations are -

x - Number of times his song played in a commercial

y - Number of times his song played in a movie.

To solve more questions on Equation modelling, visit the link below-

https://brainly.com/question/19537789

#SPJ5

Answer:

Step-by-step explanation:

The formula for finding the volume of a triangular prims is:

0.5 * b * h * length, where b is the length of the base of the triangle, h is the height of the triangle and length is prism length.

So, let's substitute those variables with the base length, height length, and prism length

The base length is 6km, the height length is 8km, and the prism length is 9km

So, we get:

0.5 * 6 * 8 * 9

= 1/2 * 6 * 8 * 9

= 1/2 * 48 * 9

= 1/2 * 432

= 216

The volume of this prism is 216km.

Answer:

[tex]14^{2}[/tex]

Step-by-step explanation:

14*14

14 is the base.  We are multiplying 14 two times.  Two would be the exponent

14 ^2

Answer:

vertex = (2, 64 )

Step-by-step explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = - 16x² + 64x ← is in standard form

with a = - 16, b = 64, c = 0 , then

x = - [tex]\frac{64}{-32}[/tex] = 2

substitute x = 2 into f(x) for corresponding y- coordinate

f(2) = - 16(2)² + 64(2) = - 16(4) + 128 = - 64 + 128 = 64

vertex = (2, 64 )

The given points of the expression is not a function because there are two different y-values for a single x-value.

Given The points are : (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4)

Function refers to a relation or expression involving one or more variables. In a function each value of x corresponds to each value of y. A relation which is having two or more values of y for x values is not a function.

We have been given points  (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4).

These are not points of a function because of a simple reason that it has two values of y for each one value of x.

Value of relation at x=-2 is -5.

Value of relation at x=-1 is 3.

Value of relation at x=1 is -2.

Value of relation at x=3 is 0.

Value of relation at x=4 is -2.

Value of relation at x=4  also equal to  4.

It has two values at x=4 one is -2 and other one is 4.

Hence the relation is not a function because there are two different y-values for a single x-value.

Learn more about function at  https://brainly.com/question/10439235

#SPJ10

The given points of the expression is not a function because there are two different y-values for a single x-value.

Given The points are : (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4)

Function refers to a relation or expression involving one or more variables. In a function each value of x corresponds to each value of y. A relation which is having two or more values of y for x values is not a function.

We have been given points  (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4).

These are not points of a function because of a simple reason that it has two values of y for each one value of x.

Value of relation at x=-2 is -5.

Value of relation at x=-1 is 3.

Value of relation at x=1 is -2.

Value of relation at x=3 is 0.

Value of relation at x=4 is -2.

Value of relation at x=4  also equal to  4.

It has two values at x=4 one is -2 and other one is 4.

Hence the relation is not a function because there are two different y-values for a single x-value.

If the top is 8 feet above the ground and ladder is 5 feet away from bottom of wall then the angle between ladder and house is 58°.

Given top is 8 feet above the ground, ladder is 5 feet away from bottom of the wall.

Trigonometric ratios are the ratios of the sides of a right angled triangle. sin is the ratio of perpendicular and hypotenuse , cos is the ratio of base and hypotenuse, tan is the ratio of perpendicular and base, cosec is the ratio of hypotenuse and perpendicular, sec is the ratio of hypotenuse and base, cot is the ratio of base and perpendicular.

Here we use tan d where d is the angle between ladder and wall of the house.

tan d= P/B

tan d=8/5

tan d=1.6

[tex]d=tan^{-1} 1.6[/tex]

d=57.99

After rounding off it will be 58°.

Hence the angle between ladder and house is 58°.

Learn more about trigonometric ratios at https://brainly.com/question/24349828

#SPJ4

Answer:

Step-by-step explanation:

What is the solution to the equation?

[tex]2^{x}[/tex] + 4 - 12 = 20

[tex]2^{x}[/tex] = 20 - 4 + 12

[tex]2^{x}[/tex] = 16 + 12

[tex]2^{x}[/tex] = 28

Answer:

x-1

Step-by-step explanation:

because i said so

If we make appropriate equation then we can find that there are 21 people and animals belong to the circus.

Given The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Double the combined number of acrobats and ballerinas is five more than three times the number of clowns.

We have to find total people and animals belong to the circus.

An equation is relationship between variables that are expressed in equal to form. It is solved to find the variables in equal to form Equations of two variables look like ax+ by=c.

let the number of acrobats be x, ballerinas be y, clowns be z, clowns be u.

According to given information in question the equations are:

x+ y-z=u-1-----------------------1

2(x+ y)=3z+5-------------------2

u=z+1----------------------------3

Put the value of u from 3 in 1

x+y- z=z+1-1

x+y-2z=0

from 2

z=2x+2y-5/3

put the value of z in x+y-2z=0

x+y-2(2x+2y-5/3)=0

-x-y+10=0

x+ y=10-------------------------4

put put the value of x+y=10 in 1

10-z=u-1

u+z=11-----------------------------5

solving 3

u-z=1------------------------6

Now add 5&6

u+z+u-z=11+12

2u=12

u=6

Put the value of u in 6

6-z=1

z=5

From above we get x+y=10, u=6, z=5

Add all three we get the total number of people and animals belong to circus.

x+y+u+z=10+6+5

=21

Hence there are total 21 people and animals belong to the circus.

Learn more about equations at https://brainly.com/question/2972832

#SPJ4

Answer:

$2,000

Step-by-step explanation:

7,440/3.72

Option 3. The effect that it has when there are exceptions to the overall trend between two variable is that It is irrelevant to the relationship.

This is used in statistics to show that there is the existence of two variables that are positively correlated.

These two variables would then have a positive slope trend line. Hence the answer to the question is option 3.

What effect does it have when there are exceptions to the overall trend in a relationship between two variables?

O It increases the relationship

O It decreases the relationship

O It is irrelevant to the relationship.

Read more on trend variables here:

https://brainly.com/question/24679525

#SPJ1

The simplest way to factor polynomials is to use the greatest common factor.

It should be noted that the polynomial simply means the expression of more than two algebraic terms.

In this case, the simplest way to factor polynomials is to use the greatest common factor. This simply had to do with the largest factor that the numbers share.

Other methods that can be utilized include the grouping method, the sum of the difference in cubes and in two squares.

Learn more about polynomial on:

brainly.com/question/2833285

#SPJ1

Answer:

a) $7.50

Step-by-step explanation:

The total cost of $85.50 includes a 5% discount, so 95% of what price is $85.50?

[tex].95x = 85.50[/tex]

[tex]x = 90[/tex]

So the original price is $90. Divide this by 12, obtaining $7.50.

Answer:

a)$7.5

Step-by-step explanation:

Solution:

Let X represents socks

Given,

Selling price (SP) of 12x=$85.50

Discount precent (d%)=5%

So,

SP=(100-d)% of MP. [this formula really exist believe it or not]

85.50= (100-5)/100 ×MP

or, 85.50×100 =95×MP

or, 8550/95=MP

So,MP=$90

Now At last ,

cost of 1 shocks before discount is 90/12

which is $7.50 ans√

Answer:

Step-by-step explanation:

The formula for the volume of a sphere of radius r is V = (4/3)(pi)r^3.

Here, with r = 3 in, the volume is

V = (4/3)(3.14)(3 in)^2, or  V  =  36(pi)(27 in)^3 = 36pi in^3

Answer: A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The range is just the y-values. You don't have to write any of the repeated values. You do need to write them in numerical order.

4, 4, 2, 5

becomes

2,4,5

Answer:

∠ ACB = 128° and ∠ABC = 32°

Step-by-step explanation:

∠ ADC = ∠ CAD (base angles theorem)

∠ ACD = 82° (angles in a triangle add to 180°)

∠ ACB = 128° (angles around a point add to 360°)

∠ ABC = 32° (angles in a triangle add to 180°)

The fabric mill produce 1,807,845 meters of fabric in 365 days.

A fabric mill produces 4953 meters of fabric in a day.

operations and interpretations to function to make function simple or more understandable called simplify and the process is called simplification.

We have 4953 meter of fabric in a day.
So for 365 days
fabric = 4953 x 365
= 1,807,845

Thus, the fabric mill produce 1,807,845 meters of fabric in 365 days.

Learn more about simplification here: https://brainly.com/question/12501526

#SPJ1

The general direction that Lin walked from the gym to his house is; B: Lin walked southwest, creating an obtuse triangle.

We are given;

Distance between the lecture hall and gym = 910 feet.

Distance between the gym and Lin apostrophe's house = 615 feet.

Distance between the lecture hall and Lin apostrophe's house = 651 feet.

Now, since this 3 distances form a triangle and the 3 distances are unequal, then we can call it an obtuse triangle since he walked west and then walked northwest.

Now, since he walked back to his house from the gym, we can say that he walked southwest if we picture the bearing of his first two directions.

Read more about Distance Bearing at; https://brainly.com/question/22719608

#SPJ1

A) The solution to m² + (1/m²) is gotten as; 14

B) The solution to m³ + ¹/₃ is gotten as; 52.312

We are given the algebraic equation;

(m² + 1)/m = 4

Multiply through by m to get;

m² + 1 = 4m

m² - 4m + 1 = 0

From online quadratic equation calculator, we have;

m = 3.732 or 0.268

A) Thus;

m² + (1/m²) = 3.732² + (1/3.732²)

⇒ 14

B) m³ + ¹/₃ gives;

3.732³ + (1/3) = 52.312

Read more about Algebra Simplification at; https://brainly.com/question/4541471

#SPJ1

Answer:

f(x)

Step-by-step explanation:

This question isn't to difficult, since all you need to know is: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. If the you're not quite sure why this is true, I'll try to express this in another way. [tex](\frac{a}{b})^x=\frac{a}{b}*\frac{a}{b}*\frac{a}{b}...\text{ x amount of times}[/tex], and as you may know when multiplying fractions, you simply multiply the numerators by the numerators and the denominators by the denominators, this means that you can simplify it to: [tex]\frac{a*a*a...\text{ x amount of times}}{b*b*b...\text{ x amount of times}}[/tex] this is literally what an exponent is which is why you can distribute the exponent as such: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. The next thing you need to know is that: [tex]1^x=1[/tex] for any real number. This is you can express this as: [tex]1*1*1...\text{ x amount of times} = 1[/tex], since 1 times 1 times 1, will always remain 1. You may think this will not apply for rational exponents, but it still does since: [tex]1^{\frac{a}{b}}=\sqrt[b]{1}^a[/tex], and no matter what b is, it's going to be 1. The square root of 1, is 1..., the cube root of 1 is 1.... This is because the very definition of a radical is what number times times it self index amount of times is equal to the number under the radical, and no matter how many times you multiply 1, you're going to get 1. If that's a bit confusing what I'm saying is: [tex]\sqrt[n]{b}\implies\text{?}^n=b[/tex].

Anyways hopefully you understand that, if not I'm sorry if I went a bit overboard trying to explain it. Anyways all you need to really know is that: [tex](\frac{1}{3})^x=\frac{1^x}{3^x}=\frac{1}{3^x}[/tex]. So this means as x increases, all you're really doing is increasing the denominator which is decreasing the number. The f function has an integer as a base, so the function will overall be increasing. This is not true for g(x) since as x increases the y-value decreases. So this means that f(x) has a faster rate. This is because the g(x) has a horizontal asymptote, since as x approaches infinity, g(x) approaches 0, since the denominator is increasing towards infinity. So the rate of change will be slowing down as x increases, since there is only so much the g(x) can change, since it has a horizontal asymptote. This is not true for f(x) as it has no horizontal asymptote and just goes towards infinity. So the f(x) has a faster rate.

Given :

Multiply Equation #1 by 3 :

Add Equations 2 and 3 :

Now, input x in Equation #3 to find y :

∴ Hence, the point of intersection is (2/3, 5/6).

Answer: A 1/2 ^4

Step-by-step explanation:

Answer:

a)1/2^4

Step-by-step explanation:

First solve 2^-4.

Use negative power rule: x^-a = 1/xa

⇒ 1/2^4

Simplify 2^4 to 16

⇒ 1/16

Just evaluate the other options.

The first one is correct.

Here's why:

⇒ Simplify 2^4 to 16.

⇒ 1/16

They have the same steps, therefore making Option A correct.

Note: This is the longer way, there is a easier way of dealing with these types of problems. Example: Without using a calculator problem.

Answer:

Can u please upload more clearer pictures ?

Answer:

300 meters per minute

Step-by-step explanation:

Step 1

Determine the fraction of the total distance for each part of the race.

Given:

1st part of race = 4/9 of total distance

2nd part of race = 2/5 of remaining distance

Step 2

Determine the distance of the third part of the race.

Given:

time = 15 minutes

speed = 300 meters per minute

Step 3

If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:

Step 4

Determine the distance of the 1st part of the race:

Step 5

Determine the speed of the 1st part of the race:

Given:

time = 20 minutes

distance = 6000 m

Answer:

-9w^2-90w

Step-by-step explanation:

You just use the distributive property and watch the negatives and positives.

[tex]\huge\boxed{-9w^2-90w}[/tex]

Distribute [tex]-9w[/tex] to both [tex]w[/tex] and [tex]10[/tex] as shown in the attached image. Then, just simplify the terms with multiplication.

[tex](-9w)\cdot w+(-9w)\cdot10\\\boxed{-9w^2-90w}[/tex]

Answer:

The inverse of the function f(x) = 64x³ - 1 is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]

Step-by-step explanation:

First replace x with y.

[tex]x=64y^3-1[/tex]

Then solve for y.

[tex]y^3=\frac{x+1}{64}[/tex]

Cube root both sides.

[tex]y=\frac{\sqrt[3]{x+1}}{4}[/tex]

Hence, the inverse is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]

Answer:

Option (2)

Step-by-step explanation:

The angle opposite the shortest side is the smallest and the angle opposite the longest side is the largest.

Since m is greater than or equal to 6, we know that:

2m+3 > m+8 > m-3