Let D = {xlx is a state in the United States} be the domain, and let f(x) - "the state capital" be the possible function. Determine if the relation is an example of a function.
Yes, f is a function.

Answer:

Step-by-step explanation:

I think its 823 ppm?

I'm not sure

Answer:

The length is 5 cm and the width is 4 cm

Step-by-step explanation:

I assume that is a rectangle

Let

x----> the length of rectangle

y ---> the width of rectangle

we know that

The area of rectangle is

A=xy

A=20 cm²

so

20=xy -----> equation A

The perimeter of rectangle is

P=2(x+y)

P=18 cm

so

18=2(x+y)

9=x+y -----> y=9-x ----> equation B

Substitute equation B in equation A and solve for x

20=x(9-x)

20=9x-x²

x²-9x+20=0

Solve the quadratic equation by graphing

The solution is x=5 cm (I assume that the length is greater than the width)

see the attached figure

Find the value of y

y=9-5=4 cm

therefore

The length is 5 cm

The width is 4 cm

Answer:

What you have to do is add all of the sums up and put 2 over it. it is 2/20 which is 1/10.

Step-by-step explanation:

in a percent it is 0.1

Can I get brainiest

The probability that Alina selects 2 cans of lemonade is

How to calculate probability?

The given question has concept of conditional probability.

Conditional probability is applied when we have to find the possibility of an event given the another event already occurred.

Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

Here, the first event is selecting the lemonade can and second event is also selecting lemonade can given one lemonade is already selected.

The probability to select 1st lemonade= 7/20

The probability to select 2nd lemonade=6/19

Multiplying them we get:

Probability:7*6/20*19=21/190

Therefore, the probability to select two lemonades is 21/190.

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Answer:

84 ft²

Step-by-step explanation:

Solve for Volume. Volume of a box is:

V = Length (base) x Width (base) x Height (of rectangular prism/square)

Change each measurement to have the same measurement (ft -> in, or vice versa).

Note that 1 ft = 12 in.

6 in = 1/2 ft, because 6/12 = 1/2

Length = 12 ft

Width = 14 ft

Height = 1/2 ft

Solve. Plug in the corresponding number to the corresponding words.

V = 12 x 14 x 1/2

Simplify. Solve.

V = 12 x (14 x 1/2)

V = 12 x (14/2)

V = 12 x 7

V = 84

84 ft² is your answer.

~

Answer:

1,008

Step-by-step explanation:

You multiply all three numbers to get your answer.

Answer:

[tex]5y^{6}\sqrt{2}[/tex]

Step-by-step explanation:

We want to  simplify:

[tex]\sqrt{50y^{12}}[/tex]

We rewrite as:

[tex]\sqrt{2\times25 \times (y^{6})^2}[/tex]

We split the radical sign to obtain:

[tex]\sqrt{25} \times \sqrt{(y^{6})^2} \times \sqrt{2}[/tex]

Simplify the square root for the perfect squares to get:

[tex]5y^{6}\sqrt{2}[/tex]

Therefore the simplified form is: [tex]5y^{6}\sqrt{2}[/tex]

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

We need two points through which the line passes.

[tex](x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 3,2)[/tex]

Substituting:

[tex]m = \frac {2-4} {3-1} = \frac {-2} {2} = - 1[/tex]

Answer:

[tex]m = -1[/tex]

Here you don’t need to solve the equation,the value of the problem is zero

For both methods I will use the quadratic formula. Look at the image below

Hope this helped!    

Answer:

y = 179x +1999

y = 249x

Step-by-step explanation:

Given:

down payment of cool cars= $1999

monthly lease rate of cool cars= $179

down payment of awesome autos= $0

monthly lease rate of awesome autos= $249

Number of months=x

total amount paid towards the lease after x months=y

Now creating a system of linear equations that describes the total amount, y, paid towards the lease after x months:

the slope intercept form of any linear function is given as y=mx +b

where m= slope  of function and b=y-intercept

In given case, slope m gives the monthly lease rate and y-intercept b gives the down payment.

So the equations for the two linear functions will be:

cool cars:

Putting the values of m=179 and b=1999, we get

y = 179x +1999

awesome autos:

Putting the values of m=249 and b=0, we get

y = 249x !

Answer:

Not a factor

Step-by-step explanation:

If (x - 3) is a factor then f(3) = 0

f(x) = x² - 4x + 30

f(3) = 2(3)² - 4(3) + 30 = 18 - 12 + 30 = 36 ≠ 0

Since f(3) ≠ 0 then (x - 3) is not a factor of f(x)

( x - 3 ) is not a factor of the polynomial 2x² - 4x + 30

What is Factor Theorem?

The Factor Theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then ( x - a ) is a factor of f ( x ) if f ( a ) = 0

Given data ,

f ( x ) = 2x² - 4x + 30

If ( x - 3 ) is a factor of f ( x ) , then by factor theorem f ( x ) = f ( 3 ) = 0

And , f ( 3 ) = 2 x 3 x 3 - 4 x 3 + 30

                            = 18 - 12 + 30

                            = 36

Therefore , f ( 3 ) ≠ 0 , so ( x - 3 ) is not a factor of 2x² - 4x + 30

Hence , ( x - 3 ) is not a factor of the polynomial 2x² - 4x + 30

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The solution of quadratic equation  [tex]3x^2 + 15x=0[/tex] is x =0 or -5.

Given Equation: [tex]3x^2 + 15x=0[/tex]

Now, factories each term as

3x² = 3 × x × x

15x = 3 × 5 × x

Now, taking the common term 3x as

[tex]3x^2 + 15x=0[/tex]

3 × x × x+ 3 × 5 × x =0

3x (x + 5)=  0

Now, equate each factor to 0 as

3x =0

x= 0/3

x= 0

or, x + 5= 0

x = -5

Thus, the value of x is -5 or 0.

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Answer:

5√2

Step-by-step explanation:

The question is on geometry

The formula for distance between two points is;

[tex]d= \sqrt{(X2-X1)^2 + (Y2-Y1)^2}[/tex]

where d is distance.

Given points;

(0,5)    and   (-5,0) ;

X1=0 ,X2= -5 , Y1= 5, Y2= 0

X2-X1 = -5 - 0= -5

Y2-Y1= 0-5= -5

[tex]d= \sqrt{(-5)^2 + (-5)^2}[/tex]

[tex]d=\sqrt{25+25}[/tex]

[tex]d=\sqrt{50}[/tex]

[tex]d=\sqrt{2*25} =\sqrt{2} *\sqrt{25} =\sqrt{2} *5\\\\\\\\d=5\sqrt{2}[/tex]

Answer:

[tex]d=5\sqrt{2}[/tex]

Step-by-step explanation:

Given : (0, 5) and (-5, 0)

To Find : Distance between the given points

Solution:

We will use distance formula :

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(0,5)[/tex]

[tex](x_2,y_2)=(-5,0)[/tex]

Substitute the values in the formula .

[tex]d=\sqrt{(-5-0)^2+(0-5)^2}[/tex]

[tex]d=\sqrt{(-5)^2+(-5)^2}[/tex]

[tex]d=\sqrt{25+25}[/tex]

[tex]d=\sqrt{50}[/tex]

[tex]d=5\sqrt{2}[/tex]

Hence the distance between the given points is 5√2 units

Final answer:

Jordan spent $14.85 in total, of which $2.85 was spent on snacks. After subtracting the cost of snacks, it's found that she spent $12.00 on bus fares.

Explanation:

The student asked how much Jordan spent on bus fares to and from the zoo if she spent a total of $14.85, including $2.85 on snacks. To find out the amount spent on bus fares, one needs to subtract the cost of the snacks from the total amount spent. Therefore, the calculation would be $14.85 (total spent) - $2.85 (snacks) = $12.00.

Hence, Jordan spent $12.00 on bus fares.

Your answer is correct

I guess you wrote the correct answer

Answer:

60

Step-by-step explanation:

Answer:

About 57.48

Step-by-step explanation:

ANSWER

[tex]2 \sqrt{3} i[/tex]

EXPLANATION

We we're given that, the real part of the complex number is 2.

Let the imaginary part be y.

Then the complex number is

[tex]z = 2 + yi[/tex]

Also, we have that, the modulus is 4.

The modulus is given by the formula;

[tex] |z| = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

This implies that,

[tex] 4 = \sqrt{ {2}^{2} + {y}^{2} } [/tex]

We square both sides to obtain;

[tex] {4}^{2} = 4 + {y}^{2} [/tex]

[tex]16 - 4 = {y}^{2} [/tex]

[tex] {y}^{2} = 12[/tex]

[tex]y = \sqrt{12} = 2 \sqrt{3} [/tex]

Therefore the complex part is

[tex]2 \sqrt{3} i[/tex]

Answer:

3.4

Step-by-step explanation:

i just did it

Answer:

2 gallons per mile

C. 5 and seventy-six hundredths sorry If I'm wrong, but I'm pretty sure I'm right

please rate my answer

Answer:

Five and seventy six hundredths

Your Welcome :3

Answer:

The interior angles are 70°,65°,80°,155° and 170°

Step-by-step explanation:

step 1

Find the sum of the interior angles of the pentagon

The sum is equal to

S=(n-2)*180°

where

n is the number of sides of polygon

n=5 (pentagon)

substitute

S=(5-2)*180°=540°

step 2

Find the value of x

Sum the given angles and equate to 540

x+(x-5)+(x+10)+(2x+15)+(2x+30)=540°

7x+50=540°

7x=490°

x=70°

step 3

Find all the angles

x=70°

(x-5)=(70-5)=65°

(x+10)=(70+10)=80°

(2x+15)=(2*70+15)=155°

(2x+30)=(2*70+30)=170°

Answer:

A=36

Step-by-step explanation:

A=s^2

A=6^2

A=36

Answer:

36

Step-by-step explanation:

Formula ⇒ A = s²

We know that s = 6, so we substitute into A = s²

A = s²

A = 6²

A = 36

Answer:

Step-by-step explanation:

C.35%

If you divide the number of hearts drawn by the number of total draws you get your answer.

14/20=0.35

Answer:

1st pic: 4

2nd pic: 70

3rd pic: 5

Step-by-step explanation:

Answer:

x° = 37°

Step-by-step explanation:

* Lets revise some facts of a circle

- The secant is a line intersect the circle in two points

- If two secants intersect each other in a point outside the circle,

 then the measure of the angle between them is half the difference

 of the measures of their intercepted arcs

* Now lets solve the problem

- There is a circle

- Two secants of this circle intersect each other in a point outside

  the circle

∴ The measure of the angle between them = 1/2 the difference of the

  measures of their intercepted arcs

∵ The measure of the angle between them is x°

∵ The measures of their intercepted arcs are 26° and 100°

- Use the rule above to find x

∴ x° = 1/2 [ measure of the large arc - measure of small arc]

∵ The measure of the large arc is 100°

∵ The measure of the small arc is 26°

∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°

∴ x° = 37°

You start with the equation V = IR, plug the value 0.5 for I and you have

V = 0.5*R

So, the first three options are equivalent and correct.

V=IR

And current, Ampere is given as 0.5 so substituting it back in the main equation gives V = 0.5R

Answer:

3 21/100

just a fraction.

The lenght of each side is 24cm, 24cm, and 8cm.

In order to solve this problem, we know that the perimeter of a triangle equation is P = a + b + c, where a, b, and c are the sides of the triangle.

The perimeter is 56cm, we can write the equation as follow:

a + b + c = 56cm (1)

If each of the two longer sides of the triangles is three times as long as the shortest side, we can assume:

c = shortest side = x

a = b = longer sides = 3x

Substituting the values in the equation (1):

3x + 3x + x = 56cm

7x = 56cm

x = 56cm/7 = 8cm

c = shortest side = 8cm

a = b = longer sides = 3(8cm) = 24cm

The ratio of the room's length to its area is 1:12, derived from length (22 feet) divided by area (264 square feet).

let's break it down step by step.

Step 1: Calculate the area of the room.

To find the area of a rectangle, you multiply its length by its width.

So, Area = Length × Width

Area = 22 feet × 12 feet

Area = 264 square feet

Step 2: Calculate the ratio of the length of the room to its area.

The ratio of length to area is:

[tex]\[ \text{Ratio} = \frac{\text{Length}}{\text{Area}} \][/tex]

Substituting the values:

[tex]\[ \text{Ratio} = \frac{22 \, \text{feet}}{264 \, \text{square feet}} \][/tex]

Step 3: Simplify the ratio.

[tex]\[ \text{Ratio} = \frac{22}{264} \][/tex]

Step 4: Simplify the fraction.

[tex]\[ \text{Ratio} = \frac{1}{12} \][/tex]

So, the ratio of the length of the room to its area is [tex]\( \frac{1}{12} \)[/tex].

Answer:

volume  =  (1/3)(area of base)(height)

area of base  =  pi * radius2  =  pi * (10/2)2  =  pi * 52  =  25pi   cm2

volume  =  (1/3)( 25pi )( 9 )   cm3

volume  =  75pi   cm3

volume  ≈  236  cm3  

ANSWER

[tex]Volume = 235.6 {cm}^{3} [/tex]

EXPLANATION

The volume of a cone is calculated the using the formula:

[tex]Volume = \frac{1}{3} \pi {r}^{2} h[/tex]

From the given information the height of the cylinder is, h=9cm.

The diameter of the base is 10cm.

The radius is half of the diameter of the base, r=5cm.

We plug in the values into the formula to get:

[tex]Volume = \frac{1}{3} \times \pi \times {5}^{2} \times 9[/tex]

[tex]Volume = 75\pi {cm}^{3} [/tex]

[tex]Volume = 235.6 {cm}^{3} [/tex]

Answer:

not geometric

Step-by-step explanation:

If the sequence is geometric then the common ratio r between consecutive terms should be equal

[tex]\frac{42}{21}[/tex] = 2

[tex]\frac{126}{42}[/tex] = 3

[tex]\frac{504}{126}[/tex] = 4

There is no common ratio between consecutive terms

Hence the sequence is not geometric

Answer:

11.2

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = B(4, 7) and (x₂, y₂ ) = C(2, - 4)

d = [tex]\sqrt{(2-4)^2+(-4-7)^2}[/tex]

   = [tex]\sqrt{(-2)^2+(-11)^2}[/tex]

   = [tex]\sqrt{4+121}[/tex]

   = [tex]\sqrt{125}[/tex] ≈ 11.2

Answer:

Part 1) [tex]P=[2\sqrt{29}+\sqrt{18}]\ units[/tex] or [tex]P=15.01\ units[/tex]

Part 2) [tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex] or [tex]P=22.36\ units[/tex]

Part 3) [tex]P=4[\sqrt{13}]\ units[/tex] or [tex]P=14.42\ units[/tex]

Part 4) [tex]P=[19+\sqrt{17}]\ units[/tex] or [tex]P=23.12\ units[/tex]

Part 5) [tex]P=2[\sqrt{17}+\sqrt{68}]\ units[/tex] or [tex]P=24.74\ units[/tex]

Part 6) [tex]A=36\ units^{2}[/tex]

Part 7) [tex]A=20\ units^{2}[/tex]

Part 8) [tex]A=16\ units^{2}[/tex]

Part 9) [tex]A=10.5\ units^{2}[/tex]

Part 10) [tex]A=6.05\ units^{2}[/tex]

Step-by-step explanation:

we know that

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Part 1) we have the triangle ABC

[tex]A(0,3),B(5,1),C(2,-2)[/tex]

step 1

Find the distance AB

[tex]A(0,3),B(5,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1-3)^{2}+(5-0)^{2}}[/tex]

[tex]AB=\sqrt{(-2)^{2}+(5)^{2}}[/tex]

[tex]AB=\sqrt{29}\ units[/tex]

step 2

Find the distance BC

[tex]B(5,1),C(2,-2)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-2-1)^{2}+(2-5)^{2}}[/tex]

[tex]BC=\sqrt{(-3)^{2}+(-3)^{2}}[/tex]

[tex]BC=\sqrt{18}\ units[/tex]

step 3

Find the distance AC

[tex]A(0,3),C(2,-2)[/tex]

substitute in the formula

[tex]AC=\sqrt{(-2-3)^{2}+(2-0)^{2}}[/tex]

[tex]AC=\sqrt{(-5)^{2}+(2)^{2}}[/tex]

[tex]AC=\sqrt{29}\ units[/tex]

step 4

Find the perimeter

The perimeter is equal to

[tex]P=AB+BC+AC[/tex]

substitute

[tex]P=[\sqrt{29}+\sqrt{18}+\sqrt{29}]\ units[/tex]

[tex]P=[2\sqrt{29}+\sqrt{18}]\ units[/tex]

or

[tex]P=15.01\ units[/tex]

Part 2) we have the rectangle ABCD

[tex]A(-4,-4),B(-2,0),C(4,-3),D(2,-7)[/tex]

Remember that in a rectangle opposite sides are congruent

step 1

Find the distance AB

[tex]A(-4,-4),B(-2,0)[/tex]

substitute in the formula

[tex]AB=\sqrt{(0+4)^{2}+(-2+4)^{2}}[/tex]

[tex]AB=\sqrt{(4)^{2}+(2)^{2}}[/tex]

[tex]AB=\sqrt{20}\ units[/tex]

step 2

Find the distance BC

[tex]B(-2,0),C(4,-3)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-3-0)^{2}+(4+2)^{2}}[/tex]

[tex]BC=\sqrt{(-3)^{2}+(6)^{2}}[/tex]

[tex]BC=\sqrt{45}\ units[/tex]

step 3

Find the perimeter

The perimeter is equal to

[tex]P=2[AB+BC][/tex]

substitute

[tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex]

or

[tex]P=22.36\ units[/tex]

Part 3) we have the rhombus ABCD

[tex]A(-3,3),B(0,5),C(3,3),D(0,1)[/tex]

Remember that  in a rhombus all sides are congruent

step 1

Find the distance AB

[tex]A(-3,3),B(0,5)[/tex]

substitute in the formula

[tex]AB=\sqrt{(5-3)^{2}+(0+3)^{2}}[/tex]

[tex]AB=\sqrt{(2)^{2}+(3)^{2}}[/tex]

[tex]AB=\sqrt{13}\ units[/tex]

step 2

Find the perimeter

The perimeter is equal to

[tex]P=4[AB][/tex]

substitute

[tex]P=4[\sqrt{13}]\ units[/tex]

or

[tex]P=14.42\ units[/tex]

Part 4) we have the quadrilateral ABCD

[tex]A(-2,-3),B(1,1),C(7,1),D(6,-3)[/tex]

step 1

Find the distance AB

[tex]A(-2,-3),B(1,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1+3)^{2}+(1+2)^{2}}[/tex]

[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]

[tex]AB=5\ units[/tex]

step 2

Find the distance BC

[tex]B(1,1),C(7,1)[/tex]

substitute in the formula

[tex]BC=\sqrt{(1-1)^{2}+(7-1)^{2}}[/tex]

[tex]BC=\sqrt{(0)^{2}+(6)^{2}}[/tex]

[tex]BC=6\ units[/tex]

step 3

Find the distance CD

[tex]C(7,1),D(6,-3)[/tex]

substitute in the formula

[tex]CD=\sqrt{(-3-1)^{2}+(6-7)^{2}}[/tex]

[tex]CD=\sqrt{(-4)^{2}+(-1)^{2}}[/tex]

[tex]CD=\sqrt{17}\ units[/tex]

step 4

Find the distance AD

[tex]A(-2,-3),D(6,-3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(-3+3)^{2}+(6+2)^{2}}[/tex]

[tex]AD=\sqrt{(0)^{2}+(8)^{2}}[/tex]

[tex]AD=8\ units[/tex]

step 5

Find the perimeter

The perimeter is equal to

[tex]P=AB+BC+CD+AD[/tex]

substitute

[tex]P=[5+6+\sqrt{17}+8]\ units[/tex]

[tex]P=[19+\sqrt{17}]\ units[/tex]

or

[tex]P=23.12\ units[/tex]

Part 5) we have the quadrilateral ABCD

[tex]A(-1,5),B(3,6),C(5,-2),D(1,-3)[/tex]

step 1

Find the distance AB

[tex]A(-1,5),B(3,6)[/tex]

substitute in the formula

[tex]AB=\sqrt{(6-5)^{2}+(3+1)^{2}}[/tex]

[tex]AB=\sqrt{(1)^{2}+(4)^{2}}[/tex]

[tex]AB=\sqrt{17}\ units[/tex]

step 2

Find the distance BC

[tex]B(3,6),C(5,-2)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-2-6)^{2}+(5-3)^{2}}[/tex]

[tex]BC=\sqrt{(-8)^{2}+(2)^{2}}[/tex]

[tex]BC=\sqrt{68}\ units[/tex]

step 3

Find the distance CD

[tex]C(5,-2),D(1,-3)[/tex]

substitute in the formula

[tex]CD=\sqrt{(-3+2)^{2}+(1-5)^{2}}[/tex]

[tex]CD=\sqrt{(-1)^{2}+(-4)^{2}}[/tex]

[tex]CD=\sqrt{17}\ units[/tex]

step 4

Find the distance AD

[tex]A(-1,5),D(1,-3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(-3-5)^{2}+(1+1)^{2}}[/tex]

[tex]AD=\sqrt{(-8)^{2}+(2)^{2}}[/tex]

[tex]AD=\sqrt{68}\ units[/tex]

step 5

Find the perimeter

The perimeter is equal to

[tex]P=\sqrt{17}+\sqrt{68}+\sqrt{17}+\sqrt{68}[/tex]

substitute

[tex]P=2[\sqrt{17}+\sqrt{68}]\ units[/tex]

or

[tex]P=24.74\ units[/tex]

Answer:

need points

Step-by-step explanation: