The price of buying gasoline varies directly with the number of gallons bought.If five gallons of gas cost $17.50,what is the rate of change of this linear equation.

The model to represent the balance in an account from an initial deposit of $200 at an annual interest of 4.2% is given by the formula A = 200(1.042)^x. Here A is the amount accrued after x years.

The subject of the given problem is related to exponential growth as it involves the growth of a principal amount in a bank account accruing annual interest. The model to represent the balance in the account after x years can be described by the formula A = P(1 + r/n)^(nt). Where, A represents the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, t is the time the money is invested for in years.

In this case, P = $200, r = 4.2/100 = 0.042 (converted percentage to decimal), n = 1 (since it is compounded annually), and t = x (number of years). Substituting these values into the formula, we obtain the model: A = 200 (1 + 0.042) ^ (1*x) simplified to, A = 200(1.042)^x. Which is used to represent the balance in the account after x years.

https://brainly.com/question/12490064

#SPJ2

The probability that her keys have landed within the forest will be C. 0.8.

From the information given, the blacked out middle section of the pyramid is 20 acres. Therefore, the probability will be:

= 20/100 = 0.2

Now, the probability that her keys have landed within the forest will be:

= 1 - 0.2

= 0.8

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ2

I think the answer is Probability is (1513+99)/(1414+99+1111+99)=1612/2723

The ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.

To find the time at which the ball reaches its maximum height, we can first determine the vertex of the quadratic function [tex]\( h(t) = -16t^2 + 32t + 6 \),[/tex] where t represents time in seconds and h represents height in feet.

The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the formula:

[tex]\[ t_{\text{max}} = \frac{-b}{2a} \][/tex]

For the function [tex]\( h(t) = -16t^2 + 32t + 6 \)[/tex], we have a = -16 and b = 32 . Plugging these values into the formula:

[tex]\[ t_{\text{max}} = \frac{-32}{2(-16)} \]\[ t_{\text{max}} = \frac{-32}{-32} = 1 \][/tex]

So, the ball reaches its maximum height at t = 1  second.

To find the maximum height, we substitute t = 1 into the function h(t) :

[tex]\[ h(1) = -16(1)^2 + 32(1) + 6 \]\[ h(1) = -16 + 32 + 6 \]\[ h(1) = 22 \][/tex]

Therefore, the ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.

Answer:

The answer is 3

Step-by-step explanation:

The value of x is 3.

The correct option is B.

Use one of your formulas from the figure we can write

x(x+21) = (x+1)(x+1+14)

Now, solving for x we get

x² + 21x = (x+1)(x+15)

x² + 21x = x² + 15x + x + 15

x² + 21x= x² + 16x+ 15

21x = 16x+ 15

21x - 16x = 15

5x= 15

x= 15/5

x= 3

Thus, the value x is 3.

Learn more about Tangent of Circle here:

https://brainly.com/question/30951227

#SPJ2

In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

The quadrilateral CDKM is a parallelogram. In this parallelogram, the side DA is perpendicular to the side CK.

The difference of the side DK and CD is,

[tex]DK - CD = 7\\DK=7+CD[/tex]

The length of the line segment CA and AK is 6 units and 15 units respectively.Then by the Pythagoras theorem,

[tex](AD)^2=(CD)^2-(AC)^2\\(AD)^2=(CD)^2-(6)^2[/tex]              ....1

Again by using the Pythagoras theorem

[tex](AD)^2=(Dk)^2-(AK)^2\\(AD)^2=(DK)^2-(15)^2[/tex]

Put the value of (AD)², from equation 1 in the above equation as,

[tex](CD)^2-6^2=(DK)^2-(15)^2\\(CD)^2-36=(DK)^2-225[/tex]

Put the value of DK in the above equation as,

[tex](CD)^2-36=(7+CD)^2-225\\(7+CD)^2-(CD)^2=225-36\\(CD)^2+14CD+49-(CD)^2=189\\CD=10[/tex]

Hence, the value of DK is,

[tex]DK=7+10DK=17[/tex]

Hence, In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/343682

Answer:

(x+9)^2

Step-by-step explanation:

Answer:

$50

Step-by-step explanation:

because I know :p

Have a good day!

The volume of figure is 877.876 yd³

1. Volume of Cone

= 1/3πr²h

= 1/3 x 3.14 x 2 x 2 x 4

= 16.746

2. Volume of cylinder

= 3.14 x 2 x 2 x 8

= 100.48

3. Volume of Hemisphere

= 2/3πr³

= 7.065

4. Volume of cylinder

= 3.14 x 1.5 x 1.5 x 9

= 63.585

5. Volume of prism

= 1/2 x ( 6 x 6) x 12

= 216

6. Volume of Cuboidal prism

= l w h

= 6 x 6 x 12

= 432

7. Volume of pyramid

= 1/3 x 3 x 2

= 2

8. Volume of cuboidal prism

= 10 x 2 x 2

= 40

So, the volume of figure is

= 16.746 + 100.48 + 7.065 + 63.585 + 216 + 432 + 2 + 40

= 877.876 yd³

Learn more about Volume here:

https://brainly.com/question/13338592

#SPJ1

The height of the giraffe whose shadow is 5 feet 9 inches at the same time will be 10 feet and 6.5 inches.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

The next stop on the road trip is the zoo.

Jacob goes to find his favorite animal, the giraffe.

Jacob wonders how tall the tallest giraffe at the zoo is.

If Jacob is 5 feet 6 inches and his shadow at the time is 3 feet long.

Then the height of the giraffe whose shadow is 5 feet 9 inches at the same time will be

Let x be the hieght of the giraffe. Then we have

The ratio will remain constant.

x / 5.75 = 5.5 / 3

x = 10.54

x = 10 feet 6.5 inches

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ2

The solution is: The retail price is $6.50.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Here, we have,

given that,

The total price of an article is $7.02, including tax.

If the tax rate is 8%

Lets price of article = x

Tax  is 8%  of article = 0.08x

so, we get,

x+0.08x=7.02

1.08x=7.02

x=7.02/1.08

x=6.5

The retail price is $6.50.

To learn more on percentage click:

brainly.com/question/13450942

#SPJ2

Answer:

Box A: 4

Box B: 6

Box C: 20

Step-by-step explanation:

Because 4+2 = 6

4 x 5 = 20

We know that co terminal angles are those angles which have a difference equal to a multiple of 360 degrees. For example co terminal angle of 45 degrees is 76 degrees because their difference is equal to 720 degrees, which is a multiple of 360.

We have been given an angle 425 degrees.

From the given choices, we need to check if angles being added or subtracted to 425 degrees are multiples of 360 or not.

Let us check each of the options one by one.

(A) The angle being subtracted is [tex]1000n[/tex]. Therefore, we have [tex]\frac{1000n}{360}=2.77n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(B)

The angle being subtracted is [tex]840n[/tex]. Therefore, we have [tex]\frac{840n}{360}=2.33n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(C)

The angle being added is [tex]960n[/tex]. Therefore, we have [tex]\frac{960n}{360}=2.67n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.

(D)

The angle being added is [tex]1440n[/tex]. Therefore, we have [tex]\frac{1440n}{360}=4n[/tex], which is an integer for all values of n. Therefore, angle given in this option is indeed a co terminate angle to 425 degrees.

Hence, correct answer is option (D).

An equation of a line that is the perpendicular bisector line segment AB is y=-x+10.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, line segment AB is defined by the endpoints A(4,2) and B(8,6).

Midpoint of line AB is (x, y) =[(x₂+x₁)/2, (y₂+y₁)/2]

= [(8+4)/2, (6+2)/2]

= (6, 4)

Slope of line AB is (y₂-y₁)/(x₂-x₁)

= (6-2)/(8-4)

= 4/4

= 1

The slope of a line perpendicular to given line is m1=-1/m2

So, the slope of a line is -1

Now, substitute m=-1 and (x, y)=(6, 4) in y=mx+c, we get

4=-1(6)+c

c=10

Substitute m=-1 and c=10 in y=mx+c, we get

y=-x+10

Therefore, an equation of a line that is the perpendicular bisector line segment AB is y=-x+10.

To learn more about the equation of a line visit:

https://brainly.com/question/2564656.

#SPJ5