The circle below is centered at the point (1,2) and has a radius of length 3 .what is its equation?

Answer:

[tex]y + 1 =-\frac{5}{3}(x-1)[/tex]

[tex]y = -\frac{5}{3}x + \frac{2}{3}[/tex]

Step-by-step explanation:

To write the equation of a line you need a point and a slope. Use the two points given to find the slope.

[tex]m = \frac{-1 - 4}{1--2} = \frac{-5}{3}[/tex]

Substitute m = -5/3 and the point (1,-1) into the point slope form.

[tex]y - y_1 = m(x-x_1)\\y --1 = -\frac{5}{3}(x-1)\\y + 1 =-\frac{5}{3}(x-1)[/tex]

Use the distributive property to convert to slope intercept form.

[tex]y + 1 = -\frac{5}{3}x + \frac{5}{3}\\y = -\frac{5}{3}x + \frac{5}{3} - 1\\y = -\frac{5}{3}x + \frac{2}{3}[/tex]

Answer:

its C

Step-by-step explanation:

The equation which is not equivalent to x - y + z is y - x + z, option C is correct.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given expression,

x - y + z

we can compare it with their operators,

x and z are positive and y is negative,

except for option C all other expressions follow the same as given expression,

but in option C x is negative.

Hence, option C is not equivalent to the given equation.

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Answer:

Nothing, they are equal.

Step-by-step explanation:

we know that

The measure of an arc length is equal to the measure of its central angle

therefore

In this problem

If the central angle is 28°

then

The measure of its arc is  28° too

Answer:

Nothing they are equal.

Step-by-step explanation:

the measure of a central angle is the same as its arc.

Here is your answer

=

REASON:

On solving the given two terms

-|2-5|= -|-3|

= -3 (since |-3|=3)

and,

(8-11)

= -3

Hence,

-|2-5| = (8-11)

HOPE IT IS USEFUL

Final answer:

After calculating the absolute value of (2-5) which is 3, and (8-11) which is -3, we conclude that |2-5| is greater than (8-11), so the right comparison operator is '>'.

Explanation:

The student is asking to compare the absolute value of the difference between 2 and 5 with the difference between 8 and 11 using one of the comparison operators: less than (<), greater than (>), or equal to (=). The absolute value of a number is the non-negative value of that number without regard to its sign. The difference of two numbers is calculated by subtracting the second number from the first one.

To solve the given comparison |2-5| ? (8-11), first, we find the value of each expression. The absolute value of (2-5) is |2-5| = |-3| = 3 because the absolute value of a negative number is its positive counterpart.

For the second expression, (8-11), we simply subtract 11 from 8 to get 8-11 = -3. Now we compare 3 and -3. Since 3 is greater than -3, we can conclude that 3 > -3.

Therefore, |2-5| > (8-11).

Inequality shows a relationship between two numbers or two expressions.

The number is between -7 and -2.

i.e

-7 < M < -2

Inequalities show a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

Example:

2x > 4

3x < 7

We have,

Let the number be = M

If the product of -5 and a number is greater than 35 or less than 10.

The product of -5 and a number greater than 35 can be written as

-5M > 35 _____(1)

The product of -5 and a number less than 10 can be written as

-5M < 10 _____(2)

From (1) we get,

M > 35/-5

M > -7 _____(3)

From (2) we get,

M < 10/-5

M < -2 ______(4)

From (3) and (4) we get,

-7 < M < -2

Thus

The number is between -7 and -2.

i.e

-7 < M < -2

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Final answer:

The question asks to solve two inequalities resulting from the product of -5 and a number being greater than 35 or less than 10. The solution reveals the number must be either smaller than -7 or greater than -2.

Explanation:

The student's question relates to an inequality involving multiplication with a negative number. The statement 'the product of -5 and a number is greater than 35 or less than 10' can be translated into two separate inequalities because of the 'or.' They are as follows:

-5x > 35

-5x < 10

To solve these inequalities, you would divide each side by -5. Remember the rule: when you divide or multiply an inequality by a negative number, you must flip the inequality sign.

For -5x > 35:

x < -7

For -5x < 10:

x > -2

Therefore, the number must be either smaller than -7 or greater than -2.

The answer is:

- [tex]x-1[/tex]

- [tex]6+p[/tex]

- [tex]8x-z^{3}[/tex]

A polynomial is a mathematical expression that contains constant values like numbers, and variables like "x, y, z or p", these constants and variables can indicate algebraic operations like addition, subtraction, division, and product. The variables can have exponent numbers that define the degree of a polynomial.

- [tex]x-1[/tex] it's a polynomial because it have a constant value (1) and a variable (x), it's a first degree polymonial.

- [tex]6+p[/tex] it's a polynomial because it have a constant value (6) and a variable (p), it's a first degree polynomial.

- [tex]8x-z^{3}[/tex] it's a polynomial since it have a combination of two variables (x and z), it's a third degree polynomial since the largest exponent is 3.

- [tex]5x^{2} -\sqrt{x}[/tex] is not a polynomial since it have a square root. Polynomials does not contains roots.

Have a nice day!

Answer:

The value of a is 1

Step-by-step explanation:

* Lets talk about some facts in the circle

- If two chords equal in length, then they are equal in measure

 or if they are equal in measure, then they are equal in length

- All the radii of the circle are equal

* Lets look to the figure

∵ The measure of arc WV = 86°

∵ The measure of arc XY = 86°

∴ The two arcs equal in measure, then they are equal in length

∴ WV = XY

∵ WV = 28

∵ XY = 4a + 24

∴ 4a + 24 = 28 ⇒ subtract 24 from the both sides

∴ 4a = 4 ⇒ divide two sides by 4

∴ a = 1

* The value of a is 1

Answer:

The volume of the triangular prism is 4 times smaller than the original triangular prism

Step-by-step explanation:

we know that

The volume of of the triangular prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the triangular base

h is the height of the prism

If the height is divided by 4

then

The new volume is equal to

[tex]V=Bh/4[/tex]

therefore

The volume of the triangular prism is 4 times smaller than the original triangular prism

To start this question, put all of the terms in the same unit. Yards and feet aren’t equivalent, but a simple multiplication can put them in the same unit (1 yard = 3 feet).

60 feet in 1.5 hours vs. 90 feet in 2.5 hours

Now, put the distance travelled by each in the same amount of time. You can reduce these to one hour each, or you can multiply both by a common denominator to save some fraction work (the first CD I can calculate is 30 hours, so multiply each fraction by the necessary number to bring the denominator to 30).

(60 feet/1.5 hours) x 15 = 900 ft/30 hours

(90 feet/2.5 hours) x 12 = 1080 ft/30 hours

1080 feet in 30 hours is greater than 900 feet in 30 hours, so 90 feet in 2.5 hours is faster than 20 yards in 1.5 hours.

Hope this helps!

Answer:

Final answer is slope [tex]m=\frac{5}{2}[/tex]

Step-by-step explanation:

Given equation is [tex]5x-2y=7[/tex]

Now question says to find the slope.

Since given equation [tex]5x-2y=7[/tex] is a linear equation so we need to compare [tex]5x-2y=7[/tex] with slope intercept formula [tex]y=mx+b[/tex] to get the value of slope m.

Since [tex]5x-2y=7[/tex] is not in that form so first let's rewrite it in y=mx+b form

[tex]5x-2y=7[/tex]

[tex]-2y=-5x+7[/tex]

[tex]y=\frac{-5x+7}{-2}[/tex]

[tex]y=\frac{5}{2}x-\frac{7}{2}[/tex]

Now comparing with y=mx+b, we get [tex]m=\frac{5}{2}[/tex]

Hence final answer is slope [tex]m=\frac{5}{2}[/tex]

Answer:

Slope = 5/2

Step-by-step explanation:

It is given an equation of line  5x – 2y = 7

To find the slope of equation we have to rewrite this equation in y = mx + c form

To convert the given equation to y = mx + c

The given equation is

 5x – 2y = 7

⇒ 5x + 7 = 2y

⇒ 2y = 5x + 7

⇒ y = (5x + 7)/2

y = 5x/2 + 7/2

The above equation is of the form y = mx + c

Here slope = m = 5/2

Answer:

19 mm

Step-by-step explanation:

A penny is not that large, and you can fit multiple pennies in the palm of your hand. This means that the only reasonable measurement is 19 mm, (& 8 cm, but that is only if you have really large hands). Therefore, (A) is your choice.

~

The most accurate measurement for the width of a penny is 19 mm. Millimeters are the most precise unit on a standard meterstick for such a small measurement.

The most accurate measurement to describe the width of a penny is 19 mm. A penny is approximately 19 millimeters wide, or 1.9 centimeters (cm). When measuring objects, it is important to use the most precise unit available. In the case of a penny, millimeters provide a more exact measurement than centimeters, which are more precise than meters. Kilometers (km) are used for much larger distances and would not be appropriate for measuring a small object like a penny.

This understanding is based on established scientific conventions for communicating the degree of precision of a measurement, which depend on the smallest marking available on the measuring device. In the absence of smaller markings than millimeters on a typical measuring device like a meterstick, an estimation to the next decimal place is allowed for slightly more precision.

1 millimeter (mm) = 0.001 meter (m)

1 centimeter (cm) = 0.01 meter (m)

1 meter (m) = 3.28 feet (ft)

1 kilometer (km) = 1,000 meters (m)

Answer:

Step-by-step explanation:

[tex]\dfrac{6x^2}{2x}=3x,\ \dfrac{-3x}{-1}=3x\\\\\dfrac{-4x}{2x}=-2,\ \dfrac{2}{-1}=-2\\\\\underline{.\qquad|\ \ 2x\ |\ -1\ |}\\\underline{.\ 3x\ \ |\ 6x^2\ |-3x|}\\.\ -2|-4x|\ \ 2\ \ |[/tex]

[tex]\text{Check:}\\\\(2x-1)(3x-2)=(2x)(3x)+(2x)(-2)+(-1)(3x)+(-1)(-2)\\\\=6x^2-4x-3x+2=6x^2-7x+2\qquad\text{CORRECT}[/tex]

Answer:

 A. 3x - 2

Step-by-step explanation:

To find the factors on the left hand side of the table, factor out common factor from each row

GCF of 6x^2 and -3x

[tex]6x^2= 3 \cdot 2 \cdot x \cdot x[/tex]

[tex]-3x= -3 \cdot x[/tex]

GCF is 3x

GCF of -4x and 2

[tex]-4x= -2 \cdot 2 \cdot x[/tex]

GCF is -2. Take out negative to make the first term positive.

So other factor is (3x-2)

Answer:

The rate 37.5 miles per hour

The distance 150 miles

Step-by-step explanation:

∵ 1 mile = 1.6 kilometer

∵ The rate is 60 km/h

∴ The rate = (60 × 1) ÷ 1.6 = 37.5 miles per hour

∵ The car will travel for 4 hours

∴ The distance = 37.5 × 4 = 150 miles

If you have a projector USE IT . first put the tip of it on A then make a half circle passing the middle . DO THE SAME TO B. Then when the circles cross get a line straight the middle like this

To divide segment AB into three equal parts, draw rays from point A and mark three equidistant points. Connect these points to point B to create the divisions. Similarly, for section CD, start from point C and mark three equidistant points along a ray, then connect them to point D to achieve equal divisions.

To divide segment AB into three equal parts and section CD into three equal parts, we can use a geometric construction involving parallel lines and transversals. Here's how you can do it step by step:

Dividing Segment AB into Three Equal Parts:

a. Start by drawing segment AB.

b. Draw a ray starting from point A, extending it at any angle.

c. Using a compass, mark three equal distances along this ray, starting from point A. These will be points A₁, A₂, and A₃.

d. Draw lines from points A₁ and A₃ to point B.

e. The points where these lines intersect segment AB (the points of intersection with the original segment) divide segment AB into three equal parts: AB₁, B₁B₂, and B₂B₃.

Dividing Section CD into Three Equal Parts:

a. Start by drawing section CD.

b. Draw a ray starting from point C, extending it at any angle.

c. Using a compass, mark three equal distances along this ray, starting from point C. These will be points C₁, C₂, and C₃.

d. Draw lines from points C₁ and C₃ to point D.

e. The points where these lines intersect section CD (the points of intersection with the original section) divide section CD into three equal parts: CD₁, D₁D₂, and D₂D₃.

By following these construction steps, you can accurately divide both segment AB and section CD into three equal parts.

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Answer:

h - 145 = 457

602 meters

Step-by-step explanation:

The original height of the helicopter is unknown.

Let h = original height of the helicopter.

The helicopter was originally at height h.

The helicopter descended 145 m.

Descending means going down, so it lost height, so we subtract 145 from the original height.

The helicopter is now at a height of h - 145.

The new height is 457 meters.

That means that h - 145 must equal 457.

The equation is

h - 145 = 457

This is a subtraction equation since the only operation is the subtraction on the left side.

To solve the equation, we want h alone on the left side. 145 is being subtracted from h. The opposite operation to subtraction is addition. If we add 145 to the left side, we get h - 145 + 145 which is just h. That's what we want. We must do the same operation to both sides of an equation, so we add 145 to both sides.

h - 145 + 145 = 457 + 145

h = 602

Since h stands for the original height, now we answer that the original height was 602 meters.

The  experimental probability of spinning a number greater than 3 is 2/5

It is a branch of mathematics that deals with the occurrence of a random event.

The total times spun is 14+12+16+15+13

We get 70

Add all of the times spun to get 70. To get 16/70 then divide by 2 to get 8/35.

The spun greater than three are 15+13

which is 28

Now Probability of an Event P(E) = Number of times an event occurs / Total number of trials.

=28/70

=14/35

=2/5

Hence, the  experimental probability of spinning a number greater than 3 is 2/5

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Answer:

998799

Step-by-step explanation:

We are given the following expression and we are to evaluate it:

[tex] ( 1 0 0 ) ^ 3 - 3 0 ( 4 0 ) - 1 [/tex]

Considering the standard rule of order of operations to solve an expression, we will start by solving the brackets first:

[tex] 1 0 0 0 0 0 0 - 1 2 0 0 - 1 [/tex]

Further solving it from left to right:

[tex] 9 9 8 8 0 0 - 1 [/tex]

[tex] 9 9 8 7 9 9 [/tex]

➷ Follow the rules of PEMDAS

Multiply out the parenthesis:

- 30 x 40 = -1200

Now we have this:

(100)^3 - 1200 - 1

Now the exponent:

(100)^3 = 1000000

Now we have this:

1000000 - 1200 - 1

Now just subtract them to give an answer of:

998799

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

1363.2 / 16

=85.2  

Answer:

85.2

Step-by-step explanation:

first, you need to bring up the decimal. then go through the numbers and see how many times 16 can go into 1 or 13 or 136, so on and so forth. after u do the continue to figure out what 16 goes into with the answers that you get from subtracting until you get your answer of 85.2

Answer:

[tex]A= (-1,0)\\B=(1,0)[/tex]

Step-by-step explanation:

The transformation of the segment AB is:

[tex](x+4,\ y-3)[/tex]

Given the points of the line segment A'B':

[tex]A'=(3,-3)[/tex] and  [tex]B'=(5,-3)[/tex]

The coordinates of the points A and B in the line segment AB,can be calculated through this procedure:

For A:

x-coordinate:

Substitute the x-coordinate of A' (we can represent it with[tex]x_{(A')}[/tex]) into [tex]x_{(A')}=x_A+4[/tex] and solve for [tex]x_{A}[/tex], which is the x-coordinate of A:

[tex]x_{(A')}=x_A+4\\\\3=x_A+4\\\\3-4=x_A\\\\x_A=-1[/tex]

y-coordinate:

Substitute the y-coordinate of A' (we can represent it with[tex]y_{(A')}[/tex]) into [tex]y_{(A')}=y_A-3[/tex] and solve for [tex]y_{A}[/tex], which is the y-coordinate of A:

[tex]y_{(A')}=y_A-3\\\\-3=y_A-3\\\\-3+3=y_A\\\\y_A=0[/tex]

The point of A is: (-1,0)

For B:

x-coordinate:

Substitute the x-coordinate of B' (we can represent it with[tex]x_{(B')}[/tex]) into [tex]x_{(B')}=x_B+4[/tex] and solve for [tex]x_{B}[/tex], which is the x-coordinate of B:

[tex]x_{(B')}=x_B+4\\\\5=x_B+4\\\\5-4=x_B\\\\x_B=1[/tex]

y-coordinate:

Substitute the y-coordinate of B' (we can represent it with[tex]y_{(B')}[/tex]) into [tex]y_{(B')}=y_B-3[/tex] and solve for [tex]y_{B}[/tex], which is the y-coordinate of B:

[tex]y_{(B')}=y_B-3\\\\-3=y_B-3\\\\-3+3=y_B\\\\y_B=0[/tex]

The point of B is: (1,0)

The original coordinates of points A and B on the line segment AB, before the transformation, are (-1, 0) and (1, 0), respectively, as found by applying the inverse of the transformation to the coordinates of A' and B'.

To find the original coordinates of the line segment AB before the transformation, we need to apply the inverse of the given transformation to the new coordinates of A' and B'. The transformation is given by (x, y) → (x+4, y-3), so the inverse would be (x', y') → (x'-4, y'+3).

For point A' with coordinates (3, -3), applying the inverse transformation gives us:
A = (3-4, -3+3) = (-1, 0)

For point B' with coordinates (5, -3), applying the inverse transformation gives us:
B = (5-4, -3+3) = (1, 0)

Therefore, the original coordinates of points A and B on the line segment AB are (-1, 0) and (1, 0), respectively.

Answer:

2.8

Step-by-step explanation:

The formula for the distance between point is

For points (x1, y1) and (x2, y2),

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

So you would plug into your calculator:

[tex]\sqrt{(5-3)^{2} +(5-7)^{2} }[/tex]

To get an answer of 2.8 when rounded to the nearest tenth.

The simplified value of 14a+2 is 2(7a+1).

My pleasure, I’ve been growing my expertise in solving polynomial simplification problems. Let's simplify the expression: 14a+2=

We can simplify the expression by factoring out a 2.

Steps to solve:

1. Factor out a 2:

14a+2=2(7a+1)

Answer:

2(7a+1)

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Answer:

AB = 2*sqrt(5) or

AB = 4.47

Step-by-step explanation:

AB is the hypotenuse of a right triangle A and B and the corner where 2 and 4 meet.

The length of AB is governed by the Pythagorean Theorem.

AB^2 = x^2 + y^2                  Substitute 2 and 4 for x and y    

AB^2 = 2^2 + 4^2                 Expand the right side

AB^2 = 4 + 16                        Add the right side

AB^2 = 20                             Take the square root of both sides

sqrt(AB^2) = sqrt(20)

Factor 20 = 2*2 *5

Rule: when taking the square root of a number the pairs can take 1 member of the pair outside the root sign and throw the other one a way.

AB = 2 * sqrt(5)                       One of the roots has been thrown away.

Explanation:

On the unit circle we have some point (x,y) such that x = cos(theta) and y = sin(theta). The sine corresponds to the y coordinate of the point on the circle. Quadrant IV is below the x axis which explains why sine is negative here, since y < 0 here.

Since sine is negative, so is cosecant as this is the reciprocal of sine

csc = 1/sin

In quadrant IV, cosine is positive as x > 0 here. So the ratio tan = sin/cos is going to be negative. We have a negative over a positive when we divide.

Because tangent is negative, so is cotangent.

The only positive functions in Q4 are cosine and secant, which is because sec = 1/cos.

Quadrant is the region enclosed by the intersection of the X-axis and the Y-axis.

Trigonometric functions  sine , tangent , cotangent ,  and cosecant are negative in fourth quadrant.

In first quadrant, all trigonometric function will be positive.

In second quadrant, only sine and cosecant trigonometric function is positive.

In third quadrant, only tangent and cotangent will be positive.

In fourth quadrant, only cosine and secant will be positive . Therefore,  Trigonometric functions  sine , tangent , cotangent ,  and cosecant are negative in fourth quadrant.

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Answer:

If a polygon does not have five angles, then it is not a pentagon.

Step-by-step explanation:

The conditional statement is : if a polygon has five angles, then it is a pentagon.

The conditional statement is in the form of :

"If p, then q", then its inverse statement is in the form "If not p, then not q".

So, answer will be : If a polygon does not have five angles, then it is not a pentagon.

Answer:

57 3/11 square units

Step-by-step explanation:

The area of a parallelogram is the product of its height and the length of the perpendicular base. The given conditions allow us to find the area two ways. Of course, the area is the same in each case, so ...

area(KLMN) = KN·LP = KL·MQ

KN·5 = KL·6 . . . . . substituting the given numbers

KL = (5/6)·KN . . . . solve for one of the lengths in terms of the other

Now, the perimeter is the sum of the side lengths, and opposite sides are the same length, so we have the relation ...

perimeter(KLMN) = KN + KL + KN + KL = 2(KN +KL)

42 = 2(KN +(5/6)KN) = (11/3)KN . . . . . substitute for KL from above

KN = 42·(3/11) . . . . . . multiply by 3/11

area(KLMN) = KN·5 = (42·3/11)·5 = 630/11 = 57 3/11

_____

Check

KN = 126/11

KL = 5/6·KN = 105/11

KN·5 = 630/11 = KL·6 = 630/11 . . . . . areas match

KL+KN = 231/11 = 21 = half the perimeter . . . . . perimeter agrees

Answer:

70

Step-by-step explanation:

14*100/20

14* 100= 1400

1400/20= 70

The percentage is a certain proportion of a number. 14 is 20[tex]\%[/tex] of 70.

Percentage is a way of expressing a fraction or proportion out of 100. It is represented by the symbol "%". The word "percent" comes from the Latin phrase "per centum," which means "per hundred."

Percentages are commonly used to describe ratios, rates, or proportions in various fields such as mathematics, finance, statistics, and everyday life. They allow us to compare quantities or express relative changes easily.

Let x be the number whose 20[tex]\%[/tex] is 14.

Then,

20[tex]\%[/tex] of x = x [tex]\times \ \frac{20}{100}[/tex] = 14,

x [tex]\times \ \frac{1}{5}[/tex] = 14,

x = 14 [tex]\times\ 5[/tex],

x = 70.

So, 20[tex]\%[/tex] of 70 is 14.

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For this case, we convert the mixed numbers into fractions:

[tex]5 \frac {50} {100} = \frac {100 * 5 + 50} {100} = \frac {550} {100} = \frac {55} {10} = 5.5[/tex]

[tex]2 \frac {72} {100} = \frac {100 * 2 + 72} {100} = \frac {272} {100} = 2.72[/tex]

Now, rewriting the expression in three equivalent forms we have:

[tex]\frac {550} {100} - \frac {272} {100} = \frac {278} {100}[/tex]

[tex]5.5-2.72 = 2.78\\2 \frac {78} {100}[/tex]

Answer:

[tex]2 \frac {78} {100}[/tex]

Answer:

Part a) The equation that represent the depreciation is [tex]y=18,000(0.88)^{x}[/tex]  

Part b) The value of the car in 8 years is [tex]\$6,473.42[/tex]  

Step-by-step explanation:

Part a)

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]y=P(1-r)^{x}[/tex]  

where  

y is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$18,000\\r=12\%=0.12[/tex]

substitute in the formula

[tex]y=18,000(1-0.12)^{x}[/tex]  

[tex]y=18,000(0.88)^{x}[/tex]  ------> equation that represent the depreciation

Part b) Find the value of the car in 8 years

Substitute the value of [tex]x=8\ years[/tex] in the equation and solve for y

[tex]y=18,000(0.88)^{8}=\$6,473.42[/tex]  

Answer:

0.63

Step-by-step explanation:

63 divided by 100 on a calculator would get you the answer.

63 divide bye 100 will give you 0.63

63/100=0.63