A doll sold for $209 in 1977 and was sold again in 1989 for $467. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V0=209
b) Find the Exponential growth function in terms of t, where t is the number of years since 1977
c) Estimate the value of the doll in 2009.
d) What is the doubling time for the value of the doll to the nearest tenth of a year?
e) Find the amount of time after which the value of the doll with be $2221

The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

In the given question,

We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.

Since we have to find the image after a dilation.

So we learn about it now,

Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.

So the given point is (-9,12).

Scale factor is 1/3.

So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as

=(-9×1/3,12×1/3)

Simplifying

=(-3,4)

Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

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Answer:

0

Step-by-step explanation:

to me you use the exponent first and then add the variable after, 30-30=0 and if you do the variable first 225-30=195. But my answer would be 0.

Answer: 78

Step-by-step explanation:

3z2-6z for z=5

Answer:  $4x4x

Step-by-step explanation:

Equation of the line is y = 3/2x + 3.

Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The "slope-intercept" form is one of the most popular methods. It is so named because it makes the slope and y-intercept of the equations in the equation more clear. The number that is placed before the x is the slope.

Given,

Slope intercept form:

Formula:

y = mx + b

Where m = slope

2y - 3x = 6

2y = 6 + 3x

Equation:

y = 3 + 3/2x

y = 3/2x + 3

Equation of the line is y = 3/2x + 3.

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Answer: i am not positive but i think 2.5 on x and 9, and 27 on y

Step-by-step explanation: just want to help asap

Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.

As given in the question,

Gabriel has 2 inches tall stack of nickel

Thickness of each nickel = 0.08inch.

Let 'n' be the number of nickels Gabriel has .

Required equation to get the number of nickel is equal to :

0.08 × n = 2

⇒ n = 2 / 0.08

⇒ n = 200/ 8

⇒ n = 25

Therefore,  Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.

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Answer 0.04

Step-by-step explanation:

because 0.08 divided by two is 0.04

Answer:

1

Step-by-step explanation:

We don't even need to calculate 3 x 2.6 considering any number raised to the power of zero equals 1.

Answer:

x ≥ 6

Step-by-step explanation:

|-3x| - 7 ≥ 11     The absolute value of -3x is 3x

3x - 7 ≥ 11        Cancel the 7 by adding it on both sides

3x ≥ 18            To get x by itself divide 3 on both sides

x ≥ 6

answer:

10

step-by-step explanation:

easy: 100 ÷ 10 = 10. you need 10

explanation: you need 100 (on the left side) to equal the right side. each weight on the right side weighs 10, but you don't know how many you need. use x for the unknown amount. now, you have:

100 = 10x. solve by dividing each side by 10.

10 = x. verify by doing 10 x 10 = 100

The straight line y = x -1 is shown figure  

To plot straight-line graphs we need to take values of x and y values to make a value table and to work out the graph.

Take x values as -1, 0, 1, etc. to make our work easy and clearer, and from that find the values of y.

After calculating the coordinates, use the resultant points to plot the line as a graph.  

Here we have a line

y = x -1  

To sketch the graph we need to make a value table as given below

First take x values as, -1,  0, 1 from that find the values of y  

At  x = -1 => y = -1 - 1 = -2

At  x = 0 => y = 0 - 1 = -1

At  x = 1 =>  y = 1 - 1 = 0  

From the above calculations, the value table is

        x   -1   0   1

        y   -2  -1  0      

Use the above value and Sketch the graph

[ the resultant graph is shown below ]

The straight line y = x -1 is shown figure    

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The set of information that is true about the relation is:

Domain: {3, 4, 5, 6}

Range: {-8, -1, 2, 7}

The relation is not a function.

A relation that represents a function will have each of its domain elements related to exactly one range element.

All the x-values in a relation are referred to as the domain of a function, while all the y-values are called the range of the function,

Therefore, for a relation to be considered a function, a domain element must not correspond to two different range elements or related to two range elements.

Given the relation, {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)}:

The domain of the relation is: {3, 4, 5, 6}

The range of the relation is: {-8, -1, 2, 7}

The relation is not a function because the domain element, 3, corresponds to two different range elements, 2 and -8.

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By assuming that the initial height of the rocket is the ground, we will get the height equation:

H(t) = -16*t^2 + 235*t

The height equation for any object near the surface of the heart that is not being subject to any other forces than the gravitational one is:

H(t) = -16*t^2 + v*t + h

Where:

t represents the time in seconds.

the first coefficient -16 is half of the gravitational acceleration in feet over squared seconds.

v is the initial velocity, which in this case is 235 ft/s

h is the initial height, in this case we assume is zero (the rocket is launched from the ground)

Replacing all that in the height equation, we will get:

H(t) = -16*t^2 + 235*t

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The estimate for the number of times Ryan should expect the spinner to land on 2 is 13.

From the information, the spanner has numbers labeled 1 - 6 and Ryan is going to spin the spinner 80 times.

It should be noted that the fraction for getting a 2 is 1 out of 6. This will be 1/6.

Therefore, when it's spinned 80 times, the expected number will be:

= 1/6 × 80

= 13

The number of times is 13.

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Complete question

A spanner has numbers labeled 1 - 6. Ryan is going to spin the spinner 80 times. Work out an estimate for the number of times he should expect the spinner to land on 2

Patrick is vegetarian and Thelma is non vegetarian.

What are vegetarian?

The practice of not eating any meat is known as vegetarianism. It might also mean avoiding eating any leftovers from animal slaughter. There are several reasons to embrace a vegetarian diet. Due to their respect for sentient animal life, many people refrain from eating meat.

Main Body:

As Thelma ordered Turkey sandwich with extra mustard and turkey is an animal , which makes her non vegetarian so it is obvious that Patrick is a vegetarian and Thelma is non vegetarian.

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The simplification of the complex fraction is found as 11/14.

For the given question, the expression is-

-2/7  +  1 1/3​

To convert mixed fraction 1 1/3​ i improper fraction, multiply 3 with 1 and add 1.

1 1/3​  = 1 x 3 + 1 /3

1 1/3​  = 4/3 Put in main equation.

-2/7  +  4/3

Simplify the expression.

= -2 x 3 + 4 x 7/ (7 x 4)

= -6 + 28 / 28

= 22/28

Divide both with 2

= 11/14

Thus, the simplification of the complex fraction is found as 11/14.

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The correct question is

Simplify the complex fraction.  

-2/7 + 1 1/3​

The area of left over wrapping paper is 380 square inches

The given dimensions are:

The surface area of the box is calculated as

Surface area = 2(lw + lh + wh)

This gives

Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches

The surface area of the wrapping paper is calculated as

Wrapper = lw

This gives

Wrapper = 2 * 3 = 6 square feet

Express the area in square inches

Wrapper = 864 square inches

The area left is the difference between the areas calculated above

i.e.  Amount left = Wrapper - Box

So, we have

Amount left = 864 square inches - 484 square inches

= 380 square inches

Hence, the amount left is 380 square inches

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Answer:

-----------------------------

A and C are congruent angles opposite to congruent sides of the isosceles triangle.

Find the measure of ∠A

Answer:

The angle A is 55°.

Step-by-step explanation:

We know that,

→ <A = <C

Now the value of x will be,

→ 3x + 40 = x + 50

→ 3x - x = 50 - 40

→ 2x = 10

→ x = 10/2

→ [ x = 5 ]

Then the value of m<A is,

→ A = 3x + 40

→ A = 3(5) + 40

→ A = 15 + 40

→ [ A = 55° ]

Hence, the answer is 55°.

The expression as power is written as 2¹⁰ and 2^9

The values are

power or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.

8• 2^7

= 2 * 2 * 2 * 2^7

= 2^10

= 1024

16•32

2^5 = 2 * 2 * 2 * 2 * 2

2^4 = 2 * 2 * 2 * 2

16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

= 2^9

= 512

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The two blanks on the left side of the equation and the solution blank should be completed with the following ratios:

2050 kg/1 m³ × 2.2 lb/1 kg × 1 m³/35.3 ft³ = 127.76 lb/ft³.

In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by dividing or multiplying.

Generally speaking, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.

Conversion:

2050 kg/1 m³ × 2.2 lb/1 kg = 4,510 lb/1 m³

4,510 lb/1 m³ × 1 m³/35.3 ft³ = 4,510 lb/35.3 ft³

4,510 lb/35.3 ft³ = 127.76 lb/ft³.

Additionally, take note of the following units of conversion:

In conclusion, we can logically deduce that the crate's density is equal to 127.76 pounds per cubic foot.

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According to the scatter plot provided, the weight for someone who is 1.5 meters tall is predicted to be 45.45 kilograms.

A line of best fit is also referred to as a trend line and it can be defined as a statistical and analytical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the weight (in kilogram) would be plotted on the y-axis of the scatter plot while the height (M) would be plotted on the x-axis of the scatter plot.

From the scatter plot (see attachment) which models the relationship between data points in the table, a linear function for the line of best fit is given by:

Weight, kg = -114.3 + 106.5M

When M = 1.5 meters, we have:

Weight, kg = -114.3 + 106.5(1.5)

Weight, kg = -114.3 + 159.75

Weight, kg = 45.45 kg.

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Complete Question:

According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be ____ kilograms.

The exact solutions of the given equation in the interval are;

A: x = 0, π/2, π, ³/₂π

We are given the equation as;

sin 4x = –2sin 2x

Writing the equation in standard form gives;

sin 4x + 2sin 2x = 0

Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;

2sin 2x cos 2x + 2sin 2x = 0

Factorize to get;

2sin 2x(cos 2x + 1) = 0

A. sin 2x = 0

The unit circle will give us 3 solutions for 2x as follows;

2x = 0

Thus; x = 0

2x = π

Thus; x = π/2

2x = 2π

Thus; x = π

B. cos 2x = - 1

The unit circle gives 2 solutions for 2x as;

2x = π

Thus; x = π/2

2x = 3π

Thus; x = ³/₂π

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Complete question is;

How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?

Answer: 5q-5r               -5q+5r

Work Shown:

4x + 13 ≥ 27

4x + 13-13 ≥ 27-13

4x ≥ 14

4x/4 ≥ 14/4

x ≥ 7/2

The inequality sign stays the same for each step. The inequality sign only flips if we were to multiply both sides by a negative number (or divide both sides by a negative number).

Note: 7/2 = 3.5

The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10

Let the number of cups be represented by x.

This will be expressed as:

2/3 = x/4.62

Cross multiply

3x = 2 × 4.62

3x = 9.24

Divide

x = 9.24 / 3

x = 3.08

Therefore, 3.08 cups are needed.

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Answer:

The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.

Step-by-step explanation:

For the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.

As given in the question,

Given system of linear equations are as follow:

6x-12y = -7           ____(1)

2x + ky = 14         _____(2)

Form equation (1)  we have,

6x -12y = -7

⇒3 ( 2x -4y) = -7

⇒ 2x - 4y = -7 /3       ____(3)

From equation (2) and (3) we have,

2x + ky = 14

2x - 4y = - 7/3

Value of k so that the given system of equations are inconsistent is given by:

k = -4

For inconsistent there is no solution.

Therefore, for the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is  k= -4.

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Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters

information given in the question

Mia stands at a horizontal distance of 15 meters from the building

The angle of elevation from her eyes to the roof ((point AA)) is 18

the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^

her eyes are 1.75 meters from the ground

The direction of movements describes a right angle triangle of

opposite = height of antenna + height of the building

adjacent = 15 meters

The  distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The  the height of the antenna is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only

tan 53  = opposite / 15

opposite = 15 * tan 53 = 19.906 meters

opposite = 15 * tan 18 = 14.266 meters

Height of the antenna

= 19.606 - 14.266

= 5.34 meters

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Answer:

(2x+6) = (x+9) ; x = 3

Step-by-step explanation:

-x both sides ; 2x-x = x and -6 both sides which is x = 3

Answer: v=2.33333333333333.........

Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......